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<div id="content">
<h1 class="title">Measurements</h1>
<div id="table-of-contents">
<h2>Table of Contents</h2>
<div id="text-table-of-contents">
<ul>
<li><a href="#org72a8967">1. Effect of the rotation of the Slip-Ring</a>
<ul>
<li><a href="#org4b8f76d">1.1. Measurement Description</a></li>
<li><a href="#org6e93e2e">1.2. Load data</a></li>
<li><a href="#org47bc1f0">1.3. Analysis</a></li>
<li><a href="#orgd87dca5">1.4. Conclusion</a></li>
</ul>
</li>
<li><a href="#org7a2f4ff">2. Measure of the noise of the Voltage Amplifier</a>
<ul>
<li><a href="#org5a4d29e">2.1. Measurement Description</a></li>
<li><a href="#orgffece30">2.2. Load data</a></li>
<li><a href="#orgec501b3">2.3. Time Domain</a></li>
<li><a href="#org7d68dd0">2.4. Frequency Domain</a></li>
<li><a href="#orgaba63f9">2.5. Conclusion</a></li>
</ul>
</li>
<li><a href="#orgded919b">3. Measure of the noise induced by the Slip-Ring</a>
<ul>
<li><a href="#orgde32f93">3.1. Measurement Description</a></li>
<li><a href="#org661917b">3.2. Load data</a></li>
<li><a href="#orgcd9a917">3.3. Time Domain</a></li>
<li><a href="#org708090d">3.4. Frequency Domain</a></li>
<li><a href="#org83ed722">3.5. Conclusion</a></li>
</ul>
</li>
<li><a href="#orgfbf06e6">4. Measure of the noise induced by the slip ring when using a geophone</a>
<ul>
<li><a href="#orgffb1bdb">4.1. First Measurement without LPF</a>
<ul>
<li><a href="#org8e8831c">4.1.1. Measurement Description</a></li>
<li><a href="#org167eeae">4.1.2. Load data</a></li>
<li><a href="#org583abb2">4.1.3. Time Domain</a></li>
<li><a href="#org35e29fe">4.1.4. Frequency Domain</a></li>
<li><a href="#org3e43efe">4.1.5. Conclusion</a></li>
</ul>
</li>
<li><a href="#orgf298379">4.2. Measurement using an oscilloscope</a>
<ul>
<li><a href="#org68d1d31">4.2.1. Measurement Setup</a></li>
<li><a href="#org5276b1f">4.2.2. Observations</a></li>
<li><a href="#org54a8d62">4.2.3. Conclusion</a></li>
</ul>
</li>
<li><a href="#orgcebb9a0">4.3. New measurements with a LPF before the Voltage Amplifiers</a>
<ul>
<li><a href="#org4bdf600">4.3.1. Setup description</a></li>
<li><a href="#org5c96c5f">4.3.2. Load data</a></li>
<li><a href="#orgbcba5cf">4.3.3. Time Domain</a></li>
<li><a href="#org0d5a581">4.3.4. Frequency Domain</a></li>
<li><a href="#orgad63dd1">4.3.5. Comparison of with and without LPF</a></li>
<li><a href="#orgdece1f2">4.3.6. Conclusion</a></li>
</ul>
</li>
</ul>
</li>
<li><a href="#org23a8137">5. Measure of the influence of the AC/DC option on the voltage amplifiers</a>
<ul>
<li><a href="#org58bc336">5.1. Measurement Description</a></li>
<li><a href="#org137ca7d">5.2. Load data</a></li>
<li><a href="#orgce0337d">5.3. Time Domain</a></li>
<li><a href="#org1ca91db">5.4. Frequency Domain</a></li>
<li><a href="#orge0411ce">5.5. Conclusion</a></li>
</ul>
</li>
<li><a href="#org6d3a86e">6. Transfer function of the Low Pass Filter</a>
<ul>
<li><a href="#org50dfe76">6.1. First LPF with a Cut-off frequency of 160Hz</a>
<ul>
<li><a href="#orge61a68e">6.1.1. Measurement Description</a></li>
<li><a href="#org229c82b">6.1.2. Load data</a></li>
<li><a href="#org78a38da">6.1.3. Transfer function of the LPF</a></li>
<li><a href="#org59dee72">6.1.4. Conclusion</a></li>
</ul>
</li>
<li><a href="#org8b09702">6.2. Second LPF with a Cut-off frequency of 1000Hz</a>
<ul>
<li><a href="#orged36cb1">6.2.1. Measurement description</a></li>
<li><a href="#org7e593d2">6.2.2. Load data</a></li>
<li><a href="#org2e7d91e">6.2.3. Transfer function of the LPF</a></li>
<li><a href="#org04a0d6e">6.2.4. Conclusion</a></li>
</ul>
</li>
</ul>
</li>
</ul>
</div>
</div>
<div id="outline-container-org72a8967" class="outline-2">
<h2 id="org72a8967"><span class="section-number-2">1</span> Effect of the rotation of the Slip-Ring</h2>
<div class="outline-text-2" id="text-1">
<p>
The data and matlab files are accessible <a href="data/meas_effect_sr.zip">here</a>.
</p>
</div>
<div id="outline-container-org4b8f76d" class="outline-3">
<h3 id="org4b8f76d"><span class="section-number-3">1.1</span> Measurement Description</h3>
<div class="outline-text-3" id="text-1-1">
<p>
Random Signal is generated by one DAC of the SpeedGoat.
</p>
<p>
The signal going out of the DAC is split into two:
</p>
<ul class="org-ul">
<li>one BNC cable is directly connected to one ADC of the SpeedGoat</li>
<li>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</li>
</ul>
<p>
Two measurements are done.
</p>
<table border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
<colgroup>
<col class="org-left" />
<col class="org-left" />
</colgroup>
<thead>
<tr>
<th scope="col" class="org-left">Data File</th>
<th scope="col" class="org-left">Description</th>
</tr>
</thead>
<tbody>
<tr>
<td class="org-left"><code>mat/data_001.mat</code></td>
<td class="org-left">Slip-ring not turning</td>
</tr>
<tr>
<td class="org-left"><code>mat/data_002.mat</code></td>
<td class="org-left">Slip-ring turning</td>
</tr>
</tbody>
</table>
<p>
For each measurement, the measured signals are:
</p>
<table border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
<colgroup>
<col class="org-left" />
<col class="org-left" />
</colgroup>
<thead>
<tr>
<th scope="col" class="org-left">Data File</th>
<th scope="col" class="org-left">Description</th>
</tr>
</thead>
<tbody>
<tr>
<td class="org-left"><code>t</code></td>
<td class="org-left">Time vector</td>
</tr>
<tr>
<td class="org-left"><code>x1</code></td>
<td class="org-left">Direct signal</td>
</tr>
<tr>
<td class="org-left"><code>x2</code></td>
<td class="org-left">Signal going through the Slip-Ring</td>
</tr>
</tbody>
</table>
<p>
The goal is to determine is the signal is altered when the spindle is rotating.
</p>
<p>
Here, the rotation speed of the Slip-Ring is set to 1rpm.
</p>
</div>
</div>
<div id="outline-container-org6e93e2e" class="outline-3">
<h3 id="org6e93e2e"><span class="section-number-3">1.2</span> Load data</h3>
<div class="outline-text-3" id="text-1-2">
<p>
We load the data of the z axis of two geophones.
</p>
<div class="org-src-container">
<pre class="src src-matlab">sr_off = load<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'mat/data_001.mat', 't', 'x1', 'x2'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
sr_on = load<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'mat/data_002.mat', 't', 'x1', 'x2'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
</pre>
</div>
</div>
</div>
<div id="outline-container-org47bc1f0" class="outline-3">
<h3 id="org47bc1f0"><span class="section-number-3">1.3</span> Analysis</h3>
<div class="outline-text-3" id="text-1-3">
<p>
Let's first look at the signal produced by the DAC (figure <a href="#orge7c2b99">1</a>).
</p>
<div class="org-src-container">
<pre class="src src-matlab"><span class="org-type">figure</span>;
hold on;
plot<span class="org-rainbow-delimiters-depth-1">(</span>sr_on.t, sr_on.x1<span class="org-rainbow-delimiters-depth-1">)</span>;
hold off;
xlabel<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Time </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">s</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">)</span></span><span class="org-string">; ylabel</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">(</span></span><span class="org-string">'Voltage </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">V</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
xlim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span><span class="org-highlight-numbers-number">0</span> <span class="org-highlight-numbers-number">10</span><span class="org-rainbow-delimiters-depth-2">]</span><span class="org-rainbow-delimiters-depth-1">)</span>;
</pre>
</div>
<div id="orge7c2b99" class="figure">
<p><img src="figs/random_signal.png" alt="random_signal.png" />
</p>
<p><span class="figure-number">Figure 1: </span>Random signal produced by the DAC</p>
</div>
<p>
We now look at the difference between the signal directly measured by the ADC and the signal that goes through the slip-ring (figure <a href="#org356df0f">2</a>).
