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a/Images/Datavis/generate_plot.py +++ b/Images/Datavis/generate_plot.py @@ -265,10 +265,13 @@ def perform_bandwidth_normalization(plot_data, plot_config): for step in plot_data['steps']: y_data = step[plot_config['y_key']] + + y_adjust = y_data[0] - plot_config.get('bandwidth_zero', 0) + new_y_data = [] for datapoint in y_data: - new_y_data.append(datapoint - y_data[0]) + new_y_data.append(datapoint - y_adjust) step[plot_config['y_key']] = new_y_data @@ -332,7 +335,7 @@ def generate_plot(plot_config): for data_process_step in plot_config.get('data_processing_steps', []): perform_processing_step(data_process_step, plot_data, plot_config) - fig = plt.figure(); + fig = plt.figure(figsize=(10, 3.5)); if(plot_config['type'] == 'lt_sweep'): plot_lt_sweep(fig, plot_config, plot_data); diff --git a/Images/Datavis/plots.yml b/Images/Datavis/plots.yml index 6c12f8e..b737944 100644 --- a/Images/Datavis/plots.yml +++ b/Images/Datavis/plots.yml @@ -7,9 +7,49 @@ defaults: Cin: $C_{in}$ plots: + - loadtype: simplecsv + load: example_spectrum.csv + type: single + + load_values: ["time", "example_voltage"] + + x_key: time + y_key: example_voltage + + xscale: linear + yscale: linear + + xmin: 0.010 + xmax: 0.0115 + ymax: 1 + xplaces: 1 + + xlabel: Zeit (s) + ylabel: TIV-Spannung (V) + + ofile: example_peak.png + - loadtype: simplecsv + load: example_spectrum.csv + type: single + + load_values: ["time", "example_voltage"] + + x_key: time + y_key: example_voltage + + xscale: linear + yscale: linear + + xmin: 0.004 + xmax: 0.0145 + + xlabel: Zeit (s) + ylabel: TIV-Spannung (V) + + ofile: example_spectrum.png - loadtype: multicsv load: - Gemitiv: IMS Measurements/Spectrum_7.csv + GemiTIV: IMS Measurements/Spectrum_7.csv HighTIME: IMS Measurements/Spectrum_23.csv load_values: ["time", "voltage"] @@ -28,13 +68,14 @@ plots: xlabel: Zeit (s) ylabel: Normalisierter Messwert (a.u.) + legend_title: TIV linewidth: 1 ofile: IMS Measurements/averaged_compare.png - loadtype: multicsv load: - Gemitiv: IMS Measurements/Spectrum_59.csv + GemiTIV: IMS Measurements/Spectrum_59.csv HighTIME: IMS Measurements/Spectrum_37.csv load_values: ["time", "voltage"] @@ -53,10 +94,34 @@ plots: xlabel: Zeit (s) ylabel: Normalisierter Messwert (a.u.) + legend_title: TIV linewidth: 0.8 ofile: IMS Measurements/raw_compare.png + - load: Parasitics/SingleStage_noise_example.txt + loadtype: ltspice + type: single + + xlabel: Frequenz (Hz) + ylabel: Rauschlevel ($V/\sqrt{Hz}$) + + xformatter: engineering + xplaces: 0 + + xmin: 10 + xmax: 1000000 + ymax: 0.00000000000008 + + yformatter: engineering + yplaces: 1 + + x_key: frequency + y_key: V(onoise)/{Rf} + + xscale: log + + ofile: Parasitics/SingleStage_noise_example.png - load: 47M N.1: V1_Measurements/V1.1-a1/47M_cap/linearity_1.csv 47M N.2: V1_Measurements/V1.1-a1/47M_cap/linearity_2.csv @@ -78,6 +143,7 @@ plots: xlabel: Eingangsstrom (nA) ylabel: Ausgansspannungsfehler (V) + legend_title: TIV ofile: V1_Measurements/V1.1-a1/47M_cap/linearity_error.png - load: @@ -96,6 +162,7 @@ plots: xlabel: Eingangsstrom (nA) ylabel: Ausgangsspannung (V) + legend_title: TIV ofile: V1_Measurements/V1.1-a1/47M_cap/linearity.png - loadtype: multicsv @@ -107,6 +174,7 @@ plots: x50: V1_Measurements/V1.1-a1/CascadeSeries/noise_47M_x50.csv ylabel: Rauschlevel ($V/\sqrt{Hz}$) + legend_title: U2A-Verstärkung load_values: ["Frequency (Hz)","Trace 1 (VHz)"] @@ -123,6 +191,51 @@ plots: yplaces: 2 ofile: V1_Measurements/V1.1-a1/CascadeSeries/noises.png + - loadtype: multicsv + load: + Ungefiltert: V1_Measurements/V1.1-a1/2M4/noise.csv + Gefiltert: V1_Measurements/V1.1-a1/2M4/noise_filt.csv + + ylabel: Rauschlevel ($V/\sqrt{Hz}$) + legend_title: Ausgang + + load_values: ["Frequency (Hz)","Trace 1 (VHz)"] + + type: lt_sweep + x_key: Frequency (Hz) + y_key: "Trace 1 (VHz)" + yformatter: engineering + yplaces: 1 + + xmin: 2000 + xmax: 5000000 + ymin: 0 + ymax: 0.00003 + + ofile: V1_Measurements/V1.1-a1/2M4/noises.png + - loadtype: multicsv + load: + Ungefiltert: V1_Measurements/V1.1-a1/2M4/bandwith.csv + Gefiltert: V1_Measurements/V1.1-a1/2M4/bandwith_filt.csv + + data_processing_steps: + - normalize_bandwidth + bandwidth_zero: 160 + + ylabel: Verstärkung ($dB\Omega$) + legend_title: Ausgang + + load_values: ["Frequency (Hz)","Channel 1 Magnitude (dB)"] + + type: lt_sweep + x_key: Frequency (Hz) + y_key: "Channel 1 Magnitude (dB)" + + xmin: 10000 + xmax: 5000000 + ymin: 120 + + ofile: V1_Measurements/V1.1-a1/2M4/bandwidths.png - loadtype: multicsv load: x2: V1_Measurements/V1.1-a1/CascadeSeries/bandwidth_47M_x2.csv @@ -134,8 +247,10 @@ plots: data_processing_steps: - normalize_bandwidth + bandwidth_zero: 180 - ylabel: Normalisierte Verstärkung (dB) + ylabel: Verstärkung ($dB\Omega$) + legend_title: U2A-Verstärkung load_values: ["Frequency (Hz)","Channel 1 Magnitude (dB)"] @@ -145,18 +260,21 @@ plots: xmin: 100 xmax: 1000000 - ymin: -25 + ymin: 120 ofile: V1_Measurements/V1.1-a1/CascadeSeries/bandwidths.png - loadtype: multicsv load: - 47M 0pF: V1_Measurements/V1.1-a1/47M_dupes/bandwidth_4K7_nocap.csv - 47M 33pF: V1_Measurements/V1.1-a1/47M_dupes/bandwidth_4K7_33pf.csv + 0pF: V1_Measurements/V1.1-a1/47M_dupes/bandwidth_4K7_nocap.csv + 33pF: V1_Measurements/V1.1-a1/47M_dupes/bandwidth_4K7_33pf.csv data_processing_steps: - normalize_bandwidth - ylabel: Normalisierte Verstärkung (dB) + bandwidth_zero: 180 + ylabel: Verstärkung ($dB\Omega$) + + legend_title: U2A-Filterkapazität load_values: ["Frequency (Hz)","Channel 1 Magnitude (dB)"] @@ -167,19 +285,21 @@ plots: xmin: 100 xmax: 1000000 - ymin: -25 + ymin: 120 ofile: V1_Measurements/V1.1-a1/midcap_bandwidth_effect.png - loadtype: multicsv load: - 47M Orig.: V1_Measurements/V1.1-a1/47M_cap/bandwidth.csv - 47M Kopie: V1_Measurements/V1.1-a1/47M_dupes/bandwidth_4K7_33pf.csv + 47M N.1: V1_Measurements/V1.1-a1/47M_cap/bandwidth.csv + 47M N.2: V1_Measurements/V1.1-a1/47M_dupes/bandwidth_4K7_33pf.csv data_processing_steps: - normalize_bandwidth + legend_title: TIV - ylabel: Normalisierte Verstärkung (dB) + bandwidth_zero: 180 + ylabel: Verstärkung ($dB\Omega$) load_values: ["Frequency (Hz)","Channel 1 Magnitude (dB)"] @@ -190,20 +310,22 @@ plots: xmin: 100 xmax: 1000000 - ymin: -25 + ymin: 120 ofile: V1_Measurements/V1.1-a1/bandwidth_consistency.png - loadtype: multicsv load: - 47M Rev. 1: V1_Measurements/bandwidth_47M.csv - 47M Rev. 2: V1_Measurements/V1.1-a1/47M_cap/bandwidth.csv + 47M V.1: V1_Measurements/bandwidth_47M.csv + 47M V.2: V1_Measurements/V1.1-a1/47M_cap/bandwidth.csv - + legend_title: TIV + data_processing_steps: - normalize_bandwidth - ylabel: Normalisierte Verstärkung (dB) + bandwidth_zero: 180 + ylabel: Verstärkung ($dB\Omega$) load_values: ["Frequency (Hz)","Channel 1 Magnitude (dB)"] @@ -214,14 +336,16 @@ plots: xmin: 100 xmax: 1000000 - ymin: -25 + ymin: 120 ofile: V1_Measurements/revision_compare_bandwidth.png - loadtype: multicsv load: - 47M Rev. 2: V1_Measurements/V1.1-a1/47M_cap/linearity_1.csv - 47M Rev. 1: V1_Measurements/1G_47M_Linearity.csv + 47M V.2: V1_Measurements/V1.1-a1/47M_cap/linearity_1.csv + 47M V.1: V1_Measurements/1G_47M_Linearity.csv + + legend_title: TIV load_values: ["Setpoint", "Measurement", "Error"] @@ -244,10 +368,11 @@ plots: - loadtype: multicsv load: - 47M Rev. 1: V1_Measurements/noise_47M.csv - 47M Rev. 2: V1_Measurements/V1.1-a1/47M_dupes/noise_4K7_nocap.csv + 47M V.1: V1_Measurements/noise_47M.csv + 47M V.2: V1_Measurements/V1.1-a1/47M_dupes/noise_4K7_nocap.csv ylabel: Rauschlevel ($V/\sqrt{Hz}$) + legend_title: TIV load_values: ["Frequency (Hz)","Trace 1 (VHz)"] @@ -259,20 +384,46 @@ plots: xmin: 500 # xmax: 1000000 ymin: 0 - ymax: 0.00004 + ymax: 0.000025 yformatter: engineering yplaces: 2 ofile: V1_Measurements/revision_compare_noise.png + - load: V1_Measurements/V1.1-a1/47M_cap/noise.csv + loadtype: simplecsv + + ylabel: Rauschlevel ($V/\sqrt{Hz}$) + + load_values: ["Frequency (Hz)","Trace 1 (VHz)"] + + type: single + xscale: log + + colourmap: default + + x_key: Frequency (Hz) + y_key: "Trace 1 (VHz)" + + xmin: 500 + xmax: 1000000 + ymin: 0 + ymax: 0.00003 + + yformatter: engineering + yplaces: 2 + + ofile: V1_Measurements/with_ims_noise.png + - loadtype: multicsv load: 20M: V1_Measurements/V1.1-a1/20M/noise.csv - 47M: V1_Measurements/V1.1-a1/47M_cap/noise.csv + 47M: V1_Measurements/V1.1-a1/47M_dupes/noise_4K7_nocap.csv 82M: V1_Measurements/V1.1-a1/82M/noise.csv 120M: V1_Measurements/V1.1-a1/120M/noise.csv ylabel: Rauschlevel ($V/\sqrt{Hz}$) + legend_title: $R_f$ load_values: ["Frequency (Hz)","Trace 1 (VHz)"] @@ -287,15 +438,16 @@ plots: ymax: 0.0001 yformatter: engineering - yplaces: 2 + yplaces: 0 ofile: V1_Measurements/V1.1-a1/noises.png - loadtype: multicsv load: - 47M 33pF: V1_Measurements/V1.1-a1/47M_cap/noise.csv - 47M 0pF: V1_Measurements/V1.1-a1/47M_dupes/noise_4K7_nocap.csv + 33pF: V1_Measurements/V1.1-a1/47M_cap/noise.csv + 0pF: V1_Measurements/V1.1-a1/47M_dupes/noise_4K7_nocap.csv ylabel: Rauschlevel ($V/\sqrt{Hz}$) + legend_title: U2B-Filterkapazität load_values: ["Frequency (Hz)","Trace 1 (VHz)"] @@ -321,6 +473,7 @@ plots: 120M: V1_Measurements/V1.1-a1/120M/noise.csv ylabel: Rauschlevel ($V/\sqrt{Hz}$) + legend_title: $R_f$ load_values: ["Frequency (Hz)","Trace 2 (VHz)"] @@ -335,7 +488,7 @@ plots: ymax: 0.0001 yformatter: engineering - yplaces: 2 + yplaces: 0 ofile: V1_Measurements/V1.1-a1/noises_ch2.png - loadtype: multicsv @@ -344,12 +497,13 @@ plots: 47M: V1_Measurements/V1.1-a1/47M_cap/bandwidth.csv 82M: V1_Measurements/V1.1-a1/82M/bandwidth.csv 120M: V1_Measurements/V1.1-a1/120M/bandwidth.csv - + legend_title: $R_f$ data_processing_steps: - normalize_bandwidth - ylabel: Normalisierte Verstärkung (dB) + bandwidth_zero: 180 + ylabel: Verstärkung ($dB\Omega$) load_values: ["Frequency (Hz)","Channel 1 Magnitude (dB)"] @@ -360,16 +514,42 @@ plots: xmin: 100 xmax: 1000000 - ymin: -25 + ymin: 120 ofile: V1_Measurements/V1.1-a1/bandwidths.png + - loadtype: multicsv + load: + 20M: V1_Measurements/V1.1-a1/20M/bandwidth.csv + 47M: V1_Measurements/V1.1-a1/47M_cap/bandwidth.csv + 82M: V1_Measurements/V1.1-a1/82M/bandwidth.csv + 120M: V1_Measurements/V1.1-a1/120M/bandwidth.csv + legend_title: $R_f$ + + data_processing_steps: + - normalize_bandwidth + bandwidth_zero: 180 + ylabel: Verstärkung ($dB\Omega$) + + load_values: ["Frequency (Hz)","Channel 2 Magnitude (dB)"] + + type: lt_sweep + colourmap: default + x_key: Frequency (Hz) + y_key: "Channel 2 Magnitude (dB)" + + xmin: 100 + xmax: 1000000 + ymin: 120 + + ofile: V1_Measurements/V1.1-a1/bandwidths_ch2.png - loadtype: multicsv load: "20M": V1_Measurements/noise_20M.csv "47M": V1_Measurements/noise_47M.csv "120M": V1_Measurements/noise_120M.csv - + legend_title: $R_f$ + ylabel: Rauschlevel ($V/\sqrt{Hz}$) load_values: ["Frequency (Hz)","Trace 1 (VHz)"] @@ -394,7 +574,8 @@ plots: "20M": V1_Measurements/noise_20M.csv "47M": V1_Measurements/noise_47M.csv "120M": V1_Measurements/noise_120M.csv - + legend_title: $R_f$ + ylabel: Rauschlevel ($V/\sqrt{Hz}$) load_values: ["Frequency (Hz)","Trace 2 (VHz)"] @@ -419,11 +600,13 @@ plots: "x0.6": V1_Measurements/compensation_47M_under.csv "x1": V1_Measurements/compensation_47M_OK.csv "x1.4": V1_Measurements/compensation_47M_over.csv + legend_title: $U_\mathrm{Schirm}/U_\mathrm{fb}$ data_processing_steps: - normalize_bandwidth - ylabel: Normalisierte Verstärkung (dB) + bandwidth_zero: 180 + ylabel: Verstärkung ($dB\Omega$) load_values: ["Frequency (Hz)","Channel 1 Magnitude (dB)"] @@ -439,11 +622,13 @@ plots: 20M: V1_Measurements/bandwidth_20M.csv 47M: V1_Measurements/bandwidth_47M.csv 120M: V1_Measurements/bandwidth_120M.csv - + legend_title: $R_f$ + data_processing_steps: - normalize_bandwidth - ylabel: Normalisierte Verstärkung (dB) + bandwidth_zero: 180 + ylabel: Verstärkung ($dB\Omega$) load_values: ["Frequency (Hz)","Channel 1 Magnitude (dB)"] @@ -454,7 +639,7 @@ plots: xmin: 100 xmax: 500000 - ymin: -25 + ymin: 140 ofile: V1_Measurements/bandwidth.png @@ -463,11 +648,13 @@ plots: 20M: V1_Measurements/bandwidth_20M.csv 47M: V1_Measurements/bandwidth_47M.csv 120M: V1_Measurements/bandwidth_120M.csv - + legend_title: $R_f$ + data_processing_steps: - normalize_bandwidth - ylabel: Normalisierte Verstärkung (dB) + bandwidth_zero: 180 + ylabel: Verstärkung ($dB\Omega$) load_values: ["Frequency (Hz)","Channel 2 Magnitude (dB)"] @@ -478,18 +665,20 @@ plots: xmin: 100 xmax: 500000 - ymin: -25 + ymin: 100 ofile: V1_Measurements/bandwidth_ch2.png - loadtype: multicsv load: Ungefiltert: V1_Measurements/bandwidth_47M.csv Gefiltert: V1_Measurements/bandwidth_47M_filter.csv - + legend_title: Ausgang + data_processing_steps: - normalize_bandwidth - ylabel: Normalisierte Verstärkung (dB) + bandwidth_zero: 180 + ylabel: Verstärkung ($dB\Omega$) load_values: ["Frequency (Hz)","Channel 1 Magnitude (dB)"] @@ -500,7 +689,7 @@ plots: xmin: 100 xmax: 500000 - ymin: -25 + ymin: 100 ofile: V1_Measurements/bandwidth_filter_compare.png @@ -583,19 +772,28 @@ plots: - load: Parasitics/Rf_series_noshield.txt loadtype: ltspice - step_parameter: $C_{f,g}$ + + legend_title: $C_{f,g}$ step_unit: F + xmin: 100 + ofile: Parasitics/Rf_series_noshield.png type: lt_sweep y_key: V(vout) dB title: Impedanzverläufe verschiedener Widerstände bei gleichbleibendem $C_p$ - ylabel: Normalisierte Verstärkung (dB) + + data_processing_steps: + - normalize_bandwidth + + bandwidth_zero: 180 + ylabel: Verstärkung ($dB\Omega$) + - load: Parasitics/Rf_series_shielded.txt loadtype: ltspice - step_parameter: $C_{\mathrm{shield}}$ + legend_title: $C_{\mathrm{shield}}$ step_unit: F ofile: Parasitics/Rf_series_shielded.png @@ -604,10 +802,14 @@ plots: y_key: V(vout) dB title: Impedanzverläufe verschiedener Widerstände bei gleichbleibendem $C_p$ - ylabel: Normalisierte Verstärkung (dB) + data_processing_steps: + - normalize_bandwidth + + bandwidth_zero: 180 + ylabel: Verstärkung ($dB\Omega$) - load: Parasitics/Examples_R_Cp_RSweep.txt loadtype: ltspice - step_parameter: $R$ + legend_title: $R$ step_unit: $\Omega$ ofile: Parasitics/Examples_R_Cp_RSweep.png @@ -619,7 +821,7 @@ plots: ylabel: Impedanz (dB$\Omega$) - load: Parasitics/SingleStage_Cfp_Sweep.txt loadtype: ltspice - step_parameter: $C_{fp}$ + legend_title: $C_{fp}$ step_unit: F ofile: Parasitics/SingleStage_Cfp_Sweep.png @@ -628,21 +830,32 @@ plots: y_key: V(n002) dB title: Verstärkung bei konstantem $R_f = 1G\Omega$ und varriertem $C_{f}$ - ylabel: Normalisierte Verstärkung (dB) + data_processing_steps: + - normalize_bandwidth + + bandwidth_zero: 180 + ylabel: Verstärkung ($dB\Omega$) - load: Parasitics/SingleStage_Rf_Sweep.txt loadtype: ltspice step_unit: $\Omega$ + legend_title: $R_f$ + ofile: Parasitics/SingleStage_Rf_Sweep.png type: lt_sweep y_key: V(n002) dB title: Verstärkung bei konstantem $C_{f} = 100fF$ und varriertem $R_{f}$ - ylabel: Normalisierte Verstärkung (dB) + data_processing_steps: + - normalize_bandwidth + + bandwidth_zero: 180 + ylabel: Verstärkung ($dB\Omega$) - load: Parasitics/SingleStage_Aol_Sweep.txt loadtype: ltspice step_unit: " " + legend_title: $A_\mathrm{ol}$ ofile: Parasitics/SingleStage_Aol_Sweep.png @@ -650,11 +863,17 @@ plots: y_key: V(n002) dB title: Verstärkung bei $C_{f} = 3fF$, $C_\mathrm{in} = 10~\mathrm{pF}$ und variieter Verstärkung - ylabel: Normalisierte Verstärkung (dB) + data_processing_steps: + - normalize_bandwidth + + bandwidth_zero: 180 + ylabel: Verstärkung ($dB\Omega$) - load: Parasitics/SingleStage_Rf_Sweep_Noise.txt loadtype: ltspice step_unit: $\Omega$ + legend_title: $R_f$ + ofile: Parasitics/SingleStage_Rf_Sweep_Noise.png type: lt_sweep @@ -669,6 +888,8 @@ plots: loadtype: ltspice step_unit: $\Omega$ + legend_title: $R_f$ + ofile: Parasitics/SingleStage_LTC_Rf_Sweep_Noise.png type: lt_sweep @@ -682,6 +903,7 @@ plots: - load: Parasitics/SingleStage_LTC6268-10_Cin_Sweep_Noise.txt loadtype: ltspice step_unit: F + legend_title: $C_\mathrm{in}$ ofile: Parasitics/SingleStage_LTC_Cin_Sweep_Noise.png @@ -696,6 +918,7 @@ plots: - load: Parasitics/SingleStage_LTC6268-10_Cin_Sweep_Noise.txt loadtype: ltspice step_unit: F + legend_title: $C_\mathrm{in}$ ofile: Parasitics/SingleStage_LTC_Cin_Sweep_Noise_log.png @@ -719,38 +942,64 @@ plots: title: Verstärkung bei variiertem GBWP legend_title: GBWP - ylabel: Normalisierte Verstärkung (dB) + + data_processing_steps: + - normalize_bandwidth + + bandwidth_zero: 180 + ylabel: Verstärkung ($dB\Omega$) - load: DesignEstimate/CompositeStage_ADA4817_StageAmpSweep_bandwidth.txt loadtype: ltspice step_unit: " " + legend_title: $A_\mathrm{U,2}$ + ofile: DesignEstimate/OpAmp_Stages_Sweep.png type: lt_sweep y_key: V(n002) dB title: Verstärkung bei variiertem GBWP - ylabel: Verstärkung (dB$\Omega$) + data_processing_steps: + - normalize_bandwidth + + bandwidth_zero: 180 + ylabel: Verstärkung ($dB\Omega$) + - load: DesignEstimate/OpAmp_GBWP_Sweep.txt loadtype: ltspice step_unit: Hz + legend_title: GBWP + ofile: DesignEstimate/OpAmp_GBWP_Sweep.png type: lt_sweep y_key: V(n002) dB title: Verstärkung bei variiertem GBWP - ylabel: Verstärkung (dB$\Omega$) + data_processing_steps: + - normalize_bandwidth + + bandwidth_zero: 180 + ylabel: Verstärkung ($dB\Omega$) - load: Parasitics/SingleStage_Cin_Sweep.txt loadtype: ltspice step_unit: F + xmin: 1000 + + legend_title: $C_\mathrm{in}$ + ofile: Parasitics/SingleStage_Cin_Sweep.png type: lt_sweep y_key: V(vout) dB title: Verstärkung bei variierter Eingangskapazität - ylabel: Normalisierte Verstärkung (dB) \ No newline at end of file + data_processing_steps: + - normalize_bandwidth + + bandwidth_zero: 180 + ylabel: Verstärkung ($dB\Omega$) diff --git a/TeX/Arbeit.tex b/TeX/Arbeit.tex index 5c457b3..652baf0 100644 --- a/TeX/Arbeit.tex +++ b/TeX/Arbeit.tex @@ -32,7 +32,7 @@ \documentclass[12pt, a4paper, openany, DIV=16, BCOR=20mm, bibliography=totoc, captions=tableheading, numbers=noenddot]{scrbook} %Book - Digitalversion (doppelseitig) -%\documentclass[12pt,a4paper,openany,bibliography=totoc,,captions=tableheading,numbers=noenddot]{scrbook} +%\documentclass[12pt, a4paper, openany, bibliography=totoc, captions=tableheading, numbers=noenddot]{scrreport} @@ -59,14 +59,18 @@ %Titelseiten für Studien- und Diplomarbeit \pagenumbering{alph} %Seitennummerierung lateinische Kleinbuchstaben -\include{Deckblatt} -\clearpage{\thispagestyle{empty}\cleardoublepage} %leere Seite für "documentclass book" +\includepdf[pages=-]{Deckblatt_Aufgabenstellung_SMT_David.pdf} -\include{Eigenstaendigkeitserklaerung} -\clearpage{\thispagestyle{empty}\cleardoublepage} %leere Seite für "documentclass book" +%\include{Deckblatt} +%\clearpage{\thispagestyle{empty}\cleardoublepage} %leere Seite für "documentclass book" -\include{Aufgabenstellung} -\clearpage{\thispagestyle{empty}\cleardoublepage} %leere Seite für "documentclass book" +%\include{Eigenstaendigkeitserklaerung} +%\clearpage{\thispagestyle{empty}\cleardoublepage} %leere Seite für "documentclass book" + +%\include{Aufgabenstellung} +%\clearpage{\thispagestyle{empty}\cleardoublepage} %leere Seite für "documentclass book" + +\clearpage{\thispagestyle{empty}\cleardoublepage} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %Inhaltsverzeichnis @@ -84,7 +88,6 @@ \listoffigures \addcontentsline{toc}{chapter}{Abbildungsverzeichnis} %Eintrag im Inhaltsverzeichnis \clearpage -\todo{Move} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% @@ -115,7 +118,7 @@ \include{Kapitel/Vermessung} \include{Kapitel/RevisionV11} -% \chapter{(Optional) Erstellung eines vollintegrierten TIV-Frontends} +\include{Kapitel/Zusammenfassung} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %Literaturverzeichnis diff --git a/TeX/Deckblatt.tex b/TeX/Deckblatt.tex index f2089a7..cdec5e4 100644 --- a/TeX/Deckblatt.tex +++ b/TeX/Deckblatt.tex @@ -1,35 +1,38 @@ \begin{titlepage} \enlargethispage{2.0cm} - \begin{center} -\vspace*{-2cm} + \vspace*{-1cm} + \begin{figure}[H] + \centering + \includegraphics[width=0.95\textwidth]{grafiken/title_header.png} + \end{figure} - \begin{figure}[h] - \centering - \includegraphics[height=4cm]{grafiken/welfenschloss_vektor.pdf} - \end{figure} + \vspace{2cm} -\vspace{1cm} + {\Large \textsc{Masterarbeit}} \\[0.2cm] + \rule{0.95\textwidth}{0.4pt}\\[3.5cm] - {\LARGE \textsc{Leibniz Universität Hannover}}\\[1.0cm] + {\LARGE \textbf{Entwicklung und Charakterisierung}} \\[0.2cm] + {\LARGE \textbf{eines rauscharmen Transimpedanzverstärkers}} \\ [0.2cm] + {\LARGE \textbf{für die Ionenmobilitätsspektrometrie}} \\ [2cm] + + {\large von} \\[0.2cm] + {\Large David Bailey} \\[0.2cm] + {\large Matrikelnummer: 10011830}\\[0.2cm] - {\Large \textsc{Fachpraktikum des Studienganges}} \\[0.2cm] - {\Large \textsc{M.Sc. Energietechnik}} \\ [2cm] + \vfill - {\Large \textbf{Implementation einer\\ - Arc-Detection der ECRH\\ - am Wendelstein W7-x\\ - Fusionsexperiment }} \\ [4cm] + {\large Betreuer:}\\[0.1cm] + {\large M. Hitzemann}\\[0.1cm] + {\large J. Winkelholz}\\[1cm] - {\Large Praktikumsbericht} \\ [1.5cm] + {\large Prüfer:}\\[0.1cm] + {\large 1. Prof. Dr.-Ing. Stefan Zimmermann}\\[0.1cm] + {\large 2. Prof. Dr.-Ing. Julia Körner}\\[1cm] - \vfil - - {\large David Bailey} \\ - {Matrikelnummer: 10011830 } \\ [1.5cm] + {September 2024}\\[2cm] \end{center} - \end{titlepage} diff --git a/TeX/Kapitel/Auslegung.tex b/TeX/Kapitel/Auslegung.tex index 8a60249..bc1fe89 100644 --- a/TeX/Kapitel/Auslegung.tex +++ b/TeX/Kapitel/Auslegung.tex @@ -1,45 +1,81 @@ -\chapter{Entwicklung des Transimpedanzverstärkers} +\cleardoublepage +\chapter{Entwicklung eines Transimpedanzverstärkers + für die Ionenmobilitätsspektrometrie} -In diesem Kapitel wird auf die Auslegung eines spezifischen TIV-Schaltkreises eingegangen. -Es werden die zu erreichenden Zielparameter des Verstärkers festgelegt und erläutert. -Hiernach werden verschiedene Bauteile zur Auswahl gezogen, wobei die limitierenden parasitären Effekte dieser dar gestellt werden. -Eine Auswahl der Bauteile wird mit Hinsicht auf die Zielparameter des Designs durchgeführt. +Dieses Kapitel beschäftigt sich mit der Auslegung eines spezifischen +TIV-Schaltkreises für die Ionenmobilitätsspektrometrie. +Zuerst erfolgt die Festlegung der zu erreichenden +Zielparameter des Verstärkers. Anschließend werden verschiedene +Bauteile untersucht und zur Auswahl gezogen, +wobei die limitierenden parasitären Effekte dieser dargestellt werden. +Eine Auswahl der Bauteile wird mit Hinsicht auf die Zielparameter +des Designs durchgeführt. \section{Zielparameter} \label{chap:tia_design_goals} Wie in Abschnitt \ref{chap:tia_in_ims} dargestellt, ist die Aufgabe eines TIVs im IMS, -die Stromflüsse der Ionenpackete auf eine messbare Spannung zu verstärken. Hierbei soll der TIV die Form eines solchen -Packetes möglichst akkurat dar stellen. Für das in dieser Arbeit ausgewählte IMS-Verfahren ist bereits die Größe der Ionen-Pakete bekannt\todo{Insert ref here}. -Somit können aus diesen Messwerten die Zielwerte des Verstärkers abgeleitet werden. +die Stromflüsse der Ionenpakete auf eine messbare Spannung zu verstärken. Hierbei soll der TIV die Form eines solchen +Paketes möglichst akkurat abbilden. +Für das in dieser Arbeit ausgewählte IMS-Verfahren ist bereits die Größe der Ionen-Pakete bekannt. -Für eine erste Auslegung wird das folgende IMS-System angestrebt: \todo[inline]{Describe IMS}. -Dieses generiert Ionenpackete mit einer Gausschen Verteilung \todo{verify this} mit einer Standardabweichung von circa $\SI{1.5}{\micro\second}$. -Um diese Packete abbilden zu können ist eine Bandbreite von mindestens $\SI{30}{\kilo\hertz}$ notwendig. -Die größte Peak-Amplitude, die hierbei zu erwarten ist, ist circa \todo{Insert peak amplitude}. Somit reicht ein Eingangsbereich des TIV von $\pm\SI{1}{\nano\ampere}$. +Der Verstärker wird so ausgelegt, dass er +für ein IMS nutzbar ist, welches am +Institut für Grundlagen der Elektrotechnik und Messtechnik +der Leibniz Universität Hannover genutzt wird. +Der Aufbau dieses IMS ist vergleichbar zu dem in +\cite{Reinecke2018Oct} dargestelltem System. +Abbildung \ref{fig:example_ims_peak} zeigt einen Peak der von einem +solchen System gemessen wurde. -\begin{figure} +\begin{figure}[ht!] \centering - \missingfigure{Include figure for an example IMS peak shape} - \caption{\label{fig:example_ims_peak}Messung eines beispielhaften Ionen-Peaks} + \includegraphics[scale=0.8]{datavis/example_peak.png} + \caption[Messung eines beispielhaften Ionen-Peaks]{ + \label{fig:example_ims_peak} + Messung eines beispielhaften Ionen-Peaks. + Zu erkennen ist die annähernd gaussche Verteilung + mit einer Breite von etwa $\SI{60}{\micro\second}$.} \end{figure} +Zu sehen ist, dass dieses System Ionenpakete mit einer +annähernd gausschen Verteilung und +mit einer Breite von circa $\SI{35}{\micro\second}$ +für die kleinsten Pakete erzeugt. +Um diese Pakete abbilden zu können ist eine Bandbreite von mindestens $\SI{30}{\kilo\hertz}$ notwendig. +Die größte Peak-Amplitude, die hierbei abgebildet werden soll, +befindet sich im Bereich von circa $\SI{1}{\nano\ampere}$. + Der Ausgang des TIV wird einen Analog-Digital-Wandler (im folgenden ADC) antreiben. Diese Bauteile wandeln ein Spannungssignal in ein digitales Signal um, welches vom Rest des Systems ausgewertet werden kann. Der im Ziel-IMS ausgewählte ADC, -der \todo{insert ADC name}, hat einen Eingangsbereich von $\pm\SI{2}{\volt}$\todo{verify}. Somit kann die Gesamtverstärkung des TIVs festgelegt werden als: -$A_\mathrm{TIV} = V_\mathrm{out}/I_\mathrm{in} = \SI{2}{\volt} / \SI{1}{\nano\ampere} = \SI{2}{\giga\ohm}$ +der {\em LTC2274}, hat einen +differentiellen Eingangsbereich von $\pm\SI{2.25}{\volt}$ \cite{DatasheetLTC2274}. +Bei gewünschtem nominalem Eingangsbereich von $\SI{1}{\nano\ampere}$ +und maximaler Ausgangsspannung von $\pm\SI{2.25}{\volt}$ wird eine +Ausgangsspannung von $\SI{1}{\volt}$ bei $\SI{1}{\nano\ampere}$ +gewählt. Hierdurch wird sicher gestellt, +dass der ADC nicht saturiert und alle Peaks korrekt abgebildet werden können. + +Somit kann die Gesamtverstärkung des TIVs festgelegt werden als: +\begin{equation*} + A_\mathrm{TIV} = V_\mathrm{out}/I_\mathrm{in} = \SI{1}{\volt} / \SI{1}{\nano\ampere} = \SI{1}{\giga\ohm} +\end{equation*} + + +\cleardoublepage \section{Analyse der Parasitäreffekte} -Im folgenden werden die bereits in Kapiteln -\ref{chap:basics_parasitics} und \ref{chap:basics_opamp} beschriebenen parasitären Effekte -im Kontext des TIVs genauer untersucht. Die Auswirkungen der verschiedenen Effekte auf das Verhalten -der Schaltung werden beschrieben, und Grenzwerte für bestimmte Parameter mithilfe der Zielparameter bestimmt. -Ebenfalls werden Möglichkeiten zur Reduktion einiger Parasitäreffekte beschrieben. + +Kapitel \ref{chap:basics_parasitics} und \ref{chap:basics_opamp} beschreiben grundlegende +parasitäre Effekte einiger Bauteil. Im Folgenden sollen diese Effekte genauer auf ihren +Einfluss auf eine TIV-Schaltung untersucht werden. +Grenzwerte für bestimmte Parameter mithilfe der Zielparameter sollen bestimmt werden und +Möglichkeiten zur Reduktion einiger Parasitäreffekte werden untersucht. \subsection{Effekte der passive Bauelemente} -In diesem Kapitel wird auf das Verhalten der passiven Bauteile eingegangen, und wie deren parasitäre +Folgend wird auf das Verhalten der passiven Bauteile eingegangen und wie deren parasitäre Effekte den Schaltkreis beeinflussen. Dies bezieht sich überwiegend auf den Rückkoppelwiderstand und die parasitären Kapazitäten der Schaltung. @@ -47,23 +83,40 @@ die parasitären Kapazitäten der Schaltung. \label{chap:r_noise} Wie bereits in Kapitel \ref{chap:basics_parasitics} beschrieben, besitzen resistive Bauteile -ein thermisches Rauschen. In diesem Abschnitt wird der Einfluss des Rauschens untersucht. +ein thermisches Rauschen. In diesem Abschnitt wird der Einfluss des Rauschens auf +die Messungen eines TIVs untersucht. In einem TIV-Schaltkreis gibt es ein Bauteil mit hohem Widerstand: Der Rückkoppelwiderstand. Somit wird vermutet, dass dieser Widerstand eine dominierende Quelle des thermischen Rauschens ist. Laut Gleichung \ref{eqn:thermal_voltage_noise} wächst die Amplitude des Spannungsrauschens mit der Wurzel des Widerstandswertes, wodurch eine erste Vermutung ist, dass ein kleinerer Widerstand besser wäre. -Für einen TIV ist der Eingang jedoch ein strombasierter Eingang. Somit muss das Stromrauschen betrachtet werden. -Dies lässt sich berechnen wie folgt:\todo{Cite or explain this} +Für einen TIV ist der Eingang jedoch ein strombasierter Eingang und die +Verstärkung des TIV nimmt proportional zur Widerstandsgröße zu. + +Das Spannungsrauschen über dem Widerstand kann +nach Ersatzschaltbild \ref{fig:example_r_noise} (Seite \pageref{fig:example_r_noise}) +in einen äquivalenten Strom durch den Widerstand umgerechnet +werden, welcher in den Eingang des TIVs fließt. +Dies kann durch Umstellung von Gleichung \ref{eqn:thermal_voltage_noise} +zusammen mit dem Ohm'schen Gesetzt erreicht werden. +Hierbei ist $I_\mathrm{n,rms}$ das Stromrauschen, +$U_\mathrm{n,rms}$ das Spannungsrauschen, $k_B$ die +Boltzmann-Konstante, $T$ die Temperatur des widerstandes +und $\Delta f$ die betrachtete Bandbreite. \begin{eqnarray} - I_\mathrm{n,rms} & = & \frac{V_\mathrm{n,rms}}{R} \\ - I_\mathrm{n,rms} & = & \frac{\sqrt{4k_BTR\Delta f}}{R} \\ - I_\mathrm{n,rms} & = & \sqrt{\frac{4k_BT\Delta f}{R}}\label{eqn:thermal_current_noise} + I_\mathrm{n,rms} & = & \frac{U_\mathrm{n,rms}}{R_f} \\ + I_\mathrm{n,rms} & = & \frac{\sqrt{4k_BTR_f\Delta f}}{R_f} \\ + I_\mathrm{n,rms} & = & \sqrt{\frac{4k_BT\Delta f}{R_f}}\label{eqn:thermal_current_noise} \end{eqnarray} -Laut Gleichung \ref{eqn:thermal_current_noise} ist somit ein {\em größerer} Widerstand von Vorteil, -um den Einfluss des thermalen Rauschens zu minimieren. Für das Design soll somit eine Maximierung des +Eine beispielhafte Rechnung mit einem $\SI{100}{\mega\ohm}$ Widerstand +bei Raumtemperatur ($\SI{25}{\celsius}$) und $\SI{30}{\kilo\hertz}$ +Bandbreite ergibt ein Rauschen von $\SI{2.22}{\pico\ampere}$. + +Laut Gleichung \ref{eqn:thermal_current_noise} ist ein {\em größerer} Widerstand von Vorteil, +um den Einfluss des thermalen Rauschens zu minimieren. +Für das Design soll somit eine Maximierung des gesamten Rückkoppelwiderstandes angestrebt werden. \subsubsection{Parasitäre Rückkopplungskapazität} @@ -71,25 +124,37 @@ gesamten Rückkoppelwiderstandes angestrebt werden. Der Rückkoppelwiderstand ist ein zentrales Bauteil des TIVs, welcher die Verstärkung des gesamten Schaltkreises festlegt. -Alle Bauteile eine parasitäre Kapazität, -wie in Kapitel \ref{chap:basics_parasitics} festgelegt wurde. -Abbildung \ref{fig:example_r_cp} in diesem Kapitel zeigt, dass diese Kapazität -an hochohmigen Widerständen schon bei geringeren Frequenzen einen Einfluss auf die Bandbreite haben kann. +Alle Bauteile besitzen parasitäre Kapazitäten, +wie in Kapitel \ref{chap:basics_parasitics} +beschrieben wurde. +Abbildung \ref{fig:example_r_cp} auf Seite \pageref{fig:example_r_cp} zeigt, dass diese Kapazität +an hochohmigen Widerständen schon bei geringeren Frequenzen einen Einfluss auf die Bandbreite hat. Im Falle des Rückkoppelwiderstandes sorgt die Verringerung der Impedanz für eine Verringerung -der Verstärkung des OpAmp, und somit für eine reduzierte Bandbreite des gesamten Verstärkers. Diese Einschränkung +der Verstärkung des OpAmp und somit für eine reduzierte Bandbreite des gesamten Verstärkers. Diese Einschränkung darf nicht unter die in Kapitel \ref{chap:tia_design_goals} festgelegte Zielbandbreite fallen. -Nun soll genauer auf den Ursprung der Kapazität, den zu erwartenden Wert, sowie mögliche Mitigationen eingegangen werden. -Um dies zu erreichen, wird eine Simulation in dem Programm ``CST Studio Suite 2021'' eingerichtet. Dieses Programm erlaubt die Simulation +Um die Ursprünge, Grenzwerte und mögliche Kompensationsmöglichkeiten +dieser Kapazität besser zu verstehen, wird genauer auf +diese eingegangen. +Hierfür wird eine Simulation in dem Programm ``CST Studio Suite 2021'' eingerichtet. Dieses Programm erlaubt die Simulation verschiedener elektrostatischer und dynamischer Modelle, um zum Beispiel die kapazitive Kopplung einer Schaltung untersuchen zu können. Als erster Ansatz wird von einem Dickfilm-Widerstand im Gehäuseformat ``1206'' ausgegangen. -Diese Größe bietet eine angemessene Auswahl von Widerstandswerten in der Größenordnung eines TIV-Rückkoppelwiderstandes an, +Diese Größe bietet eine angemessene Auswahl von Widerstandswerten in der Größenordnung eines TIV-Rückkoppelwiderstandes an und ist leicht erhältlich. Somit ist dies ein guter Kanditat für den im späteren Design verwendeten Widerstand. -Diese Art von Widerstand besteht aus einem Keramik-Kern mit zwei metallisierten Anschlüssen an den Enden und einem Kohle-Film, welcher -den eigentlichen elektrischen Widerstand bildet. Das in CST erstellte Modell diesen ist in Abbildung \ref{fig:cst_model_1206} dargestellt. +Diese Art von Widerstand besteht aus einem Keramik-Kern mit zwei metallisierten Anschlüssen an den Enden und einem +resistiven Film, often Kohle, welcher +den eigentlichen elektrischen Widerstand bildet. +Das in CST erstellte Modell hierfür ist in Abbildung \ref{fig:cst_model_1206} dargestellt. -\begin{figure}[h] +Eine weitere mögliche Bauart eines Widerstandes ist die sog. Flipchip-Terminierung. +Hierbei wird die Metallisierung nur auf einer Seite der Keramik, neben dem Widerstandsfilm, aufgebracht. +Dies soll Streueffekte und Kapazitäten verringern. Das für diese Widerstandsart erstellte Modell ist +in Abbildung \ref{fig:cst_model_1206_flipchip} dargestellt. +Bei der Modellierung wurde sich für beide Widerstandvarianten +auf \cite{VishayRFreq} bezogen. + +\begin{figure}[ht] \begin{subfigure}[t]{.5\linewidth} \centering \includegraphics[width=0.9\textwidth]{entwicklung/cst_model_r1206.png} @@ -100,45 +165,53 @@ den eigentlichen elektrischen Widerstand bildet. Das in CST erstellte Modell die \includegraphics[width=0.9\textwidth]{entwicklung/cst_model_r1206_flipchip.png} \subcaption{\label{fig:cst_model_1206_flipchip}Modell des 1206-Flipchip-Widerstandes} \end{subfigure} - \caption[CST-Widerstandsmodelle]{Die in CST Studio Suite 2021 erstellten Widerstandsmodelle. - Zu sehen ist die Keramik in weiß, die Metallkontakte in Braun, und der Kohlefilm in Dunkellila} + \caption[Simulationsmodelle der Widerstände in CST]{Die in CST Studio Suite 2021 erstellten Widerstandsmodelle. + Zu sehen ist die Keramik in weiß, die Metallkontakte in Braun, und der Kohlefilm in Dunkellila. + Eigene Modellierung nach \cite{VishayRFreq}.