nass-micro-station-measurements/slip-ring-test/index.org

#+TITLE: Measurements
:DRAWER:
#+STARTUP: overview

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#+PROPERTY: header-args:matlab  :session *MATLAB*
#+PROPERTY: header-args:matlab+ :comments org
#+PROPERTY: header-args:matlab+ :results output
#+PROPERTY: header-args:matlab+ :exports both
#+PROPERTY: header-args:matlab+ :eval no-export
#+PROPERTY: header-args:matlab+ :output-dir figs
:END:

* Effect of the rotation of the Slip-Ring
  :PROPERTIES:
  :header-args:matlab+: :tangle meas_effect_sr.m
  :header-args:matlab+: :comments org :mkdirp yes
  :END:

#+begin_src bash :exports none :results none
  zip data/meas_effect_sr \
      mat/data_001.mat \
      mat/data_002.mat \
      meas_effect_sr.m
#+end_src

The data and matlab files are accessible [[file:data/meas_effect_sr.zip][here]].

** Measurement Description
Random Signal is generated by one DAC of the SpeedGoat.

The signal going out of the DAC is split into two:
- one BNC cable is directly connected to one ADC of the SpeedGoat
- one BNC cable goes two times in the Slip-Ring (from bottom to top and then from top to bottom) and then is connected to one ADC of the SpeedGoat

Two measurements are done.
| Data File          | Description           |
|--------------------+-----------------------|
| =mat/data_001.mat= | Slip-ring not turning |
| =mat/data_002.mat= | Slip-ring turning     |

For each measurement, the measured signals are:
| Data File | Description                        |
|-----------+------------------------------------|
| =t=       | Time vector                        |
| =x1=      | Direct signal                      |
| =x2=      | Signal going through the Slip-Ring |

The goal is to determine is the signal is altered when the spindle is rotating.

Here, the rotation speed of the Slip-Ring is set to 1rpm.

** Matlab Init                                              :noexport:ignore:
#+begin_src matlab :exports none :results silent :noweb yes
  <<matlab-init>>
#+end_src

** Load data
We load the data of the z axis of two geophones.
#+begin_src matlab :results none
  sr_off = load('mat/data_001.mat', 't', 'x1', 'x2');
  sr_on  = load('mat/data_002.mat', 't', 'x1', 'x2');
#+end_src

** Analysis
Let's first look at the signal produced by the DAC (figure [[fig:random_signal]]).

#+begin_src matlab :results none
  figure;
  hold on;
  plot(sr_on.t,  sr_on.x1);
  hold off;
  xlabel('Time [s]'); ylabel('Voltage [V]');
  xlim([0 10]);
#+end_src

#+NAME: fig:random_signal
#+HEADER: :tangle no :exports results :results value raw replace :noweb yes
#+begin_src matlab :var filepath="figs/random_signal.pdf" :var figsize="wide-normal" :post pdf2svg(file=*this*, ext="png")
  <<plt-matlab>>
#+end_src

#+NAME: fig:random_signal
#+CAPTION: Random signal produced by the DAC
#+RESULTS: fig:random_signal
[[file:figs/random_signal.png]]

We now look at the difference between the signal directly measured by the ADC and the signal that goes through the slip-ring (figure [[fig:slipring_comp_signals]]).

#+begin_src matlab :results none
  figure;
  hold on;
  plot(sr_on.t,  sr_on.x1  -  sr_on.x2,  'DisplayName', 'Slip-Ring - $\omega = 1rpm$');
  plot(sr_off.t, sr_off.x1 - sr_off.x2,'DisplayName', 'Slip-Ring off');
  hold off;
  xlabel('Time [s]'); ylabel('Voltage [V]');
  xlim([0 10]);
  legend('Location', 'northeast');
#+end_src

#+NAME: fig:slipring_comp_signals
#+HEADER: :tangle no :exports results :results value raw replace :noweb yes
#+begin_src matlab :var filepath="figs/slipring_comp_signals.pdf" :var figsize="wide-normal" :post pdf2svg(file=*this*, ext="png")
  <<plt-matlab>>
#+end_src