</p>
<div class="org-src-container">
<pre class="src src-matlab"><span class="org-type">figure</span>;
hold on;
plot<span class="org-rainbow-delimiters-depth-1">(</span>sr_on.t, sr_on.x1 <span class="org-type">-</span> sr_on.x2, <span class="org-string">'DisplayName', '</span>Slip<span class="org-type">-</span>Ring <span class="org-type">-</span> $<span class="org-type">\</span>omega = <span class="org-highlight-numbers-number">1rpm$</span>'<span class="org-rainbow-delimiters-depth-1">)</span>;
plot<span class="org-rainbow-delimiters-depth-1">(</span>sr_off.t, sr_off.x1 <span class="org-type">-</span> sr_off.x2,<span class="org-string">'DisplayName', 'Slip-Ring off'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
hold off;
xlabel<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Time </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">s</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">)</span></span><span class="org-string">; ylabel</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">(</span></span><span class="org-string">'Voltage </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">V</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
xlim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span><span class="org-highlight-numbers-number">0</span> <span class="org-highlight-numbers-number">10</span><span class="org-rainbow-delimiters-depth-2">]</span><span class="org-rainbow-delimiters-depth-1">)</span>;
legend<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Location', 'northeast'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
</pre>
</div>
<div id="org356df0f" class="figure">
<p><img src="figs/slipring_comp_signals.png" alt="slipring_comp_signals.png" />
</p>
<p><span class="figure-number">Figure 2: </span>Alteration of the signal when the slip-ring is turning</p>
</div>
<div class="org-src-container">
<pre class="src src-matlab">dt = sr_on.t<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-1">)</span> <span class="org-type">-</span> sr_on.t<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-1">)</span>;
Fs = <span class="org-highlight-numbers-number">1</span><span class="org-type">/</span>dt; <span class="org-comment">% [Hz]</span>
win = hanning<span class="org-rainbow-delimiters-depth-1">(</span>ceil<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-highlight-numbers-number">1</span><span class="org-type">*</span>Fs<span class="org-rainbow-delimiters-depth-2">)</span><span class="org-rainbow-delimiters-depth-1">)</span>;
</pre>
</div>
<div class="org-src-container">
<pre class="src src-matlab"><span class="org-rainbow-delimiters-depth-1">[</span>pxx_on, f<span class="org-rainbow-delimiters-depth-1">]</span> = pwelch<span class="org-rainbow-delimiters-depth-1">(</span>sr_on.x1 <span class="org-type">-</span> sr_on.x2, win, <span class="org-rainbow-delimiters-depth-2">[]</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, Fs<span class="org-rainbow-delimiters-depth-1">)</span>;
<span class="org-rainbow-delimiters-depth-1">[</span>pxx_off, <span class="org-type">~</span><span class="org-rainbow-delimiters-depth-1">]</span> = pwelch<span class="org-rainbow-delimiters-depth-1">(</span>sr_off.x1 <span class="org-type">-</span> sr_off.x2, win, <span class="org-rainbow-delimiters-depth-2">[]</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, Fs<span class="org-rainbow-delimiters-depth-1">)</span>;
</pre>
</div>
<div id="org808978d" class="figure">
<p><img src="figs/psd_noise.png" alt="psd_noise.png" />
</p>
<p><span class="figure-number">Figure 3: </span>ASD of the measured noise</p>
</div>
</div>
</div>
<div id="outline-container-orgd87dca5" class="outline-3">
<h3 id="orgd87dca5"><span class="section-number-3">1.4</span> Conclusion</h3>
<div class="outline-text-3" id="text-1-4">
<div class="note">
<p>
<b>Remaining questions</b>:
</p>
<ul class="org-ul">
<li>Should the measurement be redone using voltage amplifiers?</li>
<li>Use higher rotation speed and measure for longer periods (to have multiple revolutions) ?</li>
</ul>
</div>
</div>
</div>
</div>
<div id="outline-container-org7a2f4ff" class="outline-2">
<h2 id="org7a2f4ff"><span class="section-number-2">2</span> Measure of the noise of the Voltage Amplifier</h2>
<div class="outline-text-2" id="text-2">
<p>
The data and matlab files are accessible <a href="data/meas_volt_amp.zip">here</a>.
</p>
</div>
<div id="outline-container-org5a4d29e" class="outline-3">
<h3 id="org5a4d29e"><span class="section-number-3">2.1</span> Measurement Description</h3>
<div class="outline-text-3" id="text-2-1">
<p>
<b>Goal</b>:
</p>
<ul class="org-ul">
<li>Determine the Voltage Amplifier noise</li>
</ul>
<p>
<b>Setup</b>:
</p>
<ul class="org-ul">
<li>The two inputs (differential) of the voltage amplifier are shunted with 50Ohms</li>
<li>The AC/DC option of the Voltage amplifier is on AC</li>
<li>The low pass filter is set to 1hHz</li>
<li>We measure the output of the voltage amplifier with a 16bits ADC of the Speedgoat</li>
</ul>
<p>
<b>Measurements</b>:
</p>
<ul class="org-ul">
<li><code>data_003</code>: Ampli OFF</li>
<li><code>data_004</code>: Ampli ON set to 20dB</li>
<li><code>data_005</code>: Ampli ON set to 40dB</li>
<li><code>data_006</code>: Ampli ON set to 60dB</li>
</ul>
</div>
</div>
<div id="outline-container-orgffece30" class="outline-3">
<h3 id="orgffece30"><span class="section-number-3">2.2</span> Load data</h3>
<div class="outline-text-3" id="text-2-2">
<div class="org-src-container">
<pre class="src src-matlab">amp_off = load<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'mat/data_003.mat', 'data'</span><span class="org-rainbow-delimiters-depth-1">)</span>; amp_off = amp_off.data<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-type">:</span>, <span class="org-rainbow-delimiters-depth-2">[</span><span class="org-highlight-numbers-number">1</span>,<span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">]</span><span class="org-rainbow-delimiters-depth-1">)</span>;
amp_20d = load<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'mat/data_004.mat', 'data'</span><span class="org-rainbow-delimiters-depth-1">)</span>; amp_20d = amp_20d.data<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-type">:</span>, <span class="org-rainbow-delimiters-depth-2">[</span><span class="org-highlight-numbers-number">1</span>,<span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">]</span><span class="org-rainbow-delimiters-depth-1">)</span>;
amp_40d = load<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'mat/data_005.mat', 'data'</span><span class="org-rainbow-delimiters-depth-1">)</span>; amp_40d = amp_40d.data<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-type">:</span>, <span class="org-rainbow-delimiters-depth-2">[</span><span class="org-highlight-numbers-number">1</span>,<span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">]</span><span class="org-rainbow-delimiters-depth-1">)</span>;
amp_60d = load<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'mat/data_006.mat', 'data'</span><span class="org-rainbow-delimiters-depth-1">)</span>; amp_60d = amp_60d.data<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-type">:</span>, <span class="org-rainbow-delimiters-depth-2">[</span><span class="org-highlight-numbers-number">1</span>,<span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">]</span><span class="org-rainbow-delimiters-depth-1">)</span>;
</pre>
</div>
</div>
</div>
<div id="outline-container-orgec501b3" class="outline-3">
<h3 id="orgec501b3"><span class="section-number-3">2.3</span> Time Domain</h3>
<div class="outline-text-3" id="text-2-3">
<p>
The time domain signals are shown on figure <a href="#org88028bf">4</a>.
</p>
<div id="org88028bf" class="figure">
<p><img src="figs/ampli_noise_time.png" alt="ampli_noise_time.png" />
</p>
<p><span class="figure-number">Figure 4: </span>Output of the amplifier</p>
</div>
</div>
</div>
<div id="outline-container-org7d68dd0" class="outline-3">
<h3 id="org7d68dd0"><span class="section-number-3">2.4</span> Frequency Domain</h3>
<div class="outline-text-3" id="text-2-4">
<p>
We first compute some parameters that will be used for the PSD computation.
</p>
<div class="org-src-container">
<pre class="src src-matlab">dt = amp_off<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">2</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-1">)</span><span class="org-type">-</span>amp_off<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">1</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-1">)</span>;
Fs = <span class="org-highlight-numbers-number">1</span><span class="org-type">/</span>dt; <span class="org-comment">% [Hz]</span>
win = hanning<span class="org-rainbow-delimiters-depth-1">(</span>ceil<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-highlight-numbers-number">10</span><span class="org-type">*</span>Fs<span class="org-rainbow-delimiters-depth-2">)</span><span class="org-rainbow-delimiters-depth-1">)</span>;
</pre>
</div>
<p>
Then we compute the Power Spectral Density using <code>pwelch</code> function.
</p>
<div class="org-src-container">
<pre class="src src-matlab"><span class="org-rainbow-delimiters-depth-1">[</span>pxoff, f<span class="org-rainbow-delimiters-depth-1">]</span> = pwelch<span class="org-rainbow-delimiters-depth-1">(</span>amp_off<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>,<span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, win, <span class="org-rainbow-delimiters-depth-2">[]</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, Fs<span class="org-rainbow-delimiters-depth-1">)</span>;
<span class="org-rainbow-delimiters-depth-1">[</span>px20d, <span class="org-type">~</span><span class="org-rainbow-delimiters-depth-1">]</span> = pwelch<span class="org-rainbow-delimiters-depth-1">(</span>amp_20d<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>,<span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, win, <span class="org-rainbow-delimiters-depth-2">[]</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, Fs<span class="org-rainbow-delimiters-depth-1">)</span>;
<span class="org-rainbow-delimiters-depth-1">[</span>px40d, <span class="org-type">~</span><span class="org-rainbow-delimiters-depth-1">]</span> = pwelch<span class="org-rainbow-delimiters-depth-1">(</span>amp_40d<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>,<span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, win, <span class="org-rainbow-delimiters-depth-2">[]</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, Fs<span class="org-rainbow-delimiters-depth-1">)</span>;
<span class="org-rainbow-delimiters-depth-1">[</span>px60d, <span class="org-type">~</span><span class="org-rainbow-delimiters-depth-1">]</span> = pwelch<span class="org-rainbow-delimiters-depth-1">(</span>amp_60d<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>,<span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, win, <span class="org-rainbow-delimiters-depth-2">[]</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, Fs<span class="org-rainbow-delimiters-depth-1">)</span>;
</pre>
</div>
<p>
We compute the theoretical ADC noise.
</p>
<div class="org-src-container">
<pre class="src src-matlab">q = <span class="org-highlight-numbers-number">20</span><span class="org-type">/</span><span class="org-highlight-numbers-number">2</span><span class="org-type">^</span><span class="org-highlight-numbers-number">16</span>; <span class="org-comment">% quantization</span>
Sq = q<span class="org-type">^</span><span class="org-highlight-numbers-number">2</span><span class="org-type">/</span><span class="org-highlight-numbers-number">12</span><span class="org-type">/</span><span class="org-highlight-numbers-number">1000</span>; <span class="org-comment">% PSD of the ADC noise</span>
</pre>
</div>
<p>
Finally, the ASD is shown on figure <a href="#org4935d97">5</a>.
