From 964052eae8c6030cf3136ea0c21e6e5073e79c4e Mon Sep 17 00:00:00 2001 From: Thomas Dehaeze Date: Tue, 19 Jan 2021 23:13:03 +0100 Subject: [PATCH] Add analysis of measured noise --- figs/asd_noise_3uF.pdf | Bin 0 -> 623943 bytes figs/asd_noise_3uF.png | Bin 0 -> 163741 bytes figs/low_noise_time_domain_3uF.pdf | Bin 0 -> 39282 bytes figs/low_noise_time_domain_3uF.png | Bin 0 -> 39491 bytes figs/noise_shunt_time_3uF.pdf | Bin 0 -> 223912 bytes figs/noise_shunt_time_3uF.png | Bin 0 -> 80367 bytes index.html | 301 ++++++++++++++++++++++------- index.org | 148 ++++++++++++++ 8 files changed, 376 insertions(+), 73 deletions(-) create mode 100644 figs/asd_noise_3uF.pdf create mode 100644 figs/asd_noise_3uF.png create mode 100644 figs/low_noise_time_domain_3uF.pdf create mode 100644 figs/low_noise_time_domain_3uF.png create mode 100644 figs/noise_shunt_time_3uF.pdf create mode 100644 figs/noise_shunt_time_3uF.png diff --git a/figs/asd_noise_3uF.pdf b/figs/asd_noise_3uF.pdf new file mode 100644 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z8g{WyRC`)XGe(?fJz0@gZ!i$IhoB`mZv~M}Bq%Z|-_7ycwWI;j?YSGrYkcisq1<8# zvT2kEe&jCr+*}N>MR36=z|V;#+tSV~{wpI_>(&id1KWcqm)(2-P+Blj^jSr=NR(L1 z$A(v@9|twO7yp - + Voltage Amplifier PD200 - Test Bench - - + +

+
+

1 Introduction

+

The goal of this test bench is to characterize the Voltage amplifier PD200 from PiezoDrive.

@@ -59,16 +76,18 @@ The documentation of the PD200 is accessible here<

-
+

amplifier_PD200.png

Figure 1: Picture of the PD200 Voltage Amplifier

+
+
-
-

1 Voltage Amplifier Requirements

-
- +
+

2 Voltage Amplifier Requirements

+
+
@@ -112,10 +131,10 @@ The documentation of the PD200 is accessible here< -
-

2 PD200 Expected characteristics

-
-
Table 1: Requirements for the Voltage Amplifier
+
+

3 PD200 Expected characteristics

+
+
@@ -190,18 +209,18 @@ The documentation of the PD200 is accessible here<
Table 2: Characteristics of the PD200

-For a load capacitance of \(10\,\mu F\), the expected \(-3\,dB\) bandwidth is \(6.4\,kHz\) (Figure 2) and the low frequency noise is \(650\,\mu V\,\text{rms}\) (Figure 3). +For a load capacitance of \(10\,\mu F\), the expected \(-3\,dB\) bandwidth is \(6.4\,kHz\) (Figure 2) and the low frequency noise is \(650\,\mu V\,\text{rms}\) (Figure 3).

-
+

pd200_expected_small_signal_bandwidth.png

Figure 2: Expected small signal bandwidth

-
+

pd200_expected_noise.png

Figure 3: Expected Low frequency noise from 0.03Hz to 20Hz

@@ -209,9 +228,9 @@ For a load capacitance of \(10\,\mu F\), the expected \(-3\,dB\) bandwidth is \(
-
-

3 Voltage Amplifier Model

-
+
+

4 Voltage Amplifier Model

+

The Amplifier is characterized by its dynamics \(G_a(s)\) from voltage inputs \(V_{in}\) to voltage output \(V_{out}\). Ideally, the gain from \(V_{in}\) to \(V_{out}\) is constant over a wide frequency band with very small phase drop. @@ -222,8 +241,16 @@ It is also characterized by its output noise \(n\). This noise is described by its Power Spectral Density.

+

+The objective is therefore to determine the transfer function \(G_a(s)\) from the input voltage to the output voltage as well as the Power Spectral Density \(S_n(\omega)\) of the amplifier output noise. +

-
+

+As both \(G_a\) and \(S_n\) depends on the load capacitance, they should be measured when loading the amplifier with a \(\SI{10}{\micro\farad}\) capacitor. +

+ + +

pd200-model-schematic.png

Figure 4: Model of the voltage amplifier

@@ -231,20 +258,20 @@ This noise is described by its Power Spectral Density.
-
-

4 Noise measurement

-
+
+

5 Noise measurement

+
-
-

4.1 Setup

-
-
+
+

5.1 Setup

+
+

Here are the documentation of the equipment used for this test bench:

@@ -262,7 +289,7 @@ If we suppose a white noise, this correspond to an amplitude spectral density:

The RMS noise begin very small compare to the ADC resolution, we must amplify the noise before digitizing the signal. The added noise of the instrumentation amplifier should be much smaller than the noise of the PD200. -We use the amplifier EG&G 5113 that have a noise of \(\approx 4 nV/\sqrt{Hz}\) referred to its input which is much smaller than the noise induced by the PD200. +We use the amplifier EG&G 5113 that has a noise of \(\approx 4 nV/\sqrt{Hz}\) referred to its input which is much smaller than the noise induced by the PD200.

