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<h1 class="title">Measurements On the Slip-Ring - Electrical Noise</h1>
<div id="table-of-contents">
<h2>Table of Contents</h2>
<div id="text-table-of-contents">
<ul>
<li><a href="#org4bb283a">1. Effect of the Slip-Ring on the signal when turned ON - Geophone measurement</a>
<ul>
<li><a href="#org539011f">1.1. Experimental Setup</a></li>
<li><a href="#orgeaa3de5">1.2. Load data</a></li>
<li><a href="#orgf3ed692">1.3. Analysis - Time Domain</a></li>
<li><a href="#org9ee7e9b">1.4. Analysis - Frequency Domain</a></li>
<li><a href="#org8c982b0">1.5. Conclusion</a></li>
</ul>
</li>
<li><a href="#orgb3f8733">2. Measure of the noise induced by the Slip-Ring using voltage amplifiers - Geophone</a>
<ul>
<li><a href="#orge58d33d">2.1. First Measurement without LPF</a>
<ul>
<li><a href="#org840c4fe">2.1.1. Measurement Description</a></li>
<li><a href="#orgc0502a3">2.1.2. Load data</a></li>
<li><a href="#org44419d0">2.1.3. Time Domain</a></li>
<li><a href="#orgeef5d2a">2.1.4. Frequency Domain</a></li>
<li><a href="#orge43131d">2.1.5. Conclusion</a></li>
</ul>
</li>
<li><a href="#org6789f18">2.2. Measurement using an oscilloscope</a>
<ul>
<li><a href="#orga1f5a57">2.2.1. Measurement Setup</a></li>
<li><a href="#orgd66bd77">2.2.2. Observations</a></li>
<li><a href="#orga118eb4">2.2.3. Conclusion</a></li>
</ul>
</li>
<li><a href="#org90c3471">2.3. New measurements with a LPF before the Voltage Amplifiers</a>
<ul>
<li><a href="#org09aed1f">2.3.1. Setup description</a></li>
<li><a href="#orgae5c732">2.3.2. Load data</a></li>
<li><a href="#org50f1c08">2.3.3. Time Domain</a></li>
<li><a href="#org778c104">2.3.4. Frequency Domain</a></li>
<li><a href="#org9e44965">2.3.5. Conclusion</a></li>
</ul>
</li>
<li><a href="#orgc48b57e">2.4. Measurement of the noise induced by the slip-ring with additional LPF at 1kHz</a>
<ul>
<li><a href="#orgb87a401">2.4.1. Measurement description</a></li>
<li><a href="#org887accb">2.4.2. Load data</a></li>
<li><a href="#org8818a95">2.4.3. Pre-processing</a></li>
<li><a href="#orgb9d52c6">2.4.4. Time Domain</a></li>
<li><a href="#org9f409d8">2.4.5. Frequency Domain</a></li>
<li><a href="#org416009b">2.4.6. Difference between the direct signal and the signal going through the slip-ring</a></li>
<li><a href="#org2a99be3">2.4.7. Conclusion</a></li>
</ul>
</li>
</ul>
</li>
</ul>
</div>
</div>
<p>
The noise induced by the slip-ring is measured when using geophones:
</p>
<ul class="org-ul">
<li>Section <a href="#org39fabc7">1</a>:
<ul class="org-ul">
<li>A geophone located at the sample location is measured with its signal going directly to the ADC and going through the slip-ring</li>
<li>The voltage amplifiers where saturating due to high frequency noise</li>
</ul></li>
<li>Section <a href="#orgc0f681e">2</a>:
<ul class="org-ul">
<li>A Low Pass Filter is added before the voltage amplifiers</li>
<li>Using a Oscilloscope, high frequency noise at 40kHz generated by the slip-ring has been identified</li>
<li>With the additional low pass filter at the input of the voltage amplifiers, the slip-ring don&rsquo;t add any measurable noise to the signal</li>
</ul></li>
</ul>
<div id="outline-container-org4bb283a" class="outline-2">
<h2 id="org4bb283a"><span class="section-number-2">1</span> Effect of the Slip-Ring on the signal when turned ON - Geophone measurement</h2>
<div class="outline-text-2" id="text-1">
<p>
<a id="org39fabc7"></a>
</p>
<div class="note" id="orgb1d7fd4">
<p>
All the files (data and Matlab scripts) are accessible <a href="data/meas_slip_ring_geophone.zip">here</a>.
</p>
</div>
</div>
<div id="outline-container-org539011f" class="outline-3">
<h3 id="org539011f"><span class="section-number-3">1.1</span> Experimental Setup</h3>
<div class="outline-text-3" id="text-1-1">
<p>
<b>Goal</b>:
The goal is to determine if some noise is added to a signal passing through the slip-ring.