</p>
<div id="org4935d97" class="figure">
<p><img src="figs/ampli_noise_psd.png" alt="ampli_noise_psd.png" />
</p>
<p><span class="figure-number">Figure 5: </span>Amplitude Spectral Density of the measured voltage at the output of the voltage amplifier</p>
</div>
</div>
</div>
<div id="outline-container-orgaba63f9" class="outline-3">
<h3 id="orgaba63f9"><span class="section-number-3">2.5</span> Conclusion</h3>
<div class="outline-text-3" id="text-2-5">
<div class="important">
<p>
<b>Questions</b>:
</p>
<ul class="org-ul">
<li>Where does those sharp peaks comes from? Can this be due to aliasing?</li>
</ul>
<p>
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.
</p>
</div>
</div>
</div>
</div>
<div id="outline-container-orgded919b" class="outline-2">
<h2 id="orgded919b"><span class="section-number-2">3</span> Measure of the noise induced by the Slip-Ring</h2>
<div class="outline-text-2" id="text-3">
<p>
The data and matlab files are accessible <a href="data/meas_slip_ring.zip">here</a>.
</p>
</div>
<div id="outline-container-orgde32f93" class="outline-3">
<h3 id="orgde32f93"><span class="section-number-3">3.1</span> Measurement Description</h3>
<div class="outline-text-3" id="text-3-1">
<p>
<b>Goal</b>:
</p>
<ul class="org-ul">
<li>Determine the noise induced by the slip-ring</li>
</ul>
<p>
<b>Setup</b>:
</p>
<ul class="org-ul">
<li>0V is generated by the DAC of the Speedgoat</li>
<li>Using a T, one part goes directly to the ADC</li>
<li>The other part goes to the slip-ring 2 times and then to the ADC</li>
<li>The parameters of the Voltage Amplifier are: 80dB, AC, 1kHz</li>
<li>Every stage of the station is OFF</li>
</ul>
<p>
First column: Direct measure
Second column: Slip-ring measure
</p>
<p>
<b>Measurements</b>:
</p>
<ul class="org-ul">
<li><code>data_008</code>: Slip-Ring OFF</li>
<li><code>data_009</code>: Slip-Ring ON</li>
<li><code>data_010</code>: Slip-Ring ON and omega=6rpm</li>
<li><code>data_011</code>: Slip-Ring ON and omega=60rpm</li>
</ul>
<div id="orgd7dd6a9" class="figure">
<p><img src="./img/VID_20190503_160831.gif" alt="VID_20190503_160831.gif" />
</p>
<p><span class="figure-number">Figure 6: </span>Slip-Ring rotating at 6rpm</p>
</div>
<div id="org4a57a9c" class="figure">
<p><img src="./img/VID_20190503_161401.gif" alt="VID_20190503_161401.gif" />
</p>
<p><span class="figure-number">Figure 7: </span>Slip-Ring rotating at 60rpm</p>
</div>
</div>
</div>
<div id="outline-container-org661917b" class="outline-3">
<h3 id="org661917b"><span class="section-number-3">3.2</span> Load data</h3>
<div class="outline-text-3" id="text-3-2">
<p>
We load the data of the z axis of two geophones.
</p>
<div class="org-src-container">
<pre class="src src-matlab">sr_off = load<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'mat/data_008.mat', 'data'</span><span class="org-rainbow-delimiters-depth-1">)</span>; sr_off = sr_off.data;
sr_on = load<span class="org-rainbow-delimiters-depth-1">(</span>'mat<span class="org-type">/</span>data_009.mat', <span class="org-string">'data'</span><span class="org-rainbow-delimiters-depth-1">)</span>; sr_on = sr_on.data;
sr_6r = load<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'mat/data_010.mat', 'data'</span><span class="org-rainbow-delimiters-depth-1">)</span>; sr_6r = sr_6r.data;
sr_60r = load<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'mat/data_011.mat', 'data'</span><span class="org-rainbow-delimiters-depth-1">)</span>; sr_60r = sr_60r.data;
</pre>
</div>
</div>
</div>
<div id="outline-container-orgcd9a917" class="outline-3">
<h3 id="orgcd9a917"><span class="section-number-3">3.3</span> Time Domain</h3>
<div class="outline-text-3" id="text-3-3">
<p>
We plot the time domain data for the direct measurement (figure <a href="#orgd6b2170">8</a>) and for the signal going through the slip-ring (figure <a href="#orga83c518">9</a>);
</p>
<div id="orgd6b2170" class="figure">
<p><img src="figs/sr_direct_time.png" alt="sr_direct_time.png" />
</p>
<p><span class="figure-number">Figure 8: </span>Direct measurement</p>
</div>
<div id="orga83c518" class="figure">
<p><img src="figs/sr_slipring_time.png" alt="sr_slipring_time.png" />
</p>
<p><span class="figure-number">Figure 9: </span>Measurement of the signal going through the Slip-Ring</p>
</div>
</div>
</div>
<div id="outline-container-org708090d" class="outline-3">
<h3 id="org708090d"><span class="section-number-3">3.4</span> Frequency Domain</h3>
<div class="outline-text-3" id="text-3-4">
<p>
We first compute some parameters that will be used for the PSD computation.
</p>
<div class="org-src-container">
<pre class="src src-matlab">dt = sr_off<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">2</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-1">)</span><span class="org-type">-</span>sr_off<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">1</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-1">)</span>;
Fs = <span class="org-highlight-numbers-number">1</span><span class="org-type">/</span>dt; <span class="org-comment">% [Hz]</span>
win = hanning<span class="org-rainbow-delimiters-depth-1">(</span>ceil<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-highlight-numbers-number">10</span><span class="org-type">*</span>Fs<span class="org-rainbow-delimiters-depth-2">)</span><span class="org-rainbow-delimiters-depth-1">)</span>;
</pre>
</div>
<p>
Then we compute the Power Spectral Density using <code>pwelch</code> function.
</p>
<div class="org-src-container">
<pre class="src src-matlab"><span class="org-rainbow-delimiters-depth-1">[</span>pxdir, f<span class="org-rainbow-delimiters-depth-1">]</span> = pwelch<span class="org-rainbow-delimiters-depth-1">(</span>sr_off<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, win, <span class="org-rainbow-delimiters-depth-2">[]</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, Fs<span class="org-rainbow-delimiters-depth-1">)</span>;
<span class="org-rainbow-delimiters-depth-1">[</span>pxoff, <span class="org-type">~</span><span class="org-rainbow-delimiters-depth-1">]</span> = pwelch<span class="org-rainbow-delimiters-depth-1">(</span>sr_off<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span>, win, <span class="org-rainbow-delimiters-depth-2">[]</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, Fs<span class="org-rainbow-delimiters-depth-1">)</span>;
<span class="org-rainbow-delimiters-depth-1">[</span>pxon, <span class="org-type">~</span><span class="org-rainbow-delimiters-depth-1">]</span> = pwelch<span class="org-rainbow-delimiters-depth-1">(</span>sr_on<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span>, win, <span class="org-rainbow-delimiters-depth-2">[]</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, Fs<span class="org-rainbow-delimiters-depth-1">)</span>;
<span class="org-rainbow-delimiters-depth-1">[</span>px6r, <span class="org-type">~</span><span class="org-rainbow-delimiters-depth-1">]</span> = pwelch<span class="org-rainbow-delimiters-depth-1">(</span>sr_6r<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span>, win, <span class="org-rainbow-delimiters-depth-2">[]</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, Fs<span class="org-rainbow-delimiters-depth-1">)</span>;
<span class="org-rainbow-delimiters-depth-1">[</span>px60r, <span class="org-type">~</span><span class="org-rainbow-delimiters-depth-1">]</span> = pwelch<span class="org-rainbow-delimiters-depth-1">(</span>sr_60r<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span>, win, <span class="org-rainbow-delimiters-depth-2">[]</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, Fs<span class="org-rainbow-delimiters-depth-1">)</span>;
</pre>
</div>
<p>
And we plot the ASD of the measured signals (figure <a href="#org7125217">10</a>);
</p>
<div class="org-src-container">
<pre class="src src-matlab"><span class="org-type">figure</span>;
hold on;
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, sqrt<span class="org-rainbow-delimiters-depth-2">(</span>pxoff<span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'OFF'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, sqrt<span class="org-rainbow-delimiters-depth-2">(</span>pxon<span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'ON'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, sqrt<span class="org-rainbow-delimiters-depth-2">(</span>px6r<span class="org-rainbow-delimiters-depth-2">)</span>, 'DisplayName', '<span class="org-highlight-numbers-number">6rpm</span>'<span class="org-rainbow-delimiters-depth-1">)</span>;
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, sqrt<span class="org-rainbow-delimiters-depth-2">(</span>px60r<span class="org-rainbow-delimiters-depth-2">)</span>, 'DisplayName', '<span class="org-highlight-numbers-number">60rpm</span>'<span class="org-rainbow-delimiters-depth-1">)</span>;
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, sqrt<span class="org-rainbow-delimiters-depth-2">(</span>pxdir<span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'k-', 'DisplayName', 'Direct'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
hold off;
<span class="org-type">set</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-variable-name">gca</span>, <span class="org-string">'xscale', 'log'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
<span class="org-type">set</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-variable-name">gca</span>, <span class="org-string">'yscale', 'log'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
xlabel<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Frequency </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">Hz</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">)</span></span><span class="org-string">; ylabel</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">(</span></span><span class="org-string">'</span>ASD of the measured Voltage $<span class="org-type">\</span>left<span class="org-rainbow-delimiters-depth-2">[</span><span class="org-type">\</span>frac<span class="org-rainbow-delimiters-depth-3">{</span>V<span class="org-rainbow-delimiters-depth-3">}{</span><span class="org-type">\</span>sqrt<span class="org-rainbow-delimiters-depth-4">{</span>Hz<span class="org-rainbow-delimiters-depth-4">}</span><span class="org-rainbow-delimiters-depth-3">}</span><span class="org-type">\</span>right<span class="org-rainbow-delimiters-depth-2">]</span>$'<span class="org-rainbow-delimiters-depth-1">)</span>
legend<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Location', 'northeast'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
xlim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span><span class="org-highlight-numbers-number">0</span>.<span class="org-highlight-numbers-number">1</span>, <span class="org-highlight-numbers-number">500</span><span class="org-rainbow-delimiters-depth-2">]</span><span class="org-rainbow-delimiters-depth-1">)</span>;
</pre>
</div>
<div id="org7125217" class="figure">
<p><img src="figs/sr_psd_compare.png" alt="sr_psd_compare.png" />
</p>
<p><span class="figure-number">Figure 10: </span>Comparison of the ASD of the measured signals when the slip-ring is ON, OFF and turning</p>
</div>
</div>
</div>
<div id="outline-container-org83ed722" class="outline-3">
<h3 id="org83ed722"><span class="section-number-3">3.5</span> Conclusion</h3>
<div class="outline-text-3" id="text-3-5">
<div class="important">
<p>
<b>Questions:</b>
</p>
<ul class="org-ul">
<li>Why is there some sharp peaks? Can this be due to aliasing?</li>
<li>It is possible that the amplifiers were saturating during the measurements => should redo the measurements with a low pass filter before the voltage amplifier</li>
</ul>
</div>
</div>
</div>
</div>
<div id="outline-container-orgfbf06e6" class="outline-2">
<h2 id="orgfbf06e6"><span class="section-number-2">4</span> Measure of the noise induced by the slip ring when using a geophone</h2>
<div class="outline-text-2" id="text-4">
<p>
The data and matlab files are accessible <a href="data/meas_sr_geophone.zip">here</a>.
