Analyze: dac noise, pre-amp noise, amp bandwidth
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figs/asd_noise_3uF_warmup.pdf
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figs/asd_noise_3uF_warmup.pdf
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figs/asd_noise_3uF_warmup.png
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figs/noise_shunt_time_3uF_warmup.pdf
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figs/noise_shunt_time_3uF_warmup.png
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index.org
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@ -179,7 +179,313 @@ addpath('./matlab/');
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addpath('./mat/');
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#+end_src
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*** Noise when shunting the input (50 Ohms)
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*** Pre-Amp Noise
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#+begin_src matlab
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preamp = load('mat/noise_preamp_5113.mat', 't', 'Vn', 'notes');
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#+end_src
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#+begin_src matlab
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preamp.Vn = preamp.Vn/preamp.notes.pre_amp.gain;
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preamp.Vn = preamp.Vn - mean(preamp.Vn);
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#+end_src
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#+begin_src matlab
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figure;
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plot(preamp.t, preamp.Vn);
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xlabel('Time [s]');
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ylabel('Voltage [V]');
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#+end_src
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#+begin_src matlab :exports none
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% Sampling time / frequency
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Ts = (preamp.t(end) - preamp.t(1))/(length(preamp.t) - 1);
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Fs = 1/Ts;
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#+end_src
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#+begin_src matlab
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win = hanning(ceil(0.5/Ts));
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[pxx, f] = pwelch(preamp.Vn, win, [], [], Fs);
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preamp.pxx = pxx;
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preamp.f = f;
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#+end_src
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#+begin_src matlab :exports none
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figure;
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hold on;
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plot(preamp.f, sqrt(preamp.pxx));
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hold off;
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set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
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xlabel('Frequency [Hz]'); ylabel('ASD [$V/\sqrt{Hz}$]');
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legend('location', 'southwest');
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xlim([1, Fs/2]);
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#+end_src
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*** DAC (16bits) Noise
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#+begin_src matlab
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dac = load('mat/noise_preamp_5113_dac.mat', 't', 'Vn', 'notes');
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#+end_src
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#+begin_src matlab
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dac.Vn = dac.Vn/dac.notes.pre_amp.gain;
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#+end_src
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#+begin_src matlab
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dac.Vn = dac.Vn - mean(dac.Vn);
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#+end_src
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#+begin_src matlab
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figure;
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plot(dac.t, 1e6*dac.Vn);
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xlabel('Time [s]');
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ylabel('Voltage [$\mu V$]');
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#+end_src
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#+begin_src matlab :exports none
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% Sampling time / frequency
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Ts = (dac.t(end) - dac.t(1))/(length(dac.t) - 1);
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Fs = 1/Ts;
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#+end_src
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The PSD of the measured noise is computed and the ASD is shown in Figure [[fig:asd_noise_3uF]].
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#+begin_src matlab
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win = hanning(ceil(0.5/Ts));
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[pxx, f] = pwelch(dac.Vn, win, [], [], Fs);
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dac.pxx = pxx;
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dac.f = f;
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#+end_src
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#+begin_src matlab :exports none
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figure;
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hold on;
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plot(dac.f, sqrt(dac.pxx), 'DisplayName', 'DAC');
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plot(dac.f, ones(size(dac.f))*(10/2^16)/sqrt(12*Fs)/dac.notes.pre_amp.gain, 'k--', 'DisplayName', 'ADC quant.');
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plot(preamp.f, sqrt(preamp.pxx), 'DisplayName', 'Pre Amp');
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hold off;
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set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
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xlabel('Frequency [Hz]'); ylabel('ASD [$V/\sqrt{Hz}$]');
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legend('location', 'southwest');
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xlim([1, Fs/2]);
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#+end_src
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*** SSI2V DAC (20bits) Noise
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#+begin_src matlab
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ssi2v = load('mat/noise_preamp_5113_SSI2V.mat', 't', 'Vn', 'notes');
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#+end_src
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#+begin_src matlab
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ssi2v.Vn = ssi2v.Vn/ssi2v.notes.pre_amp.gain;
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ssi2v.Vn = ssi2v.Vn - mean(ssi2v.Vn);
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#+end_src
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#+begin_src matlab
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figure;
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plot(ssi2v.t, 1e6*ssi2v.Vn);
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xlabel('Time [s]');
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ylabel('Voltage [$\mu V$]');
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#+end_src
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#+begin_src matlab :exports none
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% Sampling time / frequency
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Ts = (ssi2v.t(end) - ssi2v.t(1))/(length(ssi2v.t) - 1);
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Fs = 1/Ts;
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#+end_src
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The PSD of the measured noise is computed and the ASD is shown in Figure [[fig:asd_noise_3uF]].
