#+TITLE: Measurements on the instrumentation #+SETUPFILE: ../config.org * Measure of the noise of the Voltage Amplifier :PROPERTIES: :header-args:matlab+: :tangle matlab/meas_volt_amp.m :header-args:matlab+: :comments org :mkdirp yes :END: <> #+begin_src bash :exports none :results none if [ meas_volt_amp.m -nt data/meas_volt_amp.zip ]; then zip data/meas_volt_amp \ mat/data_003.mat \ mat/data_004.mat \ mat/data_005.mat \ mat/data_006.mat \ meas_volt_amp.m fi #+end_src #+begin_note All the files (data and Matlab scripts) are accessible [[file:data/meas_volt_amp.zip][here]]. #+end_note ** Measurement Description *Goal*: - Determine the Voltage Amplifier noise *Setup*: - The two inputs (differential) of the voltage amplifier are shunted with 50Ohms - The AC/DC option of the Voltage amplifier is on AC - The low pass filter is set to 1hHz - We measure the output of the voltage amplifier with a 16bits ADC of the Speedgoat *Measurements*: - =data_003=: Ampli OFF - =data_004=: Ampli ON set to 20dB - =data_005=: Ampli ON set to 40dB - =data_006=: Ampli ON set to 60dB ** 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 ** Load data #+begin_src matlab :results none amp_off = load('mat/data_003.mat', 'data'); amp_off = amp_off.data(:, [1,3]); amp_20d = load('mat/data_004.mat', 'data'); amp_20d = amp_20d.data(:, [1,3]); amp_40d = load('mat/data_005.mat', 'data'); amp_40d = amp_40d.data(:, [1,3]); amp_60d = load('mat/data_006.mat', 'data'); amp_60d = amp_60d.data(:, [1,3]); #+end_src ** Time Domain The time domain signals are shown on figure [[fig:ampli_noise_time]]. #+begin_src matlab :results none :exports none figure; hold on; plot(amp_off(:, 2), amp_off(:, 1), 'DisplayName', 'OFF'); plot(amp_20d(:, 2), amp_20d(:, 1), 'DisplayName', '20dB'); plot(amp_40d(:, 2), amp_40d(:, 1), 'DisplayName', '40dB'); plot(amp_60d(:, 2), amp_60d(:, 1), 'DisplayName', '60dB'); hold off; legend('Location', 'northeast'); xlabel('Time [s]'); ylabel('Voltage [V]'); #+end_src #+NAME: fig:ampli_noise_time #+HEADER: :tangle no :exports results :results value raw replace :noweb yes #+begin_src matlab :var filepath="figs/ampli_noise_time.pdf" :var figsize="wide-normal" :post pdf2svg(file=*this*, ext="png") <> #+end_src #+NAME: fig:ampli_noise_time #+CAPTION: Output of the amplifier #+RESULTS: fig:ampli_noise_time [[file:figs/ampli_noise_time.png]] ** Frequency Domain We first compute some parameters that will be used for the PSD computation. #+begin_src matlab :results none dt = amp_off(2, 2)-amp_off(1, 2); Fs = 1/dt; % [Hz] win = hanning(ceil(10*Fs)); #+end_src Then we compute the Power Spectral Density using =pwelch= function. #+begin_src matlab :results none [pxoff, f] = pwelch(amp_off(:,1), win, [], [], Fs); [px20d, ~] = pwelch(amp_20d(:,1), win, [], [], Fs); [px40d, ~] = pwelch(amp_40d(:,1), win, [], [], Fs); [px60d, ~] = pwelch(amp_60d(:,1), win, [], [], Fs); #+end_src We compute the theoretical ADC noise. #+begin_src matlab :results none q = 20/2^16; % quantization Sq = q^2/12/1000; % PSD of the ADC noise #+end_src Finally, the ASD is shown on figure [[fig:ampli_noise_psd]]. #+begin_src matlab :results none :exports none figure; hold on; plot(f, sqrt(pxoff), 'DisplayName', 'OFF'); plot(f, sqrt(px20d), 'DisplayName', '20dB'); plot(f, sqrt(px40d), 'DisplayName', '40dB'); plot(f, sqrt(px60d), 'DisplayName', '60dB'); plot([0.1, 500], [sqrt(Sq), sqrt(Sq)], 'k--'); hold off; set(gca, 'xscale', 'log'); set(gca, 'yscale', 'log'); xlabel('Frequency [Hz]'); ylabel('ASD of the measured Voltage $\left[\frac{V}{\sqrt{Hz}}\right]$') legend('Location', 'northeast'); xlim([0.1, 500]); #+end_src #+NAME: fig:ampli_noise_psd #+HEADER: :tangle no :exports