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<h1 class="title">Measurements On the Slip-Ring</h1>
<div id="table-of-contents">
<h2>Table of Contents</h2>
<div id="text-table-of-contents">
<ul>
<li><a href="#org2781a7a">1. Effect of the Slip-Ring on the signal</a>
<ul>
<li><a href="#org3dea630">1.1. Experimental Setup</a></li>
<li><a href="#orgf0d1f5d">1.2. Load data</a></li>
<li><a href="#org2b5c36e">1.3. Analysis - Time Domain</a></li>
<li><a href="#org22f0fdc">1.4. Analysis - Frequency Domain</a></li>
<li><a href="#org9abd380">1.5. Conclusion</a></li>
</ul>
</li>
<li><a href="#org6002a8c">2. Effect of the rotation of the Slip-Ring</a>
<ul>
<li><a href="#orgedc9c11">2.1. Measurement Description</a></li>
<li><a href="#org5e95fbe">2.2. Load data</a></li>
<li><a href="#org7a8e8fc">2.3. Analysis</a></li>
<li><a href="#org24db8f6">2.4. Conclusion</a></li>
</ul>
</li>
<li><a href="#org21fc4d2">3. Measure of the noise induced by the Slip-Ring</a>
<ul>
<li><a href="#org901cf1f">3.1. Measurement Description</a></li>
<li><a href="#org3aa7c6d">3.2. Load data</a></li>
<li><a href="#org22f6115">3.3. Time Domain</a></li>
<li><a href="#orgd6cbe96">3.4. Frequency Domain</a></li>
<li><a href="#orgbb89292">3.5. Conclusion</a></li>
</ul>
</li>
<li><a href="#orgf77f778">4. Measure of the noise induced by the slip ring when using a geophone</a>
<ul>
<li><a href="#org57fc212">4.1. First Measurement without LPF</a>
<ul>
<li><a href="#org4e633db">4.1.1. Measurement Description</a></li>
<li><a href="#orge652945">4.1.2. Load data</a></li>
<li><a href="#orgfdc44bc">4.1.3. Time Domain</a></li>
<li><a href="#org1747240">4.1.4. Frequency Domain</a></li>
<li><a href="#org2082a3e">4.1.5. Conclusion</a></li>
</ul>
</li>
<li><a href="#org0d10493">4.2. Measurement using an oscilloscope</a>
<ul>
<li><a href="#org84a4af9">4.2.1. Measurement Setup</a></li>
<li><a href="#orgba2e6ff">4.2.2. Observations</a></li>
<li><a href="#org729aaf2">4.2.3. Conclusion</a></li>
</ul>
</li>
<li><a href="#orge6ed6b4">4.3. New measurements with a LPF before the Voltage Amplifiers</a>
<ul>
<li><a href="#org4501bcc">4.3.1. Setup description</a></li>
<li><a href="#org7f64f45">4.3.2. Load data</a></li>
<li><a href="#org168648f">4.3.3. Time Domain</a></li>
<li><a href="#org18b3f68">4.3.4. Frequency Domain</a></li>
<li><a href="#org5c54c76">4.3.5. Comparison of with and without LPF</a></li>
<li><a href="#org44b238b">4.3.6. Conclusion</a></li>
</ul>
</li>
</ul>
</li>
</ul>
</div>
</div>
<div id="outline-container-org2781a7a" class="outline-2">
<h2 id="org2781a7a"><span class="section-number-2">1</span> Effect of the Slip-Ring on the signal</h2>
<div class="outline-text-2" id="text-1">
<p>
<a id="org8c43795"></a>
</p>
<p>
The data and matlab files are accessible <a href="data/meas_slip_ring_geophone.zip">here</a>.
</p>
</div>
<div id="outline-container-org3dea630" class="outline-3">
<h3 id="org3dea630"><span class="section-number-3">1.1</span> Experimental Setup</h3>
<div class="outline-text-3" id="text-1-1">
<p>
Two measurements are made with the control systems of all the stages turned OFF.
</p>
<p>
One geophone is located on the marble while the other is located at the sample location (figure <a href="#orgc4f61a9">1</a>).
