1666 lines
94 KiB
HTML
1666 lines
94 KiB
HTML
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<div id="content">
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<h1 class="title">Measurements</h1>
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<div id="table-of-contents">
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<h2>Table of Contents</h2>
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<div id="text-table-of-contents">
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<ul>
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<li><a href="#orgaf5bde7">1. Effect of the rotation of the Slip-Ring</a>
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<ul>
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<li><a href="#org0a97e9a">1.1. Measurement Description</a></li>
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<li><a href="#org029f003">1.2. Load data</a></li>
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<li><a href="#orgd16c05d">1.3. Analysis</a></li>
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<li><a href="#orgd1100d9">1.4. Conclusion</a></li>
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</ul>
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</li>
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<li><a href="#orge3831af">2. Measure of the noise of the Voltage Amplifier</a>
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<ul>
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<li><a href="#org9275c22">2.1. Measurement Description</a></li>
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<li><a href="#org076bd52">2.2. Load data</a></li>
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<li><a href="#org31a6203">2.3. Time Domain</a></li>
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<li><a href="#org2d6e818">2.4. Frequency Domain</a></li>
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<li><a href="#orgf2d618a">2.5. Conclusion</a></li>
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</ul>
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</li>
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<li><a href="#orga6037b5">3. Measure of the noise induced by the Slip-Ring</a>
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<ul>
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<li><a href="#org7a8e839">3.1. Measurement Description</a></li>
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<li><a href="#orgfd83860">3.2. Load data</a></li>
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<li><a href="#orgd7f44ae">3.3. Time Domain</a></li>
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<li><a href="#org6d9481b">3.4. Frequency Domain</a></li>
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<li><a href="#org492b214">3.5. Conclusion</a></li>
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</ul>
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</li>
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<li><a href="#orga5361d8">4. Measure of the noise induced by the slip ring when using a geophone</a>
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<ul>
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<li><a href="#orga2dfbe3">4.1. First Measurement without LPF</a>
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<ul>
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<li><a href="#orgd13160a">4.1.1. Measurement Description</a></li>
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<li><a href="#org75b1cb2">4.1.2. Load data</a></li>
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<li><a href="#org6882137">4.1.3. Time Domain</a></li>
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<li><a href="#org0ecd16d">4.1.4. Frequency Domain</a></li>
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<li><a href="#org1c6fc42">4.1.5. Conclusion</a></li>
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</ul>
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</li>
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<li><a href="#org79131d0">4.2. Measurement using an oscilloscope</a>
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<ul>
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<li><a href="#org08912ee">4.2.1. Measurement Setup</a></li>
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<li><a href="#org0f48206">4.2.2. Observations</a></li>
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<li><a href="#org72426b5">4.2.3. Conclusion</a></li>
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</ul>
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</li>
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<li><a href="#orgdbbf506">4.3. New measurements with a LPF before the Voltage Amplifiers</a>
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<ul>
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<li><a href="#orga6a384e">4.3.1. Setup description</a></li>
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<li><a href="#org30f3214">4.3.2. Load data</a></li>
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<li><a href="#orgafee079">4.3.3. Time Domain</a></li>
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<li><a href="#org21431fc">4.3.4. Frequency Domain</a></li>
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<li><a href="#org56db2e6">4.3.5. Comparison of with and without LPF</a></li>
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<li><a href="#org2d768b8">4.3.6. Conclusion</a></li>
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</ul>
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</li>
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</ul>
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</li>
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<li><a href="#orgd797cc0">5. Measure of the influence of the AC/DC option on the voltage amplifiers</a>
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<ul>
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<li><a href="#orgc085afb">5.1. Measurement Description</a></li>
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<li><a href="#orgfc17680">5.2. Load data</a></li>
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<li><a href="#org343469a">5.3. Time Domain</a></li>
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<li><a href="#orge3b762c">5.4. Frequency Domain</a></li>
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<li><a href="#org329c1e0">5.5. Conclusion</a></li>
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</ul>
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</li>
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<li><a href="#org30ed796">6. Measure of the Low Pass Filter</a>
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<ul>
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<li><a href="#org25394a2">6.1. Measurement Description</a></li>
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<li><a href="#org603ee8b">6.2. Load data</a></li>
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<li><a href="#org23355c0">6.3. Transfer function of the LPF</a></li>
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<li><a href="#org461899b">6.4. Conclusion</a></li>
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<li><a href="#org25a2b36">6.5. <span class="todo TODO">TODO</span> Low Pass Filter with a cut-off frequency of 1kHz</a></li>
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</ul>
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</li>
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</ul>
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</div>
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</div>
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<div id="outline-container-orgaf5bde7" class="outline-2">
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<h2 id="orgaf5bde7"><span class="section-number-2">1</span> Effect of the rotation of the Slip-Ring</h2>
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<div class="outline-text-2" id="text-1">
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<p>
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The data and matlab files are accessible <a href="data/meas_effect_sr.zip">here</a>.