</p>
<p>
<b>Setup</b>:
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="#orge8b7913">1</a>).
</p>
<p>
The two signals from the geophones are amplified with voltage amplifiers with the following settings:
</p>
<ul class="org-ul">
<li>Gain: 60dB</li>
<li>AC/DC switch: AC</li>
<li>Low pass filter at the output set at 1kHz</li>
</ul>
<div id="orge8b7913" 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>
<b>Measurements</b>:
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">Measurement File</th>
<th scope="col" class="org-left">Description</th>
</tr>
</thead>
<tbody>
<tr>
<td class="org-left"><code>mat/meas_018.mat</code></td>
<td class="org-left">Signal goes through the Slip-ring (as shown on the figure above)</td>
</tr>
<tr>
<td class="org-left"><code>mat/meas_019.mat</code></td>
<td class="org-left">Signal from the top geophone does not goes through the Slip-ring</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-orgeaa3de5" class="outline-3">
<h3 id="orgeaa3de5"><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">meas_sr = load(<span class="org-string">'mat/data_018.mat'</span>, <span class="org-string">'data'</span>); meas_sr = meas_sr.data;
meas_di = load(<span class="org-string">'mat/data_019.mat'</span>, <span class="org-string">'data'</span>); meas_di = meas_di.data;
</pre>
</div>
</div>
</div>
<div id="outline-container-orgf3ed692" class="outline-3">
<h3 id="orgf3ed692"><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="#org8bb42aa">2</a>).
</p>
<div class="org-src-container">
<pre class="src src-matlab"><span class="org-type">figure</span>;
hold on;
plot(meas_di(<span class="org-type">:</span>, 3), meas_di(<span class="org-type">:</span>, 2), <span class="org-string">'DisplayName'</span>, <span class="org-string">'Geophone - Direct'</span>);
plot(meas_sr(<span class="org-type">:</span>, 3), meas_sr(<span class="org-type">:</span>, 2), <span class="org-string">'DisplayName'</span>, <span class="org-string">'Geophone - Slip-Ring'</span>);
hold off;
xlabel(<span class="org-string">'Time [s]'</span>); ylabel(<span class="org-string">'Voltage [V]'</span>);
xlim([0, 50]);
legend(<span class="org-string">'location'</span>, <span class="org-string">'northeast'</span>);
</pre>
</div>
<div id="org8bb42aa" 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 of the geophone at the sample location - Time domain</p>
</div>
</div>
</div>
<div id="outline-container-org9ee7e9b" class="outline-3">
<h3 id="org9ee7e9b"><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="#org7c89484">3</a>).
</p>
<div class="org-src-container">
<pre class="src src-matlab">dt = meas_di(2, 3) <span class="org-type">-</span> meas_di(1, 3);
Fs = 1<span class="org-type">/</span>dt;
win = hanning(ceil(5<span class="org-type">*</span>Fs));
</pre>
</div>
<div class="org-src-container">
<pre class="src src-matlab">[px_di, f] = pwelch(meas_di(<span class="org-type">:</span>, 2), win, [], [], Fs);
[px_sr, <span class="org-type">~</span>] = pwelch(meas_sr(<span class="org-type">:</span>, 2), win, [], [], Fs);
</pre>
</div>
<div class="org-src-container">
<pre class="src src-matlab"><span class="org-type">figure</span>;
hold on;
plot(f, sqrt(px_sr), <span class="org-string">'DisplayName'</span>, <span class="org-string">'Slip-Ring'</span>);
plot(f, sqrt(px_di), <span class="org-string">'DisplayName'</span>, <span class="org-string">'Wire'</span>);
hold off;
<span class="org-type">set</span>(<span class="org-variable-name">gca</span>, <span class="org-string">'xscale'</span>, <span class="org-string">'log'</span>);
<span class="org-type">set</span>(<span class="org-variable-name">gca</span>, <span class="org-string">'yscale'</span>, <span class="org-string">'log'</span>);
xlabel(<span class="org-string">'Frequency [Hz]'</span>); ylabel(<span class="org-string">'Amplitude Spectral Density $\left[\frac{V}{\sqrt{Hz}}\right]$'</span>)
xlim([1, 500]);
legend(<span class="org-string">'Location'</span>, <span class="org-string">'southwest'</span>);
</pre>
</div>
<div id="org7c89484" 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 of the geophone at the sample location - Frequency domain</p>
</div>
</div>
</div>
<div id="outline-container-org8c982b0" class="outline-3">
<h3 id="org8c982b0"><span class="section-number-3">1.5</span> Conclusion</h3>
<div class="outline-text-3" id="text-1-5">
<div class="important" id="orga730da8">
<ul class="org-ul">
<li>The voltage amplifiers are saturating during the measurements (as shown by the LED on figure <a href="#orge8b7913">1</a>)</li>
<li>This saturation is mainly due to high frequency noise =&gt; a LPF will be added at the input of the voltage amplifiers in the further measurements</li>
<li>The measurements will be redone</li>
</ul>
</div>
</div>
</div>
</div>
<div id="outline-container-orgb3f8733" class="outline-2">
<h2 id="orgb3f8733"><span class="section-number-2">2</span> Measure of the noise induced by the Slip-Ring using voltage amplifiers - Geophone</h2>
<div class="outline-text-2" id="text-2">
<p>
<a id="orgc0f681e"></a>
</p>
<div class="note" id="org984d9cf">
<p>
All the files (data and Matlab scripts) are accessible <a href="data/meas_sr_geophone.zip">here</a>.