} \end{figure} - -Eine weitere mögliche Bauart eines Widerstandes ist die sog. Flipchip-Terminierung. -Hierbei wird die Metallisierung nur auf einer Seite der Keramik, neben dem Widerstandsfilm, aufgebracht. -Dies soll Streueffekte und Kapazitäten verringern. Das für diese Widerstandsart erstellte Modell ist -in Abbildung \ref{fig:cst_model_1206_flipchip} dargestellt. - -Mithilfe dieser Modelle werden nun die kapazitiven Kopplungen bestimmt. -Hierfür wird der ``Electrostatic Solver'' genutzt, welcher die elektrischen Felder im statischen Zustand, -sowie die kapazitive Kopplung von Potentialflächen, berechnet. Die Widerstände werden hierbei auf einer Grundfläche aus FR4 platziert. -Dies entspricht dem Platinenmaterial einer reellen Platine, welches durch sein Dielektrikum auch Einfluss auf die Kapazitäten hat. +Mithilfe dieser Modelle werden die kapazitiven Kopplungen bestimmt. +Hierfür wird der ``Electrostatic Solver'' von CST genutzt, +welcher die elektrischen Felder im statischen Zustand, +sowie die kapazitive Kopplung von Potentialflächen berechnet. Die Widerstände werden hierbei auf einer Grundfläche aus FR4 platziert. +Dies entspricht dem Platinenmaterial einer realen Platine, welches durch sein Dielektrikum auch Einfluss auf die Kapazitäten hat. Der Flipchip-Widerstand wird hierbei mit den Kontakten nach unten zeigend simuliert. Bei dem Standard-1206 Gehäuse werden zwei Anbringungsmöglichkeiten (Widerstandsbelag nach oben und nach unten) getestet. +Die exakte Konfiguration der Simulation ist in Abbildung \ref{fig:cst_r_sim_setup} dargestellt. -\begin{figure}[h] + +\begin{figure}[ht] \centering \scalebox{-1}[1]{ \includegraphics[width=0.7\textwidth]{entwicklung/cst_model_simsetup.png} - } - \caption[Aufbau der Simulation der parasitären Rückkoppelkapazitäten]{\label{fig:cst_r_sim_setup}Aufbau der elektrostatischen Simulation der Widerstandskapazitäten. - Aufgebaut sind der Flipchip-Widerstand (rechts), ein regulärer 1206-Format Widerstand mit dem Kohlefilm auf der Unterseite (mittig), - und ein 1206-Widerstand in normaler Aufbauweise mit dem Film nach oben zeigend (links). Die Widerstände sind auf einem FR4-Substrat angebracht (türkis)} -\end{figure} + } + \caption[Aufbau der Simulation der parasitären Rückkoppelkapazitäten]{\label{fig:cst_r_sim_setup}Aufbau der elektrostatischen Simulation der Widerstandskapazitäten. + Aufgebaut sind der Flipchip-Widerstand (rechts), ein regulärer 1206-Format Widerstand mit dem Kohlefilm auf der Unterseite (mittig), + und ein 1206-Widerstand in normaler Aufbauweise mit dem Film nach oben zeigend (links). Die Widerstände sind auf einem FR4-Substrat angebracht (türkis)} + \end{figure} + +\FloatBarrier In der Simulation werden die metallisierten Enden der Widerstände auf unterschiedliche -potentiale gelegt, um das E-, D- und Potentialfeld berechnen zu können. -Hierbei wird $\pm\SI{0.5}{\volt}$ gewählt, um ein Gesamtpotential von $\SI{1}{\volt}$ auf zu bauen, wobei -die Auswahl der Potentialwerte auf die von CST berechnete Kapazität keinen Einfluss nimmt, und lediglich zur +Potentiale gelegt, um die elektrischen Felder berechnen zu können. +Hierbei wird $\pm\SI{0.5}{\volt}$ gewählt, um ein Gesamtpotential von $\SI{1}{\volt}$ aufzubauen, wobei +die Auswahl der Potentialwerte auf die von CST berechnete Kapazität keinen Einfluss nimmt und lediglich zur Visualisierung dient. -\begin{table}[h] +Die Ergebnisse sind in Tabelle \ref{table:para_r_cf} dargestellt. Deutlich zu erkennen ist eine +Verringerung der parasitären Kapazität bei der Flipchip-Technologie. Die Anbringung des Standard-1206 +Widerstandes hat nur eine kleine Auswirkung auf die Kapazität, wobei die normale Anbringung (Film obig) +etwas besser scheint. Zusätzlich wurde die Kapazität in das Vakuum bzw. Erde berechnet. +Dies beeinflusst nicht direkt die Übertragungsfunktion des Widerstandes, trägt jedoch zuz.~B. +der Eingangskapazität bei. Zudem scheint es keine großen Unterschiede bei der Anbringung des +1206-Widerstandes zu geben, wofür im Folgenden nur noch die Standard-Anbringung betrachtet wird. + +\begin{table}[hb] \centering - \caption{\label{table:para_r_cf}Ergebnisse der Kapazitätsberechnung} + \caption{\label{table:para_r_cf}Ergebnisse der Kapazitätsberechnung aus den CST-Simulationen} \begin{tabular}{ |l|r|r| } \hline - Typ & Parallelkapazität & Erdkapazität \\ + Typ & Parallelkapazität $C_\mathrm{p}$ & Streukapazität $C_\mathrm{g}$ \\ \hline 1206, Film obig & $\SI{46.81}{\femto\farad}$ & $\SI{89.95}{\femto\farad}$ \\ 1206, Film unten & $\SI{46.93}{\femto\farad}$ & $\SI{90.17}{\femto\farad}$ \\ @@ -147,27 +220,22 @@ Visualisierung dient. \end{tabular} \end{table} -Die Ergebnisste sind in Tabelle \ref{table:para_r_cf} dargestellt. Deutlich zu erkennen ist eine -Verringerung der parasitären Kapazität bei der Flipchip-Technologie. Die Anbringung des Standard-1206 -Widerstandes hat nur eine kleine Auswirkung auf die Kapazität, wobei die normale Anbringung (Film obig) -etwas besser scheint. Zusätzlich wurde die Kapazität in das Vakuum bzw. Erde berechnet. -Dies beeinflusst nicht direkt die Übertragungsfunktion des Widerstandes, trägt jedoch zu z.B. -der Eingangskapazität bei. Zudem scheint es keine großen Unterschiede bei der Anbringung des -1206-Widerstandes zu geben, wofür im Folgenden nur noch die Standard-Anbringung betrachtet wird. - Mithilfe der ersten Kapazitätswerte und der in Kapitel \ref{chap:tia_design_goals} bestimmten Bandbreite lässt sich nun ein oberer Grenzwert des Rückkoppelwiderstandes berechnen. -Dies ergibt aus der Gleichung der Grenzfrequenz eines RC-Filters, beschrieben in Gleichung \ref{eqn:max_rf}. +Dies ergibt sich aus der Gleichung der Grenzfrequenz eines RC-Filters, +beschrieben in Gleichung \ref{eqn:max_rf}. Hierbei ist $f$ die +zu erreichende Grenzfrequenz, $R_f$ der Ohm'sche Widerstand, und +$C_f$ die parasitäre Parallelkapazität. Die berechneten Grenzwerte der Widerstände sind in Tabelle \ref{table:para_r_max} dargestellt. \begin{eqnarray} - f_c & = & 2\pi\cdot \left(R_f \cdot C_f\right)^{-1} \\ + f_c & = & \frac{1}{2\pi\cdot R_f \cdot C_p} \\ \SI{30}{\kilo\hertz} & \leq & f_c \\ - \SI{30}{\kilo\hertz} & \leq & 2\pi\cdot \left(R_f\cdot C_f\right)^{-1} \\ - R_f & \leq & 2\pi\cdot \left(\SI{30}{\kilo\hertz}\cdot C_f\right)^{-1}\label{eqn:max_rf} + \SI{30}{\kilo\hertz} & \leq & \frac{1}{2\pi\cdot R_f \cdot C_p} \\ + R_f & \leq & \frac{1}{2\pi\cdot \SI{30}{\kilo\hertz} \cdot C_p} \label{eqn:max_rf} \end{eqnarray} -\begin{table}[h] +\begin{table}[hb] \centering \caption{\label{table:para_r_max}Obere Grenzwerte der Widerstandsauswahl} \begin{tabular}{ |l|r| } @@ -182,51 +250,63 @@ Die berechneten Grenzwerte der Widerstände sind in Tabelle \ref{table:para_r_ma \end{table} Für den gesamten TIV ist nach Kapitel \ref{chap:tia_design_goals} eine Gesamtverstärkung -von ca. $\SI{2}{\giga\ohm}$ gewünscht, und entsprechend des vorherigen Kapitels ist ein möglichst großer +von circa $\SI{1}{\giga\ohm}$ angestrebt und entsprechend des vorherigen Kapitels ist ein möglichst großer Rückkoppelwiderstand vorteilhaft. Somit wird nun mithilfe der Simulationen nach der Quelle -dieser Kapazität gesucht, und Möglichkeiten zur Verringerung dieser (und somit Steigerung der Widerstandsgrenze) gesucht. +dieser Kapazität und nach Möglichkeiten zur Verringerung dieser (und somit Steigerung der Widerstandsgrenze) gesucht. Abbildungen \ref{fig:cst_r_potentials} und \ref{fig:cst_r_ds} zeigen die Ergebnisse der Feldsimulationen -auf. Vor allem die Darstellung des D-Feldes gibt Hinweise auf die Positionen der parasitären Kapazitäten, -da sich die auf einer leitenden Fläche befindende Ladung wie folgt berechnen lässt:\todo{Quote Maxwell?} +auf. Hierbei ist die Feldstärke des betrachteten Feldes entlang einer Schnittfläche +aufgezeichnet. Das Potentialfeld lässt auf die Verteilung des +Spannungsverlaufes schließen, während das +D-Feldes Hinweise auf die Positionen der parasitären Kapazitäten gibt. +Dies ist möglich, da sich durch Integration des D-Feldes die Ladungsverteilung +auf leitenden Flächen berechnen lässt, wie in Gleichung +\ref{eqn:integral_d} angegeben ist \cite{GaussLaw}. \begin{equation} - \iint \mathbf{D} \cdot dS = \iiint \rho_f dV\label{eqn:integral_d} + \iint \vec{D} \cdot d\vec{A} = \iiint \rho_f dV\label{eqn:integral_d} \end{equation} -Durch Bestimmung der Flussrichtungen des D-Feldes lassen sich somit die Quellen der -Ladungen bestimmen. Dies ist zum Verständnis der Kapazität und der späteren Verminderung dieser -nützlich.\todo{Rewrite this more understandably} +Die Quellen des D-Feldes geben so Hinweise auf die Ladungsverteilung +der Simulation, wobei diese Ladungen von den hier betrachteten +Kapazitäten verursacht werden. Die D-Felder zeigen somit auf, +welche Elemente der Simulation zur Kapazität beitragen. \begin{figure}[p] \centering \begin{subfigure}[b]{1\linewidth} \centering - \includegraphics[width=0.8\textwidth]{entwicklung/cst_estatic/potential_all.png} + \includegraphics[width=0.7\textwidth]{entwicklung/cst_estatic/potential_all.png} \subcaption{\label{fig:cst_estatic_potential_all}Potentialfeld der Widerstände aus oberer Ansicht} \end{subfigure} \vspace{2pt} - \hspace{0.1\linewidth}% - \begin{subfigure}[t]{.25\linewidth} + \hspace{0.15\linewidth}% + \begin{subfigure}[t]{.22\linewidth} \centering - \includegraphics[width=1\textwidth,trim={0 0 0 0.8cm},clip]{entwicklung/cst_estatic/potential_3t_t} + \includegraphics[width=1\textwidth,trim={0 0.8cm 0 1.6cm},clip]{entwicklung/cst_estatic/potential_3t_t} \subcaption{Potential innerhalb des nach oben zeigenden 1206 Widerstandes} \end{subfigure}\hfill% - \begin{subfigure}[t]{.25\linewidth} + \begin{subfigure}[t]{.22\linewidth} \centering - \includegraphics[width=1\textwidth]{entwicklung/cst_estatic/potential_3t_b} + \includegraphics[width=1\textwidth,trim={0 0.8cm 0 0.8cm},clip] + {entwicklung/cst_estatic/potential_3t_b} \subcaption{Potential innerhalb des herunterzeigenden 1206 Widerstandes} \end{subfigure}\hfill% - \begin{subfigure}[t]{.25\linewidth} + \begin{subfigure}[t]{.22\linewidth} \centering - \includegraphics[width=1\textwidth]{entwicklung/cst_estatic/potential_flip} + \includegraphics[width=1\textwidth,trim={0 0.8cm 0 0.8cm},clip]{entwicklung/cst_estatic/potential_flip} \subcaption{Potential innerhalb des Flipchip} - \end{subfigure}\hspace{0.1\linewidth} + \end{subfigure}\hspace{0.15\linewidth} - \caption{\label{fig:cst_r_potentials}Die Potentialfelder der elektrostatischen Simulation - der Widerstände, verschiedene Ansichten} + \caption[Potentialfelder der elektrostatischen Simulation + der Widerstände, verschiedene Ansichten]{ + \label{fig:cst_r_potentials}Potentialfelder der elektrostatischen Simulation + der Widerstände, verschiedene Ansichten, gleiche Farbskala für alle Ansichten. + Deutlich zu erkennen + ist die gleichmäßige Verteilung des Potentialfeldes um die Anschlüsse der + Widerstände herum.} \end{figure} @@ -235,47 +315,55 @@ nützlich.\todo{Rewrite this more understandably} \centering \begin{subfigure}[b]{1\linewidth} \centering - \includegraphics[width=0.8\textwidth]{entwicklung/cst_estatic/d_all} + \includegraphics[width=0.7\textwidth]{entwicklung/cst_estatic/d_all} \subcaption{\label{fig:cst_estatic_d_all}D-Feld der Widerstände von oberer Ansicht} \end{subfigure} \vspace{2pt} - \hspace{0.1\linewidth}% - \begin{subfigure}[t]{.25\linewidth} + \hspace{0.15\linewidth}% + \begin{subfigure}[t]{.22\linewidth} \centering - \includegraphics[width=1\textwidth]{entwicklung/cst_estatic/d_3t_t} + \includegraphics[width=1\textwidth,trim={0 0.8cm 0 0.8cm},clip]{entwicklung/cst_estatic/d_3t_t} \subcaption{Schnittfläche des D-Feldes in der Mitte des nach oben zeigenden 1206 Widerstandes} \end{subfigure}\hfill% - \begin{subfigure}[t]{.25\linewidth} + \begin{subfigure}[t]{.22\linewidth} \centering - \includegraphics[width=1\textwidth,clip,trim={0 0.4cm 0 0.4cm}]{entwicklung/cst_estatic/d_3t_b} + \includegraphics[width=1\textwidth,clip,trim={0 1.2cm 0 1.2cm}]{entwicklung/cst_estatic/d_3t_b} \subcaption{Schnittfläche des D-Feldes in der Mitte des herunterzeigenden 1206} \end{subfigure}\hfill% - \begin{subfigure}[t]{.25\linewidth} + \begin{subfigure}[t]{.22\linewidth} \centering - \includegraphics[width=1\textwidth,clip,trim={0cm 0.4cm 0cm 0.4cm}]{entwicklung/cst_estatic/d_flip} + \includegraphics[width=1\textwidth,clip,trim={0cm 1.2cm 0cm 1.2cm}]{entwicklung/cst_estatic/d_flip} \subcaption{\label{fig:cst_d_flipchip}Schnittfläche des D-Feldes in der Mitte des Flipchip} - \end{subfigure}\hspace{0.1\linewidth} + \end{subfigure}\hspace{0.15\linewidth} - \caption{\label{fig:cst_r_ds} Die D-Feldstärken der elektrostatischen Simulation in verschiedenen Ansichten.} + \caption[D-Felder der Widerstandssimulationen]{ + \label{fig:cst_r_ds} + D-Feldstärken der elektrostatischen Simulation in verschiedenen Ansichten, + gleiche Farbskala für alle Ansichten. + Die D-Felder geben Aufschlüsse über die Ladungsverteilung und + somit die Verteilung der Kapazitäten. Deutlich zu erkennen ist die + Konzentration der Felder um die Kontaktflächen der Widerstände herum.} \end{figure} + +\FloatBarrier + Deutlich zu erkennen ist der Grund der geringeren Kapazität des Flipchip in Abbildung \ref{fig:cst_d_flipchip} im Vergleich zu dem Standardwiderstand. Durch die geringere metallisierte Oberfläche ist die D-Feld-Intensität -innerhalb der Keramik des Widerstandes verringert, und befindet sich näher an der Unterseite. +innerhalb der Keramik des Widerstandes verringert und befindet sich näher an der Unterseite. Bei den Standardwiderständen liegt eine homogene Ausbreitung des D-Feldes in der Keramik vor. -Die D-Feld-Intensität innerhalb des PCB-Materials ist bei allen drei Widerständen gleich, und scheint ebenfalls -einen großen Einfluss auf die Kapazität zu besitzen. - +Die D-Feld-Intensität innerhalb des PCB-Materials ist bei allen drei Widerständen gleich +und scheint ebenfalls einen großen Einfluss auf die Kapazität zu besitzen. CST erlaubt die Berechnung des Feldflusses durch eine gegebene Fläche, welches dem Flächenintegral der Gleichung \ref{eqn:integral_d} entspricht. Somit können die Ladungsanteile berechnet werden, welche durch das D-Feld verursacht werden. -Abbildung \ref{fig:d_field_probe_all} zeigt die Flächen, welche zum integrieren verwendet wurden. +Abbildung \ref{fig:d_field_probe_all} zeigt die Flächen, welche zum Integrieren verwendet wurden. Die entsprechenden Ergebnisse der Integration sind in Tabelle \ref{table:d_field_integration} dargestellt. -\begin{figure}[h] +\begin{figure}[ht] \begin{subfigure}[t]{.5\linewidth} \centering \includegraphics[width=0.9\textwidth]{entwicklung/cst_estatic/d_probe_fc.png} @@ -290,11 +378,7 @@ Die entsprechenden Ergebnisse der Integration sind in Tabelle \ref{table:d_field Berechnung des D-Feld-Durchflusses} \end{figure} -Angemerkt werden muss hierbei, dass die Simulation auch die Kapazität in das Vakuum simuliert. -Die somit berechneten Ladungen entsprechen nicht nur der Parallel-, sondern auch der Erdkapazität. -Dies erklärt die leichten Diskrepanzen der berechneten Kapazität und der berechneten Feldstärken. -Aus diesem Grund können die berechneten Feldstärken nur als Richtlinie für die Verteilung der Felder genutzt werden. - +\FloatBarrier \begin{table}[h] \centering @@ -309,20 +393,33 @@ Aus diesem Grund können die berechneten Feldstärken nur als Richtlinie für di \end{tabular} \end{table} +Hierbei muss angemerkt werden, dass die Simulation auch die Kapazität in das Vakuum simuliert. +Die somit berechneten Ladungen entsprechen nicht nur der Parallel-, sondern auch der Streukapazität. +Dies erklärt die leichten Diskrepanzen der berechneten Kapazität und der berechneten Feldstärken. +Aus diesem Grund können die berechneten Feldstärken nur als Richtlinie für die Verteilung der Felder genutzt werden. -Zu sehen ist, dass sich ein erheblicher Anteil des Feldes, circa 50\%, durch das Material des PCBs bewegt. Dies +Zu sehen ist, dass sich ein erheblicher Anteil des Feldes,circa 50\%, durch das Material des PCBs bewegt. Dies trifft auf sowohl den Standard-Widerstand als auch den Flipchip zu. +\FloatBarrier + \subsubsection{Mitigation der Parallelkapazität} \label{chap:r_para_mitigations} -Im Folgenden wird untersucht, ob durch eine bestimmte Platzierung von Elektroden im PCB-Material -die Parallelkapazität verringert werden kann.\todo{Find a citation for this.} -Durch korrekte Platzierung von Elektroden mit festgelegtem Potential kann theoretisch das D-Feld auf diese umgeleitet -werden, wodurch das PCB-Material selbst eine kleinere Teilhabe an der parasitären Kapazität des Widerstandes haben sollte. + +Um den parasitären Kapazitäten entgegen zu wirken soll nun untersucht werden, +ob durch eine bestimmte Platzierung von Elektroden im PCB-Material +die Parallelkapazität verringert werden kann. +Durch korrekte Platzierung eines sog. Guard Rings bzw. +einer Abschirmungselektrode +kann theoretisch das D-Feld auf diese umgeleitet +werden, wodurch das PCB-Material selbst eine kleinere Teilhabe an der +parasitären Kapazität des Widerstandes haben sollte \cite{SierraReduceCapacitances}\cite{Yang:21}. Ein erster Versuch hierfür wird aus zwei symmetrischen Elektroden aufgebaut, welche unterhalb der Kontakte der -Widerstände aufgebaut werden, und auf das selbe Potential wie die entsprechenden Kontakte gelegt werden. -Abbildung \ref{fig:r_symmetric_shielding} zeigt den Aufbau der im folgenden verwendeten Abschirmungselektroden und +Widerstände aufgebaut werden. +Ein separater Widerstandsteiler treibt diese Elektroden auf dasselbe Potential wie die entsprechenden Kontakte, +um eine zusätzliche Last auf den hochohmigen Widerstand zu vermeiden. +Abbildung \ref{fig:r_symmetric_shielding} zeigt den Aufbau der im Folgenden verwendeten Abschirmungselektroden und deren Potentiale. \begin{figure}[h] @@ -336,43 +433,66 @@ deren Potentiale. \includegraphics[clip,trim={0 0 0.4cm 0},width=0.9\linewidth]{entwicklung/cst_estatic_shld/shielding_potential.png} \caption{\label{fig:r_symmetric_shielding_potential}Potentialfeld der Schirmungselektroden} \end{subfigure} - \caption{\label{fig:r_symmetric_shielding}Schnittbild durch das Simulatiosmodell mit eingebauten Abschirmungselektroden} + \caption[Schnittbild durch die CST-Simulation der Abschirmungselektroden]{ + \label{fig:r_symmetric_shielding} + Schnittbild + durch das Simulatiosmodell in CST, mit eingebauten Abschirmungselektroden. + Deutlich zu erkennen ist die Umverteilung des Potentialfeldes, welches + durch die Abschirmungselektroden verursacht wird.} \end{figure} Da es bei diesem Aufbau vier Potentiale gibt, sind auch entsprechend mehr Kapazitäten zu beachten. -Abbidlung \ref{fig:r_shielding_capacitances} zeigt alle Kapazitäten, welche von einem Kontakt sichtbar sind. +Abbidlung \ref{fig:r_shielding_capacitances} zeigt die in der Simulation +betrachteten Kapazitäten, welche an einem der Widerstandskontakte anliegen. \begin{figure}[h] \centering \includegraphics[width=0.6\linewidth]{entwicklung/cst_estatic_shld/shielding_capacitors.drawio.png} - \caption{\label{fig:r_shielding_capacitances}Schematische Darstellung der Kapazitäten, welche einer der Widerstandskontakte sieht.} + \caption[Schematische Darstellung der Kapazitäten, welche einer der Widerstandskontakte sieht]{ + \label{fig:r_shielding_capacitances} + Schematische Darstellung der Kapazitäten, welche einer der Widerstandskontakte sieht. + Eigene Darstellung.} \end{figure} Von Interesse sind die Parallelkapazität der Widerstandskontake, $C_\mathrm{r,p}$, -welches der im vorherigen Kapitel beschriebenen Kapazität entspricht, sowie den +welches der im vorherigen Kapitel beschriebenen Kapazität $C_p$ entspricht, sowie den Kapazitäten $C_\mathrm{sa,rb}$ und $C_\mathrm{sb,ra}$, welche zwischen dem Widerstand und den -Schirmungselektroden entstehen. Durch den hier verwendeten Aufbau sind diese Kapazitäten symmetrisch, +Schirmungselektroden entstehen. Durch den hier verwendeten Aufbau sind diese Kapazitäten symmetrisch und werden im Folgenden als $C_\mathrm{r,sp}$ bezeichnet. Die Kapazitäten $C_\mathrm{sa,ra}$ und $C_\mathrm{sb,rb}$ sind nicht relevant für die Bandbreite, da die Schirmelektrode auf das Potential des anliegenden Widerstandes getrieben wird, können -jedoch z.~B. die Eingangskapazität erhöhen. Sie werden im Folgenden als $C_\mathrm{r,s}$ bezeichnet. -Ebenso ist die Kapazität zwischen den Schirmelektroden nicht relevant, da diese separat getrieben werden und nicht hochohmig sind. +jedoch z.~B. die Eingangskapazität erhöhen. Diese werden im Folgenden als $C_\mathrm{r,s}$ bezeichnet. -\begin{table}[h] +Die Kapazität zwischen den Schirmelektroden beeinflusst nicht den hochohmigen Widerstand selbst, +da diese wie bereits beschrieben separat und niederohming mit Spannung versorgt werden. +Parasitäre Kapazitäten beeinflussen somit die Spannungen an den Schirmelektroden vernachlässigbar. + +Tabelle \ref{table:shielding_capacitances} zeigt, dass die nun berechneten gesamten +Parallelkapazitäten ($C_\mathrm{r,p} + C_\mathrm{r,sp} = C_\mathrm{p}$) wesentlich +geringer sind als diejenigen ohne Abschirmung (Vergleich $C_\mathrm{p}$ in Tabelle \ref{table:shielding_capacitances} +mit Tabelle \ref{table:para_r_cf}). Dies wird ebenfalls durch eine erneute Ladungsberechnung +mit der in Abbildung \ref{fig:d_field_probe_all} aufgezeigten Integrationsflächen bestätigt, dessen Ergebnisse in +Tabelle \ref{table:shielding_charges} dargestellt sind. +Sowohl die vom Kern als auch die im PCB verursachten Ladungen wurden verringert, was darauf schließen +lässt, dass die Abschirmungselektroden einen größeren Einfluss haben als erwartet. +Abbildung \ref{fig:shielding_d_field} zeigt die Schnittbilder der D-Felder mit Abschirmungselektroden auf. + + +\begin{table}[hbp] \centering \caption{\label{table:shielding_capacitances}Parasitäre Kapazitäten mit Abschirmungselektroden} - \begin{tabular}{ |c|c|c|c|c| } + \begin{tabular}{ |c|c|c|c|c|c| } \hline - Typ & $C_\mathrm{r,p}$ & $C_\mathrm{r,sp}$ & $C_\mathrm{r,s}$ & $C_\mathrm{r,g}$ \\ + Typ & $C_\mathrm{r,p}$ & $C_\mathrm{r,sp}$ & $C_\mathrm{r,s}$ & $C_\mathrm{r,g}$ & $C_\mathrm{p}$ \\ \hline - 1206 & $\SI{5.64}{\femto\farad}$ & $\SI{28.16}{\femto\farad}$ & $\SI{194.25}{\femto\farad}$ & $\SI{17.71}{\femto\farad}$ \\ - Flipchip & $\SI{3.51}{\femto\farad}$ & $\SI{23.39}{\femto\farad}$ & $\SI{183.53}{\femto\farad}$ & $\SI{15.99}{\femto\farad}$ \\ + 1206 & $\SI{5.64}{\femto\farad}$ & $\SI{28.16}{\femto\farad}$ & $\SI{194.25}{\femto\farad}$ & $\SI{17.71}{\femto\farad}$ & $\SI{33.8}{\femto\farad}$ \\ + Flipchip & $\SI{3.51}{\femto\farad}$ & $\SI{23.39}{\femto\farad}$ & $\SI{183.53}{\femto\farad}$ & $\SI{15.99}{\femto\farad}$ & $\SI{26.9}{\femto\farad}$ \\ \hline \end{tabular} \end{table} -\begin{table}[h] +\begin{table}[htp] \centering \caption{\label{table:shielding_charges}Ergebnisse der Feldintegration mit Abschrimung bei $\SI{1}{\volt}$ Potential} \begin{tabular}{ |c|r|r| } @@ -385,16 +505,7 @@ Ebenso ist die Kapazität zwischen den Schirmelektroden nicht relevant, da diese \end{tabular} \end{table} -Tabelle \ref{table:shielding_capacitances} zeigt, dass die nun berechneten gesamten -Parallelkapazitäten ($C_\mathrm{r,p} + C_\mathrm{r,sp}$) wesentlich -geringer sind als diejenigen ohne Abschirmung. Dies wird ebenfalls durch eine erneute Ladungsberechnung -mit der in \ref{fig:d_field_probe_all} aufgezeigten Integrationsflächen bestätigt, dessen Ergebnisse in -Tabelle \ref{table:shielding_charges} dargestellt sind. -Sowohl die vom Kern als auch die im PCB Verursachten Ladungen wurden verringert, was darauf schließen -lässt dass die Abschirmungselektroden einen größeren Einfluss haben als erwartet. -Abbildung \ref{fig:shielding_d_field} zeigt die Schnittbilder der D-Felder mit Abschirmungselektroden auf. - -\begin{figure}[h] +\begin{figure}[htp] \begin{subfigure}[t]{.5\linewidth} \centering \includegraphics[clip,trim={0 0 0 0},width=0.9\linewidth]{entwicklung/cst_estatic_shld/d_3t_t.png} @@ -405,19 +516,24 @@ Abbildung \ref{fig:shielding_d_field} zeigt die Schnittbilder der D-Felder mit A \includegraphics[clip,trim={0.5cm 0 0.5cm 0},width=0.9\linewidth]{entwicklung/cst_estatic_shld/d_fc.png} \caption{Schnittbild des Flipchip} \end{subfigure} - \caption{\label{fig:shielding_d_field}Schnittbild des D-Feldes durch das Simulatiosmodell mit eingebauten Abschirmungselektroden} + \caption[Schnittbild der D-Feld Simulation der Abschirmungselektroden]{\label{fig:shielding_d_field}Schnittbild + des D-Feldes durch das Simulatiosmodell mit eingebauten Abschirmungselektroden. + Zu erkennen ist die Umverteilung des D-Feldes von den Kontakten des Widerstandes + weg auf die Abschirmungen hin.