</p>
<div id="orgc4f61a9" class="figure">
<p><img src="./img/IMG_20190430_112615.jpg" alt="IMG_20190430_112615.jpg" width="500px" />
</p>
<p><span class="figure-number">Figure 1: </span>Experimental Setup</p>
</div>
<p>
The two measurements 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">Measurement File</th>
<th scope="col" class="org-left">Description</th>
</tr>
</thead>
<tbody>
<tr>
<td class="org-left"><code>meas_018.mat</code></td>
<td class="org-left">Signal from the top geophone does not goes through the Slip-ring</td>
</tr>
<tr>
<td class="org-left"><code>meas_019.mat</code></td>
<td class="org-left">Signal goes through the Slip-ring (as shown on the figure above)</td>
</tr>
</tbody>
</table>
<p>
Each of the measurement <code>mat</code> file contains one <code>data</code> array with 3 columns:
</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 number</th>
<th scope="col" class="org-left">Description</th>
</tr>
</thead>
<tbody>
<tr>
<td class="org-right">1</td>
<td class="org-left">Geophone - Marble</td>
</tr>
<tr>
<td class="org-right">2</td>
<td class="org-left">Geophone - Sample</td>
</tr>
<tr>
<td class="org-right">3</td>
<td class="org-left">Time</td>
</tr>
</tbody>
</table>
</div>
</div>
<div id="outline-container-orgf0d1f5d" class="outline-3">
<h3 id="orgf0d1f5d"><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">d8 = 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>; d8 = d8.data;
d9 = 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>; d9 = d9.data;
</pre>
</div>
</div>
</div>
<div id="outline-container-org2b5c36e" class="outline-3">
<h3 id="org2b5c36e"><span class="section-number-3">1.3</span> Analysis - Time Domain</h3>
<div class="outline-text-3" id="text-1-3">
<p>
First, we compare the time domain signals for the two experiments (figure <a href="#org49ef389">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>d9<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span>, d9<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>, <span class="org-string">'DisplayName', 'Slip-Ring'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
plot<span class="org-rainbow-delimiters-depth-1">(</span>d8<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span>, d8<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>, <span class="org-string">'DisplayName', 'Wire'</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">50</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="org49ef389" class="figure">
<p><img src="figs/slipring_time.png" alt="slipring_time.png" />
</p>
<p><span class="figure-number">Figure 2: </span>Effect of the Slip-Ring on the measured signal - Time domain</p>
</div>
</div>
</div>
<div id="outline-container-org22f0fdc" class="outline-3">
<h3 id="org22f0fdc"><span class="section-number-3">1.4</span> Analysis - Frequency Domain</h3>
<div class="outline-text-3" id="text-1-4">
<p>
We then compute the Power Spectral Density of the two signals and we compare them (figure <a href="#orgcc2d186">3</a>).
</p>
<div class="org-src-container">
<pre class="src src-matlab">dt = d8<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> d8<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;
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>pxx8, f<span class="org-rainbow-delimiters-depth-1">]</span> = pwelch<span class="org-rainbow-delimiters-depth-1">(</span>d8<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>pxx9, <span class="org-type">~</span><span class="org-rainbow-delimiters-depth-1">]</span> = pwelch<span class="org-rainbow-delimiters-depth-1">(</span>d9<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>
<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>pxx9<span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'Slip-Ring'</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>pxx8<span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'Wire'</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>Amplitude Spectral Density $<span class="org-type">\</span>left<span class="org-rainbow-delimiters-depth-2">[</span><span class="org-type">\</span>frac<span class="org-rainbow-delimiters-depth-3">{</span>V<span class="org-rainbow-delimiters-depth-3">}{</span><span class="org-type">\</span>sqrt<span class="org-rainbow-delimiters-depth-4">{</span>Hz<span class="org-rainbow-delimiters-depth-4">}</span><span class="org-rainbow-delimiters-depth-3">}</span><span class="org-type">\</span>right<span class="org-rainbow-delimiters-depth-2">]</span>$'<span class="org-rainbow-delimiters-depth-1">)</span>
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>;
legend<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Location', 'southwest'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
</pre>
</div>
<div id="orgcc2d186" class="figure">
<p><img src="figs/slipring_asd.png" alt="slipring_asd.png" />
</p>
<p><span class="figure-number">Figure 3: </span>Effect of the Slip-Ring on the measured signal - Frequency domain</p>
</div>
</div>
</div>
<div id="outline-container-org9abd380" class="outline-3">
<h3 id="org9abd380"><span class="section-number-3">1.5</span> Conclusion</h3>
<div class="outline-text-3" id="text-1-5">
<div class="important">
<ul class="org-ul">
<li>Connecting the geophone through the Slip-Ring seems to induce a lot of noise.</li>
</ul>
</div>
<div class="note">
<p>
<b>Remaining questions to answer</b>:
</p>
<ul class="org-ul">
<li>Why is there a sharp peak at 300Hz?</li>
<li>Why the use of the Slip-Ring does induce a noise?</li>
<li>Can the capacitive/inductive properties of the wires in the Slip-ring does not play well with the geophone? (resonant RLC circuit)</li>
</ul>
</div>
</div>
</div>
</div>
<div id="outline-container-org6002a8c" class="outline-2">
<h2 id="org6002a8c"><span class="section-number-2">2</span> Effect of the rotation of the Slip-Ring</h2>
<div class="outline-text-2" id="text-2">
<p>
<a id="org953d721"></a>
</p>
<p>
The data and matlab files are accessible <a href="data/meas_effect_sr.zip">here</a>.