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#+begin_src matlab
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win = hanning(ceil(0.5/Ts));
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[pxx, f] = pwelch(ssi2v.Vn, win, [], [], Fs);
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ssi2v.pxx = pxx;
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ssi2v.f = f;
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#+end_src
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#+begin_src matlab :exports none
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figure;
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hold on;
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plot(dac.f, sqrt(dac.pxx), 'DisplayName', 'DAC');
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plot(ssi2v.f, sqrt(ssi2v.pxx), 'DisplayName', 'SSI2V');
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plot(ssi2v.f, ones(size(ssi2v.f))*(10/2^16)/sqrt(12*Fs)/ssi2v.notes.pre_amp.gain, 'k--', 'DisplayName', 'ADC quant.');
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plot(preamp.f, sqrt(preamp.pxx), 'DisplayName', 'Pre Amp');
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hold off;
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set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
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xlabel('Frequency [Hz]'); ylabel('ASD [$V/\sqrt{Hz}$]');
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legend('location', 'southwest');
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xlim([1, Fs/2]);
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#+end_src
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*** Noise when shunting the input (50 Ohms) - After Warmup
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#+begin_src matlab :exports none
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%% Load all the measurements
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pd200w = {};
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for i = 1:7
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pd200w(i) = {load(['mat/noise_PD200_' num2str(i) '_3uF_warmup.mat'], 't', 'Vn', 'notes')};
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end
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#+end_src
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#+begin_src matlab :exports none
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%% Take into account the pre-amplifier gain
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for i = 1:7
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pd200w{i}.Vn = pd200w{i}.Vn/pd200w{i}.notes.pre_amp.gain;
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end
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#+end_src
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The time domain measurements of the amplifier noise are shown in Figure [[fig:noise_shunt_time_3uF]].
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#+begin_src matlab :exports none
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figure;
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hold on;
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for i = 1:7
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plot(pd200w{i}.t, 1e3*pd200w{i}.Vn)
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end
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hold off;
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xlabel('Time [s]');
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ylabel('Voltage [mV]');
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#+end_src
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#+begin_src matlab :tangle no :exports results :results file replace
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exportFig('figs/noise_shunt_time_3uF_warmup.pdf', 'width', 'wide', 'height', 'normal');
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#+end_src
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#+name: fig:noise_shunt_time_3uF_warmup
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#+caption: Time domain measurement of the amplifier output noise
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#+RESULTS:
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[[file:figs/noise_shunt_time_3uF_warmup.png]]
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The obtained RMS and peak to peak values of the measured noises are shown in Table [[tab:rms_pkp_noise]].
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#+begin_src matlab :exports none
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%% Compute the RMS and Peak to Peak noise
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Vn_rms = zeros(7,1); % RMS value [uV rms]
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Vn_pkp = zeros(7,1); % Peak to Peak Value in 20Hz bandwidth [mV]
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for i = 1:7
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Vn_rms(i) = 1e6*rms(pd200w{i}.Vn);
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Vn_lpf = lsim(1/(1 + s/2/pi/20), pd200w{i}.Vn, pd200w{i}.t);
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Vn_pkp(i) = 1e3*(max(Vn_lpf)-min(Vn_lpf));
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end
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#+end_src
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#+begin_src matlab :exports results :results value table replace :tangle no :post addhdr(*this*)
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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 ');
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#+end_src
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#+name: tab:rms_pkp_noise
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#+caption: RMS and Peak to Peak measured noise
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#+attr_latex: :environment tabularx :width \linewidth :align lXX
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#+attr_latex: :center t :booktabs t :float t
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#+RESULTS:
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| | *RMS [uV]* | *Peak to Peak [mV]* |
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|----------------------+------------+---------------------|
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| Specification [10uF] | 714.0 | 4.3 |
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| PD200_1 | 565.1 | 3.7 |
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| PD200_2 | 767.6 | 3.5 |
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| PD200_3 | 479.9 | 3.0 |
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| PD200_4 | 615.7 | 3.5 |
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| PD200_5 | 651.0 | 2.4 |
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| PD200_6 | 473.2 | 2.7 |
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| PD200_7 | 423.1 | 2.3 |
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#+begin_src matlab :exports none
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% Sampling time / frequency
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Ts = (pd200w{1}.t(end) - pd200w{1}.t(1))/(length(pd200w{1}.t) - 1);
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Fs = 1/Ts;
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#+end_src
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The PSD of the measured noise is computed and the ASD is shown in Figure [[fig:asd_noise_3uF]].