} \end{figure} +\FloatBarrier + Die Abschirmungselektroden sind somit in der Lage, die parasitäre Parallelkapazität des Widerstandes deutlich -zu verringern. Hierdurch jedoch entstehen größere Kapazitäten zu den jeweiligen Schirmungselektroden, welche somit +zu verringern. Hierdurch entstehen jedoch größere Kapazitäten zu den jeweiligen Schirmungselektroden, welche somit auf das gleiche Potential wie den entsprechenden Widerstandskontakt getrieben werden müssen, um negative Effekte auf die Bandbreite zu vermeiden. Mit der verringerten Parallelkapazität lassen sich somit größere Widerstände verwenden. Die erneut berechneten Grenzwerte sind in Tabelle \ref{table:para_rshield_max} aufgelistet. -\begin{table}[h] +\begin{table}[ht] \centering - \caption{\label{table:para_rshield_max}Obere Grenzwerte der Widerstandsauswahl mit Abschrimung} + \caption{\label{table:para_rshield_max}Obere Grenzwerte der Widerstandsauswahl mit Abschirmelektroden} \begin{tabular}{ |c|r| } \hline Typ & Grenzwert \\ @@ -428,93 +544,122 @@ Grenzwerte sind in Tabelle \ref{table:para_rshield_max} aufgelistet. \end{tabular} \end{table} +\FloatBarrier + Da die berechneten Werte noch nicht der in Kapitel \ref{chap:tia_design_goals} festgelegten Verstärkung entsprechen, werden zusätzlich noch andere Möglichkeiten zur Verringerung der -Parallelkapazität hinzu gezogen. +Parallelkapazität hinzugezogen. Eine dieser Möglichkeiten ist die Nutzung mehrerer Widerstände in Reihenschaltung. -Hierdurch wird der effektive Widerstand der Gesamtschaltung erhöht und die Parallelkapazität -verringert, entsprechend: +Gleichungen \ref{eqn:r_series_calc} und \ref{eqn:c_series_calc} beschreiben, wie +sich Gesamtwiderstand und -Kapazität bei Serienschaltung verhalten. \begin{eqnarray} - R_\mathrm{tot} & = & \sum_{i=1}^{n}{R_i} \\ - C_\mathrm{tot} & = & \left(\sum_{i=1}^{n}{\frac{1}{C_i}} \right)^{-1} + R_\mathrm{tot} & = & \sum_{i=1}^{n}{R_i} \label{eqn:r_series_calc}\\ + C_\mathrm{tot} & = & \left(\sum_{i=1}^{n}{\frac{1}{C_i}} \right)^{-1}\label{eqn:c_series_calc} \end{eqnarray} -Und mit einer Vereinfachung, dass alle Widerstände gleich gewählt sind, ergibt sich: - -\begin{eqnarray} - R_\mathrm{tot} & = & R\cdot n \\ - C_\mathrm{tot} & = & \frac{C}{n} \\ - f_\mathrm{c,tot} & = & 2\pi\cdot \left(R_\mathrm{tot}\cdot C_{tot}\right)^{-1} \\ - f_\mathrm{c,tot} & = & 2\pi\cdot \left(Rn \cdot \frac{C}{n}\right)^{-1} \\ - f_\mathrm{c,tot} & = & 2\pi\cdot \left(R\cdot C\right)^{-1}\label{eqn:r_series_frequency} -\end{eqnarray} +Mit der in Kapitel \ref{chap:r_para_calculations} genutzten Formel zur Berechnung +der Grenzfrequenz der RC-Schaltung kann nun die Grenzfrequenz der Serienschaltung +mehrerer Widerstände berechnet werden. +Hierfür werden $R_\mathrm{tot}$ und +$C_\mathrm{tot}$ in Gleichung \ref{eqn:rc_frequency} eingesetzt. Zusätzlich wird +vereinfacht davon ausgegangen, dass alle Widerstände gleich gewählt sind, wodurch +sich der totale Widerstand und die Kapazität entsprechend Gleichungen +\ref{eqn:series_r_rc_rsum} und \ref{eqn:series_r_rc_csum} berechnen lassen. +Gleichung \ref{eqn:r_series_frequency} beschreibt die Grenzfrequenz +der Reihenschaltung der Widerstände. Aus Gleichung \ref{eqn:r_series_frequency} lässt sich erschließen, dass die Grenzfrequenz der Gesamtschaltung der Grenzfrequenz eines einzelnen Widerstandes entspricht. Dies bedeutet, dass bei Auswahl eines geeigneten Einzelwiderstandes eine beliebig hohe -Gesamtimpedanz bei gleicher Bandbreite kreiert werden kann. +Gesamtimpedanz bei gleicher Bandbreite erreichbar ist. + +\begin{eqnarray} + R_\mathrm{tot} & = & n\cdot R \label{eqn:series_r_rc_rsum}\\ + C_\mathrm{tot} & = & \frac{C}{n} \label{eqn:series_r_rc_csum}\\ + f_\mathrm{3 db,tot} & = & \frac{1}{2\pi\cdot R_\mathrm{tot}\cdot C_{tot}} \\ + f_\mathrm{3 db,tot} & = & \frac{1}{2\pi\cdot nR \cdot \frac{C}{n}} \\ + f_\mathrm{3 db,tot} & = & \frac{1}{2\pi\cdot R\cdot C}\label{eqn:r_series_frequency} +\end{eqnarray} + + Zu beachten ist jedoch, dass die einzelnen Zweige dieser Widerstandsschaltung -hochimpedante und somit empfindliche Potentiale dar stellen. -Parasitäre Kapazitäten z.B. zu Erde, wie diejenigen in Tabelle \ref{table:shielding_capacitances} dargestellt, +hochimpedante und somit empfindliche Potentiale darstellen. +Parasitäre Kapazitäten wie z.~B. Streukapazitäten, +wie diejenigen in Tabelle \ref{table:shielding_capacitances} dargestellt, können an diesen Potentialen ebenfalls die Bandbreite beeinflussen. Mithilfe einer weiteren Simulation wird der Einfluss der Kapazitäten zu Erde untersucht. Abbildung \ref{fig:r_series_para_sim} zeigt die verwendete Schaltung auf; die Ergebnisse dieser sind in Abbildung \ref{fig:r_series_para_results} aufgezeigt. Varriert wird hierbei die Größe der einzelnen Kapazitäten zur Erde hin. -\begin{figure}[hbt!] +\begin{figure}[htb!] \centering \includegraphics[width=0.8\textwidth]{entwicklung/r_series/series_noshield.png} \caption{\label{fig:r_series_para_sim}Aufbau der Simulation zur - Analyse des Effektes der parasitären Kapazitäten auf eine Widerstands-Serienschaltung} + Analyse des Effektes der parasitären Kapazitäten auf eine Widerstands-Serienschaltung.} \end{figure} -\begin{figure}[hbt!] +\begin{figure}[htb!] \centering \includegraphics[scale=0.8]{datavis/Parasitics/Rf_series_noshield.png} - \caption{\label{fig:r_series_para_results}Ergebnisse der Simulation des - Einflusses der parasitären Erdkapazität.} + \caption[Ergebnisse der Simulation des + Einflusses der parasitären Streukapazität]{\label{fig:r_series_para_results}Ergebnisse der Simulation des + Einflusses der parasitären Streukapazität. Zu erkennen ist die starke Überhöhung der + Übertragungsfunktion des TIVs, verursacht durch eine zu hohe Streukapazität im + Rückkoppelpfad.} \end{figure} +\FloatBarrier + Deutlich zu erkennen ist eine starke Überhöhung der Bandbreite der Schaltung bei steigenden parasitären Kapazitäten, welche auf eine Instabilität der Schaltung hinweisen. Eine Verringerung der Kapazität zur Erde ist somit notwendig zum Erhalt der Stabilität bei Nutzung einer Reihenschaltung von Widerständen. - -\begin{figure}[hbt!] - \centering - \includegraphics[width=0.8\textwidth]{entwicklung/r_series/series_shielded.png} - \caption{\label{fig:r_series_para_comp_sim}Aufbau der Simulation zur - Analyse des Effektes der Schirmungskapazitäten auf eine Widerstands-Serienschaltung} -\end{figure} - -\begin{figure}[hbt!] - \centering - \includegraphics[scale=0.8]{datavis/Parasitics/Rf_series_shielded.png} - \caption{\label{fig:r_series_para_comp_results}Ergebnisse der Simulation - zur Analyse der Auswirkungen der Abschirmkapazitäten.} -\end{figure} - -Hierfür können die im vorherigen Teil beschriebenen Abschirmungselektroden genutzt werden. +Hierfür können die im vorherigen Abschnitt beschriebenen Abschirmungselektroden genutzt werden. Werden diese Elektroden über einen Widerstandsteiler auf die gleichen Potentiale wie die hochimpedanten -Widerstandszweige gelegt, so fließt kein Strom durch die parasitären Kapazitäten zur Abschirmung, und +Widerstandszweige gelegt, so fließt kein Strom durch die parasitären Kapazitäten zur Abschirmung und die Bandbreite wird nicht angehoben. Dies wird über eine weitere Simulation (Abbildung \ref{fig:r_series_para_comp_sim}) bestätigt. -Abbildung \ref{fig:r_series_para_comp_results} zeigt die berechneten Bandbreiten bei variierter +Abbildung \ref{fig:r_series_para_comp_results} zeigt die simulierten Bandbreiten bei variierter Kapazität auf. Deutlich zu erkennen ist eine wesentlich flachere Bandbreite bei größerer -Abschirmkapazität, und eine Verminderung bis hin zur kompletten Vermeidung einer Überhöhung. +Abschirmkapazität und eine Verminderung bis hin zur kompletten Vermeidung einer Überhöhung. +Es ist zu vermuten dass eine zu hohe Abschirmkapazität auch Rauschen in die Schaltung mit +ein bringt, weshalb die Kapazität der Schirmung passend ausgelegt werden muss. Dies ist +jedoch in einer Simulation schwer zu belegen, da die parasitären Rauscheffekte +einer realen Schaltung nicht einfach zu simulieren sind. -\FloatBarrier +\begin{figure}[htb!] + \centering + \includegraphics[width=0.8\textwidth]{entwicklung/r_series/series_shielded.png} + \caption[Aufbau der Simulation zur + Analyse des Effektes der Schirmungskapazitäten auf eine Widerstands-Serienschaltung]{\label{fig:r_series_para_comp_sim}Aufbau der Simulation zur + Analyse des Effektes der Schirmungskapazitäten auf eine Widerstands-Serienschaltung.} +\end{figure} + +\begin{figure}[htb!] + \centering + \includegraphics[scale=0.8]{datavis/Parasitics/Rf_series_shielded.png} + \caption[Ergebnisse der Simulation + zur Analyse der Auswirkungen der Abschirmkapazitäten]{ + \label{fig:r_series_para_comp_results}Ergebnisse der Simulation + zur Analyse der Auswirkungen der Abschirmkapazitäten. Zu erkennen + ist, dass eine zu kleine Abschirmung der Streukapazität nicht entgegen wirken + kann. Eine höhere Abschirmkapazität scheint die Bandbreite stabiler zu halten.} +\end{figure} + + +\clearpage \subsection{Effekte des OpAmp} \label{chap:effects_opamp} -Im folgenden wird auf die Effekte des OpAmp eingegangen. -Als zentrales aktives Bauteil besitzt der OpAmp einen maßgeblichen Einfluss auf die Schaltung, -und eine korrekte Auswahl ist notwendig um die festgelegten Zielparameter erreichen zu können. +Dieser Abschnitt befasst sich nun mit den Effekte des OpAmp. +Als zentrales aktives Bauteil besitzt der OpAmp einen maßgeblichen Einfluss auf die Schaltung +und eine korrekte Auswahl ist notwendig um die in Kapitel +\ref{chap:tia_design_goals} festgelegten Zielparameter zu erreichen. Dieser Auswahlprozess wird hier dargelegt. \subsubsection{Limitierungen der Verstärkung} @@ -524,50 +669,77 @@ Wie bereits in Kapitel \ref{chap:basics_opamp} beschrieben, sind zwei der zentra OpAmp seine offene Verstärkung sowie sein GBWP. Diese Parameter legen fest, welche Bandbreite bei gegebener Verstärkung erreichbar ist. Die mathematische Berechnung dieser Grenzwerte ist durch den hohen Einfluss parasitärer Effekte -wie z.B. der Eingangskapazität der Schaltung nur schwer zu erreichen. +wiez.~B. der Eingangskapazität der Schaltung nur schwer zu erreichen. Aus diesem Grund werden die benötigten Parameter mithilfe einer Simulation in der Software ``LTSpice'' berechnet, welche den Aufbau und die Simulation von elektrischen Schaltungen ermöglicht. Abbildung \ref{fig:opamp_gbwp_circuit} zeigt den in LTSpice erstellten Schaltkreis. -Hierbei werden optimistische Werte für parasitäre Eigenschaften verwendet. -Diese dürfen nicht vernachlässigt werden, da sie ebenfalls auf die Transferfunktion des OpAmp -Einfluss nehmen können, die optimistische Wahl gibt jedoch genug Freiraum für varianzen im -späteren aufgebauten Schaltkreis. -Ein Rückkoppelwiderstand von $\SI{1}{\giga\ohm}$ wird als realistischer Zielwert der Gesamtverstärkung -der Schaltung gewählt. +Hierbei werden optimistischere Werte für parasitäre Effekte wie +die Rückkoppelkapazitäten gewählt, welche +nicht vom OpAmp verursacht werden. Hierdurch ist sichergestellt dass die parasitären +Effekte des OpAmp selbst in der Simulation dominierend sind. +Ein Rückkoppelwiderstand von $\SI{1}{\giga\ohm}$ wird entsprechend +des gewählten Zielwertes gewählt. \begin{figure}[h] \centering \includegraphics[width=0.6\linewidth]{entwicklung/opamp/opamp_gbwp.png} - \caption{\label{fig:opamp_gbwp_circuit}LTSpice-Schaltkreis zur Simulation der OpAmp-Transferfunktion} + \caption[LTSpice-Schaltkreis zur Simulation der OpAmp-Übertragungsfunktion]{ + \label{fig:opamp_gbwp_circuit}LTSpice-Schaltkreis zur Simulation der OpAmp-Übertragungsfunktion. + } \end{figure} -Die Stromquelle I1 wird als Stimulus-Eingang genutzt, +\FloatBarrier + +Die Stromquelle I1 wird als Stimulus-Eingang genutzt und gibt ein Signal von $\SI{1}{\nano\ampere}$ aus. Eine parasitäre Eingangskapazität -von $\SI{10}{\pico\farad}$ wird entsprechend Erfahrungswerten bestehender Schaltkreise gewählt. +von $\SI{10}{\pico\farad}$ wird als beispielhafter +Wert der Eingangskapazität von OpAmp, PCB und Eingangsbuchse gewählt. Die parasitäre Parallelkapazität C1 wird auf $\SI{3}{\femto\farad}$ als absolutes Minimum der in Kapitel \ref{chap:r_para_calculations} berechneten Kapazitäten gesetzt. Gemessen wird die Ausgangsspannung des Verstärkers U1. In einem ersten Versuch wird die Eingangsfrequenz von $\SI{1}{\hertz}$ -bis $\SI{1}{\mega\hertz}$ varriiert, und die Ausgangsamplitude vermessen. +bis $\SI{1}{\mega\hertz}$ variiert und die Ausgangsamplitude vermessen. Verschiedene Kurven bei verändertem GBWP werden aufgezeichnet. Abbildung \ref{fig:opamp_gbwp_results} zeigt die Ergebnisse dieser Simulation auf. -\begin{figure}[h] +\begin{figure}[ht] \centering \includegraphics[scale=0.8]{datavis/DesignEstimate/OpAmp_GBWP_Sweep.png} - \caption{\label{fig:opamp_gbwp_results}Darstellung der Auswirkung eines variierten OpAmp GBWP - auf die Bandbreite und stabilität der simulierten TIV-Schaltung.} + \caption[Darstellung der Auswirkung eines variierten OpAmp GBWP + auf die Bandbreite und Stabilität der simulierten TIV-Schaltung]{\label{fig:opamp_gbwp_results} + Darstellung der Auswirkung eines variierten OpAmp GBWP + auf die Bandbreite und Stabilität der simulierten TIV-Schaltung. + Zu erkennen ist der Einfluss des GBWP auf sowohl die Bandbreite + als auch die Stabilität des Verstärkers, wobei + zu kleine GBWP-Werte instabiler werden.} \end{figure} -\begin{table}[h] +\FloatBarrier + +Deutlich zu erkennen ist die Limitierung der Bandbreite durch den OpAmp. Bei einem GBWP +von $\SI{1}{\mega\hertz}$ ist die Bandbreite des Gesamtsystems auf circa +$\SI{6}{\kilo\hertz}$ begrenzt, bei $\SI{100}{\mega\hertz}$ auf etwa +$\SI{56}{\kilo\hertz}$. +Ebenfalls zu erkennen ist einer Überhöhung der Übertragungsfunktion in den Fällen, in welchen +die Bandbreite durch den OpAmp limitiert wird. Diese Überhöhung lässt auf eine Resonanz schließen, +welche somit die Stabilität des Systems beeinflusst. +Eine solche Überhöhung muss vermieden werden, um Oszillationen sowie übermäßiges Rauschen zu vermeiden. +Ab dem $\SI{1}{\giga\hertz}$ GBWP-OpAmp ist keine solche Überhöhung zu sehen, +die Bandbreite ist hier überwiegend durch den Rückkoppelwiderstand begrenzt und das System ist stabil. +Die Reduktion der -3~dB-Bandbreite, welche in Tabelle \ref{table:opamp_gbwp_results} ab +$\SI{316.22}{\mega\hertz}$ zu sehen ist, ist durch die Resonanz zu erklären. +Diese zieht die Übertragungsfunktion nach oben und verschärft den Abfall, wodurch die -3~dB-Frequenz +nach oben gezogen wird. + +\begin{table}[ht] \centering \caption{\label{table:opamp_gbwp_results}Aus der Simulation bestimmte Bandbreiten der OpAmps bei variiertem GBWP} \begin{tabular}{ |r|r|r| } \hline - GBWP & -3dB Punk & Überhöhung \\ + GBWP & -3~dB Punk & Überhöhung \\ \hline $\SI{1.00}{\mega\hertz}$ & $\SI{6.00}{\kilo\hertz}$ & $\SI{22.03}{\decibel}$ \\ $\SI{3.16}{\mega\hertz}$ & $\SI{10.96}{\kilo\hertz}$ & $\SI{17.01}{\decibel}$ \\ @@ -581,123 +753,128 @@ Abbildung \ref{fig:opamp_gbwp_results} zeigt die Ergebnisse dieser Simulation au \hline \end{tabular} \end{table} -\FloatBarrier -Deutlich zu erkennen ist die Limitierung der Bandbreite durch den OpAmp. Bei einem GBWP -von $\SI{1}{\mega\hertz}$ ist die Bandbreite des Gesamtsystems auf circa -$\SI{6}{\kilo\hertz}$ begrenzt, bei $\SI{100}{\mega\hertz}$ auf etwa -$\SI{56}{\kilo\hertz}$. -Ebenfalls zu erkennen ist einer Überhöhung der Transferfunktion in den Fällen, in welchen -die Bandbreite durch den OpAmp limitiert wird. Diese Überhöhung lässt auf eine Resonanz schließen, -welche somit die Stabilität des Systems beeinflusst. -Eine solche Überhöhung muss vermieden werden, um Oszillationen sowie übermäßiges Rauschen zu vermeiden. -Ab dem $\SI{1}{\giga\hertz}$ GBWP-OpAmp ist keine solche Überhöhung zu sehen, -die Bandbreite ist hier überwiegend durch den Rückkoppelwiderstand begrenzt, und das System ist stabil. -Die Reduktion der -3dB-Bandbreite, welche in Tabelle \ref{table:opamp_gbwp_results} ab -$\SI{316.22}{\mega\hertz}$ zu sehen ist, ist durch die Resonanz zu erklären. -Diese zieht die Transferfunktion nach oben und verschärft den Abfall, wodurch die -3dB-Frequenz -nach oben gezogen wird. Zur Erfassung der benötigten offenen Verstärkung des OpAmp wird die LTSpice Simulation aus Abbildung \ref{fig:opamp_gbwp_circuit} erneut genutzt. Nun wird jedoch nicht das GBWP des OpAmp -variiert, sondern die offene Verstärkung. +variiert, sondern die offene Verstärkung. Abbildung \ref{fig:opamp_aol_sweep_2} +zeigt die Simulationsergebnisse auf. -\begin{figure} +\begin{figure}[ht] \centering \includegraphics[scale=0.8]{datavis/Parasitics/SingleStage_Aol_Sweep.png} - \caption{\label{fig:opamp_aol_sweep_2}Darstellung des Einflusses der offenen Verstärkung + \caption[Darstellung des Einflusses der offenen Verstärkung + eines OpAmp]{ + \label{fig:opamp_aol_sweep_2}Darstellung des Einflusses der offenen Verstärkung eines OpAmp auf die Übertragungsfunktion eines TIVs. Deutlich zu erkennen ist der Einbruch der Bandbreite bei zu geringer Verstärkung. Es ist jedoch keine Instabilität zu erkennen.} \end{figure} -Abbildung \ref{fig:opamp_aol_sweep_2} zeigt die Ergebnisse der Simulation auf. Wie beim GBWP +Wie beim GBWP ist hier ein starker Einfluss auf die Bandbreite zu erkennen, wenn die offene Verstärkung zu gering gewählt ist. So bricht die Bandbreite bereits ab einer Verstärkung von unter 10 000 -ein. -Es ist jedoch keine Überhöhung oder Instabilität zu erkennen. -Ungleich des GBWP ist so eine Begrenzung der Bandbreite durch eine zu kleine offene -Verstärkung nicht detrimental für die Stabilität der Schaltung. Lediglich die Bandbreite -selbst muss beachtet werden. +ein, wobei keine Überhöhung oder Instabilität ersichtlich ist. +Ungleich des GBWP ist eine solche Limitierung durch eine zu kleine offene +Verstärkung nicht nachteilig für die Stabilität der Schaltung. \FloatBarrier -\begin{figure}[h] - \centering - \includegraphics[scale=0.8]{datavis/Parasitics/SingleStage_Cin_Sweep.png} - \caption{\label{fig:opamp_gbwp_variation_result_1}Ergebnisse der Simulation eines idealen - OpAmp mit variierter Eingangskapazität $C_\mathrm{in}$.} -\end{figure} - -\begin{figure}[h] - \centering - \includegraphics[scale=0.8]{datavis/Parasitics/SingleStage_Cfp_Sweep.png} - \caption{\label{fig:opamp_gbwp_variation_result_2}Ergebnisse der Simulation eines idealen - OpAmp mit variierter parasitärer Widerstandskapazität $C_\mathrm{1}$.} -\end{figure} - -Um sicher zu stellen dass die Stabilität der Schaltung auch bei variierenden parasitären Effekten gegeben ist, +Um sicherzustellen dass die Stabilität der Schaltung auch bei variierenden parasitären Effekten gegeben ist, werden Simulationen mit variablem C1 und Cin (siehe Abbildung \ref{fig:opamp_gbwp_circuit}) durchgeführt. Die Ergebnisse hiervon sind in Abbildungen \ref{fig:opamp_gbwp_variation_result_1} und \ref{fig:opamp_gbwp_variation_result_2} dargestellt. -Zu erkennen ist, dass die Rückkoppelkapazitäten $C_1$ keinen Einfluss auf die Stabilität haben, und lediglich die Bandbreite + +Zu erkennen ist, dass die Rückkoppelkapazitäten $C_1$ keinen Einfluss auf die Stabilität haben und lediglich die Bandbreite begrenzen, wie bereits in Kapitel \ref{chap:basics_parasitics} beschrieben wurde. -Die Eingangskapazität $C_\mathrm{in}$ jedoch schein äquivalent zu einer variation des GBWP zu sein, wobei eine größere Kapazität +Die Eingangskapazität $C_\mathrm{in}$ jedoch scheint äquivalent zu einer Variation des GBWP zu sein, wobei eine größere Kapazität die Bandbreite verringert und die Stabilität negativ beeinflusst. Bei der Schaltungsauslegung muss somit genügend Marge bei der GBWP-Auswahl gelassen werden, um bei höher als erwartetem $C_\mathrm{in}$ stabil zu bleiben. -\FloatBarrier - Zusammengefasst ist die OpAmp-Bandbreite ein wichtiger Faktor der Schaltung. -Ein zu klein gewähltes GBWP begrenzt sowohl die Bandbreite des Schaltkreises, und kann zudem zu +Ein zu klein gewähltes GBWP begrenzt sowohl die Bandbreite des Schaltkreises und kann zudem zu Instabilitäten führen. Eine zu klein gewählte offene Verstärkung kann ebenfalls zur Begrenzung der Bandbreite führen, jedoch ohne hierbei die Stabilität zu gefährden. -Aus den Simulationen wird geschlossen dass ein Mindest-GBWP von $\SI{1}{\giga\hertz}$ +Aus den Simulationen wird geschlossen, dass ein Mindest-GBWP von $\SI{1}{\giga\hertz}$ notwendig ist, um stabil zu bleiben und die Bandbreite zu erhalten, wobei ein größeres GBWP vorteilhaft erscheint. Eine minimale offene Verstärkung von circa 10 000 ist notwendig, um die Bandbreite nicht zu beeinflussen. -\FloatBarrier +\begin{figure}[H] + \centering + \includegraphics[scale=0.8]{datavis/Parasitics/SingleStage_Cin_Sweep.png} + \caption[Ergebnisse der Simulation eines idealen + OpAmp mit variierter Eingangskapazität]{ + \label{fig:opamp_gbwp_variation_result_1}Ergebnisse der Simulation eines idealen + OpAmp mit variierter Eingangskapazität $C_\mathrm{in}$. Zu erkennen + ist eine Limitierung der Bandbreite sowie steigende + Überhöhung der Übertragungsfunktion bei größerer + Kapazität. + } +\end{figure} + +\begin{figure}[H] + \centering + \includegraphics[scale=0.8]{datavis/Parasitics/SingleStage_Cfp_Sweep.png} + \caption[Ergebnisse der Simulation eines idealen + OpAmp mit variierter parasitärer Widerstandskapazität]{ + \label{fig:opamp_gbwp_variation_result_2}Ergebnisse der Simulation eines idealen + OpAmp mit variierter parasitärer Widerstandskapazität $C_\mathrm{1}$. + Zu erkennen ist die Verringerung der Bandbreite bei steigender + Kapazität.} +\end{figure} + +\clearpage \subsubsection{Verbesserung der OpAmp Bandbreite} -Wie im vorherigen Kapitel beschrieben ist eine höhere Bandbreite des OpAmp notwendig, +Wie im vorherigen Kapitel beschrieben, ist eine höhere Bandbreite des OpAmp notwendig, um die Schaltung stabil betreiben zu können. Die berechneten Parameter sind jedoch nicht mit allen OpAmps erreichbar. -Um eine größere Auswahl von OpAmps zu ermöglichen wird nun untersucht, ob eine Erhöhung der +Um eine größere Auswahl von OpAmps zu ermöglichen, wird nun untersucht, ob eine Erhöhung der effektiven Bandbreite möglich ist. Da die Bandbreite eines einzelnen OpAmp durch seinen internen Aufbau limitiert ist, kann an diesem nichts verändert werden. Es ist jedoch möglich, durch die Verschaltung zweier oder mehr OpAmps einen gesamten Schaltkreis mit effektiv höherer Bandbreite zu erhalten. -Hierfür werden zwei Möglichkeiten hinzu gezogen: +Hierfür werden zwei Möglichkeiten erprobt: \begin{itemize} \item[a)] \textbf{Eine Reihenschaltung einzelner Verstärker-Stufen:} Es werden mehrere einzelne Stufen regulärer Verstärker hintereinander geschaltet. - Hierdurch muss jede einzelne Stufe eine geringere Verstärkung erbringen, + Hierdurch muss jede einzelne Stufe eine geringere Verstärkung erbringen und behält somit eine höhere Bandbreite. Von Vorteil ist der simple Schaltungsaufbau sowie die gute Stabilität, da jede Stufe in sich - stabil designt werden kann, und alle außer die erste Stufe als reguläre + stabil designt werden kann und alle Stufen außer die erste Stufe als reguläre Verstärker, nicht als TIV, ausgelegt werden können. - Nachteilhaft sind die akkumulierenden Fehler der OpAmps, welche mit jeder - zusätzlichen Stufe anwachsen. + Nachteilhaft ist, dass die Fehler der OpAmps, vor allem + der Eingangs-Offset, zusammen addiert werden, und + somit die Präzision verringern. \item[b)] \textbf{Eine Komposit-Schaltung von OpAmps:} Anstelle einzelne Stufen hintereinander zu schalten ist es ebenso möglich, - mehrere OpAmps zu einem gesamt-Verstärker mit insgesamt höherer Bandbreite zu verschalten.\todo{ - Find a citation for this? - } + mehrere OpAmps zu einem Gesamtverstärker mit insgesamt höherer Bandbreite zu verschalten + \cite[S.S. 332]{Horowitz:1981307}. Vorteilhaft ist die insgesamt höhere Präzision, da der Feedback-Pfad des gesamten Systems über alle OpAmps geschaltet ist. - Nachteilhaft ist hierbei die komplexere Schaltung, und dass Stabilität - durch vorsichtiges Balancieren der Stufen eingestellt werden muss. + Nachteilhaft ist hierbei die komplexere Schaltung und die Notwendigkeit der Stabilität + durch vorsichtiges Balancieren der Stufen. + Ein beispielhafter Schaltkreis ist in Abbildung \ref{fig:opamp_gbwp_increase_schematics} + dargestellt. \end{itemize} -Da für den hier betrachteten Anwendungsfall die Präzision von höherer Relevanz ist, +\begin{figure}[hb] + \centering + \includegraphics[scale=0.2]{grundlagen/CascadeOpAmp.drawio.png} + \caption[Beispielhafte Schaltungen zur Erhöhung + des OpAmp GBWP]{\label{fig:opamp_gbwp_increase_schematics}Beispielhafte Schaltungen zur Erhöhung + des OpAmp GBWP durch Kaskadierung mehrerer OpAmps.} +\end{figure} + +Da für den hier betrachteten Anwendungsfall die Präzision von höherer Relevanz ist und die vergleichsweise niedrigen Signalbandbreiten leichter stabilisierbar sind, wird der komposite Schaltungsaufbau gewählt. Es wird eine Simulation aufgebaut, mit welcher verschiedene @@ -706,48 +883,46 @@ untersuchen zu können. \label{chap:opamp_cascade_explained} -\begin{figure}[h] - \centering - \includegraphics[scale=0.2]{grundlagen/CascadeOpAmp.drawio.png} - \caption{\label{fig:opamp_gbwp_increase_schematics}Beispielhafte Schaltungen zur Erhöhung - des OpAmp GBWP.} -\end{figure} - Die Arbeitsweise dieser Verschaltung ist wie folgt: \begin{enumerate} \item Der OpAmp U1 verstärkt die am Eingang anliegende Spannungsdifferenz, welche vom - TIV-Eingangsstrom und Masse generiert wird + TIV-Eingangsstrom und Masse generiert wird. + \item Die Ausgangsspannung von U1 wird durch OpAmp U2 weiter verstärkt. - U2 besitzt hierbei eine feste Verstärkung, welche durch den Widerstandsteiler Rx/Rx + U2 besitzt hierbei eine feste Verstärkung, welche durch den Widerstandsteiler R1/R2 festgelegt wird. \item Der Ausgang von U2 wird über den Rückkoppelwiderstand an den TIV Ausgang angelegt. Hierdurch wird die Verstärkerschleife geschlossen. \item U1 regelt nun seinen eigenen Ausgang so, dass der Ausgang von U2 die - Eingangsspannung ausgleicht. Da U2 eine festgelegte Verstärkung besitzt, - übernimmt U1 zwangsweise die verbliebene Verstärkung, d.h. $R_f / A_\mathrm{U2}$. + Eingangsspannung ausgleicht.\\ + Da U2 eine festgelegte Verstärkung besitzt, + übernimmt U1 zwangsweise die verbliebene Verstärkung, d.~h. $R_f / A_\mathrm{U2}$. \end{enumerate} Durch korrekte Auswahl von U1, U2 und der Verteilung der Verstärkung zwischen den OpAmps können -so die Vorteile verschiedener OpAmps kombiniert werden. Es kann z.B. ein sensitiver und präziser -aber langsamer OpAmp in der ersten Stufe mit kleinerer Verstärkung betrieben werden, und ein +so die Vorteile verschiedener OpAmps kombiniert werden. Es kannz.~B. ein sensitiver und präziser +aber langsamer OpAmp in der ersten Stufe mit kleinerer Verstärkung betrieben werden und ein wesentlich schnellerer OpAmp in der zweiten Stufe die Gesamtverstärkung des Systems liefern. \FloatBarrier Als exemplarisches Beispiel wird der ADA4817 als erste Stufe gewählt. Dieser OpAmp hat -ein exzellent niedriges Rauschen und geringe Eingangs-Leckströme, und ist optimiert +ein exzellent niedriges Rauschen und geringe Eingangs-Leckströme und ist optimiert für Messungen an hochimpedanten Eingängen. Er besitzt jedoch eine zu geringe Verstärkung, um direkt in einer Stufe eine Verstärkung von $\SI{1}{\giga\ohm}$ zu erreichen. Mithilfe einer LTSpice-Simulation wird nun untersucht, ob eine solche kaskadierte Verschaltung zu einer nutzbaren Gesamtverstärkung führen kann. Der Aufbau der LTSpice-Simulation -ist in Abbildung \ref{fig:opamp_cascade_ltspice} dargestellt. +ist in Abbildung \ref{fig:opamp_cascade_ltspice} dargestellt, während +die Ergebnisse der Simulation in Abbildung \ref{fig:opamp_analysis_stage_sweep} +visualisiert sind. In der Simulation wird die Verstärkung der zweiten +Stufe durch Änderung der Widerstände variiert. \begin{figure}[h] \centering - \includegraphics[scale=0.8]{entwicklung/opamp/opamp_ltspice_cascade.jpg} + \includegraphics[width=0.8\textwidth]{entwicklung/opamp/opamp_ltspice_cascade.jpg} \caption{\label{fig:opamp_cascade_ltspice}Aufbau der LTSpice-Simulation zur Untersuchung einer kaskadierten OpAmp-Verschaltung.} \end{figure} @@ -755,19 +930,20 @@ ist in Abbildung \ref{fig:opamp_cascade_ltspice} dargestellt. \begin{figure}[h] \centering \includegraphics[scale=0.8]{datavis/DesignEstimate/OpAmp_Stages_Sweep.png} - \caption{\label{fig:opamp_analysis_stage_sweep} + \caption[Ergebnis der Simulation einer OpAmp-Kaskadenschaltung]{ + \label{fig:opamp_analysis_stage_sweep} Ergebnis der LTSpice-Simulation einer kaskadierten OpAmp Verschaltung, mit variierter Verteilung der Verstärkung zwischen erster und zweiter Stufe. Legendenangabe gibt die Verstärkung der zweiten Stufe an. Geasmtverstärkung - $\SI{1}{\giga\ohm}$.} + $\SI{1}{\giga\ohm}$. Zu erkennen ist eine Variation von sowohl der Bandbreite + als auch der Stabilität, wobei eine kleinere Verstärkung in der zweiten + Stufe die Bandbreite zu limitieren scheint.} \end{figure} -Abbildung \ref{fig:opamp_analysis_stage_sweep} zeigt die Ergebnisse der LTSpice-Simulation auf. -Hierbei wird die verteilung der Verstärkung zwischen den beiden Stufen variiert, um den -Einfluss dieser Verteilung charakterisieren zu können. Deutlich zu erkennen sind zwei Effekte. +Deutlich zu erkennen sind zwei Effekte. Bei zu geringer Verstärkung in der zweiten Stufe (und somit zu hoher Verstärkung in der ersten) ist die Bandbreite durch den ersten OpAmp limitiert. Bei zu hoher Verstärkung in der zweiten Stufe -scheint eine Instabilität auf zu treten. Es scheint jedoch einen nutzbaren Bereich zu geben, +scheint eine Instabilität aufzutreten. Es scheint jedoch einen nutzbaren Bereich zu geben, in welchem eine nutzbare Bandbreite ohne Instabilitäten erreicht wird. \FloatBarrier @@ -782,48 +958,64 @@ welche hier dargestellt werden sollen. Das eingangsbezogene Stromrauschen des OpAmps hat einen direkten Effekt auf das gemessene Signal. Da der Eingang des TIV Ströme misst, wird das Stromrauschen lediglich auf das -Eingangssignal hinzu addiert und mit Verstärkt. Eine Reduzierung des Effektes des Stromrauschens +Eingangssignal hinzu addiert und mit verstärkt. Eine Reduzierung des Effektes des Stromrauschens ist somit nicht möglich, lediglich die Auswahl eines OpAmps mit wenig Rauschen ist hierfür relevant. Mit hochperformanten OpAmps liegen typische Stromrausch-Werte im Bereich von circa $\SI{10}{\femto\ampere\per\sqrt{\hertz}}$, welches mit der geforderten Bandbreite von $\SI{30}{\kilo\hertz}$ ungefähr ein eingangsbezogenes Rauschen von $\SI{1.73}{\pico\ampere}$ erzeugt. Das Spannungsrauschen des OpAmp ist etwas komplexer. -Am Eingang des TIVs interagiert dieses Rauschen mit der parasitären Eingangskapazität, und wirkt +Am Eingang des TIVs interagiert dieses Rauschen mit der parasitären Eingangskapazität und wirkt somit als zusätzliches Stromrauschen, entsprechend der Formel $I = U \cdot 2\pi f \cdot C$. Dieses Rauschen steigt somit sowohl mit größerer Eingangskapazität, als auch mit der Frequenz. -Mithilfe einer LTSpice-Simulation wird dieses Rauschverhalten genauer charakterisiert. +Mithilfe einer LTSpice-Simulation wird dieses Rauschverhalten genauer charakterisiert.