</p>
</div>
</div>
<div id="outline-container-orge58d33d" class="outline-3">
<h3 id="orge58d33d"><span class="section-number-3">2.1</span> First Measurement without LPF</h3>
<div class="outline-text-3" id="text-2-1">
</div>
<div id="outline-container-org840c4fe" class="outline-4">
<h4 id="org840c4fe"><span class="section-number-4">2.1.1</span> Measurement Description</h4>
<div class="outline-text-4" id="text-2-1-1">
<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>Gain: 60dB</li>
<li>AC/DC option: AC</li>
<li>Low pass filter at the output set to 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=&gt;voltage amplifier=&gt;ADC</li>
</ul></li>
</ul>
<p>
<b>Measurements</b>:
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">Measurement File</th>
<th scope="col" class="org-left">Description</th>
</tr>
</thead>
<tbody>
<tr>
<td class="org-left"><code>data_012</code></td>
<td class="org-left">Slip-Ring OFF</td>
</tr>
<tr>
<td class="org-left"><code>data_013</code></td>
<td class="org-left">Slip-Ring ON</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">Measure of the geophone at the sample position with a direct wire</td>
</tr>
<tr>
<td class="org-right">2</td>
<td class="org-left">Measure of the geophone at the sample position going through the slip-ring</td>
</tr>
<tr>
<td class="org-right">3</td>
<td class="org-left">Time</td>
</tr>
</tbody>
</table>
</div>
</div>
<div id="outline-container-orgc0502a3" class="outline-4">
<h4 id="orgc0502a3"><span class="section-number-4">2.1.2</span> Load data</h4>
<div class="outline-text-4" id="text-2-1-2">
<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-string">'mat/data_012.mat'</span>, <span class="org-string">'data'</span>); sr_off = sr_off.data;
sr_on = load(<span class="org-string">'mat/data_013.mat'</span>, <span class="org-string">'data'</span>); sr_on = sr_on.data;
</pre>
</div>
</div>
</div>
<div id="outline-container-org44419d0" class="outline-4">
<h4 id="org44419d0"><span class="section-number-4">2.1.3</span> Time Domain</h4>
<div class="outline-text-4" id="text-2-1-3">
<p>
We compare the signal when the Slip-Ring is OFF (figure <a href="#orge5c345d">4</a>) and when it is ON (figure <a href="#orgd7e5346">5</a>).
