#+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
  if [ meas_effect_sr.m -nt data/meas_effect_sr.zip ]; then
    zip data/meas_effect_sr \
        mat/data_001.mat \
        mat/data_002.mat \
        meas_effect_sr.m
  fi
#+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
  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

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
  *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 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
  if [ meas_slip_ring.m -nt data/meas_slip_ring.zip ]; then
    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
  fi
#+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

#+name: fig:setup_sr_6rpm
#+caption: Slip-Ring rotating at 6rpm
[[file:./img/VID_20190503_160831.gif]]

#+name: fig:setup_sr_60rpm
#+caption: Slip-Ring rotating at 60rpm
[[file:./img/VID_20190503_161401.gif]]

** 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
  *Questions:*
  - Why is there some sharp peaks? Can this be due to aliasing?
  - It is possible that the amplifiers were saturating during the measurements => should redo the measurements with a low pass filter before the voltage amplifier
#+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
  if [ meas_sr_geophone.m -nt data/meas_sr_geophone.zip ]; then
    zip data/meas_sr_geophone \
        mat/data_012.mat \
        mat/data_013.mat \
        mat/data_016.mat \
        mat/data_017.mat \
        meas_sr_geophone.m
  fi
#+end_src

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

** First Measurement without LPF
*** 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 same 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 [[fig:sr_geophone_asd]]);

#+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
  - The fact that the Slip-Ring is turned ON adds some noise to the signal.
  - The signal going through the Slip-Ring is less noisy than the one going directly to the ADC.
  - This could be due to less good electromagnetic isolation.

  *Questions*:
  - Can the sharp peak on figure [[fig:sr_geophone_asd_zoom]] be due to the Aliasing?
#+end_important

** Measurement using an oscilloscope
*** Measurement Setup
Know we are measuring the same signals but using an oscilloscope instead of the Speedgoat ADC.

*** Observations
Then the Slip-Ring is ON (figure [[fig:oscilloscope_sr_on]]), we observe a signal at 40kHz with a peak-to-peak amplitude of 200mV for the direct measure and 100mV for the signal going through the Slip-Ring.

Then the Slip-Ring is OFF, we don't observe this 40kHz anymore (figure [[fig:oscilloscope_sr_off]]).

#+name: fig:oscilloscope_sr_on
#+caption: Signals measured by the oscilloscope - Slip-Ring ON - Yellow: Direct measure - Blue: Through Slip-Ring
#+attr_html: :width 500px
[[file:./img/IMG_20190506_160420.jpg]]

#+name: fig:oscilloscope_sr_off
#+caption: Signals measured by the oscilloscope - Slip-Ring OFF - Yellow: Direct measure - Blue: Through Slip-Ring
#+attr_html: :width 500px
[[file:./img/IMG_20190506_160438.jpg]]

*** Conclusion
#+begin_important
  - By looking at the signals using an oscilloscope, there is a lot of high frequency noise when turning on the Slip-Ring
  - This can eventually saturate the voltage amplifiers (seen by a led indicating saturation)
  - The choice is to *add a Low pass filter before the voltage amplifiers* to not saturate them and filter the noise.
#+end_important

** New measurements with a LPF before the Voltage Amplifiers
*** Setup description
A first order low pass filter is added before the Voltage Amplifiers with the following values:
\begin{aligned}
  R &= 1k\Omega \\
  C &= 1\mu F
\end{aligned}

And we have a cut-off frequency of $f_c = \frac{1}{RC} = 160Hz$.

We are measuring the signal from a geophone put on the marble with and without the added LPF:
- with the slip ring OFF: =mat/data_016.mat=
- with the slip ring ON: =mat/data_017.mat=

*** Load data
We load the data of the z axis of two geophones.
#+begin_src matlab :results none
  sr_lpf_off = load('mat/data_016.mat', 'data'); sr_lpf_off = sr_lpf_off.data;
  sr_lpf_on  = load('mat/data_017.mat', 'data'); sr_lpf_on  = sr_lpf_on.data;
#+end_src

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

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

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

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

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

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

#+NAME: fig:sr_lpf_geophone_time_on
#+CAPTION: Comparison of the time domain signals when the slip-ring is ON
#+RESULTS: fig:sr_lpf_geophone_time_on
[[file:figs/sr_lpf_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_lpf_off(2, 3)-sr_lpf_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
  [pxd_lpf_off, ~] = pwelch(sr_lpf_off(:, 1), win, [], [], Fs);
  [pxd_lpf_on,  ~] = pwelch(sr_lpf_on(:, 1),  win, [], [], Fs);

  % Slip-Ring measure
  [pxsr_lpf_off, f] = pwelch(sr_lpf_off(:, 2), win, [], [], Fs);
  [pxsr_lpf_on,  ~] = pwelch(sr_lpf_on(:, 2),  win, [], [], Fs);
#+end_src

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

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

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

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

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

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

*** Comparison of with and without LPF
#+begin_src matlab :results none
  figure;
  hold on;
  plot(f, sqrt(pxdon),  'DisplayName', 'Direct - ON');
  plot(f, sqrt(pxsron),  'DisplayName', 'Slip-Ring - ON');
  plot(f, sqrt(pxd_lpf_on),  'DisplayName', 'Direct - ON - LPF');
  plot(f, sqrt(pxsr_lpf_on),  'DisplayName', 'Slip-Ring - ON - LPF');
  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:comp_with_without_lpf
#+HEADER: :tangle no :exports results :results value raw replace :noweb yes
#+begin_src matlab :var filepath="figs/comp_with_without_lpf.pdf" :var figsize="full-tall" :post pdf2svg(file=*this*, ext="png")
  <<plt-matlab>>
#+end_src

#+NAME: fig:comp_with_without_lpf
#+CAPTION: Comparison of the measured signals with and without LPF
#+RESULTS: fig:comp_with_without_lpf
[[file:figs/comp_with_without_lpf.png]]

*** Conclusion
#+begin_important
  - Using the LPF, we don't have any perturbation coming from the slip-ring when it is on.
  - However, we should use a smaller value of the capacitor to have a cut-off frequency at $1kHz$.
#+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
  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

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                       |

#+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 :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', '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")
  <<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
  - 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 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 :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
  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")
  <<plt-matlab>>
#+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")
  <<plt-matlab>>
#+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