</p>
</div>
<div id="outline-container-orgffb1bdb" class="outline-3">
<h3 id="orgffb1bdb"><span class="section-number-3">4.1</span> First Measurement without LPF</h3>
<div class="outline-text-3" id="text-4-1">
</div>
<div id="outline-container-org8e8831c" class="outline-4">
<h4 id="org8e8831c"><span class="section-number-4">4.1.1</span> Measurement Description</h4>
<div class="outline-text-4" id="text-4-1-1">
<p>
<b>Goal</b>:
</p>
<ul class="org-ul">
<li>Determine if the noise induced by the slip-ring is a limiting factor when measuring the signal coming from a geophone</li>
</ul>
<p>
<b>Setup</b>:
</p>
<ul class="org-ul">
<li>The geophone is located at the sample location</li>
<li>The two Voltage amplifiers have the same following settings:
<ul class="org-ul">
<li>AC</li>
<li>60dB</li>
<li>1kHz</li>
</ul></li>
<li>The signal from the geophone is split into two using a T-BNC:
<ul class="org-ul">
<li>One part goes directly to the voltage amplifier and then to the ADC.</li>
<li>The other part goes to the slip-ring=>voltage amplifier=>ADC.</li>
</ul></li>
</ul>
<p>
First column: Direct measure
Second column: Slip-ring measure
</p>
<p>
<b>Measurements</b>:
</p>
<ul class="org-ul">
<li><code>data_012</code>: Slip-Ring OFF</li>
<li><code>data_013</code>: Slip-Ring ON</li>
</ul>
</div>
</div>
<div id="outline-container-org167eeae" class="outline-4">
<h4 id="org167eeae"><span class="section-number-4">4.1.2</span> Load data</h4>
<div class="outline-text-4" id="text-4-1-2">
<p>
We load the data of the z axis of two geophones.
</p>
<div class="org-src-container">
<pre class="src src-matlab">sr_off = load<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'mat/data_012.mat', 'data'</span><span class="org-rainbow-delimiters-depth-1">)</span>; sr_off = sr_off.data;
sr_on = load<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'mat/data_013.mat', 'data'</span><span class="org-rainbow-delimiters-depth-1">)</span>; sr_on = sr_on.data;
</pre>
</div>
</div>
</div>
<div id="outline-container-org583abb2" class="outline-4">
<h4 id="org583abb2"><span class="section-number-4">4.1.3</span> Time Domain</h4>
<div class="outline-text-4" id="text-4-1-3">
<p>
We compare the signal when the Slip-Ring is OFF (figure <a href="#org86338a6">11</a>) and when it is ON (figure <a href="#org9c8364f">12</a>).
</p>
<div id="org86338a6" class="figure">
<p><img src="figs/sr_geophone_time_off.png" alt="sr_geophone_time_off.png" />
</p>
<p><span class="figure-number">Figure 11: </span>Comparison of the time domain signals when the slip-ring is OFF</p>
</div>
<div id="org9c8364f" class="figure">
<p><img src="figs/sr_geophone_time_on.png" alt="sr_geophone_time_on.png" />
</p>
<p><span class="figure-number">Figure 12: </span>Comparison of the time domain signals when the slip-ring is ON</p>
</div>
</div>
</div>
<div id="outline-container-org35e29fe" class="outline-4">
<h4 id="org35e29fe"><span class="section-number-4">4.1.4</span> Frequency Domain</h4>
<div class="outline-text-4" id="text-4-1-4">
<p>
We first compute some parameters that will be used for the PSD computation.
</p>
<div class="org-src-container">
<pre class="src src-matlab">dt = sr_off<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">2</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-1">)</span><span class="org-type">-</span>sr_off<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">1</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-1">)</span>;
Fs = <span class="org-highlight-numbers-number">1</span><span class="org-type">/</span>dt; <span class="org-comment">% [Hz]</span>
win = hanning<span class="org-rainbow-delimiters-depth-1">(</span>ceil<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-highlight-numbers-number">10</span><span class="org-type">*</span>Fs<span class="org-rainbow-delimiters-depth-2">)</span><span class="org-rainbow-delimiters-depth-1">)</span>;
</pre>
</div>
<p>
Then we compute the Power Spectral Density using <code>pwelch</code> function.
</p>
<div class="org-src-container">
<pre class="src src-matlab"><span class="org-comment">% Direct measure</span>
<span class="org-rainbow-delimiters-depth-1">[</span>pxdoff, <span class="org-type">~</span><span class="org-rainbow-delimiters-depth-1">]</span> = pwelch<span class="org-rainbow-delimiters-depth-1">(</span>sr_off<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, win, <span class="org-rainbow-delimiters-depth-2">[]</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, Fs<span class="org-rainbow-delimiters-depth-1">)</span>;
<span class="org-rainbow-delimiters-depth-1">[</span>pxdon, <span class="org-type">~</span><span class="org-rainbow-delimiters-depth-1">]</span> = pwelch<span class="org-rainbow-delimiters-depth-1">(</span>sr_on<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, win, <span class="org-rainbow-delimiters-depth-2">[]</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, Fs<span class="org-rainbow-delimiters-depth-1">)</span>;
<span class="org-comment">% Slip-Ring measure</span>
<span class="org-rainbow-delimiters-depth-1">[</span>pxsroff, f<span class="org-rainbow-delimiters-depth-1">]</span> = pwelch<span class="org-rainbow-delimiters-depth-1">(</span>sr_off<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span>, win, <span class="org-rainbow-delimiters-depth-2">[]</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, Fs<span class="org-rainbow-delimiters-depth-1">)</span>;
<span class="org-rainbow-delimiters-depth-1">[</span>pxsron, <span class="org-type">~</span><span class="org-rainbow-delimiters-depth-1">]</span> = pwelch<span class="org-rainbow-delimiters-depth-1">(</span>sr_on<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span>, win, <span class="org-rainbow-delimiters-depth-2">[]</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, Fs<span class="org-rainbow-delimiters-depth-1">)</span>;
</pre>
</div>
<p>
Finally, we compare the Amplitude Spectral Density of the signals (figure <a href="#org4e3b998">13</a>);
</p>
<div class="org-src-container">
<pre class="src src-matlab"><span class="org-type">figure</span>;
hold on;
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, sqrt<span class="org-rainbow-delimiters-depth-2">(</span>pxdoff<span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'Direct - OFF'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, sqrt<span class="org-rainbow-delimiters-depth-2">(</span>pxsroff<span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'Slip-Ring - OFF'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, sqrt<span class="org-rainbow-delimiters-depth-2">(</span>pxdon<span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'Direct - ON'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, sqrt<span class="org-rainbow-delimiters-depth-2">(</span>pxsron<span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'Slip-Ring - ON'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
hold off;
<span class="org-type">set</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-variable-name">gca</span>, <span class="org-string">'xscale', 'log'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
<span class="org-type">set</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-variable-name">gca</span>, <span class="org-string">'yscale', 'log'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
xlabel<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Frequency </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">Hz</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">)</span></span><span class="org-string">; ylabel</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">(</span></span><span class="org-string">'</span>ASD of the measured Voltage $<span class="org-type">\</span>left<span class="org-rainbow-delimiters-depth-2">[</span><span class="org-type">\</span>frac<span class="org-rainbow-delimiters-depth-3">{</span>V<span class="org-rainbow-delimiters-depth-3">}{</span><span class="org-type">\</span>sqrt<span class="org-rainbow-delimiters-depth-4">{</span>Hz<span class="org-rainbow-delimiters-depth-4">}</span><span class="org-rainbow-delimiters-depth-3">}</span><span class="org-type">\</span>right<span class="org-rainbow-delimiters-depth-2">]</span>$'<span class="org-rainbow-delimiters-depth-1">)</span>
legend<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Location', 'northeast'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
xlim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span><span class="org-highlight-numbers-number">0</span>.<span class="org-highlight-numbers-number">1</span>, <span class="org-highlight-numbers-number">500</span><span class="org-rainbow-delimiters-depth-2">]</span><span class="org-rainbow-delimiters-depth-1">)</span>;
</pre>
</div>
<div id="org4e3b998" class="figure">
<p><img src="figs/sr_geophone_asd.png" alt="sr_geophone_asd.png" />
</p>
<p><span class="figure-number">Figure 13: </span>Comparison of the Amplitude Spectral Sensity</p>
</div>
<div id="org6078350" class="figure">
<p><img src="figs/sr_geophone_asd_zoom.png" alt="sr_geophone_asd_zoom.png" />
</p>
<p><span class="figure-number">Figure 14: </span>Comparison of the Amplitude Spectral Sensity - Zoom</p>
</div>
</div>
</div>
<div id="outline-container-org3e43efe" class="outline-4">
<h4 id="org3e43efe"><span class="section-number-4">4.1.5</span> Conclusion</h4>
<div class="outline-text-4" id="text-4-1-5">
<div class="important">
<ul class="org-ul">
<li>The fact that the Slip-Ring is turned ON adds some noise to the signal.</li>
<li>The signal going through the Slip-Ring is less noisy than the one going directly to the ADC.</li>
<li>This could be due to less good electromagnetic isolation.</li>
</ul>
<p>
<b>Questions</b>:
</p>
<ul class="org-ul">
<li>Can the sharp peak on figure <a href="#org6078350">14</a> be due to the Aliasing?</li>
</ul>
</div>
</div>
</div>
</div>
<div id="outline-container-orgf298379" class="outline-3">
<h3 id="orgf298379"><span class="section-number-3">4.2</span> Measurement using an oscilloscope</h3>
<div class="outline-text-3" id="text-4-2">
</div>
<div id="outline-container-org68d1d31" class="outline-4">
<h4 id="org68d1d31"><span class="section-number-4">4.2.1</span> Measurement Setup</h4>
<div class="outline-text-4" id="text-4-2-1">
<p>
Know we are measuring the same signals but using an oscilloscope instead of the Speedgoat ADC.