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#+begin_src matlab
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win = hanning(ceil(0.5/Ts));
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for i = 1:7
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[pxx, f] = pwelch(pd200w{i}.Vn, win, [], [], Fs);
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pd200w{i}.f = f;
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pd200w{i}.pxx = pxx;
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end
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#+end_src
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#+begin_src matlab :exports none
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figure;
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hold on;
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for i = 1:7
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plot(pd200w{i}.f, sqrt(pd200w{i}.pxx), 'DisplayName', sprintf('PD200W-%i', i));
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end
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plot(preamp.f, sqrt(preamp.pxx), 'k-', 'DisplayName', 'Pre Amp');
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plot(dac.f, ones(size(dac.f))*(10/2^16)/sqrt(12*Fs)/pd200w{1}.notes.pre_amp.gain, 'k--', 'DisplayName', 'ADC quant.');
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hold off;
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set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
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xlabel('Frequency [Hz]'); ylabel('ASD [$V/\sqrt{Hz}$]');
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legend('location', 'southwest');
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xlim([1, Fs/2]);
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% ylim([5e-7, 1e-3]);
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#+end_src
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#+begin_src matlab :tangle no :exports results :results file replace
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exportFig('figs/asd_noise_3uF_warmup.pdf', 'width', 'wide', 'height', 'tall');
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#+end_src
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#+name: fig:asd_noise_3uF_warmup
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#+caption: Amplitude Spectral Density of the measured noise
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#+RESULTS:
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[[file:figs/asd_noise_3uF_warmup.png]]
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#+begin_src matlab
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Gn = 1e-6*(s + 2*pi*40)^2/(s + 2*pi)^2;
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#+end_src
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#+begin_src matlab :exports none
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freqs = logspace(0, 4, 1000);
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figure;
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hold on;
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for i = 1:7
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plot(pd200w{i}.f, sqrt(pd200w{i}.pxx), 'DisplayName', sprintf('PD200W-%i', i));
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end
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plot(freqs, abs(squeeze(freqresp(Gn, freqs, 'Hz'))), 'k--', 'DisplayName', '$|G_n(j\omega)|$');
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hold off;
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set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
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xlabel('Frequency [Hz]'); ylabel('ASD [$V/\sqrt{Hz}$]');
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legend('location', 'southwest');
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xlim([1, Fs/2]);
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#+end_src
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*** Load / No Load :noexport:
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#+begin_src matlab
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pd200_load = load('noise_PD200_7_3uF_warmup.mat');
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pd200_no_load = load('noise_PD200_7_no_load.mat');
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#+end_src
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#+begin_src matlab
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pd200_load.Vn = pd200_load.Vn/pd200_load.notes.pre_amp.gain;
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pd200_no_load.Vn = pd200_no_load.Vn/pd200_no_load.notes.pre_amp.gain;
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#+end_src
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#+begin_src matlab :exports none
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% Sampling time / frequency
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Ts = (pd200_load.t(end) - pd200_load.t(1))/(length(pd200_load.t) - 1);
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Fs = 1/Ts;
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#+end_src
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The PSD of the measured noise is computed and the ASD is shown in Figure [[fig:asd_noise_3uF]].
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#+begin_src matlab
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win = hanning(ceil(0.5/Ts));
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[pxx_load, f] = pwelch(pd200_load.Vn, win, [], [], Fs);
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[pxx_no_load, ~] = pwelch(pd200_no_load.Vn, win, [], [], Fs);
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#+end_src
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#+begin_src matlab :exports none
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figure;
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hold on;
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plot(f, sqrt(pxx_load), 'DisplayName', 'Load');
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plot(f, sqrt(pxx_no_load), 'DisplayName', 'No Load');
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hold off;
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set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
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xlabel('Frequency [Hz]'); ylabel('ASD [$V/\sqrt{Hz}$]');
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legend('location', 'southwest');
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xlim([1, Fs/2]);
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#+end_src
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*** Noise when shunting the input (50 Ohms) :noexport:
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#+begin_src matlab :exports none
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%% Load all the measurements
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@ -310,6 +616,111 @@ exportFig('figs/asd_noise_3uF.pdf', 'width', 'wide', 'height', 'tall');
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#+RESULTS:
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[[file:figs/asd_noise_3uF.png]]
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*** Noise with DAC at the input of the PD200
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#+begin_src matlab :exports none
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%% Load all the measurements
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pd200dac = {};
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for i = 1:7
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pd200dac(i) = {load(['mat/noise_PD200_' num2str(i) '_3uF_DAC.mat'], 't', 'Vn', 'notes')};
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end
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#+end_src
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#+begin_src matlab :exports none
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%% Take into account the pre-amplifier gain
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for i = 1:7
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pd200dac{i}.Vn = pd200dac{i}.Vn/pd200dac{i}.notes.pre_amp.gain;
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pd200dac{i}.Vn = pd200dac{i}.Vn - mean(pd200dac{i}.Vn);
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end
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#+end_src
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The time domain measurements of the amplifier noise are shown in Figure [[fig:noise_shunt_time_3uF]].
