Thomas Dehaeze
6e3677eb29
Folder name is changed, rework the html templates Change the organisation.
511 lines
16 KiB
Org Mode
511 lines
16 KiB
Org Mode
#+TITLE: Measurements on the instrumentation
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#+SETUPFILE: ../config.org
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* Measure of the noise of the Voltage Amplifier
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:PROPERTIES:
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:header-args:matlab+: :tangle matlab/meas_volt_amp.m
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:header-args:matlab+: :comments org :mkdirp yes
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:END:
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<<sec:meas_volt_amp>>
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#+begin_src bash :exports none :results none
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if [ meas_volt_amp.m -nt data/meas_volt_amp.zip ]; then
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zip data/meas_volt_amp \
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mat/data_003.mat \
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mat/data_004.mat \
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mat/data_005.mat \
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mat/data_006.mat \
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meas_volt_amp.m
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fi
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#+end_src
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#+begin_note
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All the files (data and Matlab scripts) are accessible [[file:data/meas_volt_amp.zip][here]].
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#+end_note
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** Measurement Description
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*Goal*:
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- Determine the Voltage Amplifier noise
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*Setup*:
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- The two inputs (differential) of the voltage amplifier are shunted with 50Ohms
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- The AC/DC option of the Voltage amplifier is on AC
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- The low pass filter is set to 1hHz
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- We measure the output of the voltage amplifier with a 16bits ADC of the Speedgoat
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*Measurements*:
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- =data_003=: Ampli OFF
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- =data_004=: Ampli ON set to 20dB
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- =data_005=: Ampli ON set to 40dB
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- =data_006=: Ampli ON set to 60dB
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** Matlab Init :noexport:ignore:
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#+begin_src matlab :tangle no :exports none :results silent :noweb yes :var current_dir=(file-name-directory buffer-file-name)
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<<matlab-dir>>
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#+end_src
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#+begin_src matlab :exports none :results silent :noweb yes
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<<matlab-init>>
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#+end_src
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** Load data
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#+begin_src matlab :results none
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amp_off = load('mat/data_003.mat', 'data'); amp_off = amp_off.data(:, [1,3]);
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amp_20d = load('mat/data_004.mat', 'data'); amp_20d = amp_20d.data(:, [1,3]);
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amp_40d = load('mat/data_005.mat', 'data'); amp_40d = amp_40d.data(:, [1,3]);
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amp_60d = load('mat/data_006.mat', 'data'); amp_60d = amp_60d.data(:, [1,3]);
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#+end_src
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** Time Domain
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The time domain signals are shown on figure [[fig:ampli_noise_time]].
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#+begin_src matlab :results none :exports none
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figure;
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hold on;
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plot(amp_off(:, 2), amp_off(:, 1), 'DisplayName', 'OFF');
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plot(amp_20d(:, 2), amp_20d(:, 1), 'DisplayName', '20dB');
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plot(amp_40d(:, 2), amp_40d(:, 1), 'DisplayName', '40dB');
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plot(amp_60d(:, 2), amp_60d(:, 1), 'DisplayName', '60dB');
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hold off;
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legend('Location', 'northeast');
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xlabel('Time [s]');
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ylabel('Voltage [V]');
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#+end_src
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#+NAME: fig:ampli_noise_time
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#+HEADER: :tangle no :exports results :results value raw replace :noweb yes
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#+begin_src matlab :var filepath="figs/ampli_noise_time.pdf" :var figsize="wide-normal" :post pdf2svg(file=*this*, ext="png")
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<<plt-matlab>>
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#+end_src
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#+NAME: fig:ampli_noise_time
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#+CAPTION: Output of the amplifier
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#+RESULTS: fig:ampli_noise_time
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[[file:figs/ampli_noise_time.png]]
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** Frequency Domain
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We first compute some parameters that will be used for the PSD computation.
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#+begin_src matlab :results none
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dt = amp_off(2, 2)-amp_off(1, 2);
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Fs = 1/dt; % [Hz]
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win = hanning(ceil(10*Fs));
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#+end_src
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Then we compute the Power Spectral Density using =pwelch= function.