results :results value raw replace :noweb yes #+begin_src matlab :var filepath="figs/ampli_noise_psd.pdf" :var figsize="full-tall" :post pdf2svg(file=*this*, ext="png") <> #+end_src #+NAME: fig:ampli_noise_psd #+CAPTION: Amplitude Spectral Density of the measured voltage at the output of the voltage amplifier #+RESULTS: fig:ampli_noise_psd [[file:figs/ampli_noise_psd.png]] ** Conclusion #+begin_important *Questions*: - Where does those sharp peaks comes from? Can this be due to aliasing? Noise induced by the voltage amplifiers seems not to be a limiting factor as we have the same noise when they are OFF and ON. #+end_important * Measure of the influence of the AC/DC option on the voltage amplifiers :PROPERTIES: :header-args:matlab+: :tangle matlab/meas_noise_ac_dc.m :header-args:matlab+: :comments org :mkdirp yes :END: <> #+begin_src bash :exports none :results none if [ meas_noise_ac_dc.m -nt data/meas_noise_ac_dc.zip ]; then zip data/meas_noise_ac_dc \ mat/data_012.mat \ mat/data_013.mat \ meas_noise_ac_dc.m fi #+end_src #+begin_note All the files (data and Matlab scripts) are accessible [[file:data/meas_noise_ac_dc.zip][here]]. #+end_note ** Measurement Description *Goal*: - Measure the influence of the high-pass filter option of the voltage amplifiers *Setup*: - One geophone is located on the marble. - It's signal goes to two voltage amplifiers with a gain of 60dB. - One voltage amplifier is on the AC option, the other is on the DC option. *Measurements*: First measurement (=mat/data_014.mat= file): | Column | Signal | |--------+----------------------------| | 1 | Amplifier 1 with AC option | | 2 | Amplifier 2 with DC option | | 3 | Time | Second measurement (=mat/data_015.mat= file): | Column | Signal | |--------+----------------------------| | 1 | Amplifier 1 with DC option | | 2 | Amplifier 2 with AC option | | 3 | Time | #+name: fig:volt_amp_setup #+caption: Picture of the two voltages amplifiers #+attr_html: :width 500px [[file:./img/IMG_20190503_170936.jpg]] ** 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 ** Load data We load the data of the z axis of two geophones. #+begin_src matlab :results none meas14 = load('mat/data_014.mat', 'data'); meas14 = meas14.data; meas15 = load('mat/data_015.mat', 'data'); meas15 = meas15.data; #+end_src ** Time Domain The signals are shown on figure [[fig:ac_dc_option_time]]. #+begin_src matlab :results none :exports none figure; hold on; plot(meas14(:, 3), meas14(:, 1), 'DisplayName', 'Amp1 - AC'); plot(meas14(:, 3), meas14(:, 2), 'DisplayName', 'Amp2 - DC'); plot(meas15(:, 3), meas15(:, 1), 'DisplayName', 'Amp1 - DC'); plot(meas15(:, 3), meas15(:, 2), 'DisplayName', 'Amp2 - AC'); hold off; legend('Location', 'bestoutside'); xlabel('Time [s]'); ylabel('Voltage [V]'); xlim([0, 100]); #+end_src #+NAME: fig:ac_dc_option_time #+HEADER: :tangle no :exports results :results value raw replace :noweb yes #+begin_src matlab :var filepath="figs/ac_dc_option_time.pdf" :var figsize="full-normal" :post pdf2svg(file=*this*, ext="png") <> #+end_src #+NAME: fig:ac_dc_option_time #+CAPTION: Comparison of the signals going through the Voltage amplifiers #+RESULTS: fig:ac_dc_option_time [[file:figs/ac_dc_option_time.png]] ** Frequency Domain We first compute some parameters that will be used for the PSD computation. #+begin_src matlab :results none dt = meas14(2, 3)-meas14(1, 3); Fs = 1/dt; % [Hz] win = hanning(ceil(10*Fs)); #+end_src Then we compute the Power Spectral Density using =pwelch= function. #+begin_src matlab :results none [pxamp1ac, f] = pwelch(meas14(:, 1), win, [], [], Fs); [pxamp2dc, ~] = pwelch(meas14(:, 2), win, [], [], Fs); [pxamp1dc, ~] = pwelch(meas15(:, 