Add analysis of LPF, and slip-ring noise

readme.org

@@ -76,6 +76,11 @@ Then, the =f= object can be used to access the filesystem on the target computer
 | rmdir  |                                            |                                      |
 | close  |                                            |                                      |
 
-
 * ELMO
 tutorials: https://www.elmomc.com/products/application-studio/easii/easii-tutorials/
+* Low Pass Filter
+
+R = 1KOhm
+C = 1muF
+
+Fc = 1kHz

slip-ring-test/index.org

@@ -25,10 +25,12 @@
   :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]].
@@ -460,18 +462,21 @@ And we plot the ASD of the measured signals (figure [[fig:sr_psd_compare]]);
   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
 #+end_src
 
 The data and matlab files are accessible [[file:data/meas_sr_geophone.zip][here]].
 
-** Measurement Description
+** 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 following settings:
+- The two Voltage amplifiers have the same following settings:
   - AC
   - 60dB
   - 1kHz
@@ -486,19 +491,19 @@ Second column: Slip-ring measure
 - =data_012=: Slip-Ring OFF
 - =data_013=: Slip-Ring ON
 
-** Matlab Init                                              :noexport:ignore:
+*** Matlab Init                                             :noexport:ignore:
 #+begin_src matlab :exports none :results silent :noweb yes
   <<matlab-init>>
 #+end_src
 
-** Load data
+*** 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
+*** 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
@@ -545,7 +550,7 @@ We compare the signal when the Slip-Ring is OFF (figure [[fig:sr_geophone_time_o
 #+RESULTS: fig:sr_geophone_time_on
 [[file:figs/sr_geophone_time_on.png]]
 
-** Frequency Domain
+*** 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);
@@ -566,7 +571,7 @@ Then we compute the Power Spectral Density using =pwelch= function.
   [pxsron,  ~] = pwelch(sr_on(:, 2),  win, [], [], Fs);
 #+end_src
 
-Finally, we compare the Amplitude Spectral Density of the signals (figure [[]]);
+Finally, we compare the Amplitude Spectral Density of the signals (figure [[fig:sr_geophone_asd]]);
 
 #+begin_src matlab :results none
   figure;
@@ -609,10 +614,205 @@ Finally, we compare the Amplitude Spectral Density of the signals (figure [[]]);
 #+RESULTS: fig:sr_geophone_asd_zoom
 [[file:figs/sr_geophone_asd_zoom.png]]
 
-** Conclusion
+*** 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
+  - 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 will 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
@@ -681,7 +881,7 @@ The signals are shown on figure [[fig:ac_dc_option_time]].
   plot(meas15(:, 3), meas15(:, 1), 'DisplayName', 'Amp1 - DC');
   plot(meas15(:, 3), meas15(:, 2), 'DisplayName', 'Amp2 - AC');
   hold off;
-  legend('Location', 'northeast');
+  legend('Location', 'bestoutside');
   xlabel('Time [s]');
   ylabel('Voltage [V]');
   xlim([0, 100]);
@@ -689,7 +889,7 @@ The signals are shown on figure [[fig:ac_dc_option_time]].
 
 #+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")
+#+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
 
@@ -746,5 +946,138 @@ The ASD of the signals are compare on figure [[fig:ac_dc_option_asd]].
 
 ** 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
 
+ *Questions*:
+  - What option should be used for the measurements?
 #+end_important
+
+* Measure of the Low Pass Filter
+** 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) node[circ]
+          to [R=\(R\)] ++(2,0)
+          to ++(2,0)  node[circ]
+          ++(-2,0)  node[circ]
+          to [C=\(C\)] ++(0,-2)
+          ++(-2,0) node[circ]
+          to ++(2,0) node[circ]
+          to ++(2,0) node[circ];
+  \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                 |
+
+** 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
+
+** TODO Low Pass Filter with a cut-off frequency of 1kHz
+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 $f_c = 1060Hz$.

slip-ring-test/meas_effect_sr.m

@@ -0,0 +1,71 @@
+% Matlab Init                                              :noexport:ignore:
+
+clear; close all; clc;
+
+%% Intialize Laplace variable
+s = zpk('s');
+
+%% Initialize ans with org-babel
+ans = 0;
+
+% Load data
+% We load the data of the z axis of two geophones.
+
+sr_off = load('mat/data_001.mat', 't', 'x1', 'x2');
+sr_on  = load('mat/data_002.mat', 't', 'x1', 'x2');
+
+% Analysis
+% Let's first look at the signal produced by the DAC (figure [[fig:random_signal]]).
+
+
+figure;
+hold on;
+plot(sr_on.t,  sr_on.x1);
+hold off;
+xlabel('Time [s]'); ylabel('Voltage [V]');
+xlim([0 10]);
+
+
+
+% #+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]]).
+
+
+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');
+
+
+
+% #+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]]
+
+
+dt = sr_on.t(2) - sr_on.t(1);
+Fs = 1/dt; % [Hz]
+
+win = hanning(ceil(1*Fs));
+
+[pxx_on,  f] = pwelch(sr_on.x1  - sr_on.x2,  win, [], [], Fs);
+[pxx_off, ~] = pwelch(sr_off.x1 - sr_off.x2, win, [], [], Fs);
+
+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])