@@ -271,37 +298,165 @@ This gain should be around 1000.

-
+

setup-noise-measurement.png

Figure 5: Schematic of the test bench to measure the Power Spectral Density of the Voltage amplifier noise \(n\)

-
-
-
-

4.2 Results

-
-
- -
-

5 Transfer Function measurement

-
-
-
-

5.1 Setup

-

-In order to measure the transfer function from the input voltage \(V_{in}\) to the output voltage \(V_{out}\), the test bench shown in Figure 6 is used. +A low pass filter at 10kHz can be included in the EG&G amplifier in order to limit aliasing. +An high pass filter at low frequency can be added if there is a problem of large offset. +

+
+
+ +
+

5.2 Results

+
+
+
+

5.2.1 Noise when shunting the input (50 Ohms)

+
+

+The time domain measurements of the amplifier noise are shown in Figure 6.

-
+ +
+

noise_shunt_time_3uF.png +

+

Figure 6: Time domain measurement of the amplifier output noise

+
+ +

+Obtained low frequency (0.1Hz - 20Hz) noise is shown in Figure 7 which is very similar to the noise shown in the documentation (Figure 3). +

+ + +
+

low_noise_time_domain_3uF.png +

+

Figure 7: Low Frequency Noise (0.1Hz - 20Hz)

+
+ +

+The obtained RMS and peak to peak values of the measured noises are shown in Table 3. +

+ + + + +++ ++ ++ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
Table 3: RMS and Peak to Peak measured noise
 RMS [uV]Peak to Peak [mV]
Specification [10uF]714.04.3
PD200_1524.94.5
PD200_2807.76.7
PD200_3630.35.4
PD200_4619.75.5
PD200_5630.85.6
PD200_6517.34.9
PD200_7393.83.7
+ +

+The PSD of the measured noise is computed and the ASD is shown in Figure 8. +

+
+
win = hanning(ceil(0.5/Ts));
+
+[pxx, f] = pwelch(pd200{1}.Vn, win, [], [], Fs);
+
+pxx = zeros(length(pxx), 7);
+
+for i = 1:7
+    pxx(:, i) = pwelch(pd200{i}.Vn, win, [], [], Fs);
+end
+
+
+ + +
+

asd_noise_3uF.png +

+

Figure 8: Amplitude Spectral Density of the measured noise

+
+
+
+
+
+ +
+

6 Transfer Function measurement

+
+
+
+

6.1 Setup

+
+

+In order to measure the transfer function from the input voltage \(V_{in}\) to the output voltage \(V_{out}\), the test bench shown in Figure 9 is used. +

+ +

Here are the documentation of the equipment used for this test bench:

@@ -312,23 +467,23 @@ For this measurement, the sampling frequency of the Speedgoat ADC should be as h

-
+

setup-dynamics-measurement.png

-

Figure 6: Schematic of the test bench to estimate the dynamics from voltage input \(V_{in}\) to voltage output \(V_{out}\)

+

Figure 9: Schematic of the test bench to estimate the dynamics from voltage input \(V_{in}\) to voltage output \(V_{out}\)

-
-

5.2 Results

+
+

6.2 Results

-
-

6 Conclusion

-
- - +
+

7 Conclusion

+
+
Table 3: Measured characteristics, Manual characterstics and specified ones
+@@ -417,7 +572,7 @@ For this measurement, the sampling frequency of the Speedgoat ADC should be as h