\\ Hierbei wird die in Abbildung \ref{fig:opamp_vin_noise_schematic} dargestellte Schaltung verwendet. -Als OpAmp wird dabei der LTC6268-10 gewählt. Dies ist ein kommerziell erhältlicher OpAmp mit -genügend GBWP und kleinen Eingangsleckströmen, um als TIV nutzbar zu sein. +Als OpAmp wird dabei der LTC6268-10 gewählt. +Dieser OpAmp eignet sich durch sein hohes GBWP und geringe Leckströme gut +für einen TIV, und wird aus diesem Grund als vorerste Auswahl eines beispielhaften +OpAmps für die Simulationen genutzt. -\begin{figure}[h] +\begin{figure}[ht] \centering - \includegraphics[width=0.8\textwidth]{entwicklung/opamp/opamp_ltspice_noise.jpg} - \caption{\label{fig:opamp_vin_noise_schematic}Schaltkreis der LTSpice-Simulation zur + \includegraphics[width=0.7\textwidth,clip,trim={0cm 0cm 15cm 0cm}] + {entwicklung/opamp/opamp_ltspice_noise.jpg} + \caption[Schaltkreis der LTSpice-Simulation zur + Bestimmung OpAmp-Rauschens]{ + \label{fig:opamp_vin_noise_schematic}Schaltkreis der LTSpice-Simulation zur Bestimmung OpAmp-Rauschens.} \end{figure} Variiert werden $C_\mathrm{in}$ sowie $R_\mathrm{f}$, um die Auswirkungen dieser Parameter -betrachten zu können. Hierbei wird das Rauschen Eingangsbezogen gemessen, d.h. die Ausgangsspannung +betrachten zu können. Hierbei wird das Rauschen eingangsbezogen gemessen, d.~h. die Ausgangsspannung wird durch $R_\mathrm{f}$ dividiert, um den Eingangsstrom zu erhalten. Hierdurch lassen sich die Simulationswerte besser vergleichen. Die Ergebnisse sind in Abbildungen \ref{fig:opamp_vin_noise_rf} und \ref{fig:opamp_vin_noise_cin} dargestellt. -\begin{figure} +\FloatBarrier + +\begin{figure}[H] \includegraphics[scale=0.8]{datavis/Parasitics/SingleStage_LTC_Rf_Sweep_Noise.png} - \caption{\label{fig:opamp_vin_noise_rf}Rauschen in Abhängigkeit von $R_\mathrm{f}$} + \caption[Rauschen in Abhängigkeit von $R_\mathrm{f}$]{ + \label{fig:opamp_vin_noise_rf}Rauschen in Abhängigkeit von $R_\mathrm{f}$. + Zu erkennen ist die Abhängigkeit der gesamten Rauschamplitude + vom Widerstand. Die Form des Rauschens entsteht durch drei Effekte. + Im unteren Frequenzbereich ist das Spannungsrausches des OpAmp der + dominierende Effekt, welches bei steigender Frequenz abfällt. + Das Plateu ist überwiegend durch das thermische Rauschen + des Widerstandes bestimmt. Der Anstieg des Rauschens in höheren + Frequenzen entsteht durch das Stromrauschen, welches + proportional zur Frequenz wächst.} \end{figure} -\begin{figure} +\begin{figure}[H] \includegraphics[scale=0.8]{datavis/Parasitics/SingleStage_LTC_Cin_Sweep_Noise.png} \caption{\label{fig:opamp_vin_noise_cin}Rauschen in Abhängigkeit von $C_\mathrm{in}$} \end{figure} Deutlich zu erkennen ist eine starke Abhängigkeit des Rauschens von beiden Parametern. Die Eingangskapazität hat hierbei eine merkliche Auswirkung auf den frequenzabhängigen -Teil des Rauschens, welcher ab ca. $\SI{100}{\hertz}$ bis $\SI{10}{\kilo\hertz}$ +Teil des Rauschens, welcher ab circa $\SI{100}{\hertz}$ bis $\SI{10}{\kilo\hertz}$ anfängt zu dominieren. Bereits eine Kapazität von $\SI{10}{\pico\farad}$ erhöht das Rauschniveau merklich. Da die parasitäre Eingangskapazität stark vom physikalischen Schaltungsaufbau abhängig ist, diff --git a/TeX/Kapitel/Auslegung/Schaltungsdesign.tex b/TeX/Kapitel/Auslegung/Schaltungsdesign.tex index 6e5fe86..a704606 100644 --- a/TeX/Kapitel/Auslegung/Schaltungsdesign.tex +++ b/TeX/Kapitel/Auslegung/Schaltungsdesign.tex @@ -1,3 +1,4 @@ +\cleardoublepage \section{Schaltungsdesign} In diesem Kapitel wird der Aufbau einer ersten Prototypen-Schaltung beschrieben. @@ -6,14 +7,17 @@ vorherigen Kapitel ermittelten parasitären Effekten und Kompensationsmöglichke konkrete Bauteile für die Konstruktion eines ersten TIV verglichen und ausgewählt. Hiernach wird die Schaltung des TIVs ausgelegt und dessen Funktionsweise erläutert. -\subsection{TIV} +Für das Schaltungsdesign wird hierbei das Programm {\em Altium Designer} genutzt, +welches ein komerziell erhältliches Platinendesigntool ist. + +\subsection{Auslegung des TIV} \subsubsection{OpAmp Auswahl} \label{chap:v10_opamp_choice} In diesem Abschnitt wird auf die genaue Auswahl eines OpAmp für den hochimpedanten TIV-Eingang eingegangen. -Dieser OpAmp legt viele wichtige Systemparameter fest, und +Dieser OpAmp legt viele wichtige Systemparameter fest und bestimmt maßgeblich das Verhalten und das Rauschniveau des TIVs selbst. Zusammengefasst sind folgende Parameter von Bedeutung: @@ -23,35 +27,36 @@ Zusammengefasst sind folgende Parameter von Bedeutung: Messung von Signalen im $\SI{1}{\nano\ampere}$-Bereich gewollt ist, sollte der Leckstrom höchstens wenige $\SI{}{\pico\ampere}$ betragen, um die Messung nicht zu beeinflussen. - \item Hohes GBWP. Eine hohe Verstärkerbandbreite ist notwendig, um bei - den hohen Verstärkungen des TIV stabil zu bleiben (siehe Kapitel \ref{chap:basics_opamp}) + \item Hohes GBWP und Verstärkung. + Entsprechend Kapitel \ref{chap:basics_opamp} ist eine hohe Verstärkerbandbreite notwendig, um bei + den hohen Verstärkungen des TIV stabil zu bleiben. \item Niedriges Rauschen. Da das OpAmp-Spannungsrauschen mit der Eingangskapazität interagiert, ist ein geringes Rauschen ein wichtiger Auswahlfaktor (siehe Kapitel \ref{chap:opamp_noise}). \end{itemize} -Folgende OpAmps werden für die nähere Auswahl in Betracht gezogen: +Tabelle \ref{table:select_opamp_parameters} listed die in Betracht gezogenen OpAmps +zusammen mit einigen ihrer Parameter auf. \begin{table}[h] \centering - \caption{\label{table:select_opamp_parameters}Parameter der Ausgewählten OpAmps} + \caption{\label{table:select_opamp_parameters}Parameter der ausgewählten OpAmps} \begin{tabular}{ |l|r|r|r| } \hline - OpAmp & Leckstrom & GBWP & Spannungsauschen @ $\SI{10}{\kilo\hertz}$ \\ + OpAmp & Leckstrom & GBWP & Spannungsrauschen @ $\SI{10}{\kilo\hertz}$ \\ \hline - ADA4530 & $\SI{20}{\femto\ampere}$ & $\SI{2}{\mega\hertz}$ & $\SI{14}{\nano\volt\per\sqrt{\hertz}}$ \\ - ADA4817 & $\SI{2}{\pico\ampere}$ & $\SI{400}{\mega\hertz}$ & $\SI{5}{\nano\volt\per\sqrt{\hertz}}$ \\ - LTC6268-10 & $\SI{4}{\femto\ampere}$ & $\SI{4}{\giga\hertz}$ & $\SI{14}{\nano\volt\per\sqrt{\hertz}}$ \\ - LMP7721 & $\SI{20}{\femto\ampere}$ & $\SI{17}{\mega\hertz}$ & $\SI{6.5}{\nano\volt\per\sqrt{\hertz}}$ \\ + ADA4530 \cite{DatasheetADA4530} & $\SI{20}{\femto\ampere}$ & $\SI{2}{\mega\hertz}$ & $\SI{14}{\nano\volt\per\sqrt{\hertz}}$ \\ + ADA4817 \cite{DatasheetADA4817} & $\SI{2}{\pico\ampere}$ & $\SI{400}{\mega\hertz}$ & $\SI{5}{\nano\volt\per\sqrt{\hertz}}$ \\ + LTC6268-10 \cite{DatasheetLTC626810} & $\SI{4}{\femto\ampere}$ & $\SI{4}{\giga\hertz}$ & $\SI{14}{\nano\volt\per\sqrt{\hertz}}$ \\ + LMP7721 \cite{DatasheetLMP7721} & $\SI{20}{\femto\ampere}$ & $\SI{17}{\mega\hertz}$ & $\SI{6.5}{\nano\volt\per\sqrt{\hertz}}$ \\ \hline \end{tabular} \end{table} -\todo[inline]{Do we need to cite the Datasheets?} Aus diesen OpAmps werden zwei Kandidaten genauer in Betracht gezogen. Der {\em ADA4817} besitzt das niedrigste Eingangsrauschen der Auswahl und könnte somit das beste Ergebnis liefern, hat jedoch ein grenzwertiges -GBWP und braucht somit eventuell die komplexere kaskadierte Verschaltung. +GBWP und braucht somit eventuell die komplexere komposite Verschaltung. Zudem ist der Eingangsleckstrom vergleichsweise hoch. Der {\em LTC6268-10} hat ein durchschnittliches Rauschniveau und exzellenten Leckstrom sowie das beste GBWP der Sammlung, wodurch dieser @@ -63,12 +68,12 @@ Es wird somit für diese Schaltung der LTC6268-10 gewählt. \subsubsection{TIV-Schaltung} \label{chap:tia_circuit_design} -In diesem Unterkapitel wird nun die konkrete Schaltung des TIVs erstellt. +In diesem Unterkapitel wird die konkrete Schaltung des TIVs erstellt. -Der Grundlegende Aufbau eines TIV-Schaltkreises wurde bereits in Kapitel +Der grundlegende Aufbau eines TIV-Schaltkreises wurde bereits in Kapitel \ref{chap:basics_tia} beschrieben. Da der LTC6268-10 ein ausreichendes GBWP von $\SI{4}{\giga\hertz}$ hat, ist entsprechend Kapitel -\ref{chap:effects_opamp} keine kaskadierte Schaltung notwendig. +\ref{chap:effects_opamp} keine komposite Schaltung notwendig. Bezüglich des Rückkoppelwiderstandes ist sowohl für das Widerstandsrauschen aus Kapitel \ref{chap:r_noise} sowie für das @@ -80,20 +85,14 @@ der Serienschaltung sowie der Feldabschirmung aus Kapitel \ref{chap:r_para_mitigations} genutzt, um den Einfluss der Kapazitäten zu vermindern. -Da die konkreten Werte der parasitären Effekte nicht bekannt sind, und -in der Realität mit hoher Wahrscheinlichkeit größer sind als in der Simulation -(durch z.B. andere Komponenten in der Nähe, welche kapazitiv koppeln), werden -keine konkreten Werte für die Widerstände dieser Schaltung fest gelegt. Diese -werden experimentell erprobt, um eine gute Balance der Eigenschaften zu bieten. - -\begin{figure}[h] - \centering - \includegraphics[width=0.9\linewidth]{Auslegung/v1.0/tia_stage.png} - \caption{\label{fig:tia_v1_design}Schematischer Schaltkreis des TIVs} -\end{figure} +Da die konkreten Werte der parasitären Effekte nicht bekannt sind +und in der Realität mit hoher Wahrscheinlichkeit größer sind als in +der Simulation (durchz.~B. andere Komponenten in der Nähe, welche kapazitiv +mit der Schaltung verkoppelt sind), erfolgt die Auswahl der konkreten Werte +für die Widerstände dieser Schaltung experimentell. Die Auslegung der Schaltung ist in Abbildung \ref{fig:tia_v1_design} zu sehen. -U2 ist hierbei der TIVs, wofür der bereits erwähnte LTC6268-10 genutzt +U2 ist hierbei der TIV, wofür der bereits erwähnte {\em LTC6268-10} genutzt wird. Die Rückkoppelwiderstände sind R15, R16, R17, R18, welche in einer Reihe geschaltet werden um den Einfluss der Parallelkapazitäten zu verringern. Die Feldabschirmung wird hierbei durch Widerstände R10 bis R13 und R20 bis R23 @@ -107,31 +106,36 @@ Parallelkapazitäten der gewünschte Wert von $\SI{1}{\giga\ohm}$ nicht erreicht werden kann. Die Altium-Markierung ``{\em Leakage Clearance}'' passt zudem einige Abstandsregeln des Platinendesign an. +\begin{figure}[htb] + \centering + \includegraphics[width=0.9\linewidth]{Auslegung/v1.0/tia_stage.png} + \caption{\label{fig:tia_v1_design}Schematischer Schaltkreis des TIVs} +\end{figure} Bei der Auslegung der physikalischen Schaltung werden zusätzliche Einflüsse -in Betracht gezogen, welche nicht direkt auf dem Schaltplan abbildbar sind. -So ist z.B. eine vorsichtige Auslegung der Leitungen des Eingangskanals -notwendig; diese muss möglichst klein gehalten werden um Kapazitäten zu +in Betracht gezogen. +So ist z.~B. eine vorsichtige Auslegung der Leitungen des Eingangskanals +notwendig; diese müssen möglichst wenig Fläche einnehmen um Kapazitäten zu verringern. Aus dem gleichen Grund werden Kupferflächen reduziert und als Muster anstatt als ausgefüllte Flächen ausgeführt. Um einen Ladungsaufbau zu verhindern, muss der Isolations-Lack der Platine um den Rückkoppelpfad entfernt werden, während Leckströme durch -weitere Abschirmungspfade verringert werden. - -\begin{figure}[h] - \centering - \includegraphics[width=0.7\textwidth]{Auslegung/v1.0/tia_pcb.png} - \caption{\label{fig:tia_v1_pcb}Platinendesign der TIV-Schaltung} -\end{figure} +weitere Abschirmungspfade verringert werden \cite[S.S. 42]{DatasheetADA4530}. Abbildung \ref{fig:tia_v1_pcb} zeigt das Design der Platine für den Teil des TIVs selbst. Der Messeingang ist hierbei der runde Kreis des inneren Anschlusses der SMA-Buchse. Dieser ist möglichst eng an den Verstärker U2 sowie der Kaskade der Rückkoppelwiderstände angeschlossen. -Um den gesamten hochimpedanten Bereich wird der Lötstopplack entfernt, +Um den gesamten hochimpedanten Bereich wird der Lötstopplack entfernt und der Bereich des TIV-Eingangs wird mit einem geerdeten Pfad umgeben, um Oberflächenladungen und Leckströme ableiten zu können. +\begin{figure}[hbp] + \centering + \includegraphics[width=0.8\textwidth]{Auslegung/v1.0/tia_pcb.png} + \caption{\label{fig:tia_v1_pcb}Platinendesign der TIV-Schaltung} +\end{figure} + Die Abschirmungselektroden der Widerstände werden aus mehreren Kupferlagen aufgebaut. Abbildung \ref{fig:tia_v1_shielding} zeigt den Aufbau inklusive innerer Lagen von zwei Elektroden. Rot repräsentiert hierbei die oberste Lage @@ -145,7 +149,7 @@ Auf der zweiten Lage wird eine Kupferfüllung untergebracht, welche auf dem gleichen Potential der Abschirmung liegt. Diese Füllung dient zur Verringerung der Feldstärke im Platinenmaterial selbst. -\begin{figure}[h] +\begin{figure}[htp] \centering \includegraphics[width=0.7\textwidth]{Auslegung/v1.0/shielding.png} \caption{\label{fig:tia_v1_shielding}Aufbau der Schirmelektroden des @@ -155,15 +159,16 @@ Verringerung der Feldstärke im Platinenmaterial selbst. Um den Einfluss der Abschirmung abschätzen zu können, wird eine zweite Version der Schaltung ohne diese Schirmungselektroden ausgelegt. Hierfür werden die Widerstände sowie die Kupferflächen der Elektroden entfernt. Sie werden nicht durch Erdflächen -ersetzt, um keine zusätzliche Erdkapazität in den hochimpedanten Pfad ein zu koppeln. +ersetzt, um keine zusätzliche Erdkapazität in den hochimpedanten Pfad einzukoppeln. +\FloatBarrier \subsection{Unterstützende Schaltungen} -In den folgenden Paragraphen werden weitere unterstützende Schaltungen +In den folgenden Absätzen werden weitere unterstützende Schaltungen beschrieben, welche für die korrekte Funktionsweise des TIV nötig sind, jedoch selbst nicht kritisch für die Charakteristik des TIVs sind, da -sie ohne große Anforderungen an Präzision o.ä. erstellt werden können. -Dieser Schaltungselemente werden somit kurz und der vollständigkeit +sie ohne große Anforderungen an Präzision o.~ä. erstellt werden können. +Dieser Schaltungselemente werden somit kurz und der Vollständigkeit halber beschrieben. \subsubsection{Filter-Stufe} @@ -174,8 +179,8 @@ erreichen. Der im Kapitel \ref{chap:tia_circuit_design} erstellte Schaltkreis wird auf eine Bandbreite knapp über $\SI{30}{\kilo\hertz}$ abgestimmt, wobei der parasitäre RC-Filter einen Abfall von -20dB/Dekate besitzt. -Da bekannt ist dass das zu messende Signal mit einer Bandbreite von $\SI{30}{\kilo\hertz}$ -vor liegt, können alle Frequenzen hierüber möglichst stark gedämpft werden. +Da bekannt ist, dass das zu messende Signal mit einer Bandbreite von $\SI{30}{\kilo\hertz}$ +vorliegt, können alle Frequenzen hierüber möglichst stark gedämpft werden. Dies verringert das Rauschniveau, da die TIV-Schaltung selbst ein recht breites Rauschspektrum bis in die obigen $\SI{100}{\kilo\hertz}$ besitzt. Hierfür können aktive Filter verwendet werden, welche mithilfe von OpAmps, Widerständen und Kapazitäten @@ -185,33 +190,43 @@ Diese Filter werden an den Ausgang des TIV angeschlossen. Für diese Anwendung wird ein sog. Butterworth-Filter mit zwei Stufen gewählt. Dieser Filter bietet einen flachen Frequenzgang mit steilem Abfall von -80dB/Dekade ab der Grenzfrequenz. -Er besteht aus zwei in Reihe geschalteten OpAmps in aktiver Filter-Konfiguration, und -kann somit mit leicht erhältlichen Dual-Package OpAmps erstellt werden. Für die genaue +Er besteht aus zwei in Reihe geschalteten OpAmps in aktiver Filter-Konfiguration und +kann somit mit leicht erhältlichen Dual-Package OpAmps erstellt werden. +Für diesen Filter wird der generische {\em TL072} gewählt. +Für die genaue Auslegung des Filters wurde das ``Filter-Design-Tool'' von Analog Devices (siehe \cite{ADFilterDesign}) genutzt, welches für die angegebenen Filter-Parameter eine Schaltung berechnet, da die -händische Berechnung der Komponenten vor allem bei Einhaltung der -Komponentenreihen (E24) nicht trivial ist. - -\begin{figure}[h] - \centering - \includegraphics[width=0.9\linewidth]{Auslegung/filter_stage.png} - \caption{\label{fig:filter_stage_design}Schaltkreis der berechneten Filter-Stufe nach \cite{ADFilterDesign}} -\end{figure} - -\begin{figure}[h] - \centering - \includegraphics[width=0.9\linewidth]{Auslegung/filter_stage_bandwidth.png} - \caption{\label{fig:filter_stage_bandwidth}Bandbreite der berechneten Filter-Stufe nach \cite{ADFilterDesign}} -\end{figure} +händische Berechnung der Komponenten, vor allem bei Einhaltung +standardisierter +Komponentenreihen (E24), nicht trivial ist. Die erstellte Filter-Stufe ist in -Abbildung \ref{fig:filter_stage_design} dargestellt. Die berechnete Transferfunktion +Abbildung \ref{fig:filter_stage_design} dargestellt. Die berechnete Übertragungsfunktion dieses Filters ist in Abbildung \ref{fig:filter_stage_bandwidth} aufgezeichnet. -Zu sehen ist eine glatte Transferfunktion bis hin zum -3dB-Punkt bei $\SI{30}{\kilo\hertz}$, -nach welchem wie erhofft ein steiler Abfall von -80dB/Dekade vor liegt. +Zu sehen ist eine glatte Übertragungsfunktion bis hin zum -3~dB-Punkt bei $\SI{30}{\kilo\hertz}$, +nach welchem wie erhofft ein steiler Abfall von -80dB/Dekade vorliegt. Somit werden Rauschanteile sowie andere Störsignale bereits ab $\SI{50}{\kilo\hertz}$ um einen Faktor von 20dB gedämpft. +\FloatBarrier + +\begin{figure}[ht] + \centering + \includegraphics[width=0.8\linewidth]{Auslegung/filter_stage.png} + \caption[Schaltkreis der Filter-Stufe]{ + \label{fig:filter_stage_design}Schaltkreis der berechneten Filter-Stufe nach \cite{ADFilterDesign}} +\end{figure} + +\begin{figure}[hp] + \centering + \includegraphics[width=0.8\linewidth]{Auslegung/filter_stage_bandwidth.png} + \caption[Bandbreite der berechneten Filter-Stufe]{ + \label{fig:filter_stage_bandwidth}Bandbreite der berechneten Filter-Stufe nach \cite{ADFilterDesign}} +\end{figure} + +\FloatBarrier +\newpage + \subsubsection{Ausgangstreiber} \label{chap:design_output_driver} @@ -222,7 +237,7 @@ teilweise ein differentielles Signal. Aus diesem Grund wird eine Verstärkerstuf für die Umsetzung der Spannungslevel erstellt, welche durch Anpassung der Widerstände diverse Verstärkungen und Offsets ermöglicht. Die genauen Widerstände müssen je nach ADC gewählt werden, somit werden vorerst Platzhalter genutzt. -Diese Stufe ist in Abbildung \ref{fig:design_output_driver} dar gestellt. +Diese Stufe ist in Abbildung \ref{fig:design_output_driver} dargestellt. \begin{figure}[H] \centering @@ -235,8 +250,8 @@ Diese Stufe ist in Abbildung \ref{fig:design_output_driver} dar gestellt. \label{chap:power_supply_design} Für die korrekte Operation des TIV müssen die für die Verstärker benötigten Spannungen -bereit gestellt werden. Hierbei ist eine hohe Qualität, d.h. ein stabiles Spannungsniveau auch -unter Last sowie ein möglichst geringes Rauschen der Versorgung, notwendig. Zudem ist +bereitgestellt werden. Hierbei ist eine hohe Qualität, d.~h. ein stabiles Spannungsniveau auch +unter Last sowie ein möglichst geringes Rauschen der Versorgung notwendig. Zudem ist eine differentielle Spannungsversorgung notwendig. Um all dies zu erreichen, wird die Spannungsversorgung aus zwei Stufen aufgebaut: @@ -245,19 +260,19 @@ Um all dies zu erreichen, wird die Spannungsversorgung aus zwei Stufen aufgebaut \item Ein isolierender DC/DC Wandler mit dualem Ausgang, der {\em TDN 3-2423}, liefert $\SI{\pm 15}{\volt}$ Spannung mit einem weiten Eingangsspannungsbereich. Durch die Isolation können sog. Ground-Loops, - d.h. Schleifen aus Erdverbindungen, vermieden werden. Diese können als Antennen + d.~h. Schleifen aus Erdverbindungen, vermieden werden. Diese können als Antennen fungieren und somit zusätzliches Rauschen einfangen. Eine Isolation verhindert dies effektiv. Der duale Spannungsausgang des Wandlers vereinfacht zudem die Versorgung der Verstärker. Von Nachteil ist ein recht hoher Rauschanteil am Ausgang des Wandlers. Der Schaltkreis des DC/DC-Wandlers ist in Abbildung \ref{fig:design_power_dcdc} dargestellt. - \item Um das Rauschniveau zu reduzieren, und um den TIV-OpAmp mit der korrekten + \item Um das Rauschniveau zu reduzieren und um den TIV-OpAmp mit der korrekten Spannung versorgen zu können, wird ein Linearregler genutzt. Dieser Typ von Regler - bietet einen sehr stabilen und rauscharmen Ausgang, und eignet sich somit gut für die + bietet einen sehr stabilen und rauscharmen Ausgang und eignet sich somit gut für die Versorgung von sensitiven Bauteilen. Ein dedizierter Zweikanal-Linearregler, der {\em LT3032}, wird über einen - RC-Filter mit der DC/DC-Spannung versorgt, und liefert die + RC-Filter mit der DC/DC-Spannung versorgt und liefert die notwendigen Spannungen für den TIV selbst. Dieser Regler ist speziell für - niedrige Rauschlevel konzipiert, und ist somit bestens für die Bereitstellung + niedrige Rauschlevel konzipiert und ist somit bestens für die Bereitstellung einer stabilen Spannung geeignet. Der Schaltkreis des Linearreglers ist in Abbildung \ref{fig:design_power_ldo} dargestellt. \end{enumerate} @@ -276,16 +291,11 @@ Um all dies zu erreichen, wird die Spannungsversorgung aus zwei Stufen aufgebaut \subsection{Auslegung des PCB} -In diesem Abschnitt soll auf die konkrete Platzierung der im vorherigen Teil beschriebenen -Komponenten eingegangen werden. Eine korrekte Positionierung ist notwendig, um Störsignale +Nach Beschreibung der verwendeten Schaltkreise wird nun auf die +konkrete Platzierung der Komponenten eingegangen. +Eine korrekte Positionierung ist notwendig, um Störsignale zu minimieren, da gewisse Schaltungsteile eigene Rauschquellen sind. -\begin{figure}[h] - \centering - \includegraphics[width=0.95\linewidth]{Auslegung/v1.0/pcb_3d.png} - \caption{\label{fig:v1_pcb_design}3D-Modell des gesamten TIV-Schaltkreises.} -\end{figure} - Abbildung \ref{fig:v1_pcb_design} zeigt den Aufbau der Platine mit allen Komponenten. Die einzelnen Elemente des TIV sind von links nach rechts wie folgt angeordnet: @@ -296,20 +306,32 @@ Die einzelnen Elemente des TIV sind von links nach rechts wie folgt angeordnet: \item Mittig auf der Platine ist der Linearregler sowie die Filter-Stufe und der Ausgangstreiber angebracht. Der Linearregler ist hierbei möglichst nah an den Spannungseingang des TIV gelegt, um die Distanz hierzu zu - vermindern. Die Ausgangs-Stufe ist nicht rauschanfällig, und kann somit beliebig + vermindern. Die Ausgangs-Stufe ist nicht rauschanfällig und kann somit beliebig platziert werden. - \item Auf der rechten Seite der Platine wird der TIV-Teil selbst platziert. Somit + \item Auf der rechten Seite der Platine wird der TIV selbst platziert. Somit ist garantiert, dass keine unnötigen Stromflüsse durch diesen Verstärkerteil fließen können. Das gesamte TIV-System wird zur Minimierung externer Einflüsse zudem in ein Schirmgehäuse untergebracht. \end{enumerate} +\FloatBarrier + +\begin{figure}[ht] + \centering + \includegraphics[width=0.95\linewidth]{Auslegung/v1.0/pcb_3d.png} + \caption[3D-Modell des gesamten TIV-Schaltkreises]{ + \label{fig:v1_pcb_design} + 3D-Modell des gesamten TIV-Schaltkreises. + Überlagert ist die grundlegende Verteilung der + Schaltungselemente eingezeichnet.} +\end{figure} + Zusätzlich zu den bereits etablierten Komponenten der Schaltung werden einige mechanische Verbindungen zur Operation des Schaltkreises untergebracht: \begin{itemize} \item Vier M3-Schraublöcher werden an den Enden der Platine zur mechanischen - Befestigung bereit gestellt. + Befestigung bereitgestellt. \item Ein 2-Pin PSK-Stecker dient zur Stromversorgung \item Mehrere diverse PSK-Stecker sowie Testpads werden entlang der Schaltung platziert, um Spannungen sowie Signale überprüfen zu können. Dies @@ -317,15 +339,17 @@ mechanische Verbindungen zur Operation des Schaltkreises untergebracht: des Linearreglers, sowie den ungefilterten Ausgang des TIVs selbst. \item Zur Verbindung des TIV Eingangs sowie Bereitstellung des Ausgangssignals werden SMA-Steckverbindungen benutzt. Diese sind besonders gut geeignet - für Signale die einer Schirmung und präzisen Übertragung benötigen, + für Signale, die einer Schirmung und präzisen Übertragung benötigen und sind somit gut geeignet für das Eingangs- und Ausgangssignal des Verstärkers. \end{itemize} -Die Plazine wird mithilfe von Standard-Anfertigungsverfahren hergestellt. -\todo[inline]{How much of this should we write down here?} +Die Platine wird mithilfe von komerziellen Fertigungsverfahren hergestellt, +wobei die Bestückung der Komponenten durch die kleine Anzahl von Platinen +mit variierten Bauteilen von Hand durchgeführt wird. +Abbildung \ref{fig:v1_pcb_picture} zeigt ein Foto eines der erstellten Schaltkreise. \begin{figure}[h] \centering - \missingfigure{Add *good* picture of the PCB here :>} + \includegraphics[width=0.8\textwidth]{Auslegung/v1.0/pcb_photo.jpg} \caption{\label{fig:v1_pcb_picture}Bild des fertig gestellten TIV-PCBs} \end{figure} \ No newline at end of file diff --git a/TeX/Kapitel/Einleitung.tex b/TeX/Kapitel/Einleitung.tex index 5f97f47..2680781 100644 --- a/TeX/Kapitel/Einleitung.tex +++ b/TeX/Kapitel/Einleitung.tex @@ -1,20 +1,49 @@ \chapter{Einleitung} -\todo[inline]{Rework this *after* completing other chapters} +Die Analyse von Gasgemischen findet in vielen +Bereichen der Industrie- und Medizintechnik Anwendung. +Mitunter geht es um medizinisch wichtige Daten wie +die Überwachung des Metabolismus eines Patienten, +oder um sicherheitsrelevante Messungen wie die +Überprüfung einer Stoffprobe auf explosive Stoffe. -Die Analyse von Gasgemischen findet in vielen Bereichen der Industrie- und Medizintechnik Anwendung. Mitunter geht es um medizinisch wichtige Daten wie die Überwachung des Metabolismus eines Patienten, oder um sicherheitsrelevante Messungen wie die Überprüfung einer Stoffprobe auf explosive Stoffe. -Von Vorteil sind hierbei sowohl schnelle als auch sensitive Messungen, um Zuverlässig auf gegebene Zustandsänderungen reagieren zu können.\\ -Eine der Methoden dieser Analyse bietet die Ionenmobilitätsspektrometrie (im Folgenden hier IMS) an. Die IMS nutzt die variablen Ionisierbarkeiten und Mobilitäten von Molekülen in einem Gas aus um diese zu trennen und zu vermessen. Durch diese Funktionsweise können Messungen innerhalb weniger Minuten bis Sekunden durchgeführt werden, wobei Stoffkonzentrationen von \todo[inline]{Add concentration here} festgestellt werden können. +Eine der Methoden dieser Analyse bietet +das Ionenmobilitätsspektrometer (IMS) an. +Das IMS nutzt die variable Ionisierbarkeit und +Mobilität von Molekülen in einem Gas aus, um diese +zu trennen und zu vermessen. Durch diese Funktionsweise +können Messungen innerhalb weniger Minuten bis Zehntel von +Sekunden durchgeführt werden, +und es können kleinste Stoffmengen festgestellt werden \cite{Eiceman2013Oct}. -Ein zentraler Bestandteil des Aufbaus eines IMS ist nun der Transimpedanzverstärker (im Folgenden hier TIV). Dieses Element befasst sich mit der Umwandlung der zu messenden Ionen in ein Spannungssignal, welche von der Ausleseleketronik verarbeitet werden können. Somit bestimmt die Qualität und Sensitivität des TIV maßgeblich die Datenerfassung des IMS insgesamt. -Von relevanz sind hier verschiedene Parameter wie z.B. Bandbreite, Rauschverhalten und Verstärkung, welche auf den jeweiligen Anwendungsbereich des IMS angepasst werden müssen. +Ein wesentlicher Bestandteil des Aufbaus eines +IMS ist der Transimpedanzverstärker (TIV) \cite{Reinecke2018Oct}. +Dieser ist ein zentrales Element der Messkette, +welche die Ionen detektiert und für die restliche +Auswertung messbar macht. +Somit bestimmt die Performance des TIV maßgeblich +z.~B. die Detektionsgrenze und das Auflösungsvermögen +des IMS. +Bestehende TIVs bieten akzeptable Messqualität, sind jedoch +entweder sehr teuer, oder benötigen manuelle Nachjustierungen +und Korrekturen. -In dieser Arbeit wird die Auslegung und Erstellung eines kompakten, sensitiven TIVs dargestellt, welcher auf die IMS-Geräte des Institut für Grundlagen der Elektrotechnik und Messtechnik (GEM) an der Leibniz Universität Hannover angepasst ist. -Der TIV wird auf zwei verschiedene IMS-Systeme mit unterschiedlichen Anforderungen angepasst.\\ -In Kapitel 2 wird die Funktionsweise eines IMS nähergehend erklärt. Hierbei werden die jeweiligen Größen- und Zeitskalen, für die der TIV ausgelegt werden soll, erläutert, und die Aufgabe des TIV im Bezug auf das Gesamtsystem wird genauer erklärt. Zudem werden notwendige Grundlagen vermittelt.\\ -In Kapitel 3 wird ein Modell des TIVs erstellt. Zuerst werden die Zielparameter beschrieben, welche vom TIV gewünscht sind. -Neben der Erläuterung der Funktionsweise eines TIVs werden die verschiedenen parasitären Effekte genauer charakterisiert, welche die Schaltung beeinträchtigen, und es wird auf Möglichkeiten eingegangen um diesen Effekten entgegen zu wirken. Hiernach wird eine reale Schaltung ausgelegt, und mithilfe von Simulationen charakterisiert.\\ -In Kapitel 4 wird ein Prototyp der TIV-Schaltung erbaut und vermessen. Es werden hierbei vergleiche mit den erstellten Simulationen gezogen, und es wird auf Diskrepanzen zu diesen eingegangen. Abschließend werden Messungen an einem realen IMS-System ausgeführt, um die Funktionstüchtigkeit des erbauten TIV zu bestätigen.\\ -Kapitel 5 befasst sich mit der Erstellung einer vollintegrierten Schaltung auf Basis des erstellten TIV, welcher die gesamte Analogkette der IMS-Messung beinhaltet. \todo{Did this happen?}\\ -Abschließend beschreibt Kapitel 6 einen Ausblick auf zukünftige Anwendungsgebiete des erstellten TIV, und fasst die erstellten Messungen zusammen. \ No newline at end of file +Es soll in dieser Arbeit ein neuer TIV ausgelegt werden, +welcher ohne Nachjustierungen und mit leicht verfügbaren +Bauteilen gebaut werden kann, um eine kostengünstige +und reproduzierbare Alternative anzubieten. +In dieser Arbeit wird die Entwicklung, Auslegung +und Vermessung des neuen TIV-Designs beschrieben. +Hierbei werden verschiedene störende Faktoren, +wie z.