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</p>
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</div>
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<div id="outline-container-org0a97e9a" class="outline-3">
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<h3 id="org0a97e9a"><span class="section-number-3">1.1</span> Measurement Description</h3>
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<div class="outline-text-3" id="text-1-1">
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<p>
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Random Signal is generated by one DAC of the SpeedGoat.
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</p>
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<p>
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The signal going out of the DAC is split into two:
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</p>
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<ul class="org-ul">
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<li>one BNC cable is directly connected to one ADC of the SpeedGoat</li>
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<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>
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</ul>
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<p>
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Two measurements are done.
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</p>
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<table border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
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<th scope="col" class="org-left">Data File</th>
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<th scope="col" class="org-left">Description</th>
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<tbody>
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<td class="org-left"><code>mat/data_001.mat</code></td>
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<td class="org-left">Slip-ring not turning</td>
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<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-org029f003" class="outline-3">
|
|
<h3 id="org029f003"><span class="section-number-3">1.2</span> Load data</h3>
|
|
<div class="outline-text-3" id="text-1-2">
|
|
<p>
|
|
We load the data of the z axis of two geophones.
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">sr_off = load<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'mat/data_001.mat', 't', 'x1', 'x2'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
sr_on = load<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'mat/data_002.mat', 't', 'x1', 'x2'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-orgd16c05d" class="outline-3">
|
|
<h3 id="orgd16c05d"><span class="section-number-3">1.3</span> Analysis</h3>
|
|
<div class="outline-text-3" id="text-1-3">
|
|
<p>
|
|
Let's first look at the signal produced by the DAC (figure <a href="#org554b843">1</a>).
|
|
</p>
|
|
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab"><span class="org-type">figure</span>;
|
|
hold on;
|
|
plot<span class="org-rainbow-delimiters-depth-1">(</span>sr_on.t, sr_on.x1<span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
hold off;
|
|
xlabel<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Time </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">s</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">)</span></span><span class="org-string">; ylabel</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">(</span></span><span class="org-string">'Voltage </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">V</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
xlim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span><span class="org-highlight-numbers-number">0</span> <span class="org-highlight-numbers-number">10</span><span class="org-rainbow-delimiters-depth-2">]</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
</pre>
|
|
</div>
|
|
|
|
|
|
<div id="org554b843" class="figure">
|
|
<p><img src="figs/random_signal.png" alt="random_signal.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 1: </span>Random signal produced by the DAC</p>
|
|
</div>
|
|
|
|
<p>
|
|
We now look at the difference between the signal directly measured by the ADC and the signal that goes through the slip-ring (figure <a href="#orged462f9">2</a>).