#+NAME: fig:slipring_comp_signals
#+CAPTION: Alteration of the signal when the slip-ring is turning
#+RESULTS: fig:slipring_comp_signals
[[file:figs/slipring_comp_signals.png]]

#+begin_src matlab :results none
  dt = sr_on.t(2) - sr_on.t(1);
  Fs = 1/dt; % [Hz]

  win = hanning(ceil(1*Fs));
#+end_src

#+begin_src matlab :results none
  [pxx_on,  f] = pwelch(sr_on.x1  - sr_on.x2,  win, [], [], Fs);
  [pxx_off, ~] = pwelch(sr_off.x1 - sr_off.x2, win, [], [], Fs);
#+end_src

#+begin_src matlab :results none :exports none
  figure;
  hold on;
  plot(f, sqrt(pxx_on), 'DisplayName', 'Slip-Ring - $\omega = 1rpm$');
  plot(f, sqrt(pxx_off),'DisplayName', 'Slip-Ring off');
  hold off;
  set(gca, 'xscale', 'log'); set(gca, 'yscale', 'log');
  xlabel('Frequency [Hz]'); ylabel('PSD $\left[\frac{V}{\sqrt{Hz}}\right]$');
  legend('Location', 'northeast');
  xlim([1, 500]); ylim([1e-5, 1e-3])
#+end_src

#+NAME: fig:psd_noise
#+HEADER: :tangle no :exports results :results value raw replace :noweb yes
#+begin_src matlab :var filepath="figs/psd_noise.pdf" :var figsize="wide-tall" :post pdf2svg(file=*this*, ext="png")
  <<plt-matlab>>
#+end_src

#+NAME: fig:psd_noise
#+CAPTION: ASD of the measured noise
#+RESULTS: fig:psd_noise
[[file:figs/psd_noise.png]]

** Conclusion
#+begin_note
*Remaining questions*:
- Should the measurement be redone using voltage amplifiers?
- Use higher rotation speed and measure for longer periods (to have multiple revolutions) ?
#+end_note
* Measure of the noise of the Voltage Amplifier
  :PROPERTIES:
  :header-args:matlab+: :tangle meas_volt_amp.m
  :header-args:matlab+: :comments org :mkdirp yes
  :END:

#+begin_src bash :exports none :results none
  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
#+end_src

The data and matlab files are accessible [[file:data/meas_volt_amp.zip][here]].

** 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 :exports none :results silent :noweb yes
  <<matlab-init>>
#+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")
  <<plt-matlab>>
#+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")
  <<plt-matlab>>
#+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
  Noise induced by the voltage amplifiers is not a limiting factor.
#+end_important

* Measure of the noise induced by the Slip-Ring
  :PROPERTIES:
  :header-args:matlab+: :tangle meas_slip_ring.m
  :header-args:matlab+: :comments org :mkdirp yes
  :END:

#+begin_src bash :exports none :results none
  zip data/meas_slip_ring \
      mat/data_008.mat \
      mat/data_009.mat \
      mat/data_010.mat \
      mat/data_011.mat \
      meas_slip_ring.m
#+end_src

The data and matlab files are accessible [[file:data/meas_slip_ring.zip][here]].

** Measurement Description
*Goal*:
- Determine the noise induced by the slip-ring

*Setup*:
- 0V is generated by the DAC of the Speedgoat
- Using a T, one part goes directly to the ADC
- The other part goes to the slip-ring 2 times and then to the ADC
- The parameters of the Voltage Amplifier are: 80dB, AC, 1kHz
- Every stage of the station is OFF

First column: Direct measure
Second column: Slip-ring measure


*Measurements*:
- =data_008=: Slip-Ring OFF
- =data_009=: Slip-Ring ON
- =data_010=: Slip-Ring ON and omega=6rpm
- =data_011=: Slip-Ring ON and omega=60rpm