1), win, [], [], Fs); [pxamp2ac, ~] = pwelch(meas15(:, 2), win, [], [], Fs); #+end_src The ASD of the signals are compare on figure [[fig:ac_dc_option_asd]]. #+begin_src matlab :results none :exports none figure; hold on; plot(f, sqrt(pxamp1ac), 'DisplayName', 'Amp1 - AC'); plot(f, sqrt(pxamp2dc), 'DisplayName', 'Amp2 - DC'); plot(f, sqrt(pxamp1dc), 'DisplayName', 'Amp1 - DC'); plot(f, sqrt(pxamp2ac), 'DisplayName', 'Amp2 - AC'); hold off; set(gca, 'xscale', 'log'); set(gca, 'yscale', 'log'); xlabel('Frequency [Hz]'); ylabel('ASD of the measured Voltage $\left[\frac{V}{\sqrt{Hz}}\right]$') legend('Location', 'northeast'); xlim([0.1, 500]); #+end_src #+NAME: fig:ac_dc_option_asd #+HEADER: :tangle no :exports results :results value raw replace :noweb yes #+begin_src matlab :var filepath="figs/ac_dc_option_asd.pdf" :var figsize="full-tall" :post pdf2svg(file=*this*, ext="png") <> #+end_src #+NAME: fig:ac_dc_option_asd #+CAPTION: Amplitude Spectral Density of the measured signals #+RESULTS: fig:ac_dc_option_asd [[file:figs/ac_dc_option_asd.png]] ** Conclusion #+begin_important - The voltage amplifiers include some very sharp high pass filters at 1.5Hz (maybe 4th order) - There is a DC offset on the time domain signal because the DC-offset knob was not set to zero #+end_important * Transfer function of the Low Pass Filter :PROPERTIES: :header-args:matlab+: :tangle matlab/low_pass_filter_measurements.m :header-args:matlab+: :comments org :mkdirp yes :END: <> #+begin_src bash :exports none :results none if [ low_pass_filter_measurements.m -nt data/low_pass_filter_measurements.zip ]; then zip data/low_pass_filter_measurements \ mat/data_018.mat \ mat/data_019.mat \ low_pass_filter_measurements.m fi #+end_src The computation files for this section are accessible [[file:data/low_pass_filter_measurements.zip][here]]. ** First LPF with a Cut-off frequency of 160Hz *** Measurement Description *Goal*: - Measure the Low Pass Filter Transfer Function The values of the components are: \begin{aligned} R &= 1k\Omega \\ C &= 1\mu F \end{aligned} Which makes a cut-off frequency of $f_c = \frac{1}{RC} = 1000 rad/s = 160Hz$. #+NAME: fig:lpf #+HEADER: :headers '("\\usepackage{tikz}" "\\usepackage{import}" "\\import{$HOME/MEGA/These/LaTeX/}{config.tex}") #+HEADER: :imagemagick t :fit yes :iminoptions -scale 100% -density 150 :imoutoptions -quality 100 #+HEADER: :results raw replace :buffer no :eval no-export :exports both :mkdirp yes #+HEADER: :output-dir figs #+begin_src latex :file lpf.pdf :post pdf2svg(file=*this*, ext="png") :exports both \begin{tikzpicture} \draw (0,2) to [R=\(R\)] ++(2,0) node[circ] to ++(2,0) ++(-2,0) to [C=\(C\)] ++(0,-2) node[circ] ++(-2,0) to ++(2,0) to ++(2,0) \end{tikzpicture} #+end_src #+NAME: fig:lpf #+CAPTION: Schematic of the Low Pass Filter used #+RESULTS: fig:lpf [[file:figs/lpf.png]] *Setup*: - We are measuring the signal from from Geophone with a BNC T - On part goes to column 1 through the LPF - The other part goes to column 2 without the LPF *Measurements*: =mat/data_018.mat=: | Column | Signal | |--------+----------------------| | 1 | Amplifier 1 with LPF | | 2 | Amplifier 2 | | 3 | Time | #+name: fig:lpf_picture #+caption: Picture of the low pass filter used #+attr_html: :width 500px [[file:./img/IMG_20190507_102756.jpg]] *** 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 *** Load data We load the data of the z axis of two geophones. #+begin_src matlab :results none data = load('mat/data_018.mat', 'data'); data = data.data; #+end_src *** Transfer function of the LPF We compute the transfer function from the signal without the LPF to the signal measured with the LPF. #+begin_src matlab :results none