|
|
</p>
|
|
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab"><span class="org-type">figure</span>;
|
|
hold on;
|
|
plot<span class="org-rainbow-delimiters-depth-1">(</span>sr_on.t, sr_on.x1 <span class="org-type">-</span> sr_on.x2, <span class="org-string">'DisplayName', '</span>Slip<span class="org-type">-</span>Ring <span class="org-type">-</span> $<span class="org-type">\</span>omega = <span class="org-highlight-numbers-number">1rpm$</span>'<span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
plot<span class="org-rainbow-delimiters-depth-1">(</span>sr_off.t, sr_off.x1 <span class="org-type">-</span> sr_off.x2,<span class="org-string">'DisplayName', 'Slip-Ring off'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
hold off;
|
|
xlabel<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Time </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">s</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">)</span></span><span class="org-string">; ylabel</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">(</span></span><span class="org-string">'Voltage </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">V</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
xlim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span><span class="org-highlight-numbers-number">0</span> <span class="org-highlight-numbers-number">10</span><span class="org-rainbow-delimiters-depth-2">]</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
legend<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Location', 'northeast'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
</pre>
|
|
</div>
|
|
|
|
|
|
<div id="orged462f9" class="figure">
|
|
<p><img src="figs/slipring_comp_signals.png" alt="slipring_comp_signals.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 2: </span>Alteration of the signal when the slip-ring is turning</p>
|
|
</div>
|
|
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">dt = sr_on.t<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-1">)</span> <span class="org-type">-</span> sr_on.t<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
Fs = <span class="org-highlight-numbers-number">1</span><span class="org-type">/</span>dt; <span class="org-comment">% [Hz]</span>
|
|
|
|
win = hanning<span class="org-rainbow-delimiters-depth-1">(</span>ceil<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-highlight-numbers-number">1</span><span class="org-type">*</span>Fs<span class="org-rainbow-delimiters-depth-2">)</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
</pre>
|
|
</div>
|
|
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab"><span class="org-rainbow-delimiters-depth-1">[</span>pxx_on, f<span class="org-rainbow-delimiters-depth-1">]</span> = pwelch<span class="org-rainbow-delimiters-depth-1">(</span>sr_on.x1 <span class="org-type">-</span> sr_on.x2, win, <span class="org-rainbow-delimiters-depth-2">[]</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, Fs<span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
<span class="org-rainbow-delimiters-depth-1">[</span>pxx_off, <span class="org-type">~</span><span class="org-rainbow-delimiters-depth-1">]</span> = pwelch<span class="org-rainbow-delimiters-depth-1">(</span>sr_off.x1 <span class="org-type">-</span> sr_off.x2, win, <span class="org-rainbow-delimiters-depth-2">[]</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, Fs<span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
</pre>
|
|
</div>
|
|
|
|
|
|
<div id="org0c302c6" class="figure">
|
|
<p><img src="figs/psd_noise.png" alt="psd_noise.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 3: </span>ASD of the measured noise</p>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-orgd1100d9" class="outline-3">
|
|
<h3 id="orgd1100d9"><span class="section-number-3">1.4</span> Conclusion</h3>
|
|
<div class="outline-text-3" id="text-1-4">
|
|
<div class="note">
|
|
<p>
|
|
<b>Remaining questions</b>:
|
|
</p>
|
|
<ul class="org-ul">
|
|
<li>Should the measurement be redone using voltage amplifiers?</li>
|
|
<li>Use higher rotation speed and measure for longer periods (to have multiple revolutions) ?</li>
|
|
</ul>
|
|
|
|
</div>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
<div id="outline-container-orge3831af" class="outline-2">
|
|
<h2 id="orge3831af"><span class="section-number-2">2</span> Measure of the noise of the Voltage Amplifier</h2>
|
|
<div class="outline-text-2" id="text-2">
|
|
<p>
|
|
The data and matlab files are accessible <a href="data/meas_volt_amp.zip">here</a>.
|
|
</p>
|
|
</div>
|
|
|
|
<div id="outline-container-org9275c22" class="outline-3">
|
|
<h3 id="org9275c22"><span class="section-number-3">2.1</span> Measurement Description</h3>
|
|
<div class="outline-text-3" id="text-2-1">
|
|
<p>
|
|
<b>Goal</b>:
|
|
</p>
|
|
<ul class="org-ul">
|
|
<li>Determine the Voltage Amplifier noise</li>
|
|
</ul>
|
|
|
|
<p>
|
|
<b>Setup</b>:
|
|
</p>
|
|
<ul class="org-ul">
|
|
<li>The two inputs (differential) of the voltage amplifier are shunted with 50Ohms</li>
|
|
<li>The AC/DC option of the Voltage amplifier is on AC</li>
|
|
<li>The low pass filter is set to 1hHz</li>
|
|
<li>We measure the output of the voltage amplifier with a 16bits ADC of the Speedgoat</li>
|
|
</ul>
|
|
|
|
<p>
|
|
<b>Measurements</b>:
|
|
</p>
|
|
<ul class="org-ul">
|
|
<li><code>data_003</code>: Ampli OFF</li>
|
|
<li><code>data_004</code>: Ampli ON set to 20dB</li>
|
|
<li><code>data_005</code>: Ampli ON set to 40dB</li>
|
|