** Matlab Init                                              :noexport:ignore:
#+begin_src matlab :exports none :results silent :noweb yes
  <<matlab-init>>
#+end_src

** Load data
We load the data of the z axis of two geophones.
#+begin_src matlab :results none
  sr_off = load('mat/data_008.mat', 'data'); sr_off = sr_off.data;
  sr_on = load('mat/data_009.mat', 'data'); sr_on  = sr_on.data;
  sr_6r = load('mat/data_010.mat', 'data'); sr_6r  = sr_6r.data;
  sr_60r = load('mat/data_011.mat', 'data'); sr_60r = sr_60r.data;
#+end_src

** Time Domain
We plot the time domain data for the direct measurement (figure [[fig:sr_direct_time]]) and for the signal going through the slip-ring (figure [[fig:sr_slipring_time]]);

#+begin_src matlab :results none :exports none
  figure;
  hold on;
  plot(sr_60r(:, 3), sr_60r(:, 1), 'DisplayName', '60rpm');
  plot(sr_6r(:, 3),  sr_6r(:, 1),  'DisplayName', '6rpm');
  plot(sr_on(:, 3),  sr_on(:, 1),  'DisplayName', 'ON');
  plot(sr_off(:, 3), sr_off(:, 1), 'DisplayName', 'OFF');
  hold off;
  xlabel('Time [s]'); ylabel('Voltage [V]');
  legend('Location', 'northeast');
#+end_src

#+NAME: fig:sr_direct_time
#+HEADER: :tangle no :exports results :results value raw replace :noweb yes
#+begin_src matlab :var filepath="figs/sr_direct_time.pdf" :var figsize="wide-normal" :post pdf2svg(file=*this*, ext="png")
  <<plt-matlab>>
#+end_src

#+NAME: fig:sr_direct_time
#+CAPTION: Direct measurement
#+RESULTS: fig:sr_direct_time
[[file:figs/sr_direct_time.png]]


#+begin_src matlab :results none :exports none
  figure;
  hold on;
  plot(sr_60r(:, 3), sr_60r(:, 2), 'DisplayName', '60rpm');
  plot(sr_6r(:, 3),  sr_6r(:, 2),  'DisplayName', '6rpm');
  plot(sr_on(:, 3),  sr_on(:, 2),  'DisplayName', 'ON');
  plot(sr_off(:, 3), sr_off(:, 2), 'DisplayName', 'OFF');
  hold off;
  xlabel('Time [s]'); ylabel('Voltage [V]');
  legend('Location', 'northeast');
#+end_src

#+NAME: fig:sr_slipring_time
#+HEADER: :tangle no :exports results :results value raw replace :noweb yes
#+begin_src matlab :var filepath="figs/sr_slipring_time.pdf" :var figsize="wide-normal" :post pdf2svg(file=*this*, ext="png")
  <<plt-matlab>>
#+end_src

#+NAME: fig:sr_slipring_time
#+CAPTION: Measurement of the signal going through the Slip-Ring
#+RESULTS: fig:sr_slipring_time
[[file:figs/sr_slipring_time.png]]

** Frequency Domain
We first compute some parameters that will be used for the PSD computation.
#+begin_src matlab :results none
  dt = sr_off(2, 3)-sr_off(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
  [pxdir, f] = pwelch(sr_off(:, 1), win, [], [], Fs);
  [pxoff, ~] = pwelch(sr_off(:, 2), win, [], [], Fs);
  [pxon,  ~] = pwelch(sr_on(:, 2),  win, [], [], Fs);
  [px6r,  ~] = pwelch(sr_6r(:, 2),  win, [], [], Fs);
  [px60r, ~] = pwelch(sr_60r(:, 2), win, [], [], Fs);
#+end_src

And we plot the ASD of the measured signals (figure [[fig:sr_psd_compare]]);