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#+begin_src matlab :exports none
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figure;
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hold on;
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for i = 1:7
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plot(pd200dac{i}.t, 1e3*pd200dac{i}.Vn)
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end
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hold off;
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xlabel('Time [s]');
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ylabel('Voltage [mV]');
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xlim([0, 0.1]);
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#+end_src
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#+begin_src matlab :tangle no :exports results :results file replace
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exportFig('figs/noise_shunt_time_3uF_dac.pdf', 'width', 'wide', 'height', 'normal');
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#+end_src
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#+name: fig:noise_shunt_time_3uF_dac
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#+caption: Time domain measurement of the amplifier output noise
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#+RESULTS:
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[[file:figs/noise_shunt_time_3uF_dac.png]]
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#+begin_src matlab :exports none
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% Sampling time / frequency
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Ts = (pd200dac{1}.t(end) - pd200dac{1}.t(1))/(length(pd200dac{1}.t) - 1);
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Fs = 1/Ts;
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#+end_src
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The PSD of the measured noise is computed and the ASD is shown in Figure [[fig:asd_noise_3uF]].
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#+begin_src matlab
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win = hanning(ceil(0.5/Ts));
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for i = 1:7
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[pxx, f] = pwelch(pd200dac{i}.Vn, win, [], [], Fs);
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pd200dac{i}.f = f;
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pd200dac{i}.pxx = pxx;
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end
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#+end_src
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#+begin_src matlab :exports none
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figure;
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hold on;
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for i = 1:7
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plot(pd200dac{i}.f, sqrt(pd200dac{i}.pxx), 'DisplayName', sprintf('PD200DAC-%i', i));
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end
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plot(preamp.f, sqrt(preamp.pxx), 'k-', 'DisplayName', 'Pre Amp');
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plot(dac.f, 20*sqrt(dac.pxx), 'k-', 'DisplayName', 'ADC noise');
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plot(dac.f, ones(size(dac.f))*(10/2^16)/sqrt(12*Fs)/pd200dac{1}.notes.pre_amp.gain, 'k--', 'DisplayName', 'ADC quant.');
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hold off;
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set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
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xlabel('Frequency [Hz]'); ylabel('ASD [$V/\sqrt{Hz}$]');
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legend('location', 'southwest');
|
||||
xlim([1, Fs/2]);
|
||||
% ylim([5e-7, 1e-3]);
|
||||
#+end_src
|
||||
|
||||
#+begin_src matlab :tangle no :exports results :results file replace
|
||||
exportFig('figs/asd_noise_3uF_dac.pdf', 'width', 'wide', 'height', 'tall');
|
||||
#+end_src
|
||||
|
||||
#+name: fig:asd_noise_3uF_dac
|
||||
#+caption: Amplitude Spectral Density of the measured noise
|
||||
#+RESULTS:
|
||||
[[file:figs/asd_noise_3uF_dac.png]]
|
||||
|
||||
#+begin_src matlab :exports none
|
||||
figure;
|
||||
hold on;
|
||||
plot(pd200dac{1}.f, sqrt(pd200dac{1}.pxx), 'DisplayName', 'PD200 + DAC');
|
||||
plot(pd200w{1}.f, sqrt(pd200w{1}.pxx), 'DisplayName', 'PD200');
|
||||
plot(dac.f, 20*sqrt(dac.pxx), 'k-', 'DisplayName', 'DAC');
|
||||
plot(preamp.f, sqrt(preamp.pxx), 'k-', 'DisplayName', 'Pre Amp');
|
||||
plot(dac.f, ones(size(dac.f))*(10/2^16)/sqrt(12*Fs)/pd200dac{1}.notes.pre_amp.gain, 'k--', 'DisplayName', 'ADC quant.');
|
||||
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]);
|
||||
% ylim([5e-7, 1e-3]);
|
||||
#+end_src
|
||||
|
||||
#+begin_important
|
||||
The output noise of the PD200 amplifier is limited by the noise of the DAC.