</p>
</div>
</div>
<div id="outline-container-org5276b1f" class="outline-4">
<h4 id="org5276b1f"><span class="section-number-4">4.2.2</span> Observations</h4>
<div class="outline-text-4" id="text-4-2-2">
<p>
Then the Slip-Ring is ON (figure <a href="#org6ea2865">15</a>), 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.
</p>
<p>
Then the Slip-Ring is OFF, we don't observe this 40kHz anymore (figure <a href="#org2bd880f">16</a>).
</p>
<div id="org6ea2865" class="figure">
<p><img src="./img/IMG_20190506_160420.jpg" alt="IMG_20190506_160420.jpg" width="500px" />
</p>
<p><span class="figure-number">Figure 15: </span>Signals measured by the oscilloscope - Slip-Ring ON - Yellow: Direct measure - Blue: Through Slip-Ring</p>
</div>
<div id="org2bd880f" class="figure">
<p><img src="./img/IMG_20190506_160438.jpg" alt="IMG_20190506_160438.jpg" width="500px" />
</p>
<p><span class="figure-number">Figure 16: </span>Signals measured by the oscilloscope - Slip-Ring OFF - Yellow: Direct measure - Blue: Through Slip-Ring</p>
</div>
</div>
</div>
<div id="outline-container-org54a8d62" class="outline-4">
<h4 id="org54a8d62"><span class="section-number-4">4.2.3</span> Conclusion</h4>
<div class="outline-text-4" id="text-4-2-3">
<div class="important">
<ul class="org-ul">
<li>By looking at the signals using an oscilloscope, there is a lot of high frequency noise when turning on the Slip-Ring</li>
<li>This can eventually saturate the voltage amplifiers (seen by a led indicating saturation)</li>
<li>The choice is to <b>add a Low pass filter before the voltage amplifiers</b> to not saturate them and filter the noise.</li>
</ul>
</div>
</div>
</div>
</div>
<div id="outline-container-orgcebb9a0" class="outline-3">
<h3 id="orgcebb9a0"><span class="section-number-3">4.3</span> New measurements with a LPF before the Voltage Amplifiers</h3>
<div class="outline-text-3" id="text-4-3">
</div>
<div id="outline-container-org4bdf600" class="outline-4">
<h4 id="org4bdf600"><span class="section-number-4">4.3.1</span> Setup description</h4>
<div class="outline-text-4" id="text-4-3-1">
<p>
A first order low pass filter is added before the Voltage Amplifiers with the following values:
</p>
\begin{aligned}
R &= 1k\Omega \\
C &= 1\mu F
\end{aligned}
<p>
And we have a cut-off frequency of \(f_c = \frac{1}{RC} = 160Hz\).
</p>
<p>
We are measuring the signal from a geophone put on the marble with and without the added LPF:
</p>
<ul class="org-ul">
<li>with the slip ring OFF: <code>mat/data_016.mat</code></li>
<li>with the slip ring ON: <code>mat/data_017.mat</code></li>
</ul>
</div>
</div>
<div id="outline-container-org5c96c5f" class="outline-4">
<h4 id="org5c96c5f"><span class="section-number-4">4.3.2</span> Load data</h4>
<div class="outline-text-4" id="text-4-3-2">
<p>
We load the data of the z axis of two geophones.
</p>
<div class="org-src-container">
<pre class="src src-matlab">sr_lpf_off = load<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'mat/data_016.mat', 'data'</span><span class="org-rainbow-delimiters-depth-1">)</span>; sr_lpf_off = sr_lpf_off.data;
sr_lpf_on = load<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'mat/data_017.mat', 'data'</span><span class="org-rainbow-delimiters-depth-1">)</span>; sr_lpf_on = sr_lpf_on.data;
</pre>
</div>
</div>
</div>
<div id="outline-container-orgbcba5cf" class="outline-4">
<h4 id="orgbcba5cf"><span class="section-number-4">4.3.3</span> Time Domain</h4>
<div class="outline-text-4" id="text-4-3-3">
<p>
We compare the signal when the Slip-Ring is OFF (figure <a href="#org521d3fb">17</a>) and when it is ON (figure <a href="#org49d5513">18</a>).
</p>
<div id="org521d3fb" class="figure">
<p><img src="figs/sr_lpf_geophone_time_off.png" alt="sr_lpf_geophone_time_off.png" />
</p>
<p><span class="figure-number">Figure 17: </span>Comparison of the time domain signals when the slip-ring is OFF</p>
</div>
<div id="org49d5513" class="figure">
<p><img src="figs/sr_lpf_geophone_time_on.png" alt="sr_lpf_geophone_time_on.png" />
</p>
<p><span class="figure-number">Figure 18: </span>Comparison of the time domain signals when the slip-ring is ON</p>
</div>
</div>
</div>
<div id="outline-container-org0d5a581" class="outline-4">
<h4 id="org0d5a581"><span class="section-number-4">4.3.4</span> Frequency Domain</h4>
<div class="outline-text-4" id="text-4-3-4">
<p>
We first compute some parameters that will be used for the PSD computation.
</p>
<div class="org-src-container">
<pre class="src src-matlab">dt = sr_lpf_off<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">2</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-1">)</span><span class="org-type">-</span>sr_lpf_off<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">1</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-1">)</span>;
Fs = <span class="org-highlight-numbers-number">1</span><span class="org-type">/</span>dt; <span class="org-comment">% [Hz]</span>
win = hanning<span class="org-rainbow-delimiters-depth-1">(</span>ceil<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-highlight-numbers-number">10</span><span class="org-type">*</span>Fs<span class="org-rainbow-delimiters-depth-2">)</span><span class="org-rainbow-delimiters-depth-1">)</span>;
</pre>
</div>
<p>
Then we compute the Power Spectral Density using <code>pwelch</code> function.
</p>
<div class="org-src-container">
<pre class="src src-matlab"><span class="org-comment">% Direct measure</span>
<span class="org-rainbow-delimiters-depth-1">[</span>pxd_lpf_off, <span class="org-type">~</span><span class="org-rainbow-delimiters-depth-1">]</span> = pwelch<span class="org-rainbow-delimiters-depth-1">(</span>sr_lpf_off<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, win, <span class="org-rainbow-delimiters-depth-2">[]</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, Fs<span class="org-rainbow-delimiters-depth-1">)</span>;
<span class="org-rainbow-delimiters-depth-1">[</span>pxd_lpf_on, <span class="org-type">~</span><span class="org-rainbow-delimiters-depth-1">]</span> = pwelch<span class="org-rainbow-delimiters-depth-1">(</span>sr_lpf_on<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, win, <span class="org-rainbow-delimiters-depth-2">[]</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, Fs<span class="org-rainbow-delimiters-depth-1">)</span>;
<span class="org-comment">% Slip-Ring measure</span>
<span class="org-rainbow-delimiters-depth-1">[</span>pxsr_lpf_off, f<span class="org-rainbow-delimiters-depth-1">]</span> = pwelch<span class="org-rainbow-delimiters-depth-1">(</span>sr_lpf_off<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span>, win, <span class="org-rainbow-delimiters-depth-2">[]</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, Fs<span class="org-rainbow-delimiters-depth-1">)</span>;
<span class="org-rainbow-delimiters-depth-1">[</span>pxsr_lpf_on, <span class="org-type">~</span><span class="org-rainbow-delimiters-depth-1">]</span> = pwelch<span class="org-rainbow-delimiters-depth-1">(</span>sr_lpf_on<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span>, win, <span class="org-rainbow-delimiters-depth-2">[]</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, Fs<span class="org-rainbow-delimiters-depth-1">)</span>;
</pre>
</div>
<p>
Finally, we compare the Amplitude Spectral Density of the signals (figure <a href="#org09681f1">19</a>);
</p>
<div class="org-src-container">
<pre class="src src-matlab"><span class="org-type">figure</span>;
hold on;
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, sqrt<span class="org-rainbow-delimiters-depth-2">(</span>pxd_lpf_off<span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'Direct - OFF'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, sqrt<span class="org-rainbow-delimiters-depth-2">(</span>pxsr_lpf_off<span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'Slip-Ring - OFF'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, sqrt<span class="org-rainbow-delimiters-depth-2">(</span>pxd_lpf_on<span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'Direct - ON'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, sqrt<span class="org-rainbow-delimiters-depth-2">(</span>pxsr_lpf_on<span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'Slip-Ring - ON'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
hold off;
<span class="org-type">set</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-variable-name">gca</span>, <span class="org-string">'xscale', 'log'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
<span class="org-type">set</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-variable-name">gca</span>, <span class="org-string">'yscale', 'log'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
xlabel<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Frequency </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">Hz</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">)</span></span><span class="org-string">; ylabel</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">(</span></span><span class="org-string">'</span>ASD of the measured Voltage $<span class="org-type">\</span>left<span class="org-rainbow-delimiters-depth-2">[</span><span class="org-type">\</span>frac<span class="org-rainbow-delimiters-depth-3">{</span>V<span class="org-rainbow-delimiters-depth-3">}{</span><span class="org-type">\</span>sqrt<span class="org-rainbow-delimiters-depth-4">{</span>Hz<span class="org-rainbow-delimiters-depth-4">}</span><span class="org-rainbow-delimiters-depth-3">}</span><span class="org-type">\</span>right<span class="org-rainbow-delimiters-depth-2">]</span>$'<span class="org-rainbow-delimiters-depth-1">)</span>