#+begin_src matlab :results none
  figure;
  hold on;
  plot(f, sqrt(pxoff), 'DisplayName', 'OFF');
  plot(f, sqrt(pxon),  'DisplayName', 'ON');
  plot(f, sqrt(px6r),  'DisplayName', '6rpm');
  plot(f, sqrt(px60r), 'DisplayName', '60rpm');
  plot(f, sqrt(pxdir), 'k-', 'DisplayName', 'Direct');
  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:sr_psd_compare
#+HEADER: :tangle no :exports results :results value raw replace :noweb yes
#+begin_src matlab :var filepath="figs/sr_psd_compare.pdf" :var figsize="full-tall" :post pdf2svg(file=*this*, ext="png")
  <<plt-matlab>>
#+end_src

#+NAME: fig:sr_psd_compare
#+CAPTION: Comparison of the ASD of the measured signals when the slip-ring is ON, OFF and turning
#+RESULTS: fig:sr_psd_compare
[[file:figs/sr_psd_compare.png]]

** Conclusion
#+begin_important

#+end_important

* Measure of the noise induced by the slip ring when using a geophone
  :PROPERTIES:
  :header-args:matlab+: :tangle meas_sr_geophone.m
  :header-args:matlab+: :comments org :mkdirp yes
  :END:

#+begin_src bash :exports none :results none
  zip data/meas_sr_geophone \
      mat/data_012.mat \
      mat/data_013.mat \
      meas_sr_geophone.m
#+end_src

The data and matlab files are accessible [[file:data/meas_sr_geophone.zip][here]].

** Measurement Description
*Goal*:
- Determine if the noise induced by the slip-ring is a limiting factor when measuring the signal coming from a geophone

*Setup*:
- The geophone is located at the sample location
- The two Voltage amplifiers have the following settings:
  - AC
  - 60dB
  - 1kHz
- The signal from the geophone is split into two using a T-BNC:
  - One part goes directly to the voltage amplifier and then to the ADC.
  - The other part goes to the slip-ring=>voltage amplifier=>ADC.

First column: Direct measure
Second column: Slip-ring measure

*Measurements*:
- =data_012=: Slip-Ring OFF
- =data_013=: Slip-Ring ON

** Matlab Init                                              :noexport:ignore:
#+begin_src matlab :exports none :results silent :noweb yes
  <<matlab-init>>
#+end_src

** Load data
We load the data of the z axis of two geophones.
#+begin_src matlab :results none
  sr_off = load('mat/data_012.mat', 'data'); sr_off = sr_off.data;
  sr_on = load('mat/data_013.mat', 'data'); sr_on  = sr_on.data;
#+end_src

** Time Domain
We compare the signal when the Slip-Ring is OFF (figure [[fig:sr_geophone_time_off]]) and when it is ON (figure [[fig:sr_geophone_time_on]]).

#+begin_src matlab :results none :exports none
  figure;
  hold on;
  plot(sr_off(:, 3), sr_off(:, 1), 'DisplayName', 'Direct');
  plot(sr_off(:, 3), sr_off(:, 2), 'DisplayName', 'Slip-Ring');
  hold off;
  legend('Location', 'northeast');
  xlabel('Time [s]');
  ylabel('Voltage [V]');
#+end_src

#+NAME: fig:sr_geophone_time_off
#+HEADER: :tangle no :exports results :results value raw replace :noweb yes
#+begin_src matlab :var filepath="figs/sr_geophone_time_off.pdf" :var figsize="wide-normal" :post pdf2svg(file=*this*, ext="png")
  <<plt-matlab>>
#+end_src

#+NAME: fig:sr_geophone_time_off
#+CAPTION: Comparison of the time domain signals when the slip-ring is OFF
#+RESULTS: fig:sr_geophone_time_off
[[file:figs/sr_geophone_time_off.png]]

#+begin_src matlab :results none :exports none
  figure;
  hold on;
  plot(sr_on(:, 3),  sr_on(:, 1),  'DisplayName', 'Direct');
  plot(sr_on(:, 3),  sr_on(:, 2),  'DisplayName', 'Slip-Ring');
  hold off;
  legend('Location', 'northeast');
  xlabel('Time [s]');
  ylabel('Voltage [V]');
#+end_src