</p>
<div id="orge5c345d" class="figure">
<p><img src="figs/sr_geophone_time_off.png" alt="sr_geophone_time_off.png" />
</p>
<p><span class="figure-number">Figure 4: </span>Comparison of the time domain signals when the slip-ring is OFF</p>
</div>
<div id="orgd7e5346" class="figure">
<p><img src="figs/sr_geophone_time_on.png" alt="sr_geophone_time_on.png" />
</p>
<p><span class="figure-number">Figure 5: </span>Comparison of the time domain signals when the slip-ring is ON</p>
</div>
</div>
</div>
<div id="outline-container-orgeef5d2a" class="outline-4">
<h4 id="orgeef5d2a"><span class="section-number-4">2.1.4</span> Frequency Domain</h4>
<div class="outline-text-4" id="text-2-1-4">
<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(2, 3)<span class="org-type">-</span>sr_off(1, 3);
Fs = 1<span class="org-type">/</span>dt; <span class="org-comment">% [Hz]</span>
win = hanning(ceil(10<span class="org-type">*</span>Fs));
</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>
[pxdoff, <span class="org-type">~</span>] = pwelch(sr_off(<span class="org-type">:</span>, 1), win, [], [], Fs);
[pxdon, <span class="org-type">~</span>] = pwelch(sr_on(<span class="org-type">:</span>, 1), win, [], [], Fs);
<span class="org-comment">% Slip-Ring measure</span>
[pxsroff, f] = pwelch(sr_off(<span class="org-type">:</span>, 2), win, [], [], Fs);
[pxsron, <span class="org-type">~</span>] = pwelch(sr_on(<span class="org-type">:</span>, 2), win, [], [], Fs);
</pre>
</div>
<p>
Finally, we compare the Amplitude Spectral Density of the signals (figure <a href="#org4a07807">6</a>);
</p>
<div class="org-src-container">
<pre class="src src-matlab"><span class="org-type">figure</span>;
hold on;
plot(f, sqrt(pxdoff), <span class="org-string">'DisplayName'</span>, <span class="org-string">'Direct - OFF'</span>);
plot(f, sqrt(pxsroff), <span class="org-string">'DisplayName'</span>, <span class="org-string">'Slip-Ring - OFF'</span>);
plot(f, sqrt(pxdon), <span class="org-string">'DisplayName'</span>, <span class="org-string">'Direct - ON'</span>);
plot(f, sqrt(pxsron), <span class="org-string">'DisplayName'</span>, <span class="org-string">'Slip-Ring - ON'</span>);
hold off;
<span class="org-type">set</span>(<span class="org-variable-name">gca</span>, <span class="org-string">'xscale'</span>, <span class="org-string">'log'</span>);
<span class="org-type">set</span>(<span class="org-variable-name">gca</span>, <span class="org-string">'yscale'</span>, <span class="org-string">'log'</span>);
xlabel(<span class="org-string">'Frequency [Hz]'</span>); ylabel(<span class="org-string">'ASD of the measured Voltage $\left[\frac{V}{\sqrt{Hz}}\right]$'</span>)
legend(<span class="org-string">'Location'</span>, <span class="org-string">'northeast'</span>);
xlim([0.1, 500]);
</pre>
</div>
<div id="org4a07807" class="figure">
<p><img src="figs/sr_geophone_asd.png" alt="sr_geophone_asd.png" />
</p>
<p><span class="figure-number">Figure 6: </span>Comparison of the Amplitude Spectral Sensity</p>
</div>
<div id="orgfcd4cd3" class="figure">
<p><img src="figs/sr_geophone_asd_zoom.png" alt="sr_geophone_asd_zoom.png" />
</p>
<p><span class="figure-number">Figure 7: </span>Comparison of the Amplitude Spectral Sensity - Zoom</p>
</div>
</div>
</div>
<div id="outline-container-orge43131d" class="outline-4">
<h4 id="orge43131d"><span class="section-number-4">2.1.5</span> Conclusion</h4>
<div class="outline-text-4" id="text-2-1-5">
<div class="important" id="org54c3040">
<ul class="org-ul">
<li>The fact that the Slip-Ring is turned ON adds some noise to the signals</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 better electromagnetic isolation in the slip-ring</li>
</ul>
<p>
<b>Questions</b>:
</p>
<ul class="org-ul">
<li>Can the sharp peak on figure <a href="#orgfcd4cd3">7</a> be due to the Aliasing?</li>
</ul>
</div>
</div>
</div>
</div>
<div id="outline-container-org6789f18" class="outline-3">
<h3 id="org6789f18"><span class="section-number-3">2.2</span> Measurement using an oscilloscope</h3>
<div class="outline-text-3" id="text-2-2">
</div>
<div id="outline-container-orga1f5a57" class="outline-4">
<h4 id="orga1f5a57"><span class="section-number-4">2.2.1</span> Measurement Setup</h4>
<div class="outline-text-4" id="text-2-2-1">
<p>
We are now measuring the same signals than in the previous section, but with an oscilloscope instead of with the Speedgoat ADC.
</p>
</div>
</div>
<div id="outline-container-orgd66bd77" class="outline-4">
<h4 id="orgd66bd77"><span class="section-number-4">2.2.2</span> Observations</h4>
<div class="outline-text-4" id="text-2-2-2">
<p>
Then the Slip-Ring is ON (figure <a href="#orgb956278">8</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&rsquo;t observe this noise at 40kHz anymore (figure <a href="#org53e1b33">9</a>).