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#+begin_src matlab :results none
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[pxoff, f] = pwelch(amp_off(:,1), win, [], [], Fs);
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[px20d, ~] = pwelch(amp_20d(:,1), win, [], [], Fs);
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[px40d, ~] = pwelch(amp_40d(:,1), win, [], [], Fs);
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[px60d, ~] = pwelch(amp_60d(:,1), win, [], [], Fs);
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#+end_src
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We compute the theoretical ADC noise.
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#+begin_src matlab :results none
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q = 20/2^16; % quantization
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Sq = q^2/12/1000; % PSD of the ADC noise
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#+end_src
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Finally, the ASD is shown on figure [[fig:ampli_noise_psd]].
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#+begin_src matlab :results none :exports none
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figure;
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hold on;
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plot(f, sqrt(pxoff), 'DisplayName', 'OFF');
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plot(f, sqrt(px20d), 'DisplayName', '20dB');
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plot(f, sqrt(px40d), 'DisplayName', '40dB');
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plot(f, sqrt(px60d), 'DisplayName', '60dB');
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plot([0.1, 500], [sqrt(Sq), sqrt(Sq)], 'k--');
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hold off;
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set(gca, 'xscale', 'log');
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set(gca, 'yscale', 'log');
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xlabel('Frequency [Hz]'); ylabel('ASD of the measured Voltage $\left[\frac{V}{\sqrt{Hz}}\right]$')
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legend('Location', 'northeast');
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xlim([0.1, 500]);
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#+end_src
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#+NAME: fig:ampli_noise_psd
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#+HEADER: :tangle no :exports results :results value raw replace :noweb yes
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#+begin_src matlab :var filepath="figs/ampli_noise_psd.pdf" :var figsize="full-tall" :post pdf2svg(file=*this*, ext="png")
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<<plt-matlab>>
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#+end_src
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#+NAME: fig:ampli_noise_psd
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#+CAPTION: Amplitude Spectral Density of the measured voltage at the output of the voltage amplifier
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#+RESULTS: fig:ampli_noise_psd
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[[file:figs/ampli_noise_psd.png]]
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** Conclusion
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#+begin_important
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*Questions*:
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- Where does those sharp peaks comes from? Can this be due to aliasing?
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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.
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#+end_important
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* Measure of the influence of the AC/DC option on the voltage amplifiers
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:PROPERTIES:
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:header-args:matlab+: :tangle matlab/meas_noise_ac_dc.m
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:header-args:matlab+: :comments org :mkdirp yes
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:END:
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<<sec:meas_noise_ac_dc>>
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#+begin_src bash :exports none :results none
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if [ meas_noise_ac_dc.m -nt data/meas_noise_ac_dc.zip ]; then
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zip data/meas_noise_ac_dc \
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mat/data_012.mat \
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mat/data_013.mat \
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meas_noise_ac_dc.m
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fi
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#+end_src
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#+begin_note
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All the files (data and Matlab scripts) are accessible [[file:data/meas_noise_ac_dc.zip][here]].
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#+end_note
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** Measurement Description
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*Goal*:
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- Measure the influence of the high-pass filter option of the voltage amplifiers
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*Setup*:
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- One geophone is located on the marble.
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- It's signal goes to two voltage amplifiers with a gain of 60dB.
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- One voltage amplifier is on the AC option, the other is on the DC option.
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*Measurements*:
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First measurement (=mat/data_014.mat= file):
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| Column | Signal |
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|--------+----------------------------|
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| 1 | Amplifier 1 with AC option |
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| 2 | Amplifier 2 with DC option |
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| 3 | Time |
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Second measurement (=mat/data_015.mat= file):
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| Column | Signal |
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|--------+----------------------------|
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| 1 | Amplifier 1 with DC option |
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| 2 | Amplifier 2 with AC option |
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| 3 | Time |
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#+name: fig:volt_amp_setup
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#+caption: Picture of the two voltages amplifiers
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#+attr_html: :width 500px
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[[file:./img/IMG_20190503_170936.jpg]]
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** Matlab Init :noexport:ignore:
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#+begin_src matlab :tangle no :exports none :results silent :noweb yes :var current_dir=(file-name-directory buffer-file-name)
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<<matlab-dir>>
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#+end_src
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#+begin_src matlab :exports none :results silent :noweb yes
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<<matlab-init>>
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#+end_src
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** Load data
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We load the data of the z axis of two geophones.