~B. parasitären Effekte, analytisch sowie mithilfe +von Simulationen untersucht. Basierend hierauf +werden Möglichkeiten zur Reduktion und Kompensation +der negativen Effekte ausgelegt. + +Der erstellte TIV wird vermessen und charakterisiert, +wobei die Messergebnisse mit den Simulationen verglichen +werden. Eventuelle Fehler und ungewünschtes Verhalten werden +genauer analysiert und korrigiert. +Schlussendlich werden einige Vergleichsmessungen des neu +erstellten TIVs mit den bestehenden Designs durchgeführt. \ No newline at end of file diff --git a/TeX/Kapitel/Grundlagen.tex b/TeX/Kapitel/Grundlagen.tex index f2eeb0c..bff38ab 100644 --- a/TeX/Kapitel/Grundlagen.tex +++ b/TeX/Kapitel/Grundlagen.tex @@ -1,46 +1,76 @@ \chapter{Grundlagen} -Dieses Kapitel wird grundegende technische Details für diese Arbeit dar stellen, um auf diesen später auf zu bauen. -Es wird hierbei die Funktionsweise eines IMS genauer beschrieben, und die Rolle des TIVs in diesem System charakterisiert. +Dieses Kapitel stellt die grundegenden technischen Details für diese Arbeit dar. +Die Funktionsweise eines IMS wird näher beschrieben und die Rolle des TIVs in diesem System charakterisiert. Ebenfalls werden Eigenschaften relevanter elektrischer Bauteile beschrieben. -\section{Grundlagen des IMS} +\section{Grundlagen des Ionenmobilitätsspektrometers} -Im Folgenden wird die Ionenmobilitätsspektrometrie, deren Funktionsweise und Relevanz genauer beschrieben. -Es wird der Nutzen der Technologie dargestellt, und die Position des TIVs innerhalb eines IMS charakterisiert, um die Relevanz eines qualitativen Verstärkers dar stellen zu können, sowie um später die Betriebsparameter dessen festlegen zu können. +Im Folgenden ist die +Funktionsweise und Relevanz der Ionenmobilitätsspektrometrie +genauer beschrieben. Zusätzlich ist die Rolle des TIVs in +einem IMS dargestellt. -\subsection{Anwendungsgebiete eines IMS} +\subsection{Anwendungsgebiete der Ionenmobilitätsspektrometrie} -Im Folgenden soll auf die Relevanz und den Anwendungsbereich der Ionenspektrometrie eingegangen werden, um dar zu legen dass die Technologie breite praktische Anwendungen findet. Ein IMS bietet im Vergleich zu anderen Gasanalyseverfahren wie z.B. einem Massenspektrometer folgende Vorteile \cite{Eiceman2013Oct}: +Im Folgenden soll auf die Relevanz und den Anwendungsbereich von +Ionenmobilitätsspektrometern eingegangen werden, um darzulegen, +dass die Technologie breite praktische Anwendungen findet. +Ein IMS bietet im Vergleich zu anderen Gasanalyseverfahren, +wiez.~B. einem Massenspektrometer, folgende Vorteile \cite{Eiceman2013Oct}: \begin{itemize} - \item Kostengünstig. Ein IMS kann mitunter für wenige hundert Euro aufgebaut werden\cite{Reinecke2018Oct}, wodurch sie leichter in größeren Mengen aufgebaut werden können. - \item Simpler, kompakter Aufbau. Ein IMS kann unter atmosphärischem Druck betrieben werden, und braucht somit kein Vakuum-Equipment. Hierdurch sind die Systeme wesentlich transportabler als z.B. Massenspektrometer. - \item Schnelle Messungen. Messungen mit einem IMS können bis hinunter auf wenige Sekunden dauern. Hierdurch lassen sich schnell wichtige Messwerte erfassen. - \item Hohe Sensitivität. Ein IMS kann Stoffkonzentrationen im unteren ppb messen, wodurch auch kleinste Mengen eines Stoffes sicher bestimmt werden können. + \item Kostengünstig. IMS-Systeme können mitunter + für wenige hundert Euro aufgebaut werden + \cite{Reinecke2018Oct}, wodurch sie leichter + in größeren Mengen aufgebaut werden können. + \item Simpler, kompakter Aufbau \cite{Eiceman2013Oct}. + Ein IMS kann bei atmosphärischem Druck + betrieben werden und braucht somit kein + Vakuum-Equipment. Hierdurch sind die Systeme + wesentlich transportabler alsz.~B. + Massenspektrometer. + \item Schnelle, sensitive Messungen. + Messungen + mit einem IMS können bis hinunter auf wenige + Zehntel von Sekunden dauern und + zusätzlich Nachweisgrenzen + im einstelligen ppt-Bereich erreichen \cite{Reinecke2018Oct}. \end{itemize} -Hierdurch gibt es viele Anwendungsgebiete für ein IMS, mitunter in der Sicherheitstechnik zur Detektion von explosiven Stoffen\cite[Seite 269]{Eiceman2013Oct}, Drogen\cite[301]{Eiceman2013Oct}, zur Analyse von Umgebungsproben\cite[Seite 349]{Eiceman2013Oct} und zur medizinischen Untersuchung und Überwachung von Patienten\cite[Seite 366]{Eiceman2013Oct}.\\ -Ein IMS ist somit äußerst relevant für eine breite Menge an Arbeitsfeldern, und eine Weiterentwicklung der Technologie kann ebenso breit gefächerte Vorteile haben. +Hierdurch ergeben sich viele Anwendungsgebiete für ein IMS, mitunter in der +Sicherheitstechnik zur Detektion von explosiven Stoffen \cite[S.S. 269]{Eiceman2013Oct}, +Drogen \cite[S.S. 301]{Eiceman2013Oct}, zur Analyse von Umgebungsproben \cite[S.S. 349]{Eiceman2013Oct} +und zur medizinischen Untersuchung und Überwachung von Patienten \cite[S.S. 366]{Eiceman2013Oct}.\\ +Ein IMS ist somit äußerst relevant für eine breite Menge an +Arbeitsfeldern und eine Weiterentwicklung der Technologie kann ebenso breit gefächerte Vorteile haben. \subsection{Funktionsweise eines IMS} \label{chap:function_description_ims} -Das Buch ``Ion Mobility Spectrometry'' beschreibt die Ionenmobilitätsspektrometrie folgend \cite[Seite 1]{Eiceman2013Oct}: +Der Author Eiceman beschreibt im Buch ``Ion Mobility Spectrometry'' die Ionenmobilitätsspektrometrie folgend: \begin{quote} - Der Term Ionen Mobilitäts Spektrometrie (IMS) beschreibt die Prinzipien, Methoden und Instrumente zur Charakterisierung von Substanzen anhand der Geschwindigkeit von Gruppen (definiert als Gruppen von gasförmigen Ionen) entnommen von einer Substanz, in einem elektrischen Feld und einem Trägergas. + ``Der Term Ionen Mobilitäts Spektrometrie (IMS) beschreibt die Prinzipien, Methoden und Instrumente zur Charakterisierung von Substanzen anhand der Geschwindigkeit von Gruppen (definiert als Gruppen von gasförmigen Ionen) entnommen von einer Substanz, in einem elektrischen Feld und einem Driftgas.'' \cite[S.S. 1]{Eiceman2013Oct} \end{quote} -Ein IMS-System analysiert somit Gase, in dem eine Gasprobe ionisiert wird, und mithilfe eines Trägergases und eines elektrischen Feldes in diskrete Gruppen aufgespalten wird. Der Ablauf dieses Vorganges ist grundsätzlich wie folgt \cite[Seite 4]{Eiceman2013Oct}: +Ein IMS-System analysiert somit Gase, indem eine Gasprobe ionisiert +wird und mithilfe eines Trägergases und eines elektrischen Feldes +in diskrete Gruppen aufgespalten wird. Der Ablauf dieses Vorganges +ist grundsätzlich wie folgt \cite[S.S. 4]{Eiceman2013Oct}: \begin{enumerate} \item Ein Probengas wird mit einer prozessspezifischen Ionenquelle ionisiert. - \item Ein diskretes Paket dieses ionisierten Gases wird in eine Drift-Region injeziert, welche mit einem inerten Trägergas gefüllt ist und über welche eine Spannung anliegt. - \item Die angelegte Spannung beschleunigt die ionisierten Moleküle des Gaspacketes. Hierbei wird das Probegas in seine Bestandteile aufgespalten, da verschiedene Moleküle durch unterschiedliches Gewicht oder Ladung sich verschieden schnell durch die Drift-Region bewegen. - \item Die nun zeitlich aufgespaltenen Ionen-Pakete werden durch einen Detektor aufgefangen. Typischerweise ist dies eine Faraday-Platte. Hierdurch entsteht ein Stromfluss proportional zur Menge der Ionen. - \item Ein Verstärker wandelt diese Ströme in messbare Spannungen um, welche von der Sensorelektronik aufgenommen und verarbeitet werden. + + \item Ein diskretes Paket dieses ionisierten Gases wird in eine Drift-Region + injiziert, in dem sich ein Driftgas befindet. + + \item Mithilfe einer über der Driftregion anliegenden Spannung werden die + Ionen nach ihrer Mobilität getrennt. + + \item Die nun zeitlich getrennten Ionen-Pakete werden durch einen Detektor aufgefangen. Typischerweise ist dies eine Faraday-Platte. Hierdurch entsteht ein Stromfluss proportional zur Menge der Ionen. + \item Ein Verstärker wandelt diese Ströme in messbare Spannungen um, welche digitalisiert und verarbeitet werden können. \end{enumerate} Ein typischer Aufbau eines IMS ist in Abbildung \ref{fig:IMS_Schematic} dargestellt. @@ -48,162 +78,372 @@ Ein typischer Aufbau eines IMS ist in Abbildung \ref{fig:IMS_Schematic} dargeste \begin{figure}[h] \centering \includegraphics[scale=0.15]{grundlagen/IMS_Schematic.drawio.png} - \caption{\label{fig:IMS_Schematic}Schematischer Aufbau einer IMS-Röhre nach \cite[Seite 3, Abb. 1.2.b]{Eiceman2013Oct}} + \caption[Schematischer Aufbau einer IMS-Röhre]{\label{fig:IMS_Schematic}Schematischer Aufbau einer IMS-Röhre nach \cite[Seite 3, Abb. 1.2.b]{Eiceman2013Oct}} \end{figure} -Das Messergebnis eines IMS-Laufes wird as Spektrum bezeichnet, und wird meist als Strom über die Zeit dargestellt. In dieser Darstellung sind die verschiedenen Ionenpakete als Spitzen des Graphen zu erkennen. Abbildung \ref{fig:ims_example_spectrum} stellt beispielhalf ein solches Spektrum dar. +Das Messergebnis eines IMS-Laufes wird als Spektrum bezeichnet +und ist meist als Strom über die Zeit dargestellt. +Abbildung \ref{fig:ims_example_spectrum} stellt beispielhalf +ein solches Spektrum dar. +In dieser Darstellung sind die verschiedenen Ionenpakete als +Peaks des Graphen zu erkennen. \begin{figure}[h] \centering - \missingfigure{IMS SPECTRUM HERE} - \caption{\label{fig:ims_example_spectrum}Spektrum einer beispielhaften IMS-Messung} + \includegraphics[scale=0.8]{datavis/example_spectrum.png} + \caption[Spektrum einer beispielhaften IMS-Messung]{ + \label{fig:ims_example_spectrum}Spektrum einer beispielhaften IMS-Messung. + Aufgezeichnet ist die Ausgangsspannung des TIVs des IMS über die Zeit. + Zu sehen ist der Peak des Driftgases um circa + $\SI{5.5}{\milli\second}$ herum, sowie Peaks von Ionenpaketen + um $\SI{8.8}{\milli\second}$, $\SI{10.5}{\milli\second}$ + und $\SI{13}{\milli\second}$. + } \end{figure} +\FloatBarrier \subsubsection{Aufgabe eines TIV im IMS} \label{chap:tia_in_ims} -Wie in Kapitel \ref{chap:function_description_ims} beschrieben, beruht ein IMS auf der Messung der diskreten Ionenpakete, deren zeitlicher Versatz und Größe. Um die kleinen Ströme der Ione im Bereich von $\SI{100}{\pico\ampere}$ bis $\SI{10}{\nano\ampere}$ messen zu können, ist ein Verstärker notwendig. Dieser Verstärker wird als sog. Transimpedanzverstärker bezeichnet, da er als Eingangsgröße einen Strom hat, und eine Spannung als Ausgang gibt. Die Verstärkung wird somit in Ohm angegeben. Der TIV stellt hiermit ein zentrales Bauteil eines IMS dar, dessen Parameter maßgeblich die Qualität der Messungen beeinflusst. +Wie in Kapitel \ref{chap:function_description_ims} beschrieben, beruht ein IMS auf der Messung der von den Ionenpaketen hervorgerufenen Ströme und deren zeitlicher Verteilung. +Um die kleinen Ströme der Ionen im Bereich von $\SI{1}{\pico\ampere}$ bis $\SI{10}{\nano\ampere}$ messen zu können, ist ein Verstärker notwendig. Dieser Verstärker wird als TIV bezeichnet, da er als Eingangsgröße einen Strom hat und eine Spannung als Ausgang gibt. Die Verstärkung wird somit in Ohm angegeben. -Folgende Aufgaben werden an den TIV eines IMS gestellt: +Folgende Anforderungen werden an den TIV eines IMS gestellt: \begin{itemize} - \item Möglichst Stör- und Leckfreier Messeingang - \item Verstärkung von Strömen in der Größenordnung von $\SI{1}{\nano\ampere}$ - \item Bereitstellung einer messbaren Spannung im Bereich von $\SI{1}{\volt}$ - \item Genügend Bandbreite zur korrekten Abbildung der Spitzen der Ionenpackete + \item Möglichst geringes eingangsbezogenes Rauschen. Das Rauschen des TIVs + beeinflusst das Signal-Zu-Rausch-Verhältnis, woraus sichz.~B. + die Detektionsgrenzen ergeben. Ein kleineres + Rauschen erlaubt die Erkennung kleinerer Ionenströme mit größerer Sicherheit. + + \item Verstärkung von Strömen in der Größenordnung von $\SI{1}{\pico\ampere}$ + bis zu einigen $\SI{}{\nano\ampere}$. Die genaue Größe des Stromes ergibt sich durch + den Aufbau des IMS selbst. + \item Bereitstellung einer Ausgangsspannung im Bereich von $\SI{\pm2}{\volt}$. + Da der Ausgang des TIVs zur digitalisierung des Signales genutzt wird, ist eine + Ausgangsspannung gewünscht, welche mit herkömmlichen Analog-Digital-Wandlern kompatibel ist. + \item Genügend Bandbreite zur korrekten Abbildung der Ionenströme. Eine zu kleine Bandbreite + verzerrt die Form des gemessenen Ionenstromes und verschlechtert die Qualität der Messung. + Schnellere Bandbreiten erlauben die Messung schnellerer Signale und somit auch kleinerer + Ionenpakete. \end{itemize} +\cleardoublepage \section{Grundlegende Parasitäreffekte} \label{chap:basics_parasitics} -In diesem Kapitel wird auf die parasitären Effekte weiterer Bauteile eingegangen, die im folgenden relevant sind und bei der Auslegung der Schaltung beachtet werden müssen. +Im Folgenden soll auf die parasitären Effekte der verschiedenen Bauteile eingegangen werden, welche +bei der Auslegung der Schaltung beachtet werden müssen. -\paragraph*{Leckströme:} Diese treten bei fast allen Schaltungsaufbauten auf. Sie entstehen durch die hohen aber endlichen Oberflächenwiderstände des PCB-Materials sowie durch durch Verunreinigungen. Diese erlauben es kleinen Leckströmen zwischen Zweigen der Schaltung zu fließen, und können bei Zweigen mit hoher Impedanz störend wirken.\todo{Find a citation for this} +\paragraph*{Leckströme:} Diese treten bei allen Schaltungsaufbauten auf. +Sie entstehen durch die hohen, aber endlichen, Oberflächenwiderstände der Bauteile +und der Leiterkarte (engl.: Printed Circuit Board, PCB) +sowie durch Verunreinigungen \cite{AltiumLeakages}. Diese erlauben +es kleinen Leckströmen zwischen verschiedenen Zweigen der Schaltung zu fließen +und können bei Zweigen mit hoher Impedanz störend wirken +\cite[S.f. 33-34]{DatasheetADA4530}. +Abbildung \ref{fig:example_leakages} zeigt beispielhaft einige der Leckströme auf +einer Platine. -\begin{figure} +\begin{figure}[hb] \centering - \includegraphics[scale=0.25]{grundlagen/Examples_Leakages.drawio.png} - \caption{\label{fig:example_leakages}Schematische Darstellung eines PCBs mit Anschlüssen zu Bauteilen (goldene Pads) und Leiterbahnen (dunkelgrün) mit verschiedenen Leckstrompfaden entlang der Oberfläche (schraffiert dargestellt). Leckströme fließen überwiegend zwischen freigelegten Kupferflächen, können zudem auch durch Oberflächenladungen in einem Isolator wie dem PCB-Lötstopplack entstehen.} + \includegraphics[scale=0.18]{grundlagen/Examples_Leakages.drawio.png} + \caption[Schematische Darstellung der Leckströme eines PCBs]{\label{fig:example_leakages} + Schematische Darstellung eines PCBs mit Anschlüssen zu Bauteilen + und Leiterbahnen, mit verschiedenen Leckstrompfaden entlang der Oberfläche. + Leckströme fließen überwiegend durch Verunreinigungen + zwischen freigelegten Kupferflächen, + können zudem auch durch Oberflächenladungen in einem + Isolator wie dem Lötstopplack entstehen. + Eigene Darstellung nach \cite{AltiumLeakages}\cite{Horowitz:1981307}.} \end{figure} -\paragraph*{Parasitäre Kapazitäten:} Diese entstehen ebenfalls durch den physikalischen Aufbau der Schaltung. Die Nähe von Leitungen oder Kontakten zueinander, oder zu einer Kupferebene wie z.B. der Erdungsebene, erstellt eine leichte kapazitive Kopplung hierzwischen. Dieser Effekt verursacht Kapazitäten von $\SI{10}{\femto\farad}$ bis hin zu einigen $\SI{}{\pico\farad}$. Abbildung \ref{fig:example_parasitic_c} zeigt einige dieser Kapazitäten auf. +\paragraph*{Parasitäre Kapazitäten:} +\label{chap:basics_parasitics_capacitances} +Diese entstehen ebenfalls durch den physikalischen +Aufbau der Schaltung. Die Nähe von Leitungen oder Kontakten zueinander, +oder zu einer Kupferebene wiez.~B. der Erdungsebene, erstellt eine +kapazitive Kopplung hierzwischen. Dieser Effekt verursacht Kapazitäten +im Bereich von einigen $\SI{}{\femto\farad}$, bei größeren Komponenten +sogar im Bereich von $\SI{}{\pico\farad}$. +Abbildung \ref{fig:example_parasitic_c} zeigt einige dieser Kapazitäten auf. \begin{figure}[h] \centering - \includegraphics[scale=0.2]{grundlagen/Examples_Capacitances.drawio.png} - \caption{\label{fig:example_parasitic_c}Schematische Darstellung einer Schnittfläche eines PCBs mit Leitungen und einem Bauteil, mit einigen parasitären Kapazitäten eingezeichnet. Diese Kapazitäten entstehen sowohl zwischen zwei Leitungen, Leitungen und Erdflächen, sowie den Anschlüssen eines Bauteiles.} + \includegraphics[scale=0.15]{grundlagen/Examples_Capacitances.drawio.png} + \caption[Schematische Darstellung der parasitären Kapazitäten eines PCBs]{\label{fig:example_parasitic_c} + Schematische Darstellung einer Schnittfläche eines PCBs mit Leitungen und einem Bauteil, + mit einigen parasitären Kapazitäten eingezeichnet. + Diese Kapazitäten entstehen sowohl zwischen zwei Leitungen, Leitungen und Erdflächen, sowie den Anschlüssen eines Bauteiles. + Eigene Darstellung nach \cite{SierraReduceCapacitances} und \cite{AltiumReduceCapacitance}.} \end{figure} -Wichtig ist dieser Effekt in Kombination mit hochohmigen Eingängen und Widerständen. So wird z.B. die Impedanz eines $\SI{100}{\mega\ohm}$ Widerstandes bereits ab wenigen zehn Kilohertz maßgeblich durch die eigene parasitäre Kapazität beeinflust. Diese liegt bei der Standardbaugröße ``1206'' im Bereich von ca. $\SI{30}{\femto\farad}$, und bildet einen RC-Pass-Filter mit einer Eckfrequenz von $\SI{53.05}{\kilo\hertz}$. Abbildung \ref{fig:example_r_cp} zeigt beispielhaft die Verläufe verschiedener Widerstandsimpedanzen über die Frequenz, und wie diese durch die parasitäre Kapazität einbrechen. - -\begin{figure} - \centering - \includegraphics[scale=0.8]{datavis/Parasitics/Examples_R_Cp_RSweep.png} - \caption{\label{fig:example_r_cp}Impedanzverläufe verschiedener Widerstandswerte bei gleicher parasitärer Kapazität $C_p = \SI{30}{\femto\farad}$} -\end{figure} - -\paragraph*{Thermisches Rauschen:} Dieses Rauschen, genannt Johnson-Nyquist-Rauschen, betrifft resistive Komponenten. Es wird verursacht durch die thermische Bewegung von Ladungsträgern, und bildet ein weißes Rauschen aus. Das Rauschen lässt sich über die folgende Formel berechnen: +Wichtig ist dieser Effekt in Kombination mit hochohmigen Eingängen und Widerständen. +So wirdz.~B. die Impedanz eines $\SI{100}{\mega\ohm}$ Widerstandes +bereits ab wenigen zehn Kilohertz maßgeblich durch die eigene parasitäre Kapazität beeinflusst +\cite{Yang:21}\cite{JBellemann22}\cite{VishayRFreq}\cite[S.S. 45]{DatasheetADA4530}. +Hierbei wird der effektive Widerstand bei höheren Frequenzen reduziert, entsprechend der +folgenden Formel \cite[S.S. 21]{Horowitz:1981307}: \begin{equation} - V_{\mathrm{n,rms}} = \sqrt{4k_BTR\Delta f}\label{eqn:thermal_voltage_noise} + Z(f) = \left(\frac{1}{R_f} + j\cdot 2 \pi fC_p\right)^{-1} \end{equation} -Hierbei ist $V_{\mathrm{n,rms}}$ der RMS-Wert des Rauschens, $k_B$ die Boltzmann-Konstante, $T$ die Temperatur, $R$ der Widerstand des betrachteten Bauteils und $\Delta f$ die Bandbreite, über welche gemessen wird. Abbildung \ref{fig:example_r_noise} zeigt den schematischen Aufbau eines rauschenden Widerstandes. \todo{Insert citation} +Die Frequenz, ab welcher die Kapazität einen größeren Einfluss als der eigentliche +Widerstand besitzt, wird als Grenzfrequenz bezeichnet, und lässt sich wie +folgt berechnen \cite[S.S. 49]{Horowitz:1981307}: +\begin{equation} + f_{3 dB} = \frac{1}{2\pi R_f C_p} \label{eqn:rc_frequency} +\end{equation} -\begin{figure} +Die Parallelkapazität ist stark von der Bauform des Widerstandes abhängig +und liegt bei der Standardbaugröße ``1206'' im Bereich von circa $\SI{50}{\femto\farad}$ \cite{JBellemann22}. +So wird sich bei dem $\SI{100}{\mega\ohm}$ Widerstand ein RC-Pass-Filter mit einer Grenzfrequenz von $\SI{53.05}{\kilo\hertz}$ ausbilden. +Abbildung \ref{fig:example_r_cp} zeigt einige in einer Simulation berechneten Verläufe verschiedener +Widerstandsimpedanzen +über die Frequenz und wie diese durch die parasitäre Kapazität einbrechen. + +\FloatBarrier + +\begin{figure}[ht] + \centering + \includegraphics[scale=0.8]{datavis/Parasitics/Examples_R_Cp_RSweep.png} + \caption[Impedanzverläufe verschiedener Widerstandswerte]{\label{fig:example_r_cp} + Impedanzverläufe verschiedener Widerstandswerte bei gleicher parasitärer Kapazität $C_p = \SI{50}{\femto\farad}$, + dem typischen Wert für die ``1206''-Bauform \cite{JBellemann22}. + } +\end{figure} + +\paragraph*{Thermisches Rauschen:} Dieses Rauschen, genannt +Johnson-Nyquist-Rauschen, betrifft resistive Komponenten. +Es wird verursacht durch die thermische Bewegung von Ladungsträgern +und bildet ein weißes Rauschen aus. +Der Effektivwert des Rauschen lässt sich über die folgende Formel berechnen \cite[S.S. 474]{Horowitz:1981307}: + +\begin{equation} + U_{\mathrm{n,rms}} = \sqrt{4k_BTR_f\Delta f}\label{eqn:thermal_voltage_noise} +\end{equation} + +Hierbei ist $U_{\mathrm{n,rms}}$ der RMS-Wert des Rauschens, +$k_B$ die Boltzmann-Konstante, + $T$ die Temperatur, $R_f$ der Widerstand des + betrachteten Bauteils und $\Delta f$ die Bandbreite, + über welche gemessen wird. Für den beispielhaften $\SI{100}{\mega\ohm}$ + Widerstand bei Raumtemperatur ($\SI{25}{\celsius}$) und einer Bandbreite + von $\SI{30}{\kilo\hertz}$ + ergibt sich ein Rauschen von + $\SI{222.25}{´\micro\volt}$. +Abbildung \ref{fig:example_r_noise} zeigt den + schematischen Aufbau eines rauschenden Widerstandes. + +\begin{figure}[ht] \centering \includegraphics[scale=0.15]{grundlagen/Schematic_Resistor.drawio.png} - \caption{\label{fig:example_r_noise}Schematische Darstellung eines realen Widerstandes nach \cite{WikipediaResistors2024May}} + \caption[Ersatzschaltbild für die Modellierung eines + rauschenden, hochohmigen Widerstandes]{ + \label{fig:example_r_noise}Ersatzschaltbild für die Modellierung eines + rauschenden, hochohmigen Widerstandes nach \cite[S.S. 474]{Horowitz:1981307}. + Durch die niedrigen Frequenzen und hohen Impendanzen kann die parasitäre Induktivität des Widerstandes + in diesem Anwendungsfall vernachlässigt werden.} \end{figure} +\cleardoublepage + \section{Grundlagen des Operationsverstärkers} \label{chap:basics_opamp} -Im folgenden werden die Grundlagen eines Operationsverstärkers (auch genannt OpAmp) dargelegt. Hierbei wird nicht auf den exakten internen Aufbau eingegangen, sondern das relevante Verhalten sowie einige Parasitäreffekte beschrieben. +Im Folgenden werden die Grundlagen eines Operationsverstärkers (im Folgenden genannt OpAmp, aus dem Englischen ``Operational Amplifier'') dargelegt. +Hierbei ist nicht der exakte internen Aufbau entscheidend, sondern das für die Anwendung des TIVs relevante Verhalten sowie beeinflussende Parasitäreffekte. -Ein klassischer Operationsverstärker ist ein elektronisches Bauteil, welches vielseitige Anwendungen in einer Schaltung findet. Er kann als verstärkendes oder filterndes Bauteil aufgebaut werden, sowie differenzierend oder integrierend wirken. Die grundlegende Operation eines OpAmps ist bei jeder Verschaltung jedoch äquivalent:\\ -Er besitzt zwei Eingänge, positiv und negativ, und einen Ausgang (siehe Abbildung \ref{fig:example_opamp}). -Dieser Ausgang wird entsprechend der Formel $V_{\mathrm{out}} = A_\mathrm{ol} * \left(V_+ - V_-\right)$ getrieben, wobei $A_{\mathrm{ol}}$ der sog. Open-Loop-Gain, also die offene Verstärkung, ist. Für einen idealen OpAmp kann dieser Wert als quasi unendlich angenommen werden. Mithilfe eines Rückkoppelpfades wird das Ausgangssignal meist an den negativen Eingang zurück geführt. Der OpAmp wird somit den Ausgang so treiben, dass es keine Differenzspannung zwischen den Eingangssignalen gibt. Mit korrekter Auswahl der Rückkopplung können quasi-beliebige Transferfunktionen eingestellt werden. Abbildung \ref{fig:example_opamp_amplifier} zeigt einen simplen Verstärker-Schaltkreis, welcher das Eingangssignal um den Faktor 10 skaliert. +Ein klassischer OpAmp ist ein elektronisches Bauteil, welches vielseitige Anwendungen in einer Schaltung findet. +Neben dem Aufbau als verstärkendes oder filterndes Bauteil sind auch differenzierende oder integrierende Schaltungsvarianten möglich. +Das grundlegende Verhalten eines OpAmps ist bei jeder Verschaltung jedoch äquivalent:\\ +Ein OpAmp besitzt normalerweise zwei Eingänge, positiv und negativ, und einen Ausgang (siehe Abbildung \ref{fig:example_opamp}). -\begin{figure} +\begin{figure}[ht] \centering \includegraphics[scale=0.25]{grundlagen/OpAmp.drawio.png} - \caption{\label{fig:example_opamp}Schematisches Symbol eines idealen OpAmps} + \caption[Schematisches Symbol eines idealen OpAmps]{ + \label{fig:example_opamp}Schematisches Symbol eines idealen OpAmps, eigene Darstellung + nach \cite[S.S. 224]{Horowitz:1981307}.} \end{figure} -\begin{figure} +Die Spannung am Ausgang ergibt sich idealerweise durch folgende Formel: +\begin{equation} + U_{\mathrm{out}} = A_\mathrm{ol} \cdot \left(U_+ - U_-\right) +\end{equation} +Hierbei ist $A_{\mathrm{ol}}$ der sog. Open-Loop-Gain bzw. die offene Verstärkung. Für einen idealen OpAmp kann dieser Wert als quasi unendlich angenommen werden. + +Mithilfe eines Rückkoppelpfades wird das Ausgangssignal meist an den negativen Eingang +zurückgeführt. Der OpAmp wird somit den Ausgang so treiben, dass es keine Differenzspannung +zwischen den Eingangssignalen gibt. Mit korrekter Auswahl der Rückkopplung können +quasi-beliebige Transferfunktionen eingestellt werden. +Abbildung \ref{fig:example_opamp_amplifier} zeigt einen simplen +Verstärker-Schaltkreis, welcher das Eingangssignal um den Faktor 10 skaliert. + +\begin{figure}[ht] \centering \includegraphics[scale=0.25]{grundlagen/OpAmp_10x.drawio.png} - \caption{\label{fig:example_opamp_amplifier}Beispielhafte Verstärkerschaltung mit einem OpAmp} + \caption[Beispielhafte Verstärkerschaltung mit einem OpAmp]{ + \label{fig:example_opamp_amplifier}Beispielhafte Verstärkerschaltung mit einem OpAmp, + eigene Darstellung, nach \cite{Cox2002}.} \end{figure} -Ein realer OpAmp kann für viele Anwendungen als nahezu ideal angesehen werden. Da in dieser Arbeit jedoch mit hohen Verstärkungen und kleinen Strömen gearbeitet wird, müssen die parasitären Effekte des OpAmps mit beachtet werden. Diese sind wie folgt: +\FloatBarrier -\begin{itemize} - \item Eingangs-Leckströme. Die Eingänge eines realen OpAmp können kleine Ströme führen. Je nach Verstärker befinden sich diese im Bereich von $\SI{1}{\micro\ampere}$ bis hin zu $\SI{1}{\femto\ampere}$. Diese Leckströme können die Spannungen an den Eingängen, und somit das Messergebis, beeinflussen\cite{analogINBIAS2008}. - \item Parasitäre Kapazitäten. Ein OpAmp hat, bedingt durch die physikalische Auslegung des Bauteils, verschiedene ungewollte Kapazitäten sowohl gegen Masse, als auch zwischen den Kanälen selbst. Diese können die Transferfunktion beeinflussen\cite{tiOpAmpCap2000}. - \item Endliche Geschwindigkeit. Ein realer OpAmp kann auf Signaländerungen nur in endlicher Zeit reagieren. Hierdurch ergibt sich eine Grenze der Bandbreite in Relation zur Verstärkung. Dies wird als Verstärkungs-Bandpreitenprodukt\todo{Spelling OK?} charakterisiert\cite{Cox2002}. Im folgenden wird dies als GBWP aus dem Englischen ``Gain-Bandwidth-Product'' bezeichnet. Dies kann ebenfalls die Transferfunktion beeinflussen, siehe Abbildung \ref{fig:example_opamp_gbwp}. - Das GBWP gibt an, bei welcher Frequenz der OpAmp eine Verstärkung von 1 aufweist. Die effektive Bandbreite eines OpAmp kann somit durch Dividieren des GBWP mit der Verstärkung berechnet werden. - \item Endliche Verstärkung. Ein realer OpAmp kann ein Signal nur um einen +Ein realer OpAmp kann für viele Anwendungen als nahezu ideal angesehen werden. +Da in dieser Arbeit jedoch mit hohen Verstärkungen und kleinen Strömen gearbeitet +wird, müssen einige der parasitären Effekte des OpAmps mitbeachtet werden. +Diese sind wie folgt: + + +\paragraph*{Eingangs-Leckströme:} Ein idealer OpAmp besitzt Eingänge, + durch welche kein Strom fließen kann, um das Eingangssignal möglichst wenig zu stören. + Reale OpAmps haben jedoch messbare Eingangsströme. + Der exakte Wert hängt stark vom OpAmp-Typ ab, mit kleisten + Werten im Bereich von $\SI{}{\femto\ampere}$, bis hin zu + einigen $\SI{}{\micro\ampere}$. + Diese Leckströme können in der Anwendung als TIV den gemessenen Strom stark verzerren + und beeinflussen somit negativ das Messergebnis \cite[S.S. 302]{Horowitz:1981307}\cite{analogINBIAS2008}. + +\paragraph*{Parasitäre Kapazitäten:} Ein OpAmp hat, bedingt durch die physikalische Auslegung des Bauteils, + verschiedene ungewollte Kapazitäten sowohl gegen Masse, als auch zwischen den Eingängen selbst. + Diese können das Eingangssignal verzerren und stören somit die Übertragungsfunktion \cite{tiOpAmpCap2000}. + +\paragraph*{Endliche Geschwindigkeit:} + Ein realer OpAmp kann auf Signaländerungen nur in endlicher Zeit reagieren. + Hierdurch ergibt sich eine Grenze der Bandbreite in Relation zur Verstärkung. + Dies wird als Produkt aus Verstärkung und Bandbreite angegeben \cite[S.S. 247]{Horowitz:1981307}\cite{Cox2002}. + Im Folgenden wird dies als GBWP, aus dem Englischen ``Gain-Bandwidth-Product'', bezeichnet. + Dies kann ebenfalls die Übertragungsfunktion beeinflussen, + da ein zu niedriges GBWP die Übertragungsfunktion instabil werden lässt. + Abbildung \ref{fig:example_opamp_gbwp} + zeigt den Einfluss verschiedener GBWP-Werte auf die Übertragungsfunktion auf. Deutlich zu erkennen ist eine Reduktion + der Bandbreite, sowie eine Resonanz, welche bei zu kleinem GBWP auftreten kann. + +\begin{figure}[ht] + \centering + \includegraphics[scale=0.7]{datavis/Parasitics/SingleStage_GBWP_Sweep.png} + \caption[Einfluss des GBWP eines OpAmps auf einen TIV]{\label{fig:example_opamp_gbwp}Darstellung des + Einflusses des GBWP auf die Übertragungsfunktion einer OpAmp Schaltung. + Bei zu geringem GBWP ist die Bandbreite limitiert. + Zudem ensteht eine Instabilität, welche den Schaltkreis zum oszillieren bringen kann.} +\end{figure} + +\paragraph*{Endliche Verstärkung:} Ein realer OpAmp kann ein Signal nur um einen gewissen, endlichen Faktor verstärken. Dieser Faktor wird als ``offene'' Verstärkung bezeichnet, da er ohne Rückkopplung gemessen wird. Diese Begrenzung führt zu einer Limitierung der absoluten - Verstärkung einer OpAmp-Stufe. Zusammen mit einer Eingangskapazität bildet - sich hieraus ebenfalls eine Grenze der Bandbreite, da die Eingangskapazität - den Anstieg der Eingangsspannung, und durch die endliche Verstärkung auch den - Anstieg der Ausgangsspannung, begrenzt. Dies ist in Abbildung \ref{fig:opamp_aol_sweep} dargestellt. \label{chap:opamp_aol_limit_explained} - \item Rauschen. Ein realer OpAmp hat verschiedene Rauschquellen, welche in das Messsignal übergehen können. Dies sind Eingangsbezogenes Strom- und Spannungsrauschen \cite{tiNoise2007}, und sind in Abbildung \ref{fig:example_opamp_noise} dargestellt. Auf die genauen Quellen dieses Rauschens soll hier nicht weiter eingegangen werden, da diese durch die internen Schaltungen des OpAmp entstehen.