</p>
<div id="orgb956278" class="figure">
<p><img src="./img/IMG_20190506_160420.jpg" alt="IMG_20190506_160420.jpg" width="500px" />
</p>
<p><span class="figure-number">Figure 8: </span>Signals measured by the oscilloscope - Slip-Ring ON - Yellow: Direct measure - Blue: Through Slip-Ring</p>
</div>
<div id="org53e1b33" class="figure">
<p><img src="./img/IMG_20190506_160438.jpg" alt="IMG_20190506_160438.jpg" width="500px" />
</p>
<p><span class="figure-number">Figure 9: </span>Signals measured by the oscilloscope - Slip-Ring OFF - Yellow: Direct measure - Blue: Through Slip-Ring</p>
</div>
</div>
</div>
<div id="outline-container-orga118eb4" class="outline-4">
<h4 id="orga118eb4"><span class="section-number-4">2.2.3</span> Conclusion</h4>
<div class="outline-text-4" id="text-2-2-3">
<div class="important" id="org7860027">
<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-org90c3471" class="outline-3">
<h3 id="org90c3471"><span class="section-number-3">2.3</span> New measurements with a LPF before the Voltage Amplifiers</h3>
<div class="outline-text-3" id="text-2-3">
</div>
<div id="outline-container-org09aed1f" class="outline-4">
<h4 id="org09aed1f"><span class="section-number-4">2.3.1</span> Setup description</h4>
<div class="outline-text-4" id="text-2-3-1">
<p>
<b>Goal</b>:
The goal is to see if we can remove high frequency noise from the signals before the voltage amplifiers in order to not saturate them.
</p>
<p>
<b>Setup</b>:
We are measuring the signal from a geophone put at the sample position.
Using a BNC slitter, one part is going directly to the Low pass filter, voltage amplifier and ADC (first column), the other part is going through the slip ring before the low pass filter and the voltage amplifier (second column).
</p>
<p>
The two voltage amplifiers have the same following settings:
</p>
<ul class="org-ul">
<li>Gain: 60dB</li>
<li>AC/DC option: DC</li>
<li>Low pass filter at the output set to 1kHz</li>
</ul>
<p>
The low pass filter is a first order low pass filter RC circuit. It is added before the Voltage Amplifiers and has the following values:
</p>
\begin{aligned}
R &= 1k\Omega \\
C &= 1\mu F
\end{aligned}
<p>
And the cut-off frequency is \(f_c = \frac{1}{RC} = 160Hz\).
</p>
<p>
<b>Measurements</b>:
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">Measurement File</th>
<th scope="col" class="org-left">Description</th>
</tr>
</thead>
<tbody>
<tr>
<td class="org-left"><code>mat/data_016.mat</code></td>
<td class="org-left">Signal from the geophone at the sample location - Slip-Ring OFF</td>
</tr>
<tr>
<td class="org-left"><code>mat/data_017.mat</code></td>
<td class="org-left">Signal from the geophone at the sample location - Slip-Ring ON</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">Direct measurement</td>
</tr>
<tr>
<td class="org-right">2</td>
<td class="org-left">Signal going through the slip-ring</td>
</tr>
<tr>
<td class="org-right">3</td>
<td class="org-left">Time</td>
</tr>
</tbody>
</table>
</div>
</div>
<div id="outline-container-orgae5c732" class="outline-4">
<h4 id="orgae5c732"><span class="section-number-4">2.3.2</span> Load data</h4>
<div class="outline-text-4" id="text-2-3-2">
<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-string">'mat/data_016.mat'</span>, <span class="org-string">'data'</span>); sr_lpf_off = sr_lpf_off.data;
sr_lpf_on = load(<span class="org-string">'mat/data_017.mat'</span>, <span class="org-string">'data'</span>); sr_lpf_on = sr_lpf_on.data;
</pre>
</div>
</div>
</div>
<div id="outline-container-org50f1c08" class="outline-4">
<h4 id="org50f1c08"><span class="section-number-4">2.3.3</span> Time Domain</h4>
<div class="outline-text-4" id="text-2-3-3">
<p>
We compare the signal when the Slip-Ring is OFF (figure <a href="#orgef758ac">10</a>) and when it is ON (figure <a href="#orgd18f7a0">11</a>).