slip-ring-test/meas_noise_ac_dc.m

@@ -0,0 +1,66 @@
+% Matlab Init                                              :noexport:ignore:
+
+clear; close all; clc;
+
+%% Intialize Laplace variable
+s = zpk('s');
+
+%% Initialize ans with org-babel
+ans = 0;
+
+% Load data
+% We load the data of the z axis of two geophones.
+
+meas14 = load('mat/data_014.mat', 'data'); meas14 = meas14.data;
+meas15 = load('mat/data_015.mat', 'data'); meas15 = meas15.data;
+
+% Time Domain
+% The signals are shown on figure [[fig:ac_dc_option_time]].
+
+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]);
+
+% Frequency Domain
+% We first compute some parameters that will be used for the PSD computation.
+
+dt = meas14(2, 3)-meas14(1, 3);
+
+Fs = 1/dt; % [Hz]
+
+win = hanning(ceil(10*Fs));
+
+
+
+% Then we compute the Power Spectral Density using =pwelch= function.
+
+[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);
+
+
+
+% The ASD of the signals are compare on figure [[fig:ac_dc_option_asd]].
+
+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]);

slip-ring-test/meas_slip_ring.m

@@ -0,0 +1,88 @@
+% Matlab Init                                              :noexport:ignore:
+
+clear; close all; clc;
+
+%% Intialize Laplace variable
+s = zpk('s');
+
+%% Initialize ans with org-babel
+ans = 0;
+
+% Load data
+% We load the data of the z axis of two geophones.
+
+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;
+
+% 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]]);
+
+
+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');
+
+
+
+% #+NAME: fig:sr_direct_time
+% #+CAPTION: Direct measurement
+% #+RESULTS: fig:sr_direct_time
+% [[file:figs/sr_direct_time.png]]
+
+
+
+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');
+
+% Frequency Domain
+% We first compute some parameters that will be used for the PSD computation.
+
+dt = sr_off(2, 3)-sr_off(1, 3);
+
+Fs = 1/dt; % [Hz]
+
+win = hanning(ceil(10*Fs));
+
+
+
+% Then we compute the Power Spectral Density using =pwelch= function.
+
+[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);
+
+
+
+% And we plot the ASD of the measured signals (figure [[fig:sr_psd_compare]]);
+
+
+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]);

slip-ring-test/meas_sr_geophone.m

@@ -0,0 +1,194 @@
+% Matlab Init                                             :noexport:ignore:
+
+clear; close all; clc;
+
+%% Intialize Laplace variable
+s = zpk('s');
+
+%% Initialize ans with org-babel
+ans = 0;
+
+% Load data
+% We load the data of the z axis of two geophones.
+
+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;
+
+% 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]]).
+
+
+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]');
+
+
+
+% #+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]]
+
+
+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]');
+
+% Frequency Domain
+% We first compute some parameters that will be used for the PSD computation.
+
+dt = sr_off(2, 3)-sr_off(1, 3);
+
+Fs = 1/dt; % [Hz]
+
+win = hanning(ceil(10*Fs));
+
+
+
+% Then we compute the Power Spectral Density using =pwelch= function.
+
+% 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);
+
+
+
+% Finally, we compare the Amplitude Spectral Density of the signals (figure [[fig:sr_geophone_asd]]);
+
+
+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]);
+
+
+
+% #+NAME: fig:sr_geophone_asd
+% #+CAPTION: Comparison of the Amplitude Spectral Sensity
+% #+RESULTS: fig:sr_geophone_asd
+% [[file:figs/sr_geophone_asd.png]]
+
+
+xlim([100, 500]);
+
+% Load data
+% We load the data of the z axis of two geophones.
+
+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;
+
+% 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]]).
+
+
+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]');
+
+
+
+% #+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]]
+
+
+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]');
+
+% Frequency Domain
+% We first compute some parameters that will be used for the PSD computation.
+
+dt = sr_lpf_off(2, 3)-sr_lpf_off(1, 3);
+
+Fs = 1/dt; % [Hz]
+
+win = hanning(ceil(10*Fs));
+
+
+
+% Then we compute the Power Spectral Density using =pwelch= function.
+
+% 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);
+
+
+
+% Finally, we compare the Amplitude Spectral Density of the signals (figure [[fig:sr_lpf_geophone_asd]]);
+
+
+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]);
+
+
+
+% #+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]]
+
+
+xlim([100, 500]);
+
+% Comparison of with and without LPF
+
+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]);

slip-ring-test/meas_volt_amp.m

@@ -0,0 +1,74 @@
+% Matlab Init                                              :noexport:ignore:
+
+clear; close all; clc;
+
+%% Intialize Laplace variable
+s = zpk('s');
+
+%% Initialize ans with org-babel
+ans = 0;
+
+% Load data
+
+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]);
+
+% Time Domain
+% The time domain signals are shown on figure [[fig:ampli_noise_time]].
+
+
+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]');
+
+% Frequency Domain
+% We first compute some parameters that will be used for the PSD computation.
+
+dt = amp_off(2, 2)-amp_off(1, 2);
+
+Fs = 1/dt; % [Hz]
+
+win = hanning(ceil(10*Fs));
+
+
+
+% Then we compute the Power Spectral Density using =pwelch= function.
+
+[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);
+
+
+
+% We compute the theoretical ADC noise.
+
+q = 20/2^16; % quantization
+Sq = q^2/12/1000; % PSD of the ADC noise
+
+
+
+% Finally, the ASD is shown on figure [[fig:ampli_noise_psd]].
+
+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]);

slip-ring-test/readme.org

@@ -68,7 +68,6 @@ Second column: DC
 
 - meas14: col-1 = amp1+AC. col-2 = amp2+DC.
 - meas15: col-1 = amp1+DC. col-2 = amp2+AC.
-
 * Measurement of the LPF
 We are measuring the signal from from Geophone with a BNC T
 On part goes to column 1 through the LPF