dt = data(2, 3)-data(1, 3); Fs = 1/dt; % [Hz] win = hanning(ceil(10*Fs)); #+end_src #+begin_src matlab :results none [Glpf, f] = tfestimate(data(:, 2), data(:, 1), win, [], [], Fs); #+end_src We compare this transfer function with a transfer function corresponding to an ideal first order LPF with a cut-off frequency of $1000rad/s$. We obtain the result on figure [[fig:Glpf_bode]]. #+begin_src matlab :results none Gth = 1/(1+s/1000) #+end_src #+begin_src matlab :results none figure; ax1 = subplot(2, 1, 1); hold on; plot(f, abs(Glpf)); plot(f, abs(squeeze(freqresp(Gth, f, 'Hz')))); hold off; set(gca, 'xscale', 'log'); set(gca, 'yscale', 'log'); set(gca, 'XTickLabel',[]); ylabel('Magnitude'); ax2 = subplot(2, 1, 2); hold on; plot(f, mod(180+180/pi*phase(Glpf), 360)-180); plot(f, 180/pi*unwrap(angle(squeeze(freqresp(Gth, f, 'Hz'))))); hold off; set(gca, 'xscale', 'log'); ylim([-180, 180]); yticks([-180, -90, 0, 90, 180]); xlabel('Frequency [Hz]'); ylabel('Phase'); linkaxes([ax1,ax2],'x'); xlim([1, 500]); #+end_src #+NAME: fig:Glpf_bode #+HEADER: :tangle no :exports results :results value raw replace :noweb yes #+begin_src matlab :var filepath="figs/Glpf_bode.pdf" :var figsize="full-tall" :post pdf2svg(file=*this*, ext="png") <> #+end_src #+NAME: fig:Glpf_bode #+CAPTION: Bode Diagram of the measured Low Pass filter and the theoritical one #+RESULTS: fig:Glpf_bode [[file:figs/Glpf_bode.png]] *** Conclusion #+begin_important As we want to measure things up to $500Hz$, we chose to change the value of the capacitor to obtain a cut-off frequency of $1kHz$. #+end_important ** Second LPF with a Cut-off frequency of 1000Hz *** Measurement description This time, the value are \begin{aligned} R &= 1k\Omega \\ C &= 150nF \end{aligned} Which makes a low pass filter with a cut-off frequency of $f_c = 1060Hz$. *** Load data We load the data of the z axis of two geophones. #+begin_src matlab :results none data = load('mat/data_019.mat', 'data'); data = data.data; #+end_src *** Transfer function of the LPF We compute the transfer function from the signal without the LPF to the signal measured with the LPF. #+begin_src matlab :results none dt = data(2, 3)-data(1, 3); Fs = 1/dt; % [Hz] win = hanning(ceil(10*Fs)); #+end_src #+begin_src matlab :results none [Glpf, f] = tfestimate(data(:, 2), data(:, 1), win, [], [], Fs); #+end_src We compare this transfer function with a transfer function corresponding to an ideal first order LPF with a cut-off frequency of $1060Hz$. We obtain the result on figure [[fig:Glpf_bode_bis]]. #+begin_src matlab :results none Gth = 1/(1+s/1060/2/pi); #+end_src #+begin_src matlab :results none figure; ax1 = subplot(2, 1, 1); hold on; plot(f, abs(Glpf)); plot(f, abs(squeeze(freqresp(Gth, f, 'Hz')))); hold off; set(gca, 'xscale', 'log'); set(gca, 'yscale', 'log'); set(gca, 'XTickLabel',[]); ylabel('Magnitude'); ax2 = subplot(2, 1, 2); hold on; plot(f, mod(180+180/pi*phase(Glpf), 360)-180); plot(f, 180/pi*unwrap(angle(squeeze(freqresp(Gth, f, 'Hz'))))); hold off; set(gca, 'xscale', 'log'); ylim([-180, 180]); yticks([-180, -90, 0, 90, 180]); xlabel('Frequency [Hz]'); ylabel('Phase'); linkaxes([ax1,ax2],'x'); xlim([1, 500]); #+end_src #+NAME: fig:Glpf_bode_bis #+HEADER: :tangle no :exports results :results value raw replace :noweb yes #+begin_src matlab :var filepath="figs/Glpf_bode_bis.pdf" :var figsize="full-tall" :post pdf2svg(file=*this*, ext="png") <> #+end_src #+NAME: fig:Glpf_bode_bis #+CAPTION: Bode Diagram of the measured Low Pass filter and the theoritical one #+RESULTS: fig:Glpf_bode_bis [[file:figs/Glpf_bode_bis.png]] *** Conclusion #+begin_important The added LPF has the expected behavior. #+end_important