</p>
<div id="orgef758ac" 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 10: </span>Comparison of the time domain signals when the slip-ring is OFF</p>
</div>
<div id="orgd18f7a0" 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 11: </span>Comparison of the time domain signals when the slip-ring is ON</p>
</div>
</div>
</div>
<div id="outline-container-org778c104" class="outline-4">
<h4 id="org778c104"><span class="section-number-4">2.3.4</span> Frequency Domain</h4>
<div class="outline-text-4" id="text-2-3-4">
<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(2, 3)<span class="org-type">-</span>sr_lpf_off(1, 3);
Fs = 1<span class="org-type">/</span>dt; <span class="org-comment">% [Hz]</span>
win = hanning(ceil(10<span class="org-type">*</span>Fs));
</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>
[pxd_lpf_off, <span class="org-type">~</span>] = pwelch(sr_lpf_off(<span class="org-type">:</span>, 1), win, [], [], Fs);
[pxd_lpf_on, <span class="org-type">~</span>] = pwelch(sr_lpf_on(<span class="org-type">:</span>, 1), win, [], [], Fs);
<span class="org-comment">% Slip-Ring measure</span>
[pxsr_lpf_off, f] = pwelch(sr_lpf_off(<span class="org-type">:</span>, 2), win, [], [], Fs);
[pxsr_lpf_on, <span class="org-type">~</span>] = pwelch(sr_lpf_on(<span class="org-type">:</span>, 2), win, [], [], Fs);
</pre>
</div>
<p>
Finally, we compare the Amplitude Spectral Density of the signals (figure <a href="#org79403b8">12</a>);
</p>
<div class="org-src-container">
<pre class="src src-matlab"><span class="org-type">figure</span>;
hold on;
plot(f, sqrt(pxd_lpf_off), <span class="org-string">'DisplayName'</span>, <span class="org-string">'Direct - OFF'</span>);
plot(f, sqrt(pxsr_lpf_off), <span class="org-string">'DisplayName'</span>, <span class="org-string">'Slip-Ring - OFF'</span>);
plot(f, sqrt(pxd_lpf_on), <span class="org-string">'DisplayName'</span>, <span class="org-string">'Direct - ON'</span>);
plot(f, sqrt(pxsr_lpf_on), <span class="org-string">'DisplayName'</span>, <span class="org-string">'Slip-Ring - ON'</span>);
hold off;
xlim([0.1, 500]);
<span class="org-type">set</span>(<span class="org-variable-name">gca</span>, <span class="org-string">'xscale'</span>, <span class="org-string">'log'</span>); <span class="org-type">set</span>(<span class="org-variable-name">gca</span>, <span class="org-string">'yscale'</span>, <span class="org-string">'log'</span>);
xlabel(<span class="org-string">'Frequency [Hz]'</span>); ylabel(<span class="org-string">'ASD of the measured Voltage $\left[\frac{V}{\sqrt{Hz}}\right]$'</span>)
legend(<span class="org-string">'Location'</span>, <span class="org-string">'southwest'</span>);
</pre>
</div>
<div id="org79403b8" class="figure">
<p><img src="figs/sr_lpf_geophone_asd.png" alt="sr_lpf_geophone_asd.png" />
</p>
<p><span class="figure-number">Figure 12: </span>Comparison of the Amplitude Spectral Sensity</p>
</div>
<div id="orgec0976a" 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 13: </span>Comparison of the Amplitude Spectral Sensity - Zoom</p>
</div>
</div>
</div>
<div id="outline-container-org9e44965" class="outline-4">
<h4 id="org9e44965"><span class="section-number-4">2.3.5</span> Conclusion</h4>
<div class="outline-text-4" id="text-2-3-5">
<div class="important" id="orgce000ab">
<ul class="org-ul">
<li>Using the LPF, we don&rsquo;t see any additional noise coming from the slip-ring when it is turned ON</li>
<li>However, we should use a smaller value of the capacitor to have a cut-off frequency at \(1kHz\)</li>
<li>We here observe a signal at \(50Hz\) and its harmonics</li>
</ul>
</div>
</div>
</div>
</div>
<div id="outline-container-orgc48b57e" class="outline-3">
<h3 id="orgc48b57e"><span class="section-number-3">2.4</span> Measurement of the noise induced by the slip-ring with additional LPF at 1kHz</h3>
<div class="outline-text-3" id="text-2-4">
</div>
<div id="outline-container-orgb87a401" class="outline-4">
<h4 id="orgb87a401"><span class="section-number-4">2.4.1</span> Measurement description</h4>
<div class="outline-text-4" id="text-2-4-1">
<p>
<b>Setup</b>:
Voltage amplifier:
</p>
<ul class="org-ul">
<li>60db</li>
<li>AC</li>
<li>1kHz</li>
</ul>
<p>
Additionnal LPF at 1kHz
</p>
<p>
geophone at the sample location
slit into 2 BNC:
</p>
<ul class="org-ul">
<li>first one (column one): direct wire</li>
<li>second one (second column): slip-ring wire</li>
</ul>
<p>
Additionnal LPF is added before the voltage amplifiers
</p>
<p>
<b>Goal</b>:
</p>
<p>
<b>Measurements</b>:
</p>
<p>
Three 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">Measurement File</th>
<th scope="col" class="org-left">Description</th>
</tr>
</thead>
<tbody>
<tr>
<td class="org-left"><code>mat/data_035.mat</code></td>
<td class="org-left">All off</td>
</tr>
<tr>
<td class="org-left"><code>mat/data_036.mat</code></td>
<td class="org-left">Slip-Ring ON</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">Direct Wire</td>
</tr>
<tr>
<td class="org-right">2</td>
<td class="org-left">Slip-Ring Wire</td>
</tr>
<tr>
<td class="org-right">3</td>
<td class="org-left">Time</td>
</tr>
</tbody>
</table>
</div>
</div>
<div id="outline-container-org887accb" class="outline-4">
<h4 id="org887accb"><span class="section-number-4">2.4.2</span> Load data</h4>
<div class="outline-text-4" id="text-2-4-2">
<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_1khz_of = load(<span class="org-string">'mat/data_035.mat'</span>, <span class="org-string">'data'</span>); sr_lpf_1khz_of = sr_lpf_1khz_of.data;
sr_lpf_1khz_on = load(<span class="org-string">'mat/data_036.mat'</span>, <span class="org-string">'data'</span>); sr_lpf_1khz_on = sr_lpf_1khz_on.data;
</pre>
</div>
</div>
</div>
<div id="outline-container-org8818a95" class="outline-4">
<h4 id="org8818a95"><span class="section-number-4">2.4.3</span> Pre-processing</h4>
<div class="outline-text-4" id="text-2-4-3">
<p>
There is a sign difference between the signal going directly to the ADC and the signal going through the slip-ring. We add a minus sign on the signal going through the slip-ring.