#+NAME: fig:sr_geophone_time_on
#+HEADER: :tangle no :exports results :results value raw replace :noweb yes
#+begin_src matlab :var filepath="figs/sr_geophone_time_on.pdf" :var figsize="wide-normal" :post pdf2svg(file=*this*, ext="png")
  <<plt-matlab>>
#+end_src

#+NAME: fig:sr_geophone_time_on
#+CAPTION: Comparison of the time domain signals when the slip-ring is ON
#+RESULTS: fig:sr_geophone_time_on
[[file:figs/sr_geophone_time_on.png]]

** Frequency Domain
We first compute some parameters that will be used for the PSD computation.
#+begin_src matlab :results none
  dt = sr_off(2, 3)-sr_off(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
  % Direct measure
  [pxdoff, ~] = pwelch(sr_off(:, 1), win, [], [], Fs);
  [pxdon,  ~] = pwelch(sr_on(:, 1),  win, [], [], Fs);

  % Slip-Ring measure
  [pxsroff, f] = pwelch(sr_off(:, 2), win, [], [], Fs);
  [pxsron,  ~] = pwelch(sr_on(:, 2),  win, [], [], Fs);
#+end_src

Finally, we compare the Amplitude Spectral Density of the signals (figure [[]]);

#+begin_src matlab :results none
  figure;
  hold on;
  plot(f, sqrt(pxdoff), 'DisplayName', 'Direct - OFF');
  plot(f, sqrt(pxsroff), 'DisplayName', 'Slip-Ring - OFF');
  plot(f, sqrt(pxdon),  'DisplayName', 'Direct - ON');
  plot(f, sqrt(pxsron),  'DisplayName', 'Slip-Ring - ON');
  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:sr_geophone_asd
#+HEADER: :tangle no :exports results :results value raw replace :noweb yes
#+begin_src matlab :var filepath="figs/sr_geophone_asd.pdf" :var figsize="full-tall" :post pdf2svg(file=*this*, ext="png")
  <<plt-matlab>>
#+end_src

#+NAME: fig:sr_geophone_asd
#+CAPTION: Comparison of the Amplitude Spectral Sensity
#+RESULTS: fig:sr_geophone_asd
[[file:figs/sr_geophone_asd.png]]

#+begin_src matlab :results none :exports none
  xlim([100, 500]);
#+end_src

#+NAME: fig:sr_geophone_asd_zoom
#+HEADER: :tangle no :exports results :results value raw replace :noweb yes
#+begin_src matlab :var filepath="figs/sr_geophone_asd_zoom.pdf" :var figsize="full-tall" :post pdf2svg(file=*this*, ext="png")
  <<plt-matlab>>
#+end_src

#+NAME: fig:sr_geophone_asd_zoom
#+CAPTION: Comparison of the Amplitude Spectral Sensity - Zoom
#+RESULTS: fig:sr_geophone_asd_zoom
[[file:figs/sr_geophone_asd_zoom.png]]

** Conclusion
#+begin_important
- When the slip-ring is OFF, it does not add any noise to the measurement
- When the slip-ring is ON, it adds significant noise to the signal
#+end_important

* Measure of the influence of the AC/DC option on the voltage amplifiers
  :PROPERTIES:
  :header-args:matlab+: :tangle meas_noise_ac_dc.m
  :header-args:matlab+: :comments org :mkdirp yes
  :END:

#+begin_src bash :exports none :results none
  zip data/meas_noise_ac_dc \
      mat/data_012.mat \
      mat/data_013.mat \
      meas_noise_ac_dc.m
#+end_src

The data and matlab files are accessible [[file:data/meas_noise_ac_dc.zip][here]].

** 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                       |

** Matlab Init                                              :noexport:ignore:
#+begin_src matlab :exports none :results silent :noweb yes
  <<matlab-init>>
#+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', 'northeast');
  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="wide-normal" :post pdf2svg(file=*this*, ext="png")
  <<plt-matlab>>
#+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")
  <<plt-matlab>>
#+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

#+end_important