legend<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Location', 'northeast'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
xlim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span><span class="org-highlight-numbers-number">0</span>.<span class="org-highlight-numbers-number">1</span>, <span class="org-highlight-numbers-number">500</span><span class="org-rainbow-delimiters-depth-2">]</span><span class="org-rainbow-delimiters-depth-1">)</span>;
</pre>
</div>
<div id="org09681f1" class="figure">
<p><img src="figs/sr_lpf_geophone_asd.png" alt="sr_lpf_geophone_asd.png" />
</p>
<p><span class="figure-number">Figure 19: </span>Comparison of the Amplitude Spectral Sensity</p>
</div>
<div id="orgc8c197a" class="figure">
<p><img src="figs/sr_lpf_geophone_asd_zoom.png" alt="sr_lpf_geophone_asd_zoom.png" />
</p>
<p><span class="figure-number">Figure 20: </span>Comparison of the Amplitude Spectral Sensity - Zoom</p>
</div>
</div>
</div>
<div id="outline-container-orgad63dd1" class="outline-4">
<h4 id="orgad63dd1"><span class="section-number-4">4.3.5</span> Comparison of with and without LPF</h4>
<div class="outline-text-4" id="text-4-3-5">
<div class="org-src-container">
<pre class="src src-matlab"><span class="org-type">figure</span>;
hold on;
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, sqrt<span class="org-rainbow-delimiters-depth-2">(</span>pxdon<span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'Direct - ON'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, sqrt<span class="org-rainbow-delimiters-depth-2">(</span>pxsron<span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'Slip-Ring - ON'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, sqrt<span class="org-rainbow-delimiters-depth-2">(</span>pxd_lpf_on<span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'Direct - ON - LPF'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, sqrt<span class="org-rainbow-delimiters-depth-2">(</span>pxsr_lpf_on<span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'Slip-Ring - ON - LPF'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
hold off;
<span class="org-type">set</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-variable-name">gca</span>, <span class="org-string">'xscale', 'log'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
<span class="org-type">set</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-variable-name">gca</span>, <span class="org-string">'yscale', 'log'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
xlabel<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Frequency </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">Hz</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">)</span></span><span class="org-string">; ylabel</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">(</span></span><span class="org-string">'</span>ASD of the measured Voltage $<span class="org-type">\</span>left<span class="org-rainbow-delimiters-depth-2">[</span><span class="org-type">\</span>frac<span class="org-rainbow-delimiters-depth-3">{</span>V<span class="org-rainbow-delimiters-depth-3">}{</span><span class="org-type">\</span>sqrt<span class="org-rainbow-delimiters-depth-4">{</span>Hz<span class="org-rainbow-delimiters-depth-4">}</span><span class="org-rainbow-delimiters-depth-3">}</span><span class="org-type">\</span>right<span class="org-rainbow-delimiters-depth-2">]</span>$'<span class="org-rainbow-delimiters-depth-1">)</span>
legend<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Location', 'northeast'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
xlim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span><span class="org-highlight-numbers-number">0</span>.<span class="org-highlight-numbers-number">1</span>, <span class="org-highlight-numbers-number">500</span><span class="org-rainbow-delimiters-depth-2">]</span><span class="org-rainbow-delimiters-depth-1">)</span>;
</pre>
</div>
<div id="org85b75e8" class="figure">
<p><img src="figs/comp_with_without_lpf.png" alt="comp_with_without_lpf.png" />
</p>
<p><span class="figure-number">Figure 21: </span>Comparison of the measured signals with and without LPF</p>
</div>
</div>
</div>
<div id="outline-container-orgdece1f2" class="outline-4">
<h4 id="orgdece1f2"><span class="section-number-4">4.3.6</span> Conclusion</h4>
<div class="outline-text-4" id="text-4-3-6">
<div class="important">
<ul class="org-ul">
<li>Using the LPF, we don't have any perturbation coming from the slip-ring when it is on.</li>
<li>However, we should use a smaller value of the capacitor to have a cut-off frequency at \(1kHz\).</li>
</ul>
</div>
</div>
</div>
</div>
</div>
<div id="outline-container-org23a8137" class="outline-2">
<h2 id="org23a8137"><span class="section-number-2">5</span> Measure of the influence of the AC/DC option on the voltage amplifiers</h2>
<div class="outline-text-2" id="text-5">
<p>
The data and matlab files are accessible <a href="data/meas_noise_ac_dc.zip">here</a>.
</p>
</div>
<div id="outline-container-org58bc336" class="outline-3">
<h3 id="org58bc336"><span class="section-number-3">5.1</span> Measurement Description</h3>
<div class="outline-text-3" id="text-5-1">
<p>
<b>Goal</b>:
</p>
<ul class="org-ul">
<li>Measure the influence of the high-pass filter option of the voltage amplifiers</li>
</ul>
<p>
<b>Setup</b>:
</p>
<ul class="org-ul">
<li>One geophone is located on the marble.</li>
<li>It's signal goes to two voltage amplifiers with a gain of 60dB.</li>
<li>One voltage amplifier is on the AC option, the other is on the DC option.</li>
</ul>
<p>
<b>Measurements</b>:
First measurement (<code>mat/data_014.mat</code> file):
</p>
<table border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
<colgroup>
<col class="org-right" />
<col class="org-left" />
</colgroup>
<thead>
<tr>
<th scope="col" class="org-right">Column</th>
<th scope="col" class="org-left">Signal</th>
</tr>
</thead>
<tbody>
<tr>
<td class="org-right">1</td>
<td class="org-left">Amplifier 1 with AC option</td>
</tr>
<tr>
<td class="org-right">2</td>
<td class="org-left">Amplifier 2 with DC option</td>
</tr>
<tr>
<td class="org-right">3</td>
<td class="org-left">Time</td>
</tr>
</tbody>
</table>
<p>
Second measurement (<code>mat/data_015.mat</code> file):
</p>
<table border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
<colgroup>
<col class="org-right" />
<col class="org-left" />
</colgroup>
<thead>
<tr>
<th scope="col" class="org-right">Column</th>
<th scope="col" class="org-left">Signal</th>
</tr>
</thead>
<tbody>
<tr>
<td class="org-right">1</td>
<td class="org-left">Amplifier 1 with DC option</td>
</tr>
<tr>
<td class="org-right">2</td>
<td class="org-left">Amplifier 2 with AC option</td>
</tr>
<tr>
<td class="org-right">3</td>
<td class="org-left">Time</td>
</tr>
</tbody>
</table>
<div id="orgde4e8ac" class="figure">
<p><img src="./img/IMG_20190503_170936.jpg" alt="IMG_20190503_170936.jpg" width="500px" />
</p>
<p><span class="figure-number">Figure 22: </span>Picture of the two voltages amplifiers</p>
</div>
</div>
</div>
<div id="outline-container-org137ca7d" class="outline-3">
<h3 id="org137ca7d"><span class="section-number-3">5.2</span> Load data</h3>
<div class="outline-text-3" id="text-5-2">
<p>
We load the data of the z axis of two geophones.
</p>
<div class="org-src-container">
<pre class="src src-matlab">meas14 = load<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'mat/data_014.mat', 'data'</span><span class="org-rainbow-delimiters-depth-1">)</span>; meas14 = meas14.data;
meas15 = load<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'mat/data_015.mat', 'data'</span><span class="org-rainbow-delimiters-depth-1">)</span>; meas15 = meas15.data;
</pre>
</div>
</div>
</div>
<div id="outline-container-orgce0337d" class="outline-3">
<h3 id="orgce0337d"><span class="section-number-3">5.3</span> Time Domain</h3>
<div class="outline-text-3" id="text-5-3">
<p>
The signals are shown on figure <a href="#org24fe5db">23</a>.
</p>
<div id="org24fe5db" class="figure">
<p><img src="figs/ac_dc_option_time.png" alt="ac_dc_option_time.png" />
</p>
<p><span class="figure-number">Figure 23: </span>Comparison of the signals going through the Voltage amplifiers</p>
</div>
</div>
</div>
<div id="outline-container-org1ca91db" class="outline-3">
<h3 id="org1ca91db"><span class="section-number-3">5.4</span> Frequency Domain</h3>
<div class="outline-text-3" id="text-5-4">
<p>
We first compute some parameters that will be used for the PSD computation.
</p>
<div class="org-src-container">
<pre class="src src-matlab">dt = meas14<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">2</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-1">)</span><span class="org-type">-</span>meas14<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">1</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-1">)</span>;
Fs = <span class="org-highlight-numbers-number">1</span><span class="org-type">/</span>dt; <span class="org-comment">% [Hz]</span>
win = hanning<span class="org-rainbow-delimiters-depth-1">(</span>ceil<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-highlight-numbers-number">10</span><span class="org-type">*</span>Fs<span class="org-rainbow-delimiters-depth-2">)</span><span class="org-rainbow-delimiters-depth-1">)</span>;
</pre>
</div>
<p>
Then we compute the Power Spectral Density using <code>pwelch</code> function.