</p>
<p>
We also subtract the mean value as the voltage amplifiers were on the DC option.
</p>
<div class="org-src-container">
<pre class="src src-matlab">sr_lpf_1khz_of(<span class="org-type">:</span>, 1) = sr_lpf_1khz_of(<span class="org-type">:</span>, 1)<span class="org-type">-</span>mean(sr_lpf_1khz_of(<span class="org-type">:</span>, 1));
sr_lpf_1khz_of(<span class="org-type">:</span>, 2) = <span class="org-type">-</span>(sr_lpf_1khz_of(<span class="org-type">:</span>, 2)<span class="org-type">-</span>mean(sr_lpf_1khz_of(<span class="org-type">:</span>, 2)));
sr_lpf_1khz_on(<span class="org-type">:</span>, 1) = sr_lpf_1khz_on(<span class="org-type">:</span>, 1)<span class="org-type">-</span>mean(sr_lpf_1khz_on(<span class="org-type">:</span>, 1));
sr_lpf_1khz_on(<span class="org-type">:</span>, 2) = <span class="org-type">-</span>(sr_lpf_1khz_on(<span class="org-type">:</span>, 2)<span class="org-type">-</span>mean(sr_lpf_1khz_on(<span class="org-type">:</span>, 2)));
</pre>
</div>
</div>
</div>
<div id="outline-container-orgb9d52c6" class="outline-4">
<h4 id="orgb9d52c6"><span class="section-number-4">2.4.4</span> Time Domain</h4>
<div class="outline-text-4" id="text-2-4-4">
<p>
We compare the signal when the Slip-Ring is OFF (figure <a href="#org58deeed">14</a>) and when it is ON (figure <a href="#org74abed5">15</a>).
</p>
<div id="org58deeed" class="figure">
<p><img src="figs/sr_lpf_1khz_geophone_time_off.png" alt="sr_lpf_1khz_geophone_time_off.png" />
</p>
<p><span class="figure-number">Figure 14: </span>Comparison of the time domain signals when the slip-ring is OFF</p>
</div>
<div id="org74abed5" class="figure">
<p><img src="figs/sr_lpf_1khz_geophone_time_on.png" alt="sr_lpf_1khz_geophone_time_on.png" />
</p>
<p><span class="figure-number">Figure 15: </span>Comparison of the time domain signals when the slip-ring is ON</p>
</div>
</div>
</div>
<div id="outline-container-org9f409d8" class="outline-4">
<h4 id="org9f409d8"><span class="section-number-4">2.4.5</span> Frequency Domain</h4>
<div class="outline-text-4" id="text-2-4-5">
<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_1khz_of(2, 3)<span class="org-type">-</span>sr_lpf_1khz_of(1, 3);
Fs = 1<span class="org-type">/</span>dt; <span class="org-comment">% [Hz]</span>
win = hanning(ceil(10<span class="org-type">*</span>Fs));
</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>
[pxdi_lpf_1khz_of, f] = pwelch(sr_lpf_1khz_of(<span class="org-type">:</span>, 1), win, [], [], Fs);
[pxdi_lpf_1khz_on, <span class="org-type">~</span>] = pwelch(sr_lpf_1khz_on(<span class="org-type">:</span>, 1), win, [], [], Fs);
<span class="org-comment">% Slip-Ring measure</span>
[pxsr_lpf_1khz_of, <span class="org-type">~</span>] = pwelch(sr_lpf_1khz_of(<span class="org-type">:</span>, 2), win, [], [], Fs);
[pxsr_lpf_1khz_on, <span class="org-type">~</span>] = pwelch(sr_lpf_1khz_on(<span class="org-type">:</span>, 2), win, [], [], Fs);
</pre>
</div>
<p>
Finally, we compare the Amplitude Spectral Density of the signals (figure <a href="#org767055e">16</a>);
</p>
<div class="org-src-container">
<pre class="src src-matlab"><span class="org-type">figure</span>;
hold on;
plot(f, sqrt(pxdi_lpf_1khz_of), <span class="org-string">'DisplayName'</span>, <span class="org-string">'Direct - OFF'</span>);
plot(f, sqrt(pxsr_lpf_1khz_of), <span class="org-string">'DisplayName'</span>, <span class="org-string">'Slip-Ring - OFF'</span>);