\\ - Das Spannungsrauschen ist hierbei im unteren Frequenzbereich proportional zu $1/\omega$ und flacht ab einer Eckfrequenz zu einem konstanten Wert ab, während das Stromrauschen konstant anfängt und im höheren Frequenzbereich proportional zu $\omega$ zu nimmt. -\end{itemize} + Verstärkung einer OpAmp-Stufe \cite[S.S. 249]{Horowitz:1981307}. + Zusammen mit einer Eingangskapazität bildet + sich im Falle eines TIVs hieraus ebenfalls eine Grenze der Bandbreite, da die Eingangskapazität + den Anstieg der Eingangsspannung und durch die endliche Verstärkung auch den + Anstieg der Ausgangsspannung begrenzt \cite[S.S.541]{Horowitz:1981307}. + Dieser Effekt ist in Abbildung \ref{fig:opamp_aol_sweep} dargestellt, + welche einen klaren Einbruch der Bandbreite bei zu geringer offener Verstärkung zeigt. + \label{chap:opamp_aol_limit_explained} -\begin{figure} + +\begin{figure}[ht] \centering \includegraphics[scale=0.8]{datavis/Parasitics/SingleStage_Aol_Sweep.png} - \caption{\label{fig:opamp_aol_sweep}Darstellung des Einflusses der offenen Verstärkung + \caption[Einfluss der offenen Verstärkung auf einen TIV]{\label{fig:opamp_aol_sweep} + Ergebnisse einer Simulation zur Darstellung + des Einflusses der offenen Verstärkung eines OpAmp auf die Übertragungsfunktion eines TIVs. Bei zu geringer Verstärkung bricht die Verstärkung frühzeitig ein, und es bildet sich ein Tiefpassverhalten aus. Es sind jedoch keine Instabilitäten zu erkennen.} \end{figure} -\begin{figure}[h] - \centering - \includegraphics[scale=0.8]{datavis/Parasitics/SingleStage_GBWP_Sweep.png} - \caption{\label{fig:example_opamp_gbwp}Darstellung des Einflusses des GBWP auf die Übertragungsfunktion einer OpAmp Schaltung. Bei zu geringem GBWP ist die Bandbreite limitiert. Zudem ensteht eine Instabilität, welche den Schaltkreis zum oszillieren bringen kann.} -\end{figure} +\FloatBarrier -\begin{figure}[h] +\paragraph*{Rauschen:} + Ein realer OpAmp hat verschiedene Rauschquellen, welche in das Messsignal übergehen können. + Diese treten sowohl als Spannungs- als auch als Stromquellen auf \cite{tiNoise2007}. + Zusätzlich ist die Amplitude des Rauschens meist Frequenzabhängig. + Abbildung \ref{fig:example_opamp_noise} stellt ein vereinfachtes Ersatzschaltbild der Rauschquellen dar. + +\begin{figure}[htb] \centering - \includegraphics[scale=0.25]{grundlagen/OpAmp_Noise.drawio.png} - \caption{\label{fig:example_opamp_noise}Schematische, vereinfachte Darstellung der zusammengefassten Rauschquellen eines OpAmp nach \cite{tiNoise2007}. + \includegraphics[scale=0.22]{grundlagen/OpAmp_Noise.drawio.png} + \caption[Schematisches Ersatzschaltbild der Rauschquellen eines OpAmp]{\label{fig:example_opamp_noise}Schematisches, + vereinfachtes Ersatzschaltbild der zusammengefassten Rauschquellen eines OpAmp nach \cite{tiNoise2007}. Hierbei sind die Rauschquellen eingangsbezogen dargestellt.} \end{figure} + +Auf die physikalischen Ursachen dieses Rauschens soll hier nicht weiter eingegangen werden, +da diese durch die internen Schaltungen des OpAmp entstehen.\\ +Das Spannungsrauschen ist hierbei im unteren Frequenzbereich proportional zu $1/f$ und flacht ab einer Eckfrequenz zu einem konstanten Wert ab, während das Stromrauschen konstant anfängt und im höheren Frequenzbereich proportional zu $f$ zu nimmt. +Abbildung \ref{fig:example_opamp_noise_plot} zeigt das Rauschen eines beispielhaft gewählten realen OpAmps. + + +\begin{figure}[ht] + \centering + \includegraphics[scale=0.8]{datavis/Parasitics/SingleStage_noise_example.png} + \caption[ + Darstellung des Rauschens eines beispielhaft gewählten OpAmps + ]{\label{fig:example_opamp_noise_plot}Darstellung des Rauschens eines beispielhaft gewählten OpAmps. + Deutlich zu erkennen ist das Spannungsrauschen in den unteren Frequenzen, welches bis circa + $\SI{1}{\kilo\hertz}$ dominiert, sowie das Stromrauschen in den oberen Frequenzen, welches ab + $\SI{100}{\kilo\hertz}$ stark ansteigt.} +\end{figure} + +\cleardoublepage \section{Aufbau eines Transimpedanzverstärkers} \label{chap:basics_tia} -Im Folgenden wird auf den grundlegenden Aufbau und die Funktionalität eines TIVs eingegangen. +Im Folgenden wird auf den grundlegenden Aufbau +und die Funktionalität eines TIVs eingegangen, +basierend auf \cite{Reinecke2018Oct} und \cite[S.S. 233]{Horowitz:1981307}. -Ein TIV ist eine variante einer OpAmp-Verschaltung, dessen Aufgabe es ist, einen Strom in eine Spannung um zu wandeln. Somit wird die Verstärkung der Schaltung in $\Omega$ angegeben. Die grundlegende Schaltung ist hierbei in \ref{fig:example_tia_circuit} aufgeführt. +Wie bereits beschrieben ist ein TIV eine OpAmp-Verschaltung, welche einen +Strom in eine Spannung umwandelt. +Die Verstärkung wird hierbei in $\Omega$ angegeben. +Abbildung \ref{fig:example_tia_circuit} zeigt den grundlegenden +Aufbau eines TIVs. -\begin{figure}[h] +\begin{figure}[hb] \centering \includegraphics[scale=0.2]{grundlagen/OpAmp_TIA.drawio.png} - \caption{\label{fig:example_tia_circuit}Grundlegender Schaltkreis eines Transimpedanzverstärkers.} + \caption[Grundlegender Schaltkreis eines Transimpedanzverstärkers]{ + \label{fig:example_tia_circuit}Grundlegender Schaltkreis eines Transimpedanzverstärkers, + eigene Darstellung nach \cite{Reinecke2018Oct} und \cite[S.S. 233]{Horowitz:1981307}.} \end{figure} Die Funktionsweise ist wie folgt: \begin{itemize} - \item Der OpAmp steuert den Ausgang, um die Differenz der Eingangsspannungen zu minimieren. Da der positive Eingang fest auf $\SI{0}{\volt}$ gelegt ist, wird der negative Eingang ebenfalls auf $\SI{0}{\volt}$ gesteuert. - \item Ein Eingangsstrom fließt in den Eingang des TIV. Durch den Strom kombiniert mit einer (parasitären) Eingangskapazität bildet sich eine Spannung aus. - \item Durch die aufbauende differenzielle Spannung am Eingang steuert der OpAmp eine neue Ausgangsspannung an. - \item Die Ausgangsspannung lässt über den Rückkoppelwiderstand $R_f$ einen Strom fließen. Dieser Strom gleicht den Eingangsstrom so aus, dass die Spannung am negativen Eingang zurück auf $\SI{0}{\volt}$ getrieben wird. Die Ausgangsspannung wird somit auf $R_\mathrm{f} \cdot I_\mathrm{in}$ getrieben. + \item Der OpAmp regelt seinen Ausgang entsprechend Kapitel \ref{chap:basics_opamp}, + um die Differenz der Eingangsspannungen zu minimieren. + Da der positive Eingang fest auf $\SI{0}{\volt}$ gelegt ist, wird der negative Eingang ebenfalls auf $\SI{0}{\volt}$ gesteuert. + \item Ein Eingangsstrom fließt in den Eingang des TIV. + Dieser Strom ändert die Spannung am negativen Eingang des OpAmps, wobei ein positiver Strom + die Spannung ansteigen lässt bzw. ein negativer Strom die Spannung absenkt. + + \item Durch die aufbauende differenzielle Spannung am Eingang ändert der OpAmp seine Ausgangsspannung. + Fließtz.~B. ein positiver Strom, steigt die Spannung am invertiernden OpAmp Eingang und die Ausgangsspannung + senkt sich ab. + + \item Die neue Ausgangsspannung lässt über den Rückkoppelwiderstand $R_f$ einen Strom fließen. + Dieser Strom gleicht den Eingangsstrom so aus, dass die Spannung am negativen Eingang zurück auf $\SI{0}{\volt}$ getrieben wird. \end{itemize} +Für einen idealen TIV ergibt sich somit die Ausgangsspannung wie folgt: +\begin{equation} + U_\mathrm{out} = - R_\mathrm{f} \cdot I_\mathrm{in} +\end{equation} + Die Vor- und Nachteile dieser Schaltungsart sind wie folgt: \begin{itemize} \item[+] Leicht einstellbare Verstärkung. Der Rückkoppelwiderstand legt direkt die Verstärkung fest. - \item[+] Sehr hohe Verstärkungen sind durch Auswahl eines hohen Widerstandes möglich. - \item[+] Konstante Eingangsspannung. Der TIV-Eingang wird konstant auf $\SI{0}{\volt}$ getrieben. Hierdurch werden Effekte von z.B. parasitären Kapazitäten am Eingang verringert. Zudem können Abschirmungen an $\SI{0}{\volt}$, d.h. Erde, angeschlossen werden. - \item[-] Parasitäre Effekte begrenzen oft die Bandbreite. + \item[+] Durch Auswahl eines geeigneten OpAmps und Rückkoppelwiderstandes sind sehr hohe Verstärkungen + mit geringem Aufwand möglich. + + \item[+] Konstante Eingangsspannung. Der TIV-Eingang wird konstant auf $\SI{0}{\volt}$ getrieben. Hierdurch werden Effekte vonz.~B. parasitären Kapazitäten am Eingang verringert. Zudem können Abschirmungen an $\SI{0}{\volt}$, d.~h. Erde, angeschlossen werden. + + \item[-] Die Bandbreite kann stark durch parasitäre Effekte beeinflusst werden, und das Design + der Schaltung muss diese Effekte einbeziehen. + \item[-] Ein OpAmp mit sehr hohem GBWP ist notwendig, um stabil zu bleiben. - \item[-] Durch die hohe Verstärkung ist die Schaltung sehr Rauschanfällig. + \item[-] Durch die hohe Verstärkung ist die Schaltung sehr anfällig für + das eingangsbezogene Rauschen des OpAmps sowie anderer Störquellen. \end{itemize} \ No newline at end of file diff --git a/TeX/Kapitel/RevisionV11.tex b/TeX/Kapitel/RevisionV11.tex index e8642fd..e716b27 100644 --- a/TeX/Kapitel/RevisionV11.tex +++ b/TeX/Kapitel/RevisionV11.tex @@ -1,8 +1,9 @@ +\cleardoublepage \chapter{Revision des TIVs} -In diesem Kapitel wird auf die zweite Revision der Platine eingegangen. -Diese Revision ist notwendig, um die Instabilität der ersten Revision +In diesem Kapitel wird auf die Revision der Platine eingegangen. +Diese Revision ist notwendig, um die Instabilität der ersten Version der Platine zu beheben, welche in Kapitel \ref{chap:v10_instability} gemessen wurde, da diese Instabilität einer Verwendung der Platine in einem echten IMS im Wege steht. @@ -11,7 +12,7 @@ in einem echten IMS im Wege steht. In Kapitel \ref{chap:v10_instability} wurde eine Instabilität der Schaltung bei angeschlossenem IMS festgestellt. -Zusätzlich hierzu wurden andere Effekte wie z.B. die Steigerung +Zusätzlich hierzu wurden andere Effekte wiez.~B. die Steigerung des Rauschniveaus bei angelegten externen Schaltungen festgestellt. Eine Vermutung ist, dass die Sensitivität des Schaltkreises auf externe @@ -25,7 +26,7 @@ Effekten führen kann. Eine Simulation der Instabilität war nicht erfolgreich, da der simulierte Schaltkreis in LTSpice mit einem reelen Verstärkermodell keine Instabilitäten -aufwies. Es ist somit zu vermuten dass es sich um nicht akkurat modellierte Effekte +aufwies. Es ist somit zu vermuten, dass es sich um nicht akkurat modellierte Effekte des Verstärkers handelt. Eine händisch modifizierte Schaltung wird genutzt, um andere Verstärkungen sowie @@ -36,11 +37,11 @@ Zusätzlich wird bei anderen OpAmps keine Instabilität festgestellt. \section{Korrektur der Schaltung} Im folgenden Abschnitt werden die Änderung der Schaltung beschrieben, welche für -die nächste Revision vorgenommen werden. +die Revision vorgenommen werden. Da der erkannte Fehler vermutlich durch den Verstärker selbst verursacht wird, soll nun ein anderer OpAmp genutzt werden. Kapitel \ref{chap:v10_opamp_choice} listet andere Möglichkeiten auf. Da das Eingangsspannungsrauschen vermutlich -an den Problemen teil nimmt, wird nun ein OpAmp mit möglichst geringem Rauschen +an den Problemen teilnimmt, wird nun ein OpAmp mit möglichst geringem Rauschen gewählt, der {\em ADA4817}. Der {\em ADA4817} bietet mit einem Rauschlevel von nur $\SI{5}{\nano\volt\per\sqrt{\hertz}}$ @@ -51,28 +52,34 @@ Somit soll eine kaskadierte Schaltung entsprechend Kapitel \ref{chap:opamp_casca genutzt werden, um die notwendige Bandbreite erreichen zu können. Da die Abschirmung sowie die Reihenschaltung der Rückkoppelwiderstände der -vorherigen Version beide als Funktionsfähig befunden wurden, wird an diesem Teilen +vorherigen Version beide als funktionsfähig befunden wurden, wird an diesen Teilen der Schaltung keine Änderung vorgenommen. Lediglich der OpAmp wird durch eine kaskadierte Schaltung des {\em ADA4817 } ersetzt. - -\begin{figure}[h] - \centering - \includegraphics[width=0.9\textwidth]{Auslegung/v1.1/tia_stage.png} - \caption{\label{fig:v11_tia_schematic}Schaltkreis der zweiten Revision des - Verstärkerteils des TIVs.} -\end{figure} - Abbildung \ref{fig:v11_tia_schematic} zeigt den geänderten Schaltkreis auf. + Hierbei sind U2B und U2A die zwei ADA4817-OpAmps der kaskadierten Verschaltung. Widerstände R33 und R34 setzten hierbei die Verstärkung von U2A fest. U2B übernimmt den Rest der Verstärkung, wobei die Gesamtverstärkung nur durch die Rückkoppelwiderstände R15 bis R18 sowie den Rückkoppelteiler R14+R19 festgelegt wird. +Da viele der Widerstandswerte vom Rückkoppelwiderstand abhängig sind, +und mehrere Varianten dieses Schaltkreises mit verschiedenen +$R_f$ angefertigt werden, werden für diese Widerstände Platzhalter +(``{\em Val?}'') eingetragen. + +\begin{figure}[htb] + \centering + \includegraphics[width=0.9\textwidth]{Auslegung/v1.1/tia_stage.png} + \caption[Schaltkreis der Revision des + Verstärkerteils des TIVs]{\label{fig:v11_tia_schematic}Schaltkreis der Revision des + Verstärkerteils des TIVs.} +\end{figure} + Es ist bei einer kaskadierten Verschaltung gewünscht, so viel Verstärkung in die erste Stufe zu legen wie möglich, um das Rauschen zu minimieren und die Stabilität zu erhöhen. Zu viel Verstärkung in der ersten Stufe reduziert jedoch die Bandbreite. -Die exakte Verteilung der Verstärkung hängt vom Systemverhalten ab, +Die exakte Verteilung der Verstärkung hängt vom Systemverhalten ab und muss experimentell bestimmt werden. R9 und R32 erlauben das Umschalten der Schaltung von einer kaskadierten Schaltung @@ -84,37 +91,38 @@ Die Rückkoppelwiderstände und Abschirmwiderstände (R19 bis 13, R15 bis 18, R2 plus die anpassenden Spannungsteiler (R24, R14, R19) sind unverändert vom ersten Schaltungsdesign. -\begin{figure}[h] +Abbildung \ref{fig:v11_tia_pcb} zeigt die Auslegung des PCBs der Revision. +Hierbei werden die vorherigen Konstruktionen für Rückkoppelpfad und Abschirmung der +Widerstände beibehalten. +Aus diesem Grund wird hierauf nicht mehr genauer eingegangen. + +\begin{figure}[hb] \centering - \includegraphics[width=0.7\textwidth]{Auslegung/v1.1/tia_pcb.png} - \caption{\label{fig:v11_tia_pcb}Auslegung des PCBs der zweiten Revision + \includegraphics[width=0.8\textwidth]{Auslegung/v1.1/tia_pcb.png} + \caption{\label{fig:v11_tia_pcb}Auslegung des PCBs der Revision des TIVs} \end{figure} -Abbildung \ref{fig:v11_tia_pcb} zeigt die Auslegung des PCBs der zweiten Revision. -Hierbei werden die vorherigen Konstruktionen für Rückkoppelpfad und Abschirmung der -Widerstände bei behalten. -Aus diesem Grund wird hierauf nicht mehr genauer eingegangen. - Die Kaskadenschaltung der zwei Verstärker ist um U2 herum gelegt. U2 ist -ein sog. {\em Dual Package OpAmp}, d.h. es liegen zwei unabhängige -ADA4817 im selben Packet vor. Dies ermöglicht eine möglichst kleine Auslegung +ein sog. {\em Dual Package OpAmp}, d.~h. es liegen zwei unabhängige +ADA4817 im selben Paket vor. Dies ermöglicht eine möglichst kleine Auslegung des Rückkoppelpfades für die zweite Stufe des Verstärkers, welches für die Stabilität -notwendig ist sowie weniger Störquellen einkoppelt. +notwendig ist und weniger Störquellen einkoppelt. Der Vollständigkeit halber zeigt Abbildung \ref{fig:v11_pcb_3d_image} ein 3D-Modell -der zweiten Revision der Platine. Die restlichen Schaltungsteile wurden nicht modifiziert, +der Revision der Platine. Die restlichen Schaltungsteile wurden nicht modifiziert, weshalb auf diese hier nicht mehr eingegangen wird. -\begin{figure}[h] +\begin{figure}[hb] \centering \includegraphics[width=0.9\textwidth]{Auslegung/v1.1/pcb_3d.png} - \caption{\label{fig:v11_pcb_3d_image}3D-Modell der zweiten Revision des PCBs} + \caption{\label{fig:v11_pcb_3d_image}3D-Modell der Revision des PCBs} \end{figure} +\cleardoublepage \section{Vermessung der Revision} -In diesem Kapitel wird die zweite Revision der Platine +In diesem Kapitel wird die Revision der Platine vermessen und auf weitere Fehler überprüft. Es werden, wenn nicht anders beschrieben, dieselben Methoden wie aus Kapitel \ref{chap:measurements} genutzt. Wo angemessen, sollen Vergleiche mit der vorherigen Version gezogen werden. @@ -122,82 +130,134 @@ genutzt. Wo angemessen, sollen Vergleiche mit der vorherigen Version gezogen wer \subsection{Stabilität am IMS} \label{chap:v11_measurement_ims_stability} -Es wird nun als aller erstes die Stabilität an einer IMS-Röhre vermessen. Hierfür wird dieselbe -Röhre wie in der Vermessung der ersten Revision genutzt, an den Eingang des TIVs -angeschlossen, und vermessen. Hierbei wird die $\SI{47}{\mega\ohm}$ Variante genutzt. +Es wird nun als Allererstes die Stabilität an einer IMS-Röhre vermessen. Hierfür wird dieselbe +Röhre wie in der Vermessung der ursprünglichen Version genutzt, an den Eingang des TIVs +angeschlossen und vermessen. Hierbei wird die $\SI{47}{\mega\ohm}$ Variante genutzt. Im Falle der neuen Schaltung liegt nun die erwartete stabile, statische Ausgangsspannung bei $\SI{0}{\volt}$ mit einem akzeptablem Rauschen. Abbildung \ref{fig:v11_ims_noise} zeigt das Spektrum des Rauschens dieser Variante. -\begin{figure}[h] +\begin{figure}[hb] \centering - \missingfigure{Add figure of with-IMS noise} + \includegraphics[scale=0.8]{datavis/V1_Measurements/with_ims_noise.png} \caption{\label{fig:v11_ims_noise}Rauschlevel der $\SI{47}{\mega\ohm}$ Variante mit angeschlossenem IMS.} \end{figure} Diese Messung bestätigt, dass diese Revision der Schaltung keine Oszillationen bei Anschluss einer IMS-Röhre -aufweist. Der Fehler der ersten Revision wurde somit erfolgreich behoben. +aufweist. Das Rauschlevel ist nur minimal beeinträchtigt. +Der Fehler der ursprünglichen Version wurde somit erfolgreich behoben. -\subsection{Linearität} +\FloatBarrier -In diesem Abschnitt wird die Linearität der neuen Revision vermessen. Die Messung erfolgt hierbei mit den -gleichen Messgeräten wie in Kapitel \ref{chap:v10_measurement_linearity}, es wird jedoch durch die höhere -Versorgungsspannung des ADA4817 ein größerer Eingangsstrombereich von \todo{Measure this} vermessen. +\subsection[Linearität]{Untersuchung der Linearität} -\begin{figure}[h] +In diesem Abschnitt wird die Linearität der Revision vermessen. +Die Messung erfolgt hierbei mit denselben Messgeräten wie in Kapitel +\ref{chap:v10_measurement_linearity}, d.~h. dem {\em Keithley 6221} +sowie dem {\em Keysight 34461A}. +Es wird jedoch durch die höhere +Versorgungsspannung des ADA4817 ein größerer Eingangsstrombereich von +$\SI{\pm3.5}{\nano\ampere}$ vermessen. +Abbildung \ref{fig:v11_linearity} zeigt die vermessene Linearität von +zwei verschiedenen Platinen der +$\SI{47}{\mega\ohm}$-Variante. + +\begin{figure}[ht] \centering - \missingfigure{Measure linearity of v11} - \caption{\label{fig:v11_linearity}Vermessung der Linearität der zweiten Revision, - $\SI{47}{\mega\ohm}$-Variante} + \includegraphics[scale=0.75]{datavis/V1_Measurements/V1.1-a1/47M_cap/linearity.png} + \caption[Vermessung der Linearität der Revision, + $\SI{47}{\mega\ohm}$-Variante]{\label{fig:v11_linearity}Vermessung der Linearität der zwei Platinen der $\SI{47}{\mega\ohm}$-Variante. + + Es ist ein konsistent lineares Verhalten zu erkennen, wobei der + Verstärker eine maximale Ausgangsspannung von circa $\SI{\pm3.2}{\nano\ampere}$ + aufweist. } \end{figure} -Abbildung \ref{fig:v11_linearity} zeigt die vermessene Linearität an der -$\SI{47}{\mega\ohm}$-Variante. \todo{Fill this out after measurement} +Zu sehen ist eine maximale Ausgangsspannung von circa $\SI{\pm3.2}{\volt}$, und +somit ein Eingangsstrombereich von $\SI{\pm3.2}{\nano\ampere}$. Hierbei scheinen +sich beide vermessenen Platinen gleich zu verhalten. -\newpage -\subsection{Bandbreite} +\FloatBarrier -In diesem Abschnitt werden die Übertragungsfunktionen und Bandbreiten der erstellten -Platinen genauer untersucht. +Um eventuelle Fehler in der Linearität besser erkennen zu können, wird zudem der Fehler +der Messung aufgezeichnet, d.~h. die Differenz zwischen der erwarteten und gemessenen +Spannung. Dies ist in Abbildung \ref{fig:v11_linearity_error} aufgezeichnet. + +\begin{figure}[H] + \centering + \includegraphics[scale=0.75]{datavis/V1_Measurements/V1.1-a1/47M_cap/linearity_error.png} + \caption[Fehler der Linearität, + $\SI{47}{\mega\ohm}$-Variante]{\label{fig:v11_linearity_error} + Fehler der Ausgangsspannung der zwei vermessenen $\SI{47}{\mega\ohm}$ + TIVs. Zu sehen sind nur leichte Abweichungen der Ausgangsspannung + von höchstens $\SI{1.5}{\milli\volt}$ sowie einige Sprünge. + } +\end{figure} + +Deutlich zu erkennen ist eine sehr geringe Abweichung der Ausgangsspannung +vom Sollwert von höchstens $\SI{1.5}{\milli\volt}$, wobei meistens +eine Abweichung von besser als $\SI{\pm1}{\milli\volt}$ eingehalten wird. +Dies stellt merklich kleinere Abweichungen als bei der ersten Version dar und +ist somit eine deutliche Verbesserung. Zu sehen sind ebenfalls einige kleine Sprünge +in beiden vermessenen Platinen, $+\SI{0.7}{\milli\volt}$ bei etwa +$\SI{-0.8}{\nano\ampere}$ sowie $+\SI{1}{\milli\volt}$ bei etwa $\SI{2}{\nano\ampere}$. +Die genaue Ursache dieser Sprünge ist nicht bekannt. Die Amplitude der Sprünge stellt +jedoch eine Änderung von nur 0.1\% dar und ist somit akzeptabel. + +Insgesamt ist die Linearität des neuen Schaltkreises somit eine wesentliche Verbesserung +im Vergleich zur ersten Version und ist mehr als ausreichend für die +hier gesetzten Zielparameter. + +\FloatBarrier + +\subsection[Bandbreite]{Untersuchung der Bandbreite} + +Um zu bestätigen, dass der neue Schaltkreis des TIVs eine ausreichende Bandbreite +liefert, werden folgend die Übertragungsfunktionen der Revision vermessen. Es wird hierfür dieselbe Methode wie aus Kapitel \ref{chap:v10_measurement_bandwidth} -genutzt. +genutzt. Abbildung \ref{fig:v11_measurement_bandwidth} zeigt die gemessenen Übertragungsfunktionen +der zweiten Platinenversion, wobei mehrere Platinen mit variiertem Rückkoppelwiderstand +aufgebaut wurden. -\begin{figure}[h] +\begin{figure}[hb] \centering \includegraphics[scale=0.8]{datavis/V1_Measurements/V1.1-a1/bandwidths.png} - \caption{\label{fig:v11_measurement_bandwidth}Messungen der Übertragungsfunktionen - der Platinen der zweiten Revision.} + \caption[Messungen der Übertragungsfunktionen + der Platinen der Revision]{\label{fig:v11_measurement_bandwidth} + Messungen der Übertragungsfunktionen + der Platinen der Revision. Zu erkennen + ist die Abhängigkeit der Bandbreite vom Rückkoppelwiderstand.} \end{figure} -Abbildung \ref{fig:v11_measurement_bandwidth} zeigt die gemessenen Übertragungsfunktionen -der zweiten Platinenrevision. Deutlich zu erkennen ist die gewünschte glatte Übertragungsfunktion bis hin zur Eckfrequenz. -Hiernach fallen die Verstärkungen der Platinenvarianten jedoch unterschiedlich schnell ab. +Hiernach fallen die Verstärkungen der Platinenvarianten jedoch unterschiedlich\\ +schnell ab. Alle Platinen bis auf die $\SI{47}{\mega\ohm}$ Variante weisen einen Abfall von circa -20dB/Dekade auf, welcher durch das RC-Verhalten der Rückkoppelwiderstände bestimmt wird. -Die $\SI{47}{\mega\ohm}$ Variante weist jedoch einen Abfall von -40dB/Dekate auf, welches +Die $\SI{47}{\mega\ohm}$ Variante weist jedoch einen Abfall von -40dB/Dekade auf, welches auf einen gedämpften Oszillator schließen lässt. Ebenfalls ist ein Knick in der -$\SI{82}{\mega\ohm}$ Variante bei circa $\SI{300}{\kilo\hertz}$ zu erkennen, und ein deutlicher +$\SI{82}{\mega\ohm}$ Variante bei circa $\SI{300}{\kilo\hertz}$ zu erkennen und ein deutlicher Resonanz-Peak in der $\SI{120}{\mega\ohm}$ Variante bei $\SI{600}{\kilo\hertz}$. Diese Diskrepanzen stören das Verhalten der Übertragungsfunktion für die hier gesetzten -Zielparameter nicht, da die beobachteten Frequenzen gänzlich überhalb der Filter-Eckfrequenz +Zielparameter nicht, da die beobachteten Frequenzen gänzlich oberhalb der Eckfrequenz +des Filters von $\SI{30}{\kilo\hertz}$ liegen. Im Falle der $\SI{47}{\mega\ohm}$ ist der stärkere Abfall der Verstärkung sogar vorteilhaft. -Eine Vermutung der Ursache dieser Resonanz ist der kaskadierte Aufbau des Verstärkers selbst. -Die zweite Stufe des Verstärkers kann zu einer Phasenverschiebung führen, welches diverse -Einflüsse auf den Frequenzverlauf der Verstärkung haben kann. +Eine Vermutung der Ursache dieser Resonanz ist der kaskadierte Aufbau des Verstärkers selbst, +wobei das GBWP der ersten oder zweiten Stufe zu einer leichten Überhöhung der Bandbreite +führen kann. +Aus der Messung der Übertragungsfunktionen können nun die -3~dB-Punkte der Platinen +entnommen werden. Diese sind in Tabelle \ref{table:v11_bandwidths} dargestellt. -\todo[inline]{Check with our LTSpice simulation if we see these!} - -\begin{table}[H] +\begin{table}[hb] \centering - \caption{\label{table:v11_bandwidths}-3dB-Frequenzen des ungefilterten - TIV-Ausgangs der zweiten Revision} + \caption{\label{table:v11_bandwidths}-3~dB-Frequenzen des ungefilterten + TIV-Ausgangs der Revision} \begin{tabular}{ |r|r|r| } \hline - Widerstand & -3dB Punk \\ + Widerstand & -3~dB Punk \\ \hline $\SI{20}{\mega\ohm}$ & $\SI{97.556}{\kilo\hertz}$ \\ $\SI{47}{\mega\ohm}$ & $\SI{54.747}{\kilo\hertz}$ \\ @@ -207,56 +267,55 @@ Einflüsse auf den Frequenzverlauf der Verstärkung haben kann. \end{tabular} \end{table} -Tabelle \ref{table:v11_bandwidths} zeigt die -3dB-Frequenzen der gemessenen -Übertragungsfunktionen. Im Vergleich zur ersten Revision -bieten die $\SI{20}{\mega\ohm}$ und $\SI{47}{\mega\ohm}$ varianten der Platinen -eine höhere Bandbreite als die Platinen der ersten Revision, während die +Im Vergleich +bieten die $\SI{20}{\mega\ohm}$ und $\SI{47}{\mega\ohm}$ Varianten der Platinen +eine höhere Bandbreite als die Platinen der ursprünglichen Version, während die $\SI{120}{\mega\ohm}$ Variante eine niedrigere Bandbreite aufweist. -Diese Diskrepanz liegt vermutlich ebenfalls am beobachteten Verhalten der Kaskadenschaltung, und -ist erneut im Falle der $\SI{47}{\mega\ohm}$ Variante von Vorteil. - -\begin{figure}[h] - \centering - \includegraphics[scale=0.8]{datavis/V1_Measurements/revision_compare_bandwidth.png} - \caption{\label{fig:v11_comparison_bandwidth}Vergleich der Bandbreiten der - $\SI{47}{\mega\ohm}$ Varianten von der alten und neuen Revision.} -\end{figure} +Diese Diskrepanz liegt vermutlich ebenfalls am beobachteten Verhalten der Kaskadenschaltung +und ist erneut im Falle der $\SI{47}{\mega\ohm}$ Variante von Vorteil. Abbildung \ref{fig:v11_comparison_bandwidth} zeigt einen direkten Vergleich der -Bandbreiten der TIV-Stufen der vorherigen und neuen Revison für +Bandbreiten der TIV-Stufen der vorherigen und neuen Version für die $\SI{47}{\mega\ohm}$ Variante. Der steilere Abfall sowie die -leicht höhere -3dB-Frequenz der zweiten Revision +leicht höhere -3~dB-Frequenz der Revision ist hierbei deutlich zu erkennen. -Da die Filterstufe zwischen den Revisionen nicht geändert wurde, -da das Filterverhalten bereits als ausreichend empfunden wurde, wird hier nicht -erneut darauf eingegangen. +\begin{figure}[ht] + \centering + \includegraphics[scale=0.8]{datavis/V1_Measurements/revision_compare_bandwidth.png} + \caption[Vergleich der Bandbreiten der + $\SI{47}{\mega\ohm}$ Varianten von der alten und neuen Version]{\label{fig:v11_comparison_bandwidth}Vergleich der Bandbreiten der + $\SI{47}{\mega\ohm}$ Varianten von der alten und neuen Version.} +\end{figure} + +Die Filterstufe zwischen den Versionen wurde nicht geändert, +da das Filterverhalten bereits als ausreichend empfunden wurde. +Somit wird hier nicht erneut darauf eingegangen. Zusammengefasst besitzen die Varianten der $\SI{82}{\mega\ohm}$ und $\SI{120}{\mega\ohm}$ eine zu geringe Bandbreite, während die $\SI{47}{\mega\ohm}$ und $\SI{20}{\mega\ohm}$ Varianten beide mehr als ausreichend -Bandbreite besitzen. Die neue Revision der Platine erfüllt somit die Anforderungen. - -\FloatBarrier -\newpage +Bandbreite besitzen. Die neue Version der Platine erfüllt somit die Anforderungen. \subsection{Rauschen} -In diesem Abschnitt wird das Rauschen der neuen Revision vermessen, und mit der vorherigen -Revision verglichen. Es wird beschrieben ob und wie sich das Rauschverhalten geändert hat. +Folgend wird das Rauschen der Revision vermessen und mit der originalen Version +verglichen. Es wird beschrieben, ob und wie sich das Rauschverhalten geändert hat. Das Spektrum des Rauschens wird mit dem selben Aufbau aus Kapitel \ref{chap:v10_measurement_noise} -vermessen. +vermessen. Abbildung \ref{fig:v11_measurement_noise} zeigt die Rauschspektren der Revision. -\begin{figure}[h] +\begin{figure}[ht] \centering \includegraphics[scale=0.8]{datavis/V1_Measurements/V1.1-a1/noises.png} - \caption{\label{fig:v11_measurement_noise}Durchschnittliches Rauschspektrum der Platinen - der zweiten Revision.} + \caption[Durchschnittliches Rauschspektrum der Platinen + der Revision]{\label{fig:v11_measurement_noise}Durchschnittliches Rauschspektrum der Platinen + der Revision. + Erkennbar ist die Abhängigkeit des Rauschlevels vom Rückkoppelwiderstand. + Ebenfalls sind einige Frequenzen mit erhöhtem Rauschen erkennbar.} \end{figure} -Abbildung \ref{fig:v11_measurement_noise} zeigt die Rauschspektren der zweiten -Platinenrevision. -Wie in der ersten Revision ist hier deutlich eine Abhängigkeit des Rauschlevels + +Wie in der ursprünglichen Version ist hier deutlich eine Abhängigkeit des Rauschlevels vom Rückkoppelwiderstand zu erkennen, wobei erneut ein kleinerer Widerstand ein höheres Rauschniveau einbringt. Zusätzlich ist die Verteilung des Rauschens merklich anders. Für alle Versionen @@ -264,43 +323,50 @@ scheint eine kleine Erhöhung um $\SI{30}{\kilo\hertz}$ zu liegen, wobei diese in der $\SI{47}{\mega\ohm}$ Variante merklich stärker ausfällt. Ebenso sind Spitzen im Rauschspektrum zu erkennen. Für $\SI{20}{\mega\ohm}$ liegt eine deutliche Spitze bei $\SI{7}{\kilo\hertz}$ vor, -für $\SI{47}{\mega\ohm}$ die Erhöhung bei $\SI{30}{\kilo\hertz}$, und für die +für $\SI{47}{\mega\ohm}$ die Erhöhung bei $\SI{30}{\kilo\hertz}$ und für die $\SI{120}{\mega\ohm}$ Variante eine deutliche Erhöhung bei -circa $\SI{700}{\kilo\hertz}$. Diese Eröhungen des Rauschens liegen auf den +circa $\SI{700}{\kilo\hertz}$. Diese Erhöhungen des Rauschens liegen auf den gleichen Frequenzen wie die Resonanzen in der Bandbreite. Somit ist zu vermuten, dass die gleiche Ursache für beide Effekte zuständig ist. -\begin{figure}[H] - \centering - \includegraphics[scale=0.8]{datavis/V1_Measurements/revision_compare_noise.png} - \caption{\label{fig:v11_v10_comparison_noise}Vergleich des Rauschspektrums - der Revisionen der $\SI{47}{\mega\ohm}$ Variante.