</p>
<div class="org-src-container">
<pre class="src src-matlab"><span class="org-rainbow-delimiters-depth-1">[</span>pxamp1ac, f<span class="org-rainbow-delimiters-depth-1">]</span> = pwelch<span class="org-rainbow-delimiters-depth-1">(</span>meas14<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, win, <span class="org-rainbow-delimiters-depth-2">[]</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, Fs<span class="org-rainbow-delimiters-depth-1">)</span>;
<span class="org-rainbow-delimiters-depth-1">[</span>pxamp2dc, <span class="org-type">~</span><span class="org-rainbow-delimiters-depth-1">]</span> = pwelch<span class="org-rainbow-delimiters-depth-1">(</span>meas14<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span>, win, <span class="org-rainbow-delimiters-depth-2">[]</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, Fs<span class="org-rainbow-delimiters-depth-1">)</span>;
<span class="org-rainbow-delimiters-depth-1">[</span>pxamp1dc, <span class="org-type">~</span><span class="org-rainbow-delimiters-depth-1">]</span> = pwelch<span class="org-rainbow-delimiters-depth-1">(</span>meas15<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, win, <span class="org-rainbow-delimiters-depth-2">[]</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, Fs<span class="org-rainbow-delimiters-depth-1">)</span>;
<span class="org-rainbow-delimiters-depth-1">[</span>pxamp2ac, <span class="org-type">~</span><span class="org-rainbow-delimiters-depth-1">]</span> = pwelch<span class="org-rainbow-delimiters-depth-1">(</span>meas15<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span>, win, <span class="org-rainbow-delimiters-depth-2">[]</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, Fs<span class="org-rainbow-delimiters-depth-1">)</span>;
</pre>
</div>
<p>
The ASD of the signals are compare on figure <a href="#orgf2f8049">24</a>.
</p>
<div id="orgf2f8049" class="figure">
<p><img src="figs/ac_dc_option_asd.png" alt="ac_dc_option_asd.png" />
</p>
<p><span class="figure-number">Figure 24: </span>Amplitude Spectral Density of the measured signals</p>
</div>
</div>
</div>
<div id="outline-container-orge0411ce" class="outline-3">
<h3 id="orge0411ce"><span class="section-number-3">5.5</span> Conclusion</h3>
<div class="outline-text-3" id="text-5-5">
<div class="important">
<ul class="org-ul">
<li>The voltage amplifiers include some very sharp high pass filters at 1.5Hz (maybe 4th order)</li>
<li>There is a DC offset on the time domain signal because the DC-offset knob was not set to zero</li>
</ul>
</div>
</div>
</div>
</div>
<div id="outline-container-org6d3a86e" class="outline-2">
<h2 id="org6d3a86e"><span class="section-number-2">6</span> Transfer function of the Low Pass Filter</h2>
<div class="outline-text-2" id="text-6">
<p>
The computation files for this section are accessible <a href="data/low_pass_filter_measurements.zip">here</a>.
</p>
</div>
<div id="outline-container-org50dfe76" class="outline-3">
<h3 id="org50dfe76"><span class="section-number-3">6.1</span> First LPF with a Cut-off frequency of 160Hz</h3>
<div class="outline-text-3" id="text-6-1">
</div>
<div id="outline-container-orge61a68e" class="outline-4">
<h4 id="orge61a68e"><span class="section-number-4">6.1.1</span> Measurement Description</h4>
<div class="outline-text-4" id="text-6-1-1">
<p>
<b>Goal</b>:
</p>
<ul class="org-ul">
<li>Measure the Low Pass Filter Transfer Function</li>
</ul>
<p>
The values of the components are:
</p>
\begin{aligned}
R &= 1k\Omega \\
C &= 1\mu F
\end{aligned}
<p>
Which makes a cut-off frequency of \(f_c = \frac{1}{RC} = 1000 rad/s = 160Hz\).
</p>
<div class="org-src-container">
<pre class="src src-latex" id="org1bfb14a"><span class="org-font-latex-sedate"><span class="org-keyword">\begin</span></span>{<span class="org-function-name">tikzpicture</span>}
<span class="org-font-latex-sedate">\draw</span> (0,2)
to [R=<span class="org-font-latex-sedate"><span class="org-font-latex-math">\(R\)</span></span>] ++(2,0) node[circ]
to ++(2,0)
++(-2,0)
to [C=<span class="org-font-latex-sedate"><span class="org-font-latex-math">\(C\)</span></span>] ++(0,-2) node[circ]
++(-2,0)
to ++(2,0)
to ++(2,0)
<span class="org-font-latex-sedate"><span class="org-keyword">\end</span></span>{<span class="org-function-name">tikzpicture</span>}
</pre>
</div>
<div id="orge941987" class="figure">
<p><img src="figs/lpf.png" alt="lpf.png" />
</p>
<p><span class="figure-number">Figure 25: </span>Schematic of the Low Pass Filter used</p>
</div>
<p>
<b>Setup</b>:
</p>
<ul class="org-ul">
<li>We are measuring the signal from from Geophone with a BNC T</li>
<li>On part goes to column 1 through the LPF</li>
<li>The other part goes to column 2 without the LPF</li>
</ul>
<p>
<b>Measurements</b>:
<code>mat/data_018.mat</code>:
</p>
<table border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
<colgroup>
<col class="org-right" />
<col class="org-left" />
</colgroup>
<thead>
<tr>
<th scope="col" class="org-right">Column</th>
<th scope="col" class="org-left">Signal</th>
</tr>
</thead>
<tbody>
<tr>
<td class="org-right">1</td>
<td class="org-left">Amplifier 1 with LPF</td>
</tr>
<tr>
<td class="org-right">2</td>
<td class="org-left">Amplifier 2</td>
</tr>
<tr>
<td class="org-right">3</td>
<td class="org-left">Time</td>
</tr>
</tbody>
</table>
</div>
</div>
<div id="outline-container-org229c82b" class="outline-4">
<h4 id="org229c82b"><span class="section-number-4">6.1.2</span> Load data</h4>
<div class="outline-text-4" id="text-6-1-2">
<p>
We load the data of the z axis of two geophones.
</p>
<div class="org-src-container">
<pre class="src src-matlab">data = load<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'mat/data_018.mat', 'data'</span><span class="org-rainbow-delimiters-depth-1">)</span>; data = data.data;
</pre>
</div>
</div>
</div>
<div id="outline-container-org78a38da" class="outline-4">
<h4 id="org78a38da"><span class="section-number-4">6.1.3</span> Transfer function of the LPF</h4>
<div class="outline-text-4" id="text-6-1-3">
<p>
We compute the transfer function from the signal without the LPF to the signal measured with the LPF.
</p>
<div class="org-src-container">
<pre class="src src-matlab">dt = data<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">2</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-1">)</span><span class="org-type">-</span>data<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">1</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-1">)</span>;
Fs = <span class="org-highlight-numbers-number">1</span><span class="org-type">/</span>dt; <span class="org-comment">% [Hz]</span>
win = hanning<span class="org-rainbow-delimiters-depth-1">(</span>ceil<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-highlight-numbers-number">10</span><span class="org-type">*</span>Fs<span class="org-rainbow-delimiters-depth-2">)</span><span class="org-rainbow-delimiters-depth-1">)</span>;
</pre>
</div>
<div class="org-src-container">
<pre class="src src-matlab"><span class="org-rainbow-delimiters-depth-1">[</span>Glpf, f<span class="org-rainbow-delimiters-depth-1">]</span> = tfestimate<span class="org-rainbow-delimiters-depth-1">(</span>data<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span>, data<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, win, <span class="org-rainbow-delimiters-depth-2">[]</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, Fs<span class="org-rainbow-delimiters-depth-1">)</span>;
</pre>
</div>
<p>
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 <a href="#org9c29fd5">26</a>.
</p>
<div class="org-src-container">
<pre class="src src-matlab">Gth = <span class="org-highlight-numbers-number">1</span><span class="org-type">/</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">1</span><span class="org-type">+</span>s<span class="org-type">/</span><span class="org-highlight-numbers-number">1000</span><span class="org-rainbow-delimiters-depth-1">)</span>
</pre>
</div>
<div class="org-src-container">
<pre class="src src-matlab"><span class="org-type">figure</span>;
ax1 = subplot<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">2</span>, <span class="org-highlight-numbers-number">1</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-1">)</span>;
hold on;
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, abs<span class="org-rainbow-delimiters-depth-2">(</span>Glpf<span class="org-rainbow-delimiters-depth-2">)</span><span class="org-rainbow-delimiters-depth-1">)</span>;
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, abs<span class="org-rainbow-delimiters-depth-2">(</span>squeeze<span class="org-rainbow-delimiters-depth-3">(</span>freqresp<span class="org-rainbow-delimiters-depth-4">(</span>Gth, f, <span class="org-string">'Hz'</span><span class="org-rainbow-delimiters-depth-4">)</span><span class="org-rainbow-delimiters-depth-3">)</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-rainbow-delimiters-depth-1">)</span>;
hold off;
<span class="org-type">set</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-variable-name">gca</span>, <span class="org-string">'xscale', 'log'</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">)</span></span><span class="org-string">; set</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">(</span></span><span class="org-string">gca, 'yscale', 'log'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
<span class="org-type">set</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-variable-name">gca</span>, <span class="org-string">'XTickLabel'</span>,<span class="org-rainbow-delimiters-depth-2">[]</span><span class="org-rainbow-delimiters-depth-1">)</span>;
ylabel<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Magnitude'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
ax2 = subplot<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">2</span>, <span class="org-highlight-numbers-number">1</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-1">)</span>;
hold on;
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, mod<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-highlight-numbers-number">180</span><span class="org-type">+</span><span class="org-highlight-numbers-number">180</span><span class="org-type">/</span><span class="org-constant">pi</span><span class="org-type">*</span>phase<span class="org-rainbow-delimiters-depth-3">(</span>Glpf<span class="org-rainbow-delimiters-depth-3">)</span>, <span class="org-highlight-numbers-number">360</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-type">-</span><span class="org-highlight-numbers-number">180</span><span class="org-rainbow-delimiters-depth-1">)</span>;
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, <span class="org-highlight-numbers-number">180</span><span class="org-type">/</span><span class="org-constant">pi</span><span class="org-type">*</span>unwrap<span class="org-rainbow-delimiters-depth-2">(</span>angle<span class="org-rainbow-delimiters-depth-3">(</span>squeeze<span class="org-rainbow-delimiters-depth-4">(</span>freqresp<span class="org-rainbow-delimiters-depth-5">(</span>Gth, f, <span class="org-string">'Hz'</span><span class="org-rainbow-delimiters-depth-5">)</span><span class="org-rainbow-delimiters-depth-4">)</span><span class="org-rainbow-delimiters-depth-3">)</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-rainbow-delimiters-depth-1">)</span>;
hold off;
<span class="org-type">set</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-variable-name">gca</span>, <span class="org-string">'xscale', 'log'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
ylim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span><span class="org-type">-</span><span class="org-highlight-numbers-number">180</span>, <span class="org-highlight-numbers-number">180</span><span class="org-rainbow-delimiters-depth-2">]</span><span class="org-rainbow-delimiters-depth-1">)</span>;
yticks<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span><span class="org-type">-</span><span class="org-highlight-numbers-number">180</span>, <span class="org-type">-</span><span class="org-highlight-numbers-number">90</span>, <span class="org-highlight-numbers-number">0</span>, <span class="org-highlight-numbers-number">90</span>, <span class="org-highlight-numbers-number">180</span><span class="org-rainbow-delimiters-depth-2">]</span><span class="org-rainbow-delimiters-depth-1">)</span>;
xlabel<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Frequency </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">Hz</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">)</span></span><span class="org-string">; ylabel</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">(</span></span><span class="org-string">'Phase'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
linkaxes<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span>ax1,ax2<span class="org-rainbow-delimiters-depth-2">]</span>,<span class="org-string">'x'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
xlim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span><span class="org-highlight-numbers-number">1</span>, <span class="org-highlight-numbers-number">500</span><span class="org-rainbow-delimiters-depth-2">]</span><span class="org-rainbow-delimiters-depth-1">)</span>;
</pre>
</div>
<div id="org9c29fd5" class="figure">
<p><img src="figs/Glpf_bode.png" alt="Glpf_bode.png" />
</p>
<p><span class="figure-number">Figure 26: </span>Bode Diagram of the measured Low Pass filter and the theoritical one</p>
</div>
</div>
</div>
<div id="outline-container-org59dee72" class="outline-4">
<h4 id="org59dee72"><span class="section-number-4">6.1.4</span> Conclusion</h4>
<div class="outline-text-4" id="text-6-1-4">
<div class="important">
<p>
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 \(1kHz\).