plot(f, sqrt(pxdi_lpf_1khz_on), <span class="org-string">'DisplayName'</span>, <span class="org-string">'Direct - ON'</span>);
plot(f, sqrt(pxsr_lpf_1khz_on), <span class="org-string">'DisplayName'</span>, <span class="org-string">'Slip-Ring - ON'</span>);
hold off;
xlim([1, 500]);
<span class="org-type">set</span>(<span class="org-variable-name">gca</span>, <span class="org-string">'xscale'</span>, <span class="org-string">'log'</span>); <span class="org-type">set</span>(<span class="org-variable-name">gca</span>, <span class="org-string">'yscale'</span>, <span class="org-string">'log'</span>);
xlabel(<span class="org-string">'Frequency [Hz]'</span>); ylabel(<span class="org-string">'ASD of the measured Voltage $\left[\frac{V}{\sqrt{Hz}}\right]$'</span>)
legend(<span class="org-string">'Location'</span>, <span class="org-string">'southwest'</span>);
</pre>
</div>
<div id="org767055e" class="figure">
<p><img src="figs/sr_lpf_1khz_geophone_asd.png" alt="sr_lpf_1khz_geophone_asd.png" />
</p>
<p><span class="figure-number">Figure 16: </span>Comparison of the Amplitude Spectral Sensity</p>
</div>
</div>
</div>
<div id="outline-container-org416009b" class="outline-4">
<h4 id="org416009b"><span class="section-number-4">2.4.6</span> Difference between the direct signal and the signal going through the slip-ring</h4>
<div class="outline-text-4" id="text-2-4-6">
<p>
We subtract the signal coming from the direct wire to the signal going through the slip-ring when the slip-ring is ON and when it is OFF (figure <a href="#orga7bd62b">17</a>).
</p>
<div id="orga7bd62b" class="figure">
<p><img src="figs/diff_sr_direct.png" alt="diff_sr_direct.png" />
</p>
<p><span class="figure-number">Figure 17: </span>Difference between the signal going directly to the ADC and the signal going through the slip-ring before the ADC</p>
</div>
<p>
Then we compute the Power Spectral Density using <code>pwelch</code> function (figure <a href="#orga12f709">18</a>).
</p>
<div class="org-src-container">
<pre class="src src-matlab"><span class="org-comment">% Direct measure</span>
[px_diff_lpf_1khz_of, f] = pwelch(sr_lpf_1khz_of(<span class="org-type">:</span>, 1)<span class="org-type">-</span>sr_lpf_1khz_of(<span class="org-type">:</span>, 2), win, [], [], Fs);
[px_diff_lpf_1khz_on, <span class="org-type">~</span>] = pwelch(sr_lpf_1khz_on(<span class="org-type">:</span>, 1)<span class="org-type">-</span>sr_lpf_1khz_on(<span class="org-type">:</span>, 2), win, [], [], Fs);
</pre>
</div>
<div id="orga12f709" class="figure">
<p><img src="figs/diff_sr_direct_psd.png" alt="diff_sr_direct_psd.png" />
</p>
<p><span class="figure-number">Figure 18: </span>Amplitude Spectral Density of the difference between the signal going directly to the ADC and the signal going through the slip-ring before the ADC</p>
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<h4 id="org2a99be3"><span class="section-number-4">2.4.7</span> Conclusion</h4>
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<li>Using the LPF, we don&rsquo;t see any additional noise coming from the slip-ring when it is turned ON</li>
<li>The signal going through the slip-ring only differs from the direct signal by some 50Hz and its harmonics</li>
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<div id="postamble" class="status">
<p class="author">Author: Dehaeze Thomas</p>
<p class="date">Created: 2020-11-12 jeu. 10:29</p>
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