</p>
</div>
<div id="outline-container-orgedc9c11" class="outline-3">
<h3 id="orgedc9c11"><span class="section-number-3">2.1</span> Measurement Description</h3>
<div class="outline-text-3" id="text-2-1">
<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-org5e95fbe" class="outline-3">
<h3 id="org5e95fbe"><span class="section-number-3">2.2</span> Load data</h3>
<div class="outline-text-3" id="text-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">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-org7a8e8fc" class="outline-3">
<h3 id="org7a8e8fc"><span class="section-number-3">2.3</span> Analysis</h3>
<div class="outline-text-3" id="text-2-3">
<p>
Let's first look at the signal produced by the DAC (figure <a href="#org340bcf5">4</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="org340bcf5" class="figure">
<p><img src="figs/random_signal.png" alt="random_signal.png" />
</p>
<p><span class="figure-number">Figure 4: </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="#org7a50ceb">5</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="org7a50ceb" class="figure">
<p><img src="figs/slipring_comp_signals.png" alt="slipring_comp_signals.png" />
</p>
<p><span class="figure-number">Figure 5: </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="org5986467" class="figure">
<p><img src="figs/psd_noise.png" alt="psd_noise.png" />
</p>
<p><span class="figure-number">Figure 6: </span>ASD of the measured noise</p>
</div>
</div>
</div>
<div id="outline-container-org24db8f6" class="outline-3">
<h3 id="org24db8f6"><span class="section-number-3">2.4</span> Conclusion</h3>
<div class="outline-text-3" id="text-2-4">
<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-org21fc4d2" class="outline-2">
<h2 id="org21fc4d2"><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>
<a id="orgddb1e83"></a>
</p>
<p>
The data and matlab files are accessible <a href="data/meas_slip_ring.zip">here</a>.
</p>
</div>
<div id="outline-container-org901cf1f" class="outline-3">
<h3 id="org901cf1f"><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="org1e3bbb6" class="figure">
<p><img src="./img/VID_20190503_160831.gif" alt="VID_20190503_160831.gif" />
</p>
<p><span class="figure-number">Figure 7: </span>Slip-Ring rotating at 6rpm</p>
</div>
<div id="orgc9e3e39" class="figure">
<p><img src="./img/VID_20190503_161401.gif" alt="VID_20190503_161401.gif" />
</p>
<p><span class="figure-number">Figure 8: </span>Slip-Ring rotating at 60rpm</p>
</div>
</div>
</div>
<div id="outline-container-org3aa7c6d" class="outline-3">
<h3 id="org3aa7c6d"><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-org22f6115" class="outline-3">
<h3 id="org22f6115"><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="#org841f525">9</a>) and for the signal going through the slip-ring (figure <a href="#orgdc9de69">10</a>);
</p>
<div id="org841f525" class="figure">
<p><img src="figs/sr_direct_time.png" alt="sr_direct_time.png" />
</p>
<p><span class="figure-number">Figure 9: </span>Direct measurement</p>
</div>
<div id="orgdc9de69" class="figure">
<p><img src="figs/sr_slipring_time.png" alt="sr_slipring_time.png" />
</p>
<p><span class="figure-number">Figure 10: </span>Measurement of the signal going through the Slip-Ring</p>
</div>
</div>
</div>
<div id="outline-container-orgd6cbe96" class="outline-3">
<h3 id="orgd6cbe96"><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="#org70efd75">11</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="org70efd75" class="figure">
<p><img src="figs/sr_psd_compare.png" alt="sr_psd_compare.png" />
</p>
<p><span class="figure-number">Figure 11: </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-orgbb89292" class="outline-3">
<h3 id="orgbb89292"><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-orgf77f778" class="outline-2">
<h2 id="orgf77f778"><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>
<a id="org34dee33"></a>
</p>
<p>
The data and matlab files are accessible <a href="data/meas_sr_geophone.zip">here</a>.
</p>
</div>
<div id="outline-container-org57fc212" class="outline-3">
<h3 id="org57fc212"><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-org4e633db" class="outline-4">
<h4 id="org4e633db"><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-orge652945" class="outline-4">
<h4 id="orge652945"><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-orgfdc44bc" class="outline-4">
<h4 id="orgfdc44bc"><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="#org2b29bbb">12</a>) and when it is ON (figure <a href="#org0c98be5">13</a>).