</p>
</div>
</div>
</div>
</div>
<div id="outline-container-org8b09702" class="outline-3">
<h3 id="org8b09702"><span class="section-number-3">6.2</span> Second LPF with a Cut-off frequency of 1000Hz</h3>
<div class="outline-text-3" id="text-6-2">
</div>
<div id="outline-container-orged36cb1" class="outline-4">
<h4 id="orged36cb1"><span class="section-number-4">6.2.1</span> Measurement description</h4>
<div class="outline-text-4" id="text-6-2-1">
<p>
This time, the value are
</p>
\begin{aligned}
R &= 1k\Omega \\
C &= 150nF
\end{aligned}
<p>
Which makes a low pass filter with a cut-off frequency of \(f_c = 1060Hz\).
</p>
</div>
</div>
<div id="outline-container-org7e593d2" class="outline-4">
<h4 id="org7e593d2"><span class="section-number-4">6.2.2</span> Load data</h4>
<div class="outline-text-4" id="text-6-2-2">
<p>
We load the data of the z axis of two geophones.
</p>
<div class="org-src-container">
<pre class="src src-matlab">data = load<span class="org-rainbow-delimiters-depth-1">(</span>'mat<span class="org-type">/</span>data_019.mat', <span class="org-string">'data'</span><span class="org-rainbow-delimiters-depth-1">)</span>; data = data.data;
</pre>
</div>
</div>
</div>
<div id="outline-container-org2e7d91e" class="outline-4">
<h4 id="org2e7d91e"><span class="section-number-4">6.2.3</span> Transfer function of the LPF</h4>
<div class="outline-text-4" id="text-6-2-3">
<p>
We compute the transfer function from the signal without the LPF to the signal measured with the LPF.
</p>
<div class="org-src-container">
<pre class="src src-matlab">dt = data<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">2</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-1">)</span><span class="org-type">-</span>data<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">1</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-1">)</span>;
Fs = <span class="org-highlight-numbers-number">1</span><span class="org-type">/</span>dt; <span class="org-comment">% [Hz]</span>
win = hanning<span class="org-rainbow-delimiters-depth-1">(</span>ceil<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-highlight-numbers-number">10</span><span class="org-type">*</span>Fs<span class="org-rainbow-delimiters-depth-2">)</span><span class="org-rainbow-delimiters-depth-1">)</span>;
</pre>
</div>
<div class="org-src-container">
<pre class="src src-matlab"><span class="org-rainbow-delimiters-depth-1">[</span>Glpf, f<span class="org-rainbow-delimiters-depth-1">]</span> = tfestimate<span class="org-rainbow-delimiters-depth-1">(</span>data<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span>, data<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, win, <span class="org-rainbow-delimiters-depth-2">[]</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, Fs<span class="org-rainbow-delimiters-depth-1">)</span>;
</pre>
</div>
<p>
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 <a href="#org60b202b">27</a>.
</p>
<div class="org-src-container">
<pre class="src src-matlab">Gth = <span class="org-highlight-numbers-number">1</span><span class="org-type">/</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">1</span><span class="org-type">+</span>s<span class="org-type">/</span><span class="org-highlight-numbers-number">1060</span><span class="org-type">/</span><span class="org-highlight-numbers-number">2</span><span class="org-type">/</span><span class="org-constant">pi</span><span class="org-rainbow-delimiters-depth-1">)</span>;
</pre>
</div>
<div class="org-src-container">
<pre class="src src-matlab"><span class="org-type">figure</span>;
ax1 = subplot<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">2</span>, <span class="org-highlight-numbers-number">1</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-1">)</span>;
hold on;
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, abs<span class="org-rainbow-delimiters-depth-2">(</span>Glpf<span class="org-rainbow-delimiters-depth-2">)</span><span class="org-rainbow-delimiters-depth-1">)</span>;
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, abs<span class="org-rainbow-delimiters-depth-2">(</span>squeeze<span class="org-rainbow-delimiters-depth-3">(</span>freqresp<span class="org-rainbow-delimiters-depth-4">(</span>Gth, f, <span class="org-string">'Hz'</span><span class="org-rainbow-delimiters-depth-4">)</span><span class="org-rainbow-delimiters-depth-3">)</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-rainbow-delimiters-depth-1">)</span>;
hold off;
<span class="org-type">set</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-variable-name">gca</span>, <span class="org-string">'xscale', 'log'</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">)</span></span><span class="org-string">; set</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">(</span></span><span class="org-string">gca, 'yscale', 'log'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
<span class="org-type">set</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-variable-name">gca</span>, <span class="org-string">'XTickLabel'</span>,<span class="org-rainbow-delimiters-depth-2">[]</span><span class="org-rainbow-delimiters-depth-1">)</span>;
ylabel<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Magnitude'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
ax2 = subplot<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">2</span>, <span class="org-highlight-numbers-number">1</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-1">)</span>;
hold on;
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, mod<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-highlight-numbers-number">180</span><span class="org-type">+</span><span class="org-highlight-numbers-number">180</span><span class="org-type">/</span><span class="org-constant">pi</span><span class="org-type">*</span>phase<span class="org-rainbow-delimiters-depth-3">(</span>Glpf<span class="org-rainbow-delimiters-depth-3">)</span>, <span class="org-highlight-numbers-number">360</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-type">-</span><span class="org-highlight-numbers-number">180</span><span class="org-rainbow-delimiters-depth-1">)</span>;
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, <span class="org-highlight-numbers-number">180</span><span class="org-type">/</span><span class="org-constant">pi</span><span class="org-type">*</span>unwrap<span class="org-rainbow-delimiters-depth-2">(</span>angle<span class="org-rainbow-delimiters-depth-3">(</span>squeeze<span class="org-rainbow-delimiters-depth-4">(</span>freqresp<span class="org-rainbow-delimiters-depth-5">(</span>Gth, f, <span class="org-string">'Hz'</span><span class="org-rainbow-delimiters-depth-5">)</span><span class="org-rainbow-delimiters-depth-4">)</span><span class="org-rainbow-delimiters-depth-3">)</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-rainbow-delimiters-depth-1">)</span>;
hold off;
<span class="org-type">set</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-variable-name">gca</span>, <span class="org-string">'xscale', 'log'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
ylim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span><span class="org-type">-</span><span class="org-highlight-numbers-number">180</span>, <span class="org-highlight-numbers-number">180</span><span class="org-rainbow-delimiters-depth-2">]</span><span class="org-rainbow-delimiters-depth-1">)</span>;
yticks<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span><span class="org-type">-</span><span class="org-highlight-numbers-number">180</span>, <span class="org-type">-</span><span class="org-highlight-numbers-number">90</span>, <span class="org-highlight-numbers-number">0</span>, <span class="org-highlight-numbers-number">90</span>, <span class="org-highlight-numbers-number">180</span><span class="org-rainbow-delimiters-depth-2">]</span><span class="org-rainbow-delimiters-depth-1">)</span>;
xlabel<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Frequency </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">Hz</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">)</span></span><span class="org-string">; ylabel</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">(</span></span><span class="org-string">'Phase'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
linkaxes<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span>ax1,ax2<span class="org-rainbow-delimiters-depth-2">]</span>,<span class="org-string">'x'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
xlim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span><span class="org-highlight-numbers-number">1</span>, <span class="org-highlight-numbers-number">500</span><span class="org-rainbow-delimiters-depth-2">]</span><span class="org-rainbow-delimiters-depth-1">)</span>;
</pre>
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<div id="org60b202b" class="figure">
<p><img src="figs/Glpf_bode_bis.png" alt="Glpf_bode_bis.png" />
</p>
<p><span class="figure-number">Figure 27: </span>Bode Diagram of the measured Low Pass filter and the theoritical one</p>
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<div id="outline-container-org04a0d6e" class="outline-4">
<h4 id="org04a0d6e"><span class="section-number-4">6.2.4</span> Conclusion</h4>
<div class="outline-text-4" id="text-6-2-4">
<div class="important">
<p>
The added LPF has the expected behavior.
</p>
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<div id="postamble" class="status">
<p class="author">Author: Thomas Dehaeze</p>
<p class="date">Created: 2019-05-07 mar. 16:56</p>
<p class="validation"><a href="http://validator.w3.org/check?uri=referer">Validate</a></p>
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