} -\end{figure} - -Abbildund \ref{fig:v11_v10_comparison_noise} zeigt den direkten -Vergleich der ungefilterten Rauschspektren der ersten und zweiten Revision +Abbildung \ref{fig:v11_v10_comparison_noise} zeigt den direkten +Vergleich der ungefilterten Rauschspektren der originalen Platine und der +Revision der $\SI{47}{\mega\ohm}$ Version des Schaltkreise. Trotz des kleineren Eingangsspannungsrauschens des ADA4817 liegt ein insgesamt leicht größeres Rauschniveau vor. Dies stimmt jedoch nur bei offenem -Eingang. Das Rauschen der ersten Revision mit dem LTC6268-10 vergrößert sich bei -steigender Eingangskapazität, während das Rauschen der zweiten Revision +Eingang. Das Rauschen der ursprünglichen Version mit dem LTC6268-10 vergrößert sich bei +steigender Eingangskapazität, während das Rauschen der Revision kaum von der Eingangskapazität abhängt (siehe Kapitel \ref{chap:v11_measurement_ims_stability}). Unter realen Bedingungen ist somit das -Rauschen der zweiten Revision besser. +Rauschen der Revision besser. -\begin{figure}[H] +\begin{figure}[ht] \centering - \includegraphics[scale=0.8]{datavis/V1_Measurements/V1.1-a1/noises_ch2.png} - \caption{\label{fig:v11_measurement_noise_ch2}Rauschspektren des - gefilterten Ausgangs der zweiten Revision des TIVs.} + \includegraphics[scale=0.8]{datavis/V1_Measurements/revision_compare_noise.png} + \caption[Vergleich des Rauschspektrums + der Revision der $\SI{47}{\mega\ohm}$ Variante]{\label{fig:v11_v10_comparison_noise}Vergleich des Rauschspektrums + der Revision der $\SI{47}{\mega\ohm}$ Variante.} \end{figure} +\FloatBarrier + Abbildung \ref{fig:v11_measurement_noise_ch2} zeigt die Rauschspektren der gefilterten Ausgänge. Wie in der vorherigen Version ist zu erkennen, dass die Filterstufe das Rauschlevel deutlich und effektiv senkt. Die bereits identifizierten Erhöhungen im Rauschen werden, mit Ausnahme der Spitze des $\SI{20}{\mega\ohm}$ TIVs, herausgefiltert. +\begin{figure}[ht] + \centering + \includegraphics[scale=0.8]{datavis/V1_Measurements/V1.1-a1/noises_ch2.png} + \caption[Rauschspektren des + gefilterten Ausgangs der Revision des TIVs]{\label{fig:v11_measurement_noise_ch2}Rauschspektren des + gefilterten Ausgangs der Revision des TIVs. + Wie bei der ersten Platine ist die Filterung des Rauschens durch die Filterstufe ab $\SI{30}{\kilo\hertz}$ + erkennbar.} +\end{figure} + Die RMS-Werte der Rauschlevel für den ungefilterten und gefilterten Ausgang sind in Tabelle \ref{table:v11_noise_table} aufgelistet. Dort ist deutlich zu erkennen, dass die Filterstufe das Rauschen merklich verringert, da der @@ -324,45 +390,48 @@ genutzte LTC6268-10. \end{tabular} \end{table} -Insgesamt ist somit das Rauschen der zweiten Revision des TIVs nutzbar. -Zwar ist das Rauschen im Vergleich zur ersten Revision geringfügig erhöht, jedoch +Insgesamt ist somit das Rauschen der Revision des TIVs nutzbar. +Zwar ist das Rauschen im Vergleich zur ursprünglichen Version geringfügig erhöht, jedoch bieten alle Versionen der Schaltung mit Ausnahme des $\SI{20}{\mega\ohm}$ TIVs ein akzeptabel geringes Rauschen. \FloatBarrier -\newpage \subsection{Konsistenz des Schaltkreises} In diesem Abschnitt wird darauf eingegangen, wie wiederholbar -der Aufbau der zweiten Revision der Platine ist. +der Aufbau der Revision der Platine ist. Ein wichtiger Aspekt des in dieser Arbeit entwickelten TIVs ist der reproduzierbare Aufbau ohne größere manuelle Abstimmungen der Abschirmung oder anderer Komponenten. -Um dies zu belegen wird eine zweite Platine der $\SI{47}{\mega\ohm}$ +Um dies zu belegen, wird eine zweite Platine der $\SI{47}{\mega\ohm}$ Variante hergestellt. Diese Platine wird nicht experimentell abgestimmt, -sondern mit denselben Komponentenwerten verlötet wie die Platine +sondern mit denselben Komponentenwerten verlötet wie die Platine, welche bereits vermessen wurde. Das gewollte Verhalten ist nun, dass diese Kopie dasselbe Verhalten aufweist wie die original vermessene Platine. \begin{figure}[h] \centering \includegraphics[scale=0.8]{datavis/V1_Measurements/V1.1-a1/bandwidth_consistency.png} - \caption{\label{fig:v11_bandwidth_consistency_check}Vergleich der Bandbreiten + \caption[Vergleich der Bandbreiten + zweier identischer TIV-Platinen]{\label{fig:v11_bandwidth_consistency_check}Vergleich der Bandbreiten zweier identischer TIV-Platinen.} \end{figure} Abbildung \ref{fig:v11_bandwidth_consistency_check} zeigt die Bandbreiten der originalen Platine und der Kopie im direkten Vergleich. Es ist zu erkennen, dass eine leichte -Diskrepanz der Bandbreiten um die Eckfrequenz herum vor liegt. Diese beträgt -jedoch nur ca. 2dB, und liegt in einem Bereich der durch den nachfolgenden +Diskrepanz der Bandbreiten um die Eckfrequenz herum vorliegt. Diese beträgt +jedoch nur circa 2 dB und liegt in einem Bereich, der durch den nachfolgenden Filter herausgefiltert wird. Für den relevanten Bereich bis $\SI{30}{\kilo\hertz}$ sind beide TIVs jedoch nahezu identisch. -Das Verhalten der TIVs scheint somit eine gute Konsistenz auf zu weisen. -Es ist somit nicht notwendig, die Platinen nach der Anfertigung noch weiter -ab zu stimmen. +Das Verhalten der TIVs scheint somit eine gute Konsistenz aufzuweisen. +Es ist somit vermutlich nicht notwendig, +die Platinen nach der Anfertigung noch weiter +abzustimmen. + +\FloatBarrier \subsection{Einfluss der Kaskadenschaltung} @@ -376,16 +445,20 @@ Einbringung einer Kapazität mit dem Rückkoppelpfad der zweiten Stufe von Vorteil ist. Diese Filterung könnte theoretisch Rauschen in der ersten Stufe abfangen. Hierfür wird eine $\SI{47}{\mega\ohm}$-Variante -modifiziert, und eine Kapazität parallel zu Widerstand R34 -(siehe Abbildung \ref{fig:v11_tia_schematic}) eingebracht. Diese Kapazität ist -so ausgelegt, dass sie die Verstärkung der zweiten Stufe ab ca. $\SI{60}{\kilo\hertz}$ +modifiziert, indem eine Kapazität parallel zu Widerstand R34 +(siehe Abbildung \ref{fig:v11_tia_schematic}) eingebracht wird. Diese Kapazität ist +so ausgelegt, dass sie die Verstärkung der zweiten Stufe ab circa $\SI{60}{\kilo\hertz}$ absenkt. \begin{figure}[h] \centering \includegraphics[scale=0.8]{datavis/V1_Measurements/V1.1-a1/midcap_bandwidth_effect.png} - \caption{\label{fig:v11_midcap_bandwidth}Einfluss eines Tiefpassfilters in - der zweiten Stufe des kaskadierten TIVs auf die Übertragungsfunktion.} + \caption[Einfluss eines Tiefpassfilters in + der zweiten Stufe des kaskadierten TIVs auf die Übertragungsfunktion]{ + \label{fig:v11_midcap_bandwidth}Einfluss eines Tiefpassfilters in + der zweiten Stufe des kaskadierten TIVs auf die Übertragungsfunktion. + Zu erkennen ist die Verschärfung des Abfalls in der Bandbreite bei + genutztem Tiefpassfilter.} \end{figure} Abbildung \ref{fig:v11_midcap_bandwidth} zeigt die Ergebnisse der Messung @@ -396,8 +469,12 @@ in der Version mit Tiefpassfilter. Dies ist generell von Vorteil. \begin{figure}[h] \centering \includegraphics[scale=0.8]{datavis/V1_Measurements/V1.1-a1/midcap_noise_influence.png} - \caption{\label{fig:v11_midcap_noise}Einfluss eines Tiefpassfilters in - der zweiten Stufe des kaskadierten TIVs auf das Rauschspektrum.} + \caption[Einfluss eines Tiefpassfilters in + der zweiten Stufe des kaskadierten TIVs auf das Rauschspektrum]{ + \label{fig:v11_midcap_noise}Einfluss eines Tiefpassfilters in + der zweiten Stufe des kaskadierten TIVs auf das Rauschspektrum. + Zu erkennen ist die geänderte Verteilung des Rauschens bei Nutzen + des Filters.} \end{figure} Abbildung \ref{fig:v11_midcap_noise} zeigt die aufgenommenen Rauschspektren. @@ -407,13 +484,13 @@ Frequenzen höher ist. Zwar weist die Version ohne Tiefpassfilter in den höhere Frequenzen stärkeres Rauschen auf, dieses wird jedoch von der nachfolgenden Filterstufe entfernt. -Da die Bandbreite beider Versionen ausreichend ist, und die Variante +Da die Bandbreite beider Versionen ausreichend ist und die Variante ohne Tiefpassfilter ein niedrigeres Rauschen aufwies, ist somit keine Filterung in der zweiten Stufe von Vorteil. \FloatBarrier -\newpage -\subsubsection{Verstärkungsverteilung} + +\subsubsection{Einfluss der Verstärkungsverteilung} In diesem Kapitel soll nun untersucht werden, welche Verteilung der Verstärkungen zwischen erster und zweiter Stufe am besten ist. @@ -426,14 +503,6 @@ Gemessen werden die Bandbreite sowie das Rauschen der Schaltung, mit den gleichen Messsystemen wie in den vorherigen Messungen (siehe Kapitel \ref{chap:v10_measurement_bandwidth} und \ref{chap:v10_measurement_noise}). -\begin{figure}[h] - \centering - \includegraphics[scale=0.8]{datavis/V1_Measurements/V1.1-a1/CascadeSeries/bandwidths.png} - \caption{\label{fig:v11_cascade_bandwidths}Übertragungsfunktionen eines - $\SI{47}{\mega\ohm}$ TIVs mit varriierter Verstärkung der zweiten - Stufe der Kaskade.} -\end{figure} - Abbildung \ref{fig:v11_cascade_bandwidths} zeigt die Übertragungsfunktionen der getesteten Varianten. Deutlich zu erkennen ist die Abhängigkeit der Grenzfrequenz von der Verteilung @@ -442,19 +511,33 @@ Grenzfrequenz der gesamten Schaltung nach oben verschiebt. Entsprechend Kapitel \ref{chap:opamp_aol_limit_explained} und \ref{chap:opamp_cascade_explained} lässt dies darauf schließen, dass die Bandbreite der $\SI{47}{\mega\ohm}$ -durch die offene Verstärkung des OpAmps limitiert ist, +durch die offene Verstärkung des OpAmps limitiert ist und nicht durch das GBWP oder die Rückkoppelwiderstände. Dies ist von Vorteil, da sich hierdurch die Bandbreite der Schaltung durch Umverteilung der Verstärkung beliebig einstellen lässt, ohne hierbei die Stabilität des Schaltkreises zu gefährden. -Generell ist nur die Einhaltung der Zielparameter von -3dB bei $\SI{30}{\kilo\hertz}$ +\begin{figure}[h] + \centering + \includegraphics[scale=0.8]{datavis/V1_Measurements/V1.1-a1/CascadeSeries/bandwidths.png} + \caption[Übertragungsfunktionen eines + $\SI{47}{\mega\ohm}$ TIVs mit varriierter Verstärkung der zweiten + Stufe der Kaskade]{ + \label{fig:v11_cascade_bandwidths}Übertragungsfunktionen eines + $\SI{47}{\mega\ohm}$ TIVs mit varriierter Verstärkung der zweiten + Stufe der Kaskade. Erkennbar ist ein starker Einfluss auf die + Bandbreite.} +\end{figure} + +Generell ist nur die Einhaltung der Zielparameter von -3~dB bei $\SI{30}{\kilo\hertz}$ wichtig. Höhere Bandbreiten werden durch die Filterstufe entfernt. \begin{figure}[h] \centering \includegraphics[scale=0.8]{datavis/V1_Measurements/V1.1-a1/CascadeSeries/noises.png} - \caption{\label{fig:v11_cascade_noises}Rauschspektren eines + \caption[Rauschspektren eines + $\SI{47}{\mega\ohm}$ TIVs mit varriierter Verstärkung der zweiten + Stufe der Kaskade]{\label{fig:v11_cascade_noises}Rauschspektren eines $\SI{47}{\mega\ohm}$ TIVs mit varriierter Verstärkung der zweiten Stufe der Kaskade.} \end{figure} @@ -465,21 +548,182 @@ verschieden eingestellten Stufen. Hierbei ist eine starke Abhängigkeit des Rauschens von der Verteilung zu beobachten, wobei eine höhere Verstärkung der zweiten Stufe mit wesentich höherem Rauschen verbunden ist. Das höhere Rauschen scheint mit der höheren Bandbreite in Verbindung zu stehen, -da in den niedrigen Frequenzen alle TIV-Varianten das gleiche Rauschen aufweisen, +da in den niedrigen Frequenzen alle TIV-Varianten das gleiche Rauschen aufweisen und die einzelnen Rauschlevel entsprechend der Bandbreite des jeweiligen TIVs abknicken. Somit ist bestätigt, dass die Verteilung der Verstärkungen der TIV-Stufen ein wichtiger Paramter ist. Generell soll die Verstärkung der ersten Stufe so groß wie möglich gehalten -werden, d.h. die zweite Stufe so klein wie möglich, um das Rauschen zu vermindern. +werden, d.~h. die zweite Stufe so klein wie möglich, um das Rauschen zu vermindern. +\cleardoublepage +\section{Messung an einem IMS} + +Mit der Funktionalität des erstellten TIVs bestätigt, wird nun eine +Messung an einem aktivem IMS durchgeführt. +Hierbei soll das Auflösungsvermögen sowie das Rauschniveau des neu +erstellten TIVs mit dem Verhalten des vorherig genutzten Verstärkers +verglichen werden. + +Anhand der bereits durchgeführten Messungen wird der $\SI{47}{\mega\ohm}$ +TIV als Verstärker für dieses Experiment genutzt. Dieser besitzt +das niedrigste Rauschen bei der gewollten Bandbreite von $\SI{30}{\kilo\hertz}$, +und ist somit die beste Auswahl. +Das genutzte IMS-System ist ein 75 mm PEEK-Röhren IMS, mit +einer Driftspannung von $\SI{7.5}{\kilo\volt}$, +welches bereits durch vorherige Messungen im Labor charakterisiert wurde +und somit eine gut verstandene Platform darstellt. +Zum Vergleich wird der bestehende Verstärker, der {\em GemiTIV}, +genutzt. Dieser ist auf eine vergleichbare Bandbreite von +circa $\SI{25}{\kilo\hertz}$ eingestellt. + +Es werden insgesamt vier Messungen durchgeführt, zwei als +Referenz mit dem bestehendem Verstärker und zwei mit dem neu +erstellten TIV. Für jeden Verstärker wird eine Messung +mit zehnfacher Mittlung zur Reduktion des Rauschens und eine +Messung ohne Mittlung durchgeführt. Da die Verstärker +leicht unterschiedliche DC-Offsets und Verstärkungen besitzen, +wird bei den gemessenen Spektren der DC-Anteil entfernt und +auf die Amplitude des Peaks normalisiert. + +Die aufgenommenen +Spektren sind in Abbildungen \ref{fig:v11_real_meas_avg} +und \ref{fig:v11_real_meas_noavg} dargestellt. + +\begin{figure}[htb] + \centering + \includegraphics[scale=0.8]{datavis/IMS Measurements/averaged_compare.png} + \caption[Ergebnisse der gemittelten Messung am IMS]{ + \label{fig:v11_real_meas_avg} + Ergebnisse der gemittelten Messungen der zwei Verstärker + im Vergleich, normalisiert auf die gleiche Peak-Höhe. + + Zu erkennen ist eine sehr gute Übereinstimmung der + Messergebnisse und vergleichbares Rauschen. Die Peak-Form + ist bei beiden TIVs fast exakt gleich. + } +\end{figure} + +\begin{figure}[htb] + \centering + \includegraphics[scale=0.8]{datavis/IMS Measurements/raw_compare.png} + \caption[Ergebnisse der ungemittelten Messung am IMS]{ + \label{fig:v11_real_meas_noavg} + Ergebnisse der ungemittelten Messungen der zwei Verstärker + im Vergleich, normalisiert auf die gleiche Peak-Höhe. + + In dieser Messung lässt sich das Rauschen besser vergleichen. + Hierbei ist zu erkennen dass der neu erstellte TIV ein insgesamt + kleineres Rauschen hat. + } +\end{figure} + +\FloatBarrier + +Zu erkennen ist die gute Übereinstimmung der Messungen. +Die für die Datenauswertung relevanten Formen der +Gauss-Peaks werden vom neuen TIV gut dargestellt, es +sind keine Verzerrungen im Vergleich zum bestehenden +Verstärker zu erkennen. +Bezüglich des Rauschens weist der neu erstellte TIV eine +kleinere Amplitude auf, wobei anzumerken ist, dass +die mechanische Schwingung des Aperturgitters innerhalb des +IMS merklich zum Rauschen beitragen kann. + +Somit ist bewiesen, dass der hier erstellte +TIV erfolgreich in einem echten IMS-System genutzt werden kann +und hierbei vergleichbar gute Messergebnisse liefert +wie die bestehenden Systeme. + +\clearpage +\section{Erprobung einer schnellen Variante} + +Die in Kapitel \ref{chap:tia_design_goals} festgelegten Ziele +sind für einen bestimmten Typ von IMS geeignet. Es gibt jedoch +andere Arten von IMS, welche schnellere Messungen benötigen, so +z.~B. dem Hike-IMS. +Dieses System benötigt Bandbreiten von mindestens +$\SI{250}{\kilo\hertz}$, mit +einem maximalen Eingangssignal von $\SI{10}{\nano\ampere}$. +Somit wird eine TIV-Verstärkung von $\SI{100}{\mega\ohm}$ angestrebt. + +Aus diesem Grund wird im folgenden eine Variante des TIV-Schaltkreises +erprobt, welche auf diese Parameter eingestellt ist. Hierfür +wird als Rückkoppelwiderstand ein Wert von $\SI{2.4}{\mega\ohm}$ +genutzt. Zusätzlich wird der Ausgangsfilters auf eine Grenzfrequenz +von $\SI{280}{\kilo\hertz}$ eingestellt. + +Vermessen werden Bandbreite und Rauschen mit den gleichen Methodiken +wie in den vorherigen Kapiteln (vgl. Kapitel \ref{chap:v10_measurement_bandwidth} +und Kapitel \ref{chap:v10_measurement_noise}). Abbildungen \ref{fig:v24_bandwidth} +und \ref{fig:v24_noise} zeigen die Messwerte auf. + +\begin{figure}[ht] + \centering + \includegraphics[scale=0.8]{datavis/V1_Measurements/V1.1-a1/2M4/bandwidths.png} + \caption[Bandbreite der $\SI{2.4}{\mega\hertz}$-Variante]{ + \label{fig:v24_bandwidth} + Bandbreite der $\SI{2.4}{\mega\hertz}$-Variante. Aufgezeichnet sind + die Bandbreiten des ungefilteren und gefilterten Ausgangs. + Zu erkennen ist ein flacher Frequenzgang bis circa $\SI{100}{\kilo\hertz}$, + ab welchem eine Überhöhung der Bandbreite erkennbar ist. + } +\end{figure} + + +Zu erkennen ist ein flacher Frequenzgang bis circa $\SI{100}{\kilo\hertz}$, mit +einer darauf folgenden Instabilität, mit einer leichten +Erhöhung von circa 3dB um $\SI{500}{\kilo\hertz}$ herum. +Diese Erhöhung lässt darauf schließen, dass entweder das Limit +des OpAmp GBWP erreicht wird (entsprechend Kapitel \ref{chap:opamp_parasitics_gbwp}), oder dass die Abschirmung für +die höheren Frequenzen nicht ausreichend ist. Da die Überhöhung +recht gering ist und keine Instabilität darstellt, ist +zu vermuten dass durch leichte Anpassungen die Übertragungsfunktion +abgeflacht werden kann. + + +\begin{figure}[ht] + \centering + \includegraphics[scale=0.8]{datavis/V1_Measurements/V1.1-a1/2M4/noises.png} + \caption[Rauschspektrum der $\SI{2.4}{\mega\hertz}$-Variante]{ + \label{fig:v24_noise} + Rauschspektrum der $\SI{2.4}{\mega\hertz}$-Variante. Aufgezeichnet sind + die Spektren des ungefilteren und gefilterten Ausgangs. + Zu erkennen ist ein sehr geringes Rauschen bis hin zu + $\SI{100}{\kilo\hertz}$, ab welchem Punkt das Rauschen stark + ansteigt. + } +\end{figure} + +Das Rauschspektrum der erstellten Variante ist ebenfalls sehr gut für den +Einsatz an einem IMS geeignet. +Das Rauschlevel ist mit durchschnittlich $\SI{10}{\micro\volt\per\sqrt{\hertz}}$ +bis zur Filter-Grenzfrequenz sehr niedrig. Die in der Bandbreite erkennbare Überhöhung ist +ebenso im Rauschen zu erkennen, da ab $\SI{100}{\kilo\hertz}$ das Rauschen stark ansteigt. +Der Ausgangsfilter verringert teilweise das Rauschen, und mit +einem maximalen Rauschlevel von $\SI{25}{\micro\volt\per\sqrt{\hertz}}$ +sind diese Messwerte dennoch sehr gut nutzbar. + +Insgesamt ist die erstellte Variante sehr gut für die Nutzung an schnelleren IMS-Systemen +geeignet, da sie ein niedriges Rauschen und stabile Bandbreite anbietet. +Bei weiterer Feineinstellung des TIVs ist zudem zu erwarten, dass die Überhöhungen +korrigiert werden kann, um noch höhere Bandbreiten bei gleicher Verstärkung erreichen +zu können. + +Eine Messung an einem echten IMS-System war durch technische Probleme +unabhängig vom TIV nicht möglich. + +\clearpage \section{Fazit} -Die zweite Revision korrigiert erfolgreich die Instabilität, welche in der ersten Revision -festgestellt wurde. -In den restlichen Parametern schneidet sie vergleichbar gut wie die erste Revision ab. +Die Revision korrigiert erfolgreich die Instabilität, welche in der ersten Version +des in dieser Arbeit erstellten TIVs festgestellt wurde. +In den restlichen Parametern schneidet sie vergleichbar gut wie die erste Version ab. Zudem lässt sich durch die korrekte Einstellung der Verstärkungsverteilung der kaskadierten Stufe die Bandbreite des Schaltkreises arbiträr limitieren, was eine zusätzliche Rauschreduktion -ermöglicht. -Somit wurde ein erfolgreicher und für ein IMS nutzbarer TIV entwickelt. \ No newline at end of file +ermöglicht. In der Messung am echten IMS konnte bestätigt werden, dass der TIV +Messwerte mit gleicher Qualität wie bestehende Systeme liefern kann. + +Zusammengefasst wurde somit bestätigt, dass erfolgreich ein TIV für die IMS entwickelt +wurde. \ No newline at end of file diff --git a/TeX/Kapitel/Vermessung.tex b/TeX/Kapitel/Vermessung.tex index 7d476b6..fd535f9 100644 --- a/TeX/Kapitel/Vermessung.tex +++ b/TeX/Kapitel/Vermessung.tex @@ -1,42 +1,54 @@ - +\cleardoublepage \chapter{Vermessung} \label{chap:measurements} In diesem Kapitel wird der erstellte Schaltkreis auf seine Funktionstüchtigkeit untersucht. -Es wird beurteilt, ob die Schaltung die festgelegten Zielparameter erreichen kann, -und welche Parameter einer Verbesserung bedürfen. +Es wird beurteilt, ob die Schaltung die festgelegten Zielparameter erreichen kann +und welche Parameter einer Verbesserung bedürfen. Zusätzlich werden +verschiedene Auslegungen des Schaltkreises getestet, um den Einfluss verschiedener +Komponenten und Design-Varianten zu erproben. -Hierbei werden verschiedene Variationen des Schaltkreises vermessen, um -einige Systemparameter bestimmen zu können. Diese sind: +Relevant ist hierbei vor allem die Größe des Rückkoppelwiderstandes, welcher +entsprechend der Simulationen das Rauschen stark beeinflusst und die Bandbreite +des Schaltkreises fest legt. Aus diesem Grund sollen verschiedene +Rückkoppelwiderstände getestet werden. +Ebenso relevant ist der Einfluss der Abschirmung, welche genauer betrachtet +wird. + +Somit sind folgende Schaltkreise zu vermessen: \begin{itemize} \item Ein Schaltkreis ohne Abschirmungen und mit $4\cdot\SI{47}{\mega\ohm}$ - Rückkoppelwiderständen, zur Bestätigung der Notwendigkeit der Abschirmungen + Rückkoppelwiderständen zur Bestätigung der Notwendigkeit der Abschirmungen. \item Drei Schaltkreise mit jeweils $4\cdot\SI{47}{\mega\ohm}$, $4\cdot\SI{20}{\mega\ohm}$ sowie $4\cdot\SI{120}{\mega\ohm}$ Rückkoppelwiderständen, um den Einfluss der verschiedenen Widerstände charakterisieren zu können. \end{itemize} +Die Auswahl dieser Widerstände wurde entsprechend der Abschätzungen aus +Kapitel \ref{chap:r_para_mitigations} getroffen. + +\clearpage \section{Messergebnisse} \subsection{Linearität} \label{chap:v10_measurement_linearity} In diesem Abschnitt wird die Linearität des erstellten -Schaltkreises erprobt. Diese Art der Vermessung gibt an, +Schaltkreises evaluiert. Diese Art der Vermessung gibt an, auf welche Art Eingangs- und Ausgangssignal in Relation stehen. Für die meisten Sensorsysteme ist eine möglichst lineare -Relation gewünscht, d.h.: +Relation gewünscht, d.~h.: \begin{equation*} - V_\mathrm{out} = I_\mathrm{in} \cdot R_\mathrm{f} + U_\mathrm{out} = I_\mathrm{in} \cdot R_\mathrm{f} \end{equation*} Wobei $R_\mathrm{f}$ der Rückkoppelwiderstand des TIVs ist. In einem echten System gibt es jedoch zusätzliche Fehlerquellen, -welche diese Relation verändern, so z.B. +welche diese Relation verändern, soz.~B. Nichtlinearitäten und Leckströme. Um die Relation zwischen Aus- und Eingang charakterisieren @@ -45,59 +57,79 @@ genutzt. Diese Quelle liefert Ströme mit einer Auflösung von $\SI{10}{\pico\am Der Ausgang dieser Quelle wird an den Eingang des gebauten TIVs angeschlossen. Der Ausgang des TIVs wird mit einem digitalem Multimeter, dem {\em Keysight 34461A}, vermessen, -wobei eine Mittlung von $100\cdot\SI{20}{\milli\second}$ eingestellt wird. -Dies mittelt über 100 Perioden des 50Hz-Stromnetzes hinweg, um +wobei eine Mittlung von $\SI{2000}{\milli\second}$ eingestellt wird. +Dies mittelt über 100 Perioden des $\SI{50}{\hertz}$-Stromnetzes hinweg, um den Einfluss dieser Störquelle zu vermindern. Vermessen wird nur die abgeschirmte $4\cdot\SI{47}{\mega\ohm}$ Variante des TIVs, da Nichtlinearitäten sowie Leckströme eine Funktion des Verstärkers selbst sind. Abschirmung, -Widerstandsgröße etc. beeinflusst lediglich die dynamischen +Widerstandsgröße etc. beeinflussen lediglich die dynamischen Eigenschaften des Schaltkreises, da Widerstände generell keine Nichtlinearitäten bei DC aufweisen. Es wird ein Strombereich von $\SI{\pm2.6}{\nano\ampere}$ Eingangsstrom in Schritten von $\SI{0.1}{\nano\ampere}$ vermessen. +Abbildung \ref{fig:measurement_v1_linearity} zeigt das Ergebnis der Vermessung +und Abbildung \ref{fig:measurement_v1_linearity_error} zeigt die Abweichung +der Messung vom Sollwert. -\begin{figure}[h] +\begin{figure}[ht] \centering \includegraphics[scale=0.8]{datavis/V1_Measurements/1G_47M_Linearity.png} - \caption{\label{fig:measurement_v1_linearity} - Messergebnisse der Linearitätsmessung.} + \caption[Messergebnisse der Linearitätsmessung]{\label{fig:measurement_v1_linearity} + Messergebnisse der Linearitätsmessung des $\SI{47}{\mega\ohm}$ TIVs. + Es sind wie gewünscht keine merklichen Nichtlinearitäten zu erkennen.} \end{figure} -Abbildung \ref{fig:measurement_v1_linearity} zeigt das Ergebnis der Vermessung. -Deutlich zu erkennen ist eine saubere, lineare Abhängigkeit der Ausgangsspannung -vom Eingangsstrom ohne merkliche Abweichungen vom linearen Zusammenhang. Auch -der Verstärkungsfaktor von $\SI{1}{\giga\ohm}$ wird präzise erreicht. -Lediglich an den Extremen des Messbereiches ab ca. $\SI{\pm2.4}{\nano\ampere}$ ist ein +\begin{figure}[ht] + \centering + \includegraphics[scale=0.8]{datavis/V1_Measurements/1G_47M_Linearity_Error.png} + \caption[Abweichung der Linearität des TIVs]{ + \label{fig:measurement_v1_linearity_error} + Abweichung des Messwerts des $\SI{47}{\mega\ohm}$ TIVs vom + Erwartungswert. Zu sehen ist ein leichter Fehler der Verstärkung + von circa +0.5\%, ein Nullpunkt-Offset von $\SI{+5}{\milli\volt}$, + sowie die Grenzen des nutzbaren Bereichs des Verstärkers. + } +\end{figure} + +Deutlich zu erkennen ist eine nutzbare lineare Abhängigkeit der Ausgangsspannung +vom Eingangsstrom ohne starke Abweichungen vom linearen Zusammenhang. +Es scheint ein leichter Fehler im Verstärkungsfaktor von 0.5\% vorzuliegen +und der Nullpunkt ist um circa $\SI{5}{\milli\volt}$ nach oben verschoben. +Beide dieser Fehler lassen sich durch eine lineare Kalibration entfernen, +der Schaltkreis besitzt somit ein nutzbares lineares Ausgangssignal. +Lediglich an den Extremen des Messbereiches ab circa $\SI{\pm2.4}{\nano\ampere}$ ist ein Einknicken der Ausgangsspannung zu erkennen. Dies lässt sich durch die Versorgungsspannung -des Verstärkers erklären, welche bei ca. $\SI{\pm2.5}{\volt}$ liegt, wodurch die +des Verstärkers erklären, welche bei circa $\SI{\pm2.5}{\volt}$ liegt, wodurch die Ausgangsspannung begrenzt ist. -In Zusammenfassung ist die Linearität des Schaltkreises mehr als Ausreichend, und +In Zusammenfassung ist die Linearität des Schaltkreises mehr als ausreichend und für den gewünschten Eingangsstrom von $\SI{\pm1}{\nano\ampere}$ liegt ein komplett -lineares Verhalten vor. +lineares Verhalten vor. -\subsection{Bandbreite} +\clearpage + +\subsection[Verstärkerbandbreite]{Untersuchung der Verstärkerbandbreite} \label{chap:v10_measurement_bandwidth} -In diesem Abschnitt wird die Bandbreite des Systems untersucht. -Hierbei wird sowohl die Bandbreite der TIV-Stufe ohne Filterung, -als auch die gesamte Bandbreite mit Filterung, vermessen. +Nun wird die Übertratungsfunktion der TIVs betrachtet. +Hierbei werden sowohl die Bandbreite der TIV-Stufe ohne Filterung, +als auch die gesamte Bandbreite mit Filterung vermessen. Für einen Verstärker wie den TIV ist eine Übertragungsfunktion gewünscht, welche möglichst flach verläuft und erst ab einer gewissen Grenzfrequenz dann möglichst steil abfällt. Der glatte Verlauf unterhalb der Grenzfrequenz erlaubt für eine verzerrungsfreie Übertragung eines Signals, während der steile -Abfall nach der Grenzfrequenz ungewünschte Signale heraus filtert. +Abfall nach der Grenzfrequenz ungewünschte Signale herausfiltert. Die Übertragungsfunktionen werden mithilfe eines {\em Analog Discovery Pro 3} Oszilloskop + Funktionsgenerator aufgenommen. -Der Ausgang des Funktionsgenerators an eine Photodioden-Box angeschlossen, +Der Ausgang des Funktionsgenerators wird an eine Photodiodenbox angeschlossen, welche die Ausgangsspannung des Generators auf einen Strom im Bereich von 0 bis $\SI{0.7}{\nano\ampere}$ umwandelt. Der Frequenzgang dieser Box ist hierbei -bis in die oberen $\SI{100}{\kilo\hertz}$ flach und konstant, und muss somit +bis in die oberen $\SI{100}{\kilo\hertz}$ flach und konstant und muss somit nicht weiter beachtet werden. Der Ausgang der Photodioden-Box wird an den Eingang des TIVs angeschlossen. Der gefilterte und ungefilterte Ausgang des TIVs werden jeweils mit dem {\em Analog Discovery Pro 3} vermessen. @@ -106,19 +138,20 @@ Durch Anlegen einer Sinus-Ausgangsspannung an die Dioden-Box und Vermessung der Amplitude und Phase des Sinus an den Ausgängen des TIVs kann berechnet werden, mit welcher Verstärkung bzw. Dämpfung die verschiedenen Frequenzen übertragen wurden. Hierbei werden Frequenzen im Bereich von $\SI{100}{\hertz}$ bis $\SI{500}{\kilo\hertz}$ -genutzt. - -\begin{figure}[ht] - \centering - \includegraphics[scale=0.8]{datavis/V1_Measurements/bandwidth.png} - \caption{\label{fig:v10_bandwidth}Bandbreiten des TIV-Teils der aufgebauten Varianten - der ersten Platinenrevision, mit verschiedenen - Rückkoppelwiderständen.} -\end{figure} - -Abbildung \ref{fig:v10_bandwidth} zeigt die aufgenommenen Bandbreiten +genutzt. Abbildung \ref{fig:v10_bandwidth} zeigt die aufgenommenen Bandbreiten des abgeschirmten Schaltkreises mit verschiedenen Rückkoppelwiderständen. + +\begin{figure}[H] + \centering + \includegraphics[scale=0.8]{datavis/V1_Measurements/bandwidth.png} + \caption[Messung der TIV Übertragungsfunktionen]{ + \label{fig:v10_bandwidth}Bandbreiten des TIV-Teils der aufgebauten Varianten + der ersten Platinenrevision mit variierten + Rückkoppelwiderständen. Zu erkennen ist die Abhängigkeit der Bandbreite + vom Widerstand.} +\end{figure} + Deutlich zu erkennen ist die Abhängigkeit der Bandbreite vom Rückkoppelwiderstand, wie in vorherigen Kapiteln dargelegt und berechnet wurde. Die tatsächliche Bandbreite ist hierbei wie erwartet geringer als die simulierten Werte @@ -126,14 +159,14 @@ aus Kapitel \ref{chap:r_para_mitigations}, da sich vermutlich nicht alle parasitären Eigenschaften akkurat modellieren ließen. Dennoch ist eine klare Verbindung zwischen Widerstandsgröße und Bandbreite erkennbar. Die gemessenen --3dB Grenzfrequenzen sind in Tabelle \ref{table:v10_bandwidths} aufgelistet. +-3~dB Grenzfrequenzen sind in Tabelle \ref{table:v10_bandwidths} aufgelistet. \begin{table}[H] \centering - \caption{\label{table:v10_bandwidths}-3dB-Frequenzen des ungefilterten TIV-Ausgangs} + \caption{\label{table:v10_bandwidths}-3~dB-Frequenzen des ungefilterten TIV-Ausgangs} \begin{tabular}{ |r|r|r| } \hline - Widerstand & -3dB Punk \\ + Widerstand & -3~dB Punk \\ \hline $\SI{20}{\mega\ohm}$ & $\SI{58.484}{\kilo\hertz}$ \\ $\SI{47}{\mega\ohm}$ & $\SI{49.355}{\kilo\hertz}$ \\ @@ -143,86 +176,103 @@ Die gemessenen \end{table} Die Übertragungsfunktionen aller drei Platinen weisen akzeptables Verhalten -auf, d.h. einen glatten Verlauf vor der Grenzfrequenz und einen -Abfall von ca. -20dB/Dekade. Lediglich die Grenzfrequenz des -$\SI{120}{\mega\ohm}$ Schaltkreises ist relativ gering, und bietet somit +auf, d.