|
||||
#+end_important
|
||||
|
||||
*** TODO Noise with SSI2V at the input of the PD200
|
||||
|
||||
* Transfer Function measurement
|
||||
** 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 [[fig:setup-dynamics-measurement]] is used.
|
||||
@ -327,7 +738,98 @@ For this measurement, the sampling frequency of the Speedgoat ADC should be as h
|
||||
#+caption: Schematic of the test bench to estimate the dynamics from voltage input $V_{in}$ to voltage output $V_{out}$
|
||||
[[file:figs/setup-dynamics-measurement.png]]
|
||||
|
||||
** Maximum Frequency/Voltage to not overload the amplifier
|
||||
|
||||
The maximum current is 1A [rms] which corresponds to 0.7A in amplitude of the sin wave.
|
||||
|
||||
The impedance of the capacitance is:
|
||||
\[ Z_C(\omega) = \frac{1}{jC\omega} \]
|
||||
|
||||
Therefore the relation between the output current and the output voltage is (in amplitude):
|
||||
\[ V_{out} = \frac{1}{C\omega} I_{out} \]
|
||||
|
||||
There is a gain of 20 between the input voltage and the output voltage:
|
||||
\[ 20 V_{in} = \frac{1}{C\omega} I_{out} \]
|
||||
|
||||
For a specified voltage input amplitude $V_{in}$, the maximum frequency is then:
|
||||
\[ \omega_{\text{max}} = \frac{1}{20 C V_{in}} I_{out,\text{max}} \]
|
||||
|
||||
#+begin_src matlab
|
||||
Iout_max = 0.7; % Maximum output current [A]
|
||||
C = 3e-6; % Load Capacitance [F]
|
||||
|
||||
V_in = linspace(0, 5, 100); % Input Voltage [V]
|
||||
|
||||
w_max = 1./(20*C*V_in) * Iout_max; % [rad/s]
|
||||
|
||||
figure;
|
||||
plot(V_in, w_max/2/pi);
|
||||
xlabel('Input Voltage Amplitude [V]');
|
||||
ylabel('Maximum Frequency [Hz]');
|
||||
set(gca, 'yscale', 'log');
|
||||
#+end_src
|
||||
|
||||
** 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)
|
||||
<<matlab-dir>>
|
||||
#+end_src
|
||||
|
||||
#+begin_src matlab :exports none :results silent :noweb yes
|
||||
<<matlab-init>>
|
||||
#+end_src
|
||||
|
||||
#+begin_src matlab :tangle no
|
||||
addpath('./matlab/mat/');
|
||||
addpath('./matlab/');
|
||||
#+end_src
|
||||
|
||||
#+begin_src matlab :eval no
|
||||
addpath('./mat/');
|
||||
#+end_src
|
||||
|
||||
*** First test
|
||||
#+begin_src matlab
|
||||
pd200_1V_1 = load('mat/tf_pd200_7_1V.mat', 't', 'Vin', 'Vout', 'Iout');
|
||||
#+end_src
|
||||
|
||||
#+begin_src matlab
|
||||
Ts = (pd200_1V_1.t(end) - pd200_1V_1.t(1))/(length(pd200_1V_1.t)-1);
|
||||
Fs = 1/Ts;
|
||||
#+end_src
|
||||
|
||||
#+begin_src matlab
|
||||
win = hanning(ceil(1*Fs));
|
||||
|
||||
[tf_1, f] = tfestimate(pd200_1V_1.Vin, pd200_1V_1.Vout, win, [], [], 1/Ts);
|
||||
#+end_src
|
||||
|
||||
#+begin_src matlab :exports none
|
||||
figure;
|
||||
tiledlayout(3, 1, 'TileSpacing', 'None', 'Padding', 'None');
|
||||
|
||||
ax1 = nexttile([2,1]);
|
||||
hold on;
|
||||
plot(f, abs(tf_1));
|
||||
hold off;
|
||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
||||
ylabel('Amplitude $V_{out}/V_{in}$ [V/V]'); set(gca, 'XTickLabel',[]);
|
||||
hold off;
|
||||
ylim([1e-1, 1e1]);
|
||||
|
||||
ax2 = nexttile;
|
||||
hold on;
|
||||
plot(f, 180/pi*angle(tf_1));
|
||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin');
|
||||
yticks(-360:15:360);
|
||||
xlabel('Frequency [Hz]'); ylabel('Phase [deg]');
|
||||
hold off;
|
||||
ylim([-45, 15]);
|
||||
|
||||
linkaxes([ax1,ax2],'x');
|
||||
xlim([1, 2e3]);
|
||||
#+end_src
|
||||
|
||||
* Conclusion
|
||||
|
||||
#+name: tab:table_name
|
||||
|
||||
Loading…
Reference in New Issue
Block a user