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#+begin_src matlab :results none
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meas14 = load('mat/data_014.mat', 'data'); meas14 = meas14.data;
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meas15 = load('mat/data_015.mat', 'data'); meas15 = meas15.data;
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#+end_src
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** Time Domain
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The signals are shown on figure [[fig:ac_dc_option_time]].
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#+begin_src matlab :results none :exports none
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figure;
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hold on;
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plot(meas14(:, 3), meas14(:, 1), 'DisplayName', 'Amp1 - AC');
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plot(meas14(:, 3), meas14(:, 2), 'DisplayName', 'Amp2 - DC');
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plot(meas15(:, 3), meas15(:, 1), 'DisplayName', 'Amp1 - DC');
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plot(meas15(:, 3), meas15(:, 2), 'DisplayName', 'Amp2 - AC');
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hold off;
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legend('Location', 'bestoutside');
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xlabel('Time [s]');
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ylabel('Voltage [V]');
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xlim([0, 100]);
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#+end_src
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#+NAME: fig:ac_dc_option_time
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#+HEADER: :tangle no :exports results :results value raw replace :noweb yes
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#+begin_src matlab :var filepath="figs/ac_dc_option_time.pdf" :var figsize="full-normal" :post pdf2svg(file=*this*, ext="png")
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<<plt-matlab>>
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#+end_src
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#+NAME: fig:ac_dc_option_time
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#+CAPTION: Comparison of the signals going through the Voltage amplifiers
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#+RESULTS: fig:ac_dc_option_time
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[[file:figs/ac_dc_option_time.png]]
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** Frequency Domain
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We first compute some parameters that will be used for the PSD computation.
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#+begin_src matlab :results none
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dt = meas14(2, 3)-meas14(1, 3);
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Fs = 1/dt; % [Hz]
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win = hanning(ceil(10*Fs));
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#+end_src
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Then we compute the Power Spectral Density using =pwelch= function.
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#+begin_src matlab :results none
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[pxamp1ac, f] = pwelch(meas14(:, 1), win, [], [], Fs);
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[pxamp2dc, ~] = pwelch(meas14(:, 2), win, [], [], Fs);
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[pxamp1dc, ~] = pwelch(meas15(:, 1), win, [], [], Fs);
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[pxamp2ac, ~] = pwelch(meas15(:, 2), win, [], [], Fs);
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#+end_src
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The ASD of the signals are compare on figure [[fig:ac_dc_option_asd]].
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#+begin_src matlab :results none :exports none
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figure;
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hold on;
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plot(f, sqrt(pxamp1ac), 'DisplayName', 'Amp1 - AC');
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plot(f, sqrt(pxamp2dc), 'DisplayName', 'Amp2 - DC');
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plot(f, sqrt(pxamp1dc), 'DisplayName', 'Amp1 - DC');
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plot(f, sqrt(pxamp2ac), 'DisplayName', 'Amp2 - AC');
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hold off;
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set(gca, 'xscale', 'log');
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set(gca, 'yscale', 'log');
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xlabel('Frequency [Hz]'); ylabel('ASD of the measured Voltage $\left[\frac{V}{\sqrt{Hz}}\right]$')
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legend('Location', 'northeast');
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xlim([0.1, 500]);
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#+end_src
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#+NAME: fig:ac_dc_option_asd
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#+HEADER: :tangle no :exports results :results value raw replace :noweb yes
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#+begin_src matlab :var filepath="figs/ac_dc_option_asd.pdf" :var figsize="full-tall" :post pdf2svg(file=*this*, ext="png")
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<<plt-matlab>>
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#+end_src
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#+NAME: fig:ac_dc_option_asd
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#+CAPTION: Amplitude Spectral Density of the measured signals
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#+RESULTS: fig:ac_dc_option_asd
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[[file:figs/ac_dc_option_asd.png]]
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** Conclusion
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#+begin_important
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- The voltage amplifiers include some very sharp high pass filters at 1.5Hz (maybe 4th order)
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- There is a DC offset on the time domain signal because the DC-offset knob was not set to zero
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#+end_important
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* Transfer function of the Low Pass Filter
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:PROPERTIES:
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:header-args:matlab+: :tangle matlab/low_pass_filter_measurements.m
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:header-args:matlab+: :comments org :mkdirp yes
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:END:
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<<sec:low_pass_filter_measurements>>
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#+begin_src bash :exports none :results none
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if [ low_pass_filter_measurements.m -nt data/low_pass_filter_measurements.zip ]; then
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zip data/low_pass_filter_measurements \
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mat/data_018.mat \
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mat/data_019.mat \
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low_pass_filter_measurements.m
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fi
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#+end_src
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The computation files for this section are accessible [[file:data/low_pass_filter_measurements.zip][here]].