~h. einen glatten Verlauf vor der Grenzfrequenz und einen +Abfall von circa -20dB/Dekade. Lediglich die Grenzfrequenz des +$\SI{120}{\mega\ohm}$ Schaltkreises ist relativ gering und bietet somit wenig Spielraum für die nachfolgende Filterung. -\begin{figure}[ht] +Ebenfalls von Interesse ist die Übertragungsfunktion des gefilterten Ausgangs. +Dieser wird mit der bereits genutzten Messung vermessen. +Die Ergebnisse dieser Messung sind in Abbildung \ref{fig:v10_bandwidths_ch2} +dargestellt. + +\begin{figure}[htb] \centering \includegraphics[scale=0.8]{datavis/V1_Measurements/bandwidth_ch2.png} - \caption{\label{fig:v10_bandwidths_ch2}Übertragungsfunktionen des gefilterten Ausgangs - der Platinen bei variiertem Rückkoppelwiderstand.} + \caption[Übertragungsfunktionen des gefilterten Ausgangs + der Platinen bei variiertem Rückkoppelwiderstand]{ + \label{fig:v10_bandwidths_ch2}Übertragungsfunktionen des gefilterten Ausgangs + der Platinen bei variiertem Rückkoppelwiderstand. Zu erkennen ist die Eckfrequenz + des Filters bei $\SI{30}{\kilo\hertz}$} \end{figure} - -Abbildung \ref{fig:v10_bandwidths_ch2} zeigt die Messungen der gefilterten -Ausgänge derselben Platinen. Die Auslegung der Filterstufe soll erst ab der Grenzfrequenz von $\SI{30}{\kilo\hertz}$ einen Abfall von -40dB/Dekate einbringen, wobei Frequenzen unterhalb der Grenzfrequenz nicht beeinflusst werden sollten. -Diese Verhalten ist auch deutlich in der Messung zu erkennen. Die -3dB-Frequenzen +Dieses Verhalten ist auch deutlich in der Messung zu erkennen. Die -3~dB-Frequenzen der gefilterten Ausgänge sind in Tabelle \ref{table:v10_bandwidth_filters} aufgelistet. -Wie bereits theorisiert ist die Bandbreite der $\SI{120}{\mega\ohm}$-Variante zu gering +Wie bereits theorisiert, ist die Bandbreite der $\SI{120}{\mega\ohm}$-Variante zu gering für die vollen $\SI{30}{\kilo\hertz}$. Die anderen beiden Varianten besitzen genug Bandbreite. \begin{table}[H] \centering - \caption{\label{table:v10_bandwidth_filters}-3dB-Frequenzen der gefilterten Ausgänge des TIVs} + \caption{\label{table:v10_bandwidth_filters}-3~dB-Frequenzen der gefilterten Ausgänge des TIVs} \begin{tabular}{ |r|r|r| } \hline - Widerstand & -3dB Punk \\ + Widerstand & -3~dB Punk \\ \hline - $\SI{20}{\mega\ohm}$ & $\SI{30.22057}{\kilo\hertz}$ \\ + $\SI{20}{\mega\ohm}$ & $\SI{30.220}{\kilo\hertz}$ \\ $\SI{47}{\mega\ohm}$ & $\SI{30.199}{\kilo\hertz}$ \\ $\SI{120}{\mega\ohm}$ & $\SI{25.118}{\kilo\hertz}$ \\ \hline \end{tabular} \end{table} - -\begin{figure}[htb] - \centering - \includegraphics[scale=0.8]{datavis/V1_Measurements/bandwidth_filter_compare.png} - \caption{\label{fig:v10_bandwidth_filter_compare}Vergleich der Übertragungsfunktion - des gefilterten und ungefilterten Ausangs des $\SI{47}{\mega\ohm}$ TIVs.} -\end{figure} - Abbildung \ref{fig:v10_bandwidth_filter_compare} zeigt zum Vergleich die Bandbreiten des ungefilterten und gefilterten Ausgangs des $\SI{47}{\mega\ohm}$ TIVs. Die Eckfrequenz des Filters sowie der -40dB/Dekade-Abfall ist deutlich zu erkennen. +\begin{figure}[ht] + \centering + \includegraphics[scale=0.8]{datavis/V1_Measurements/bandwidth_filter_compare.png} + \caption[Vergleich der Übertragungsfunktion + des gefilterten und ungefilterten Ausangs des $\SI{47}{\mega\ohm}$ TIVs]{ + \label{fig:v10_bandwidth_filter_compare}Vergleich der Übertragungsfunktion + des gefilterten und ungefilterten Ausangs des $\SI{47}{\mega\ohm}$ TIVs. + Die Filterung ist deutlich ab $\SI{30}{\kilo\hertz}$ zu erkennen, mit + einem wesentlich schnelleren Abfall des gefilterten Ausgangs. + } +\end{figure} + \FloatBarrier -\newpage \subsubsection{Einfluss der Abschirmung} \label{chap:measurements_v10_shielding} -In diesem Abschnitt wird der Einfluss der Abschirmung genauer untersucht. +Ein relevantes Element des Schaltungsdesigns ist die Abschirmung, welche +zum Ausgleich der parasitären Kapazitäten ausgelegt wurde. +Der konkrete Effekt dieser Abschirmung wird nun betrachtet. Um diesen zu messen, werden die Abschirmungselektroden durch Änderung des Widerstandsteilers auf zu hohe/zu niedrige Spannungen im Vergleich zum Sollwert gelegt. Hiernach werden die Übertragungsfunktionen vermessen und ausgewertet. +Abbildung \ref{fig:v10_compensation_comparison} zeigt die Übertragungsfunktionen +in Abhängigkeit zum Verstärkungsfaktor der Abschirmung zur Signalspannung. -\begin{figure}[H] +\FloatBarrier + +\begin{figure}[ht] \centering \includegraphics[scale=0.8]{datavis/V1_Measurements/compensation.png} - \caption{\label{fig:v10_compensation_comparison}Übertragungsfunktionen - des $\SI{47}{\mega\ohm}$ TIVs bei variierten Abschirmungselektrodenspannungen} + \caption[Messung der Übertragungsfunktionen + bei variierter Abschirmungsspannung]{ + \label{fig:v10_compensation_comparison}Übertragungsfunktionen + des $\SI{47}{\mega\ohm}$ TIVs bei variierten Abschirmungselektrodenspannungen. + Zu erkennen ist die starke Änderung der Übertragungsfunktion bei + falsch angepasster Abschirmung.} \end{figure} -Abbildung \ref{fig:v10_compensation_comparison} zeigt die Übertragungsfunktionen -bei variierten Abschirmungs-Spannungen. Deutlich zu erkennen ist ein starker Einfluss +Deutlich zu erkennen ist ein starker Einfluss der Abschirmung auf die Verstärkungen selbst bei kleineren Frequenzen ab $\SI{500}{\hertz}$, wobei die Abschirmung den Frequenzgang sowohl anheben als auch absenken kann. -So kann z.B. bei weiterer Anhebung des Frequenzganges +So kannz.~B. bei weiterer Anhebung des Frequenzganges eine Instabilität und Oszillation auftreten. Zudem ist ein möglichst flacher Frequenzgang gewünscht. Die flachste, und somit am besten geeignetste, Übertragungsfunktion ergibt sich mit einer leicht zu hohen Filterspannung, zwischen x1 und x1.1. -Dies lässt sich leicht mit der E24-Serie von Widerständen erreichen, und benötigt +Dies lässt sich leicht mit der E24-Serie von Widerständen erreichen und benötigt somit keine teureren Widerstände zur Einstellung der Abschirmung. Hieraus kann geschlossen werden, dass die Abschirmungen einen merklichen und wichtigen Einfluss auf @@ -233,93 +283,112 @@ notwendig für die Funktionalität des TIVs. \subsubsection{Messung ohne Abschirmung} -In diesem Kapitel soll die Übertragungsfunktion der Variante -ohne Abschirmung vermessen werden. +Um zu bestätigen dass die Abschirmung notwendig ist, wird +ein separates Platinendesign ohne jegliche Abschirmungen angefertigt +und dessen Übertragungsfunktion sollte vermessen werden. Dies war jedoch nicht möglich, da die Platine keinen stabilen Ausgang besaß. Der Ausgangspegel des TIVs ohne Abschirmung der Rückkoppelwiderstände bildet eine Rechteckwelle aus, welche zwischen dem maximalen und minimalen Pegel wechselt. Somit ist keine Bandbreitenmessung möglich, da die Eingangs-Sinus-Welle -nie korrekt übertragen wird. +nie korrekt übertragen wird. Die Messung dieses instabilen +Ausgangssignals ist in Abbildung \ref{fig:v10_unshielded_waveform} +dargestellt. -\begin{figure}[H] +\begin{figure}[ht] \centering \includegraphics[scale=0.8]{datavis/V1_Measurements/unshielded_47M.png} - \caption{\label{fig:v10_unshielded_waveform} - Ausgangsspannung des TIV-Schaltkreises ohne Abschirmung.} + \caption[Ausgangsspannung des TIV-Schaltkreises ohne Abschirmung]{\label{fig:v10_unshielded_waveform} + Ausgangsspannung des TIV-Schaltkreises ohne Abschirmung. + Deutlich zu erkennen ist die starke Oszillation der Ausgangsspannung, + welche bis an die Spannungsgrenzen des Ausgangs geht.} \end{figure} -Abbilding \ref{fig:v10_unshielded_waveform} zeigt die bereits -genannte Ausgangs-Wellenform. Deutlich zu erkennen ist die oszilliernde Natur -der Spannung. Die Wellenform ist zu erklären durch den Einfluss parasitärer -Erdungskapazitäten auf die hochohmigen Potentiale der Rückkoppelwiderstände. -Dies wurde bereits in Kapitel \ref{chap:r_para_mitigations} theorisiert, und +Die oszilliernde Natur +der Spannung ist deutlich zu erkennen. Die Wellenform ist durch den Einfluss parasitärer +Erdungskapazitäten auf die hochohmigen Potentiale der Rückkoppelwiderstände zu erklären. +Dies wurde bereits in Kapitel \ref{chap:r_para_mitigations} theorisiert und die Messungen in \ref{chap:measurements_v10_shielding} wiesen auch auf eine Instabilität bei zu kleiner Abschirmung hin. -Die Instabilität bei keiner Abschirmung ist somit erwartet, und weißt zusätzlich darauf hin -dass die bestehende Abschirmungsgeometrie ausreichend ist um diese Instabilität zu vermeiden. +Die Instabilität bei keiner Abschirmung ist somit erwartet und weist zusätzlich darauf hin, +dass die bestehende Abschirmungsgeometrie ausreichend ist, um diese Instabilität zu vermeiden. +Eine Operation gänzlich ohne Abschirmungselektroden ist nicht möglich. \FloatBarrier -\newpage \subsection{Rauschen} \label{chap:v10_measurement_noise} -In diesem Abschnitt wird das Rauschen des Schaltkreises genauer untersucht. -Das Rauschverhalten ist relevant für die Signalqualität, und somit für die -Detektionsgrenzen, welche erreicht werden können. Generell sind niedrigere +Das Rauschverhalten ist relevant für die Signalqualität und somit für die +Detektionsgrenzen, welche erreicht werden können. Aus diesem Grund wird dieses +nun genauer vermessen. +Generell sind niedrigere Rauschwerte besser, wobei auch die Verteilung der Rauschenergie relevant ist, -d.h. ob es gewisse Frequenzen mit Spitzen oder Frequenbereiche mit erhöhtem +d.~h. ob es gewisse Frequenzen mit Spitzen oder Frequenbereiche mit erhöhtem oder niedrigerem Rauschen gibt. -Um das Rauschen der Platinen auf zu nehmen, wird der Eingang des TIVs +Um das Rauschen der Platinen aufzunehmen, wird der Eingang des TIVs mit einer Abschirmkappe abgedeckt. Zusätzlich wird der Aufbau in ein Metallgehäuse eingebaut, um äußere Störsignale zu verringern. Es wird für jede Platine das FFT-Spektrum von $\SI{500}{\hertz}$ bis $\SI{1}{\mega\hertz}$ aufgenommen, wobei jeweils 1000 Spektren -summiert und der Durchschnitt berechnet wird, um die durchschnittliche Verteilung -des Rauschens zu berechnen. +genutzt werden, um die durchschnittliche Verteilung +des Rauschens zu berechnen. Die Aufnahme der Spektren erfolgt mit dem +{\em Analog Discovery 3}, +wobei die Rauschgrenze dieses Messgerätes bei circa $\SI{0.5}{\micro\volt\per\sqrt{\hertz}}$ +liegt und somit die gemessenen Rauschlevel nicht +merklich beeinflusst. +Die aufgenommenen Spektren sind in +Abbildung \ref{fig:v10_noises_ch1} dargestellt. -\begin{figure}[H] +\begin{figure}[ht] \centering \includegraphics[scale=0.8]{datavis/V1_Measurements/noises.png} - \caption{\label{fig:v10_noises_ch1}Durchschnittliches Rauschspektrum + \caption[Durchschnittliches Rauschspektrum des ungefilterten Ausgangs - der drei Platinen.} + der drei Platinen]{\label{fig:v10_noises_ch1}Durchschnittliches Rauschspektrum + des ungefilterten Ausgangs + der drei Platinen bei abgeschirmtem, offenem Eingang. + Die gleichmäßige Verteilung des Rauschens ist sichtbar.} \end{figure} -Abbildung \ref{fig:v10_noises_ch1} zeigt die Rausch-Spektren der drei Platinen. -Deutlich zu erkennen ist die Abhängigkeit des Rauschens von der Widerstands-Größe, +Deutlich zu erkennen ist die Abhängigkeit des Rauschens von der Widerstandsgröße, welches der Vorhersage aus Kapitel \ref{chap:r_noise} entspricht. Das Rauschen ist bei allen drei Platinen relativ gleichmäßig -verteilt, mit einer flachen Spitze bei ca. $\SI{30}{\kilo\hertz}$. -Es sind keine Frequenz-Spitzen zu erkennen, und keine Resonanzen. +verteilt, mit einer flachen Spitze bei circa $\SI{30}{\kilo\hertz}$. +Es sind keine Frequenz-Spitzen und keine Resonanzen zu erkennen. Zusätzlich wird das Verhalten der Filter-Stufe auf das Rauschen -betrachtet. Es wird mithilfe des selben Messaufbaus das Rauschen -des gefilterten Ausgangs aufgenommen und aufgezeichnet. +betrachtet. Mithilfe desselben Messaufbaus wird das Rauschen +des gefilterten Ausgangs aufgenommen und aufgezeichnet. Abbildung +\ref{fig:v10_noises_ch2} zeigt die aufgenommenen Spektren. -\begin{figure}[h] +\begin{figure}[htb] \centering \includegraphics[scale=0.8]{datavis/V1_Measurements/noises_ch2.png} - \caption{\label{fig:v10_noises_ch2}Durchschnittliches Rauschspektrum + \caption[Durchschnittliches Rauschspektrum + des gefilterten Ausgangs + der drei Platinen]{\label{fig:v10_noises_ch2}Durchschnittliches Rauschspektrum des gefilterten Ausgangs - der drei Platinen.} + der drei Platinen. + Erkennbar ist die Wirkung des Ausgangsfilters ab $\SI{30}{\kilo\hertz}$, + welche das Rauschen stark verringert.} \end{figure} -Abbildung \ref{fig:v10_noises_ch2} zeigt die Rauschspektren der gefilterten Ausgänge. -Deutlich zu erkennen ist eine starke Reduktion des Rauschens ab der $\SI{30}{\kilo\hertz}$ -Grenzfrequenz des Filters, welches das gewünschte Verhalten ist. Der Filter reduziert +\FloatBarrier + +Deutlich zu erkennen ist eine starke Reduktion des Rauschens ab $\SI{30}{\kilo\hertz}$ +, welches das gewünschte Verhalten ist. Der Filter reduziert somit effektiv das Rauschen des TIV Ausgangs. Es wird zudem das RMS-Level des Rauschens sowohl vor als auch nach der -Filterung gemessen, und ist in Tabelle \ref{table:v10_noise_table} aufgelistet. -Deutlich zu erkennen ist das niedrigere Rauschniveau der Varianten mit größeren -Widerständen, sowie die effektivität der Filterung des Ausganges. +Filterung gemessen. Diese sind in Tabelle \ref{table:v10_noise_table} aufgelistet. +Das niedrigere Rauschniveau der Varianten mit größeren +Widerständen, sowie die Effektivität der Filterung des Ausganges, sind deutlich zu erkennen. -\begin{table}[H] +\begin{table}[htb] \centering - \caption{\label{table:v10_noise_table}AC-RMS-Spannungen des Rauschens der Platinen} + \caption{\label{table:v10_noise_table}RMS-Spannungen des Rauschens der Platinen} \begin{tabular}{ |r|r|r|r| } \hline Widerstand & Rauschen des @@ -338,36 +407,43 @@ für die Messungen, mit einem breit verteiltem Rauschen ohne spezifische Töne u einem niedrigen Rauschlevel. \FloatBarrier -\newpage \subsection{Stabilität am IMS} \label{chap:v10_instability} -In diesem Abschnitt soll auf das Verhalten des Schaltkreises bei -angeschlossenem IMS eingegangen werden. Die Präsenz des restlichen -Systems kann Einflüsse auf das Rauschniveau der Umgebung haben, -der Eingang des TIVs wird kapazitiv beeinflusst, etc. +Bisher wurde der erstellte TIV lediglich unter +Laborbedingungen getestet. Um korrekt beurteilen zu +können ob der TIV für den realen Einsatz geeignet ist, +muss zudem das Verhalten innerhalb eines realen Systems +betrachtet werden. So können Teile eines IMS +einen negativen Einfluss auf die Stabilität oder das +Rauschen des TIVs haben. Diese Einflüsse sollen +nun genauer betrachtet werden. -Beim Verbinden des bestehenden TIVs an eine IMS-Röhre mit Faraday-Elektrode -entsteht eine Störung: Der Ausgang des TIVs wird instabil, wobei eine +Als erstes wird eine Rauschmessung mit angeschlossener +Faraday-Elektrode, dem Detektor-Teil einer IMS-Röhre, angestrebt. +Dies ist jedoch nicht möglich, da beim Anschluss der Elektrode +eine Störung auftritt: Der Ausgang des TIVs wird instabil, wobei eine Rechteckwelle mit variabler Frequenz anstelle eines gefilterten und gleichmäßigen Signals ausgegeben wird. +Abbildung \ref{fig:measurement_v10_ims_instability} zeigt die Ausgangsspannung bei +angeschlossener IMS-Röhre auf. -\begin{figure}[htb] +\begin{figure}[ht] \centering \includegraphics[scale=0.8]{datavis/V1_Measurements/V1.0-a1/Instability.png} - \caption{\label{fig:measurement_v10_ims_instability}Ausgangsspannung des + \caption[Ausgangsspannung des + TIVs bei angeschlossener IMS-Röhre]{ + \label{fig:measurement_v10_ims_instability}Ausgangsspannung des TIVs bei angeschlossener IMS-Röhre, mit deutlich zu erkennender Instabilität der Messung.} \end{figure} -Abbildung \ref{fig:measurement_v10_ims_instability} zeigt die Ausgangsspannung bei -angeschlossener IMS-Röhre auf. Zu erwarten ist eine stabile, statische Ausgangsspannung, da keine Ionen auf die Röhre gegeben werden. Die gemessene Ausgangsspannung jedoch zeigt ein stark variables, schwingendes Signal, welches bis an die Ausgangsspannungen schwingt. Dieses Verhalten weist auf eine erhöhte Sensitivität der Schaltung auf -Eingangskapazitäten hin. Eine Vermutung wird aufgestellt dass das +Eingangskapazitäten hin. Eine Vermutung wird aufgestellt, dass das Eingangs-Spannungsrauschen des OpAmps selbst einen virtuellen Rausch-Strom erzeugt, welcher vom Verstärker mit verstärkt wird. Somit ist das Eingangsspannungsrauschen für die korrekte Funktionalität @@ -376,20 +452,21 @@ eines TIVs von größerer Bedeutung als anfänglich erwartet. Es ist anzumerken, dass eine solche Instabilität nicht korrekt in den Simulationen mit LTSpice abgebildet wird. Simulationen können nicht alle realen Vorgänge korrekt abbilden, wodurch vor allem -bei transienten Vorgängen oder denen in der Nähe der Arbeitsgrenzen, so z.B. der -maximalen Ausgangsspannung, Abweichungen von der Realität auftreten. Diese -Instabilität ist somit nur experimentell aufweislich. +bei transienten Vorgängen oder denen in der Nähe der Arbeitsgrenzen, soz.~B. der +maximalen Ausgangsspannung, Abweichungen von der Realität auftreten. +Diese Instabilität kann somit nur experimentell untersucht werden. Die Präsenz dieser Instabilität ist für den Einsatz in einem IMS ungeeignet. Der instabile und schwingende Ausgang erlaubt keine Messung der feinen Ionenströme, wodurch dieser Schaltkreis für eben solche Messungen nicht geeignet ist. +\clearpage \section{Diskussion der Messergebnisse} In diesem Kapitel werden die aufgenommenen Messwerte diskutiert. Es wird geprüft, ob die erstellte Schaltung die Anforderungen aus -Kapitel \ref{chap:tia_design_goals} erfüllt, und es werden mögliche +Kapitel \ref{chap:tia_design_goals} erfüllt und es werden mögliche Gründe für Abweichungen und unerwartete Werte etabliert. Die erstellte Platine erfüllt in fast allen Varianten die @@ -400,13 +477,13 @@ Sowohl $\SI{47}{\mega\ohm}$ und $\SI{20}{\mega\ohm}$ besitzen ausreichend Bandbreite. Die in Kapitel \ref{chap:r_para_mitigations} theorisierten Abschirmungen -ist als notwendig und angemessen ausgelegt identifiziert. Die Platinen +sind als notwendig und angemessen ausgelegt identifiziert. Die Platinen ohne Abschirmungen weisen eine starke Instabilität auf, während Platinen mit korrekt eingestellter Abschirmung einen glatten Frequenzgang bis hin zu ihrer Grenzfrequenz aufweisen. Das Rauschen der Platinen ist angemessen für den Nutzen in IMS-Systemen, -wobei die Platine ein breit verteiltes Rauschen ohne Peak-Frequenzen +wobei die Platinen ein breit verteiltes Rauschen ohne Peak-Frequenzen besitzt, welches für Messungen von Vorteil ist. Das Rauschlevel aller drei Platinen ist nutzbar, wobei jedoch die $\SI{120}{\mega\ohm}$ und $\SI{47}{\mega\ohm}$ Varianten die besten Rauschlevel besitzen. diff --git a/TeX/Kapitel/Zusammenfassung.tex b/TeX/Kapitel/Zusammenfassung.tex new file mode 100644 index 0000000..e5cb4c6 --- /dev/null +++ b/TeX/Kapitel/Zusammenfassung.tex @@ -0,0 +1,41 @@ +\cleardoublepage +\chapter{Zusammenfassung} + +In dieser Arbeit konnte erfolgreich ein neues +Design eines TIVs erstellt werden. +Hierbei wurden wichtige parasitären Effekte des Schaltkreises +dargestellt und neuartige +Kompensationsmöglichkeiten zur Reduktion des Einflusses +dieser ausgelegt. + +Mithilfe des durch Simulation vertieften Verständisses +über die parasitären Effekte sowie der Arbeitsweise +der Operationsverstärker konnte ein erstes Design +ausgelegt werden, welches die Anforderungen +an Bandbreite und Rauschlevel erfüllte. +Lediglich die Stabilität des Schaltkreises führte +zu Problemen. + +Die Ursprünge der Instabilität wurde thematisiert, +wobei das Rauschen des verwendeten OpAmps zusammen mit +einer möglichen Instabilität durch das GBWP vermutet wurde. +Es konnte in einer Revision der Schaltung die Stabilität +deutlich verbessert werden, in dem eine kaskadierte +OpAmp-Struktur mit ausreichendem GBWP und stabilisierender +Limitierung durch eine passend eingestellte offene Verstärkung +entwicklet wurde. + +Der somit erstellte Schaltkreis konnte in einer Messung +an einem der IMS-Systeme des GEM an der Leibniz Universität +Hannover vermessen werden und wurde mit den bestehenden +Systemen verglichen. Somit konnte bestätigt werden, dass +das neu erstellte System Messwerte mit guter Qualität liefert +und seine Zielanforderungen erfüllt. +Es wurde ebenfalls eine Variation des TIVs aufgebaut, welche +mit höherer Bandbreite arbeitet und somit den erstellten +TIV für einen breiteren Anwendungsbereich einsetzbar macht. + +Hierbei konnte der TIV so ausgelegt werden, dass keine manuellen +Nachjustierungen für eine korrekte Operation notwendig sind, +und der Preis sowie die Größe des Schaltkreises konnten im +Vergleich zur Vorgängerversion deutlich verringert werden. \ No newline at end of file diff --git a/TeX/Literaturverzeichnis.bib b/TeX/Literaturverzeichnis.bib index c4a8746..dfa7052 100644 --- a/TeX/Literaturverzeichnis.bib +++ b/TeX/Literaturverzeichnis.bib @@ -1,3 +1,13 @@ +@book{Horowitz:1981307, + author = "Horowitz, Paul and Hill, Winfield", + title = "{The art of electronics; 3rd ed.}", + publisher = "Cambridge University Press", + address = "Cambridge", + year = "2015", + url = "https://cds.cern.ch/record/1981307", +} + + @article{Reinecke2018Oct, author = {Reinecke, Tobias and Clowers, Brian H.}, title = {{Implementation of a flexible, open-source platform for ion mobility spectrometry}}, @@ -58,20 +68,119 @@ eid = {MT-038} } -@misc{WikipediaResistors2024May, - author = {{Contributors to Wikimedia projects}}, - title = {{Johnson{\textendash}Nyquist noise - Wikipedia}}, - year = {2024}, - month = may, - note = {[Online; accessed 13. May 2024]}, - url = {https://en.wikipedia.org/w/index.php?title=Johnson-Nyquist_noise&oldid=1222085733} -} - @misc{ADFilterDesign, author = {{Analog Devices}}, title = {{Filter Design Tool}}, year = {2024}, - month = july, + month = jul, note = {[Online; accessed 05. July 2024]}, url = {https://tools.analog.com/en/filterwizard/} } + +@misc{JBellemann22, + author = {{Jeroen Belleman}}, + title = {{Shunt capacitance of 1206 SMD resistors}}, + year = {2010}, + month = dec, + note = {[Online; accessed 28th August 2024]}, + url = {http://jeroen.web.cern.ch/jeroen/resistor/shuntC.html} +} + +@misc{VishayRFreq, + title = {{Frequency Response of Thin Film Chip Resistors}}, + year = {2009}, + month = feb, + note = {[Online; accessed 28th August 2024]}, + url = {https://www.vishay.com/docs/60107/freqresp.pdf} +} + +@misc{DatasheetADA4530, + title = {{Datasheet ADA4530 - Femtoampere Input Bias Current Electrometer Amplifier}}, + year = {2024}, + month = jun, + note = {[Online; accessed 12th June 2024]}, + url = {https://www.analog.com/media/en/technical-documentation/data-sheets/ada4530-1.pdf} +} + +@misc{DatasheetLTC2274, + title = {{Datasheet LTC2274 - 16-Bit, 105Msps Serial Output ADC}}, + year = {2009}, + month = jun, + note = {[Online; accessed 21th June 2024]}, + url = {https://www.analog.com/media/en/technical-documentation/data-sheets/2274fb.pdf} +} + +@misc{DatasheetLTC626810, + title = {{Datasheet LTC6268-10 - 4GHz Ultra-Low Bias Current FET Input Op Amp}}, + year = {2015}, + month = feb, + note = {[Online; accessed 21th June 2024]}, + url = {https://www.analog.com/media/en/technical-documentation/data-sheets/626810f.pdf} +} + +@misc{DatasheetADA4817, + title = {{Datasheet ADA4817 - Low Noise, 1 GHz FastFET Op Amps}}, + year = {2008}, + month = oct, + note = {[Online; accessed 21th June 2024]}, + url = {https://www.analog.com/media/en/technical-documentation/data-sheets/ADA4817-1_4817-2.pdf} +} + +@misc{DatasheetLMP7721, + title = {{Datasheet LMP7721 - 3-Femtoampere Input Bias Current Precision Amplifier}}, + year = {2014}, + month = dec, + note = {[Online; accessed 21th June 2024]}, + url = {https://www.ti.com/lit/ds/symlink/lmp7721.pdf} +} + +@misc{SierraReduceCapacitances, + title = {{How to reduce parasitic capacitance in PCB layout}}, + year = {2021}, + month = feb, + note = {[Online; accessed 10th June 2024]}, + url = {https://www.protoexpress.com/blog/how-to-reduce-parasitic-capacitance-pcb-layout/} +} + +@misc{AltiumReduceCapacitance, + title = {{How to Reduce Parasitic Capacitance in a PCB Layout}}, + author = {{Zachariah Peterson }}, + year = {2022}, + month = mar, + note = {[Online; accessed 10th June 2024]}, + url = {https://resources.altium.com/p/how-reduce-parasitic-capacitance-pcb-layout} +} + +@misc{AltiumLeakages, + title = {{PCB Leakage Current and Breakdown in High Voltage Design}}, + author = {{Zachariah Peterson}}, + year = {2020}, + month = jan, + note = {[Online; accessed 3rd June 2024]}, + url = {https://resources.altium.com/p/pcb-leakage-current-and-breakdown-in-high-voltage-design} +} + +@misc{GaussLaw, + title = {{Maxwell’s equations}}, + author = {{Wikimedia Foundation}}, + year = {2024}, + month = sep, + note = {[Online; accessed 15th March 2024]}, + url = {https://en.wikipedia.org/wiki/Maxwell’s_equations } +} + +@article{Yang:21, +author = {Jinqing Yang and Minjie Wan and Weixian Qian and Kan Ren and Dongming Lu and Jun Zhang and Guohua Gu and Qian Chen}, +journal = {Appl. Opt.}, +keywords = {Avalanche photodiodes; Fiber optic gyroscopes; Optical signals; Phase compensation; Photodetectors; Photodiodes}, +number = {31}, +pages = {9748--9756}, +publisher = {Optica Publishing Group}, +title = {Bandwidth extension method based on the field-shunting effect in a high-gain photoelectric receiver circuit}, +volume = {60}, +month = {Nov}, +year = {2021}, +url = {https://opg.optica.org/ao/abstract.cfm?URI=ao-60-31-9748}, +doi = {10.1364/AO.442413}, +abstract = {In the high-gain photoelectric receiver circuit, the method based on the field-shunting effect is applied to improve the bandwidth of the transimpedance amplifier. This method is implemented by adding a ground trace under the gain resistor, which reduces the parasitic capacitance of the gain resistor and thus increases the bandwidth. To obtain the specific impact of this method on bandwidth, a series of simulations are carried out, including electromagnetic simulations of a three-dimensional structure of circuit gain part and simulation program with integrated circuit emphasis (SPICE) simulations of the high-gain voltage-current feedback transimpedance amplifier. Finally, the optimal simulation result shows that selecting a 1206 size chip fixed resistor and setting the ground trace width to 1.1 mm can greatly reduce the influence of resistor parasitic effects on the circuit, thereby achieving the best performance of bandwidth extension. Further, the comparative experiment also verifies the effectiveness of the method for bandwidth enhancement.}, +} \ No newline at end of file diff --git a/TeX/config/Konfiguration.tex b/TeX/config/Konfiguration.tex index 101cd35..dd5f302 100644 --- a/TeX/config/Konfiguration.tex +++ b/TeX/config/Konfiguration.tex @@ -30,7 +30,7 @@ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % Literaturverzeichnis -\bibliographystyle{plain} %Literaturangaben nach Erscheinen im Text sortiert, "DIN 1505 Teil 2" +\bibliographystyle{unsrt} %Literaturangaben nach Erscheinen im Text sortiert, "DIN 1505 Teil 2" %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % Zusätzliche Worttrennungen diff --git a/TeX/config/Pakete.tex b/TeX/config/Pakete.tex index 73d64df..4f1fe27 100644 --- a/TeX/config/Pakete.tex +++ b/TeX/config/Pakete.tex @@ -73,9 +73,9 @@ \usepackage{listings} % Paket für Quelltexte \usepackage{pdfpages} \usepackage{import} % Erlaubt relative Pfadangaben -\usepackage[output-decimal-marker={,}]{siunitx} % Paket für Einheiten +\usepackage[output-decimal-marker={,},number-unit-product={~}]{siunitx} % Paket für Einheiten \usepackage{xfrac} \DeclareSIUnit \var {var} -\usepackage{todonotes} % Todo-Notes im Text erstellen -%\usepackage[disable]{todonotes} % Vor dem Drucken Todo Notes hier global deaktivieren! \ No newline at end of file +%\usepackage{todonotes} % Todo-Notes im Text erstellen +\usepackage[disable]{todonotes} % Vor dem Drucken Todo Notes hier global deaktivieren! \ No newline at end of file diff --git a/TeX/config/hyphenation.tex b/TeX/config/hyphenation.tex index 45e9d82..ae5a0a9 100644 --- a/TeX/config/hyphenation.tex +++ b/TeX/config/hyphenation.tex @@ -6,4 +6,5 @@ \hyphenation{STMCubeIDE} \hyphenation{Span-nungs-rau-schen} \hyphenation{Komponenten-reihen} -\hyphenation{GBWP} \ No newline at end of file +\hyphenation{GBWP} +\hyphenation{Photo-dioden-box} \ No newline at end of file diff --git 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Rückkoppel-widerstände + + + + OpAmp + + TIV Eingang + + Gain-Einstellung + + diff --git a/TeX/grafiken/Auslegung/v1.0/tia_stage.png b/TeX/grafiken/Auslegung/v1.0/tia_stage.png index f6901da..d16de86 100644 Binary files a/TeX/grafiken/Auslegung/v1.0/tia_stage.png and b/TeX/grafiken/Auslegung/v1.0/tia_stage.png differ diff --git a/TeX/grafiken/Auslegung/v1.1/tia_pcb.png b/TeX/grafiken/Auslegung/v1.1/tia_pcb.png index a94f812..99e8f75 100644 Binary files a/TeX/grafiken/Auslegung/v1.1/tia_pcb.png and b/TeX/grafiken/Auslegung/v1.1/tia_pcb.png differ diff --git a/TeX/grafiken/Auslegung/v1.1/tia_pcb.svg b/TeX/grafiken/Auslegung/v1.1/tia_pcb.svg new file mode 100644 index 0000000..3fa2950 --- /dev/null +++ b/TeX/grafiken/Auslegung/v1.1/tia_pcb.svg @@ -0,0 +1,17921 @@ + + + +AbschirmungRückkoppel-widerständeOpAmpTIV EingangGain-EinstellungZweitstufen- +einstellung diff --git a/TeX/grafiken/Auslegung/v1.1/tia_stage.png b/TeX/grafiken/Auslegung/v1.1/tia_stage.png index f08c9a6..9d2e9b0 100644 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