</p>
<div id="org2b29bbb" class="figure">
<p><img src="figs/sr_geophone_time_off.png" alt="sr_geophone_time_off.png" />
</p>
<p><span class="figure-number">Figure 12: </span>Comparison of the time domain signals when the slip-ring is OFF</p>
</div>
<div id="org0c98be5" class="figure">
<p><img src="figs/sr_geophone_time_on.png" alt="sr_geophone_time_on.png" />
</p>
<p><span class="figure-number">Figure 13: </span>Comparison of the time domain signals when the slip-ring is ON</p>
</div>
</div>
</div>
<div id="outline-container-org1747240" class="outline-4">
<h4 id="org1747240"><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="#org6f7187f">14</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="org6f7187f" class="figure">
<p><img src="figs/sr_geophone_asd.png" alt="sr_geophone_asd.png" />
</p>
<p><span class="figure-number">Figure 14: </span>Comparison of the Amplitude Spectral Sensity</p>
</div>
<div id="orgacb2d5e" class="figure">
<p><img src="figs/sr_geophone_asd_zoom.png" alt="sr_geophone_asd_zoom.png" />
</p>
<p><span class="figure-number">Figure 15: </span>Comparison of the Amplitude Spectral Sensity - Zoom</p>
</div>
</div>
</div>
<div id="outline-container-org2082a3e" class="outline-4">
<h4 id="org2082a3e"><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="#orgacb2d5e">15</a> be due to the Aliasing?</li>
</ul>
</div>
</div>
</div>
</div>
<div id="outline-container-org0d10493" class="outline-3">
<h3 id="org0d10493"><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-org84a4af9" class="outline-4">
<h4 id="org84a4af9"><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-orgba2e6ff" class="outline-4">
<h4 id="orgba2e6ff"><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="#org8cbaa23">16</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="#orgeeac555">17</a>).
</p>
<div id="org8cbaa23" class="figure">
<p><img src="./img/IMG_20190506_160420.jpg" alt="IMG_20190506_160420.jpg" width="500px" />
</p>
<p><span class="figure-number">Figure 16: </span>Signals measured by the oscilloscope - Slip-Ring ON - Yellow: Direct measure - Blue: Through Slip-Ring</p>
</div>
<div id="orgeeac555" class="figure">
<p><img src="./img/IMG_20190506_160438.jpg" alt="IMG_20190506_160438.jpg" width="500px" />
</p>
<p><span class="figure-number">Figure 17: </span>Signals measured by the oscilloscope - Slip-Ring OFF - Yellow: Direct measure - Blue: Through Slip-Ring</p>
</div>
</div>
</div>
<div id="outline-container-org729aaf2" class="outline-4">
<h4 id="org729aaf2"><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-orge6ed6b4" class="outline-3">
<h3 id="orge6ed6b4"><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-org4501bcc" class="outline-4">
<h4 id="org4501bcc"><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-org7f64f45" class="outline-4">
<h4 id="org7f64f45"><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-org168648f" class="outline-4">
<h4 id="org168648f"><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="#org82abb68">18</a>) and when it is ON (figure <a href="#org7701819">19</a>).
</p>
<div id="org82abb68" 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 18: </span>Comparison of the time domain signals when the slip-ring is OFF</p>
</div>
<div id="org7701819" 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 19: </span>Comparison of the time domain signals when the slip-ring is ON</p>
</div>
</div>
</div>
<div id="outline-container-org18b3f68" class="outline-4">
<h4 id="org18b3f68"><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="#org58407c0">20</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="org58407c0" class="figure">
<p><img src="figs/sr_lpf_geophone_asd.png" alt="sr_lpf_geophone_asd.png" />
</p>
<p><span class="figure-number">Figure 20: </span>Comparison of the Amplitude Spectral Sensity</p>
</div>
<div id="orge9dc071" 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 21: </span>Comparison of the Amplitude Spectral Sensity - Zoom</p>
</div>
</div>
</div>
<div id="outline-container-org5c54c76" class="outline-4">
<h4 id="org5c54c76"><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="org9493d78" class="figure">
<p><img src="figs/comp_with_without_lpf.png" alt="comp_with_without_lpf.png" />
</p>
<p><span class="figure-number">Figure 22: </span>Comparison of the measured signals with and without LPF</p>
</div>
</div>
</div>
<div id="outline-container-org44b238b" class="outline-4">
<h4 id="org44b238b"><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>
<div id="postamble" class="status">
<p class="author">Author: Thomas Dehaeze</p>
<p class="date">Created: 2019-05-10 ven. 10:06</p>
<p class="validation"><a href="http://validator.w3.org/check?uri=referer">Validate</a></p>
</div>
</body>
</html>