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** First LPF with a Cut-off frequency of 160Hz
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*** Measurement Description
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*Goal*:
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- Measure the Low Pass Filter Transfer Function
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The values of the components are:
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\begin{aligned}
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R &= 1k\Omega \\
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C &= 1\mu F
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\end{aligned}
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Which makes a cut-off frequency of $f_c = \frac{1}{RC} = 1000 rad/s = 160Hz$.
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#+NAME: fig:lpf
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#+HEADER: :headers '("\\usepackage{tikz}" "\\usepackage{import}" "\\import{$HOME/MEGA/These/LaTeX/}{config.tex}")
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#+HEADER: :imagemagick t :fit yes :iminoptions -scale 100% -density 150 :imoutoptions -quality 100
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#+HEADER: :results raw replace :buffer no :eval no-export :exports both :mkdirp yes
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#+HEADER: :output-dir figs
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#+begin_src latex :file lpf.pdf :post pdf2svg(file=*this*, ext="png") :exports both
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\begin{tikzpicture}
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\draw (0,2)
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to [R=\(R\)] ++(2,0) node[circ]
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to ++(2,0)
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++(-2,0)
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to [C=\(C\)] ++(0,-2) node[circ]
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++(-2,0)
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to ++(2,0)
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to ++(2,0)
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\end{tikzpicture}
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#+end_src
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#+NAME: fig:lpf
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#+CAPTION: Schematic of the Low Pass Filter used
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#+RESULTS: fig:lpf
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[[file:figs/lpf.png]]
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*Setup*:
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- We are measuring the signal from from Geophone with a BNC T
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- On part goes to column 1 through the LPF
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- The other part goes to column 2 without the LPF
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*Measurements*:
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=mat/data_018.mat=:
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| Column | Signal |
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|--------+----------------------|
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| 1 | Amplifier 1 with LPF |
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| 2 | Amplifier 2 |
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| 3 | Time |
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#+name: fig:lpf_picture
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#+caption: Picture of the low pass filter used
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#+attr_html: :width 500px
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[[file:./img/IMG_20190507_102756.jpg]]
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*** Matlab Init :noexport:ignore:
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#+begin_src matlab :tangle no :exports none :results silent :noweb yes :var current_dir=(file-name-directory buffer-file-name)
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<<matlab-dir>>
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#+end_src
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#+begin_src matlab :exports none :results silent :noweb yes
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<<matlab-init>>
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#+end_src
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*** Load data
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We load the data of the z axis of two geophones.
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#+begin_src matlab :results none
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data = load('mat/data_018.mat', 'data'); data = data.data;
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#+end_src
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*** Transfer function of the LPF
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We compute the transfer function from the signal without the LPF to the signal measured with the LPF.
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#+begin_src matlab :results none
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dt = data(2, 3)-data(1, 3);
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Fs = 1/dt; % [Hz]
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win = hanning(ceil(10*Fs));
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#+end_src
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#+begin_src matlab :results none
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[Glpf, f] = tfestimate(data(:, 2), data(:, 1), win, [], [], Fs);
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#+end_src
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We compare this transfer function with a transfer function corresponding to an ideal first order LPF with a cut-off frequency of $1000rad/s$.
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We obtain the result on figure [[fig:Glpf_bode]].