Author: Dehaeze Thomas

-

Created: 2021-01-04 lun. 11:09

+

Created: 2021-01-19 mar. 23:00

diff --git a/index.org b/index.org index b97bf4b..d689cb0 100644 --- a/index.org +++ b/index.org @@ -161,6 +161,154 @@ A low pass filter at 10kHz can be included in the EG&G amplifier in order to lim An high pass filter at low frequency can be added if there is a problem of large offset. ** Results +*** Matlab Init :noexport:ignore: +#+begin_src matlab :tangle no :exports none :results silent :noweb yes :var current_dir=(file-name-directory buffer-file-name) +<> +#+end_src + +#+begin_src matlab :exports none :results silent :noweb yes +<> +#+end_src + +#+begin_src matlab :tangle no +addpath('./matlab/mat/'); +addpath('./matlab/'); +#+end_src + +#+begin_src matlab :eval no +addpath('./mat/'); +#+end_src + +*** Noise when shunting the input (50 Ohms) + +#+begin_src matlab :exports none +%% Load all the measurements +pd200 = {}; +for i = 1:7 + pd200(i) = {load(['mat/noise_PD200_' num2str(i) '.mat'], 't', 'Vn', 'notes')}; +end + +%% Take into account the pre-amplifier gain +for i = 1:7 + pd200{i}.Vn = pd200{i}.Vn/pd200{i}.notes.pre_amp.gain; +end +#+end_src + +The time domain measurements of the amplifier noise are shown in Figure [[fig:noise_shunt_time_3uF]]. + +#+begin_src matlab :exports none +figure; +hold on; +for i = 1:7 + plot(pd200{i}.t, 1e3*pd200{i}.Vn) +end +hold off; +xlabel('Time [s]'); +ylabel('Voltage [mV]'); +#+end_src + +#+begin_src matlab :tangle no :exports results :results file replace +exportFig('figs/noise_shunt_time_3uF.pdf', 'width', 'wide', 'height', 'normal'); +#+end_src + +#+name: fig:noise_shunt_time_3uF +#+caption: Time domain measurement of the amplifier output noise +#+RESULTS: +[[file:figs/noise_shunt_time_3uF.png]] + +Obtained low frequency (0.1Hz - 20Hz) noise is shown in Figure [[fig:low_noise_time_domain_3uF]] which is very similar to the noise shown in the documentation (Figure [[fig:pd200_expected_noise]]). + +#+begin_src matlab :exports none +figure; +hold on; +plot(pd200{1}.t, lsim(1/(1 + s/2/pi/20), 1e3*pd200{1}.Vn, pd200{1}.t)) +hold off; +xlabel('Time [s]'); +ylabel('Voltage [mV]'); +xlim([0, 40]); ylim([-3, 3]); +#+end_src + +#+begin_src matlab :tangle no :exports results :results file replace +exportFig('figs/low_noise_time_domain_3uF.pdf', 'width', 'wide', 'height', 'normal'); +#+end_src + +#+name: fig:low_noise_time_domain_3uF +#+caption: Low Frequency Noise (0.1Hz - 20Hz) +#+RESULTS: +[[file:figs/low_noise_time_domain_3uF.png]] + +The obtained RMS and peak to peak values of the measured noises are shown in Table [[tab:rms_pkp_noise]]. + +#+begin_src matlab :exports none +%% Compute the RMS and Peak to Peak noise +Vn_rms = zeros(7,1); % RMS value [uV rms] +Vn_pkp = zeros(7,1); % Peak to Peak Value [mV] +for i = 1:7 + Vn_rms(i) = 1e6*rms(pd200{i}.Vn); + Vn_pkp(i) = 1e3*(max(pd200{i}.Vn)-min(pd200{i}.Vn)); +end +#+end_src + +#+begin_src matlab :exports results :results value table replace :tangle no :post addhdr(*this*) +data2orgtable([[714; Vn_rms], [4.3; Vn_pkp]], {'Specification [10uF]', 'PD200_1', 'PD200_2', 'PD200_3', 'PD200_4', 'PD200_5', 'PD200_6', 'PD200_7'}, {'*RMS [uV]*', '*Peak to Peak [mV]*'}, ' %.1f '); +#+end_src + +#+name: tab:rms_pkp_noise +#+caption: RMS and Peak to Peak measured noise +#+attr_latex: :environment tabularx :width \linewidth :align lXX +#+attr_latex: :center t :booktabs t :float t +#+RESULTS: +| | *RMS [uV]* | *Peak to Peak [mV]* | +|----------------------+------------+---------------------| +| Specification [10uF] | 714.0 | 4.3 | +| PD200_1 | 524.9 | 4.5 | +| PD200_2 | 807.7 | 6.7 | +| PD200_3 | 630.3 | 5.4 | +| PD200_4 | 619.7 | 5.5 | +| PD200_5 | 630.8 | 5.6 | +| PD200_6 | 517.3 | 4.9 | +| PD200_7 | 393.8 | 3.7 | + +#+begin_src matlab :exports none +% Sampling time / frequency +Ts = (pd200{1}.t(end) - pd200{1}.t(1))/(length(pd200{1}.t) - 1); +Fs = 1/Ts; +#+end_src + +The PSD of the measured noise is computed and the ASD is shown in Figure [[fig:asd_noise_3uF]]. +#+begin_src matlab +win = hanning(ceil(0.5/Ts)); + +[pxx, f] = pwelch(pd200{1}.Vn, win, [], [], Fs); + +pxx = zeros(length(pxx), 7); + +for i = 1:7 + pxx(:, i) = pwelch(pd200{i}.Vn, win, [], [], Fs); +end +#+end_src + +#+begin_src matlab :exports none +figure; +hold on; +for i = 1:7 + plot(f, sqrt(pxx(:, i)), 'DisplayName', sprintf('PD200-%i', i)); +end +hold off; +set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log'); +xlabel('Frequency [Hz]'); ylabel('ASD [$V/\sqrt{Hz}$]'); +legend('location', 'southwest'); +xlim([1, Fs/2]); +#+end_src + +#+begin_src matlab :tangle no :exports results :results file replace +exportFig('figs/asd_noise_3uF.pdf', 'width', 'wide', 'height', 'tall'); +#+end_src + +#+name: fig:asd_noise_3uF +#+caption: Amplitude Spectral Density of the measured noise +#+RESULTS: +[[file:figs/asd_noise_3uF.png]] * Transfer Function measurement ** Setup
Table 4: Measured characteristics, Manual characterstics and specified ones

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