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#+begin_src matlab :results none
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Gth = 1/(1+s/1000)
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#+end_src
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#+begin_src matlab :results none
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figure;
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ax1 = subplot(2, 1, 1);
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hold on;
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plot(f, abs(Glpf));
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plot(f, abs(squeeze(freqresp(Gth, f, 'Hz'))));
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hold off;
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set(gca, 'xscale', 'log'); set(gca, 'yscale', 'log');
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set(gca, 'XTickLabel',[]);
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ylabel('Magnitude');
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ax2 = subplot(2, 1, 2);
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hold on;
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plot(f, mod(180+180/pi*phase(Glpf), 360)-180);
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plot(f, 180/pi*unwrap(angle(squeeze(freqresp(Gth, f, 'Hz')))));
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hold off;
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set(gca, 'xscale', 'log');
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ylim([-180, 180]);
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yticks([-180, -90, 0, 90, 180]);
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xlabel('Frequency [Hz]'); ylabel('Phase');
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linkaxes([ax1,ax2],'x');
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xlim([1, 500]);
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#+end_src
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#+NAME: fig:Glpf_bode
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#+HEADER: :tangle no :exports results :results value raw replace :noweb yes
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#+begin_src matlab :var filepath="figs/Glpf_bode.pdf" :var figsize="full-tall" :post pdf2svg(file=*this*, ext="png")
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<<plt-matlab>>
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#+end_src
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#+NAME: fig:Glpf_bode
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#+CAPTION: Bode Diagram of the measured Low Pass filter and the theoritical one
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#+RESULTS: fig:Glpf_bode
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[[file:figs/Glpf_bode.png]]
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*** Conclusion
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#+begin_important
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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 $1kHz$.
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#+end_important
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** Second LPF with a Cut-off frequency of 1000Hz
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*** Measurement description
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This time, the value are
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\begin{aligned}
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R &= 1k\Omega \\
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C &= 150nF
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\end{aligned}
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Which makes a low pass filter with a cut-off frequency of $f_c = 1060Hz$.
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*** Load data
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We load the data of the z axis of two geophones.
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#+begin_src matlab :results none
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data = load('mat/data_019.mat', 'data'); data = data.data;
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#+end_src
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*** Transfer function of the LPF
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We compute the transfer function from the signal without the LPF to the signal measured with the LPF.
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#+begin_src matlab :results none
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dt = data(2, 3)-data(1, 3);
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Fs = 1/dt; % [Hz]
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win = hanning(ceil(10*Fs));
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#+end_src
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#+begin_src matlab :results none
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[Glpf, f] = tfestimate(data(:, 2), data(:, 1), win, [], [], Fs);
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#+end_src
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We compare this transfer function with a transfer function corresponding to an ideal first order LPF with a cut-off frequency of $1060Hz$.
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We obtain the result on figure [[fig:Glpf_bode_bis]].
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#+begin_src matlab :results none
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Gth = 1/(1+s/1060/2/pi);
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#+end_src
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#+begin_src matlab :results none
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figure;
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ax1 = subplot(2, 1, 1);
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hold on;
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plot(f, abs(Glpf));
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plot(f, abs(squeeze(freqresp(Gth, f, 'Hz'))));
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hold off;
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set(gca, 'xscale', 'log'); set(gca, 'yscale', 'log');
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set(gca, 'XTickLabel',[]);
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ylabel('Magnitude');
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ax2 = subplot(2, 1, 2);
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|
hold on;
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|
plot(f, mod(180+180/pi*phase(Glpf), 360)-180);
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plot(f, 180/pi*unwrap(angle(squeeze(freqresp(Gth, f, 'Hz')))));
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|
hold off;
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|
set(gca, 'xscale', 'log');
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|
ylim([-180, 180]);
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|
yticks([-180, -90, 0, 90, 180]);
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|
xlabel('Frequency [Hz]'); ylabel('Phase');
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|
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|
linkaxes([ax1,ax2],'x');
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|
xlim([1, 500]);
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|
#+end_src
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|
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|
#+NAME: fig:Glpf_bode_bis
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|
#+HEADER: :tangle no :exports results :results value raw replace :noweb yes
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|
#+begin_src matlab :var filepath="figs/Glpf_bode_bis.pdf" :var figsize="full-tall" :post pdf2svg(file=*this*, ext="png")
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|
<<plt-matlab>>
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|
#+end_src
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|
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|
#+NAME: fig:Glpf_bode_bis
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|
#+CAPTION: Bode Diagram of the measured Low Pass filter and the theoritical one
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|
#+RESULTS: fig:Glpf_bode_bis
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|
[[file:figs/Glpf_bode_bis.png]]
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|
*** Conclusion
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|
#+begin_important
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|
The added LPF has the expected behavior.
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|
#+end_important
|