<li><code>data_006</code>: Ampli ON set to 60dB</li>
|
|
</ul>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org076bd52" class="outline-3">
|
|
<h3 id="org076bd52"><span class="section-number-3">2.2</span> Load data</h3>
|
|
<div class="outline-text-3" id="text-2-2">
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">amp_off = load<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'mat/data_003.mat', 'data'</span><span class="org-rainbow-delimiters-depth-1">)</span>; amp_off = amp_off.data<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-type">:</span>, <span class="org-rainbow-delimiters-depth-2">[</span><span class="org-highlight-numbers-number">1</span>,<span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">]</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
amp_20d = load<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'mat/data_004.mat', 'data'</span><span class="org-rainbow-delimiters-depth-1">)</span>; amp_20d = amp_20d.data<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-type">:</span>, <span class="org-rainbow-delimiters-depth-2">[</span><span class="org-highlight-numbers-number">1</span>,<span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">]</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
amp_40d = load<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'mat/data_005.mat', 'data'</span><span class="org-rainbow-delimiters-depth-1">)</span>; amp_40d = amp_40d.data<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-type">:</span>, <span class="org-rainbow-delimiters-depth-2">[</span><span class="org-highlight-numbers-number">1</span>,<span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">]</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
amp_60d = load<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'mat/data_006.mat', 'data'</span><span class="org-rainbow-delimiters-depth-1">)</span>; amp_60d = amp_60d.data<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-type">:</span>, <span class="org-rainbow-delimiters-depth-2">[</span><span class="org-highlight-numbers-number">1</span>,<span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">]</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org31a6203" class="outline-3">
|
|
<h3 id="org31a6203"><span class="section-number-3">2.3</span> Time Domain</h3>
|
|
<div class="outline-text-3" id="text-2-3">
|
|
<p>
|
|
The time domain signals are shown on figure <a href="#orgac0ea26">4</a>.
|
|
</p>
|
|
|
|
|
|
<div id="orgac0ea26" class="figure">
|
|
<p><img src="figs/ampli_noise_time.png" alt="ampli_noise_time.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 4: </span>Output of the amplifier</p>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org2d6e818" class="outline-3">
|
|
<h3 id="org2d6e818"><span class="section-number-3">2.4</span> Frequency Domain</h3>
|
|
<div class="outline-text-3" id="text-2-4">
|
|
<p>
|
|
We first compute some parameters that will be used for the PSD computation.
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">dt = amp_off<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">2</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-1">)</span><span class="org-type">-</span>amp_off<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">1</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
|
|
Fs = <span class="org-highlight-numbers-number">1</span><span class="org-type">/</span>dt; <span class="org-comment">% [Hz]</span>
|
|
|
|
win = hanning<span class="org-rainbow-delimiters-depth-1">(</span>ceil<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-highlight-numbers-number">10</span><span class="org-type">*</span>Fs<span class="org-rainbow-delimiters-depth-2">)</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
</pre>
|
|
</div>
|
|
|
|
<p>
|
|
Then we compute the Power Spectral Density using <code>pwelch</code> function.
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab"><span class="org-rainbow-delimiters-depth-1">[</span>pxoff, f<span class="org-rainbow-delimiters-depth-1">]</span> = pwelch<span class="org-rainbow-delimiters-depth-1">(</span>amp_off<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>,<span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, win, <span class="org-rainbow-delimiters-depth-2">[]</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, Fs<span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
<span class="org-rainbow-delimiters-depth-1">[</span>px20d, <span class="org-type">~</span><span class="org-rainbow-delimiters-depth-1">]</span> = pwelch<span class="org-rainbow-delimiters-depth-1">(</span>amp_20d<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>,<span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, win, <span class="org-rainbow-delimiters-depth-2">[]</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, Fs<span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
<span class="org-rainbow-delimiters-depth-1">[</span>px40d, <span class="org-type">~</span><span class="org-rainbow-delimiters-depth-1">]</span> = pwelch<span class="org-rainbow-delimiters-depth-1">(</span>amp_40d<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>,<span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, win, <span class="org-rainbow-delimiters-depth-2">[]</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, Fs<span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
<span class="org-rainbow-delimiters-depth-1">[</span>px60d, <span class="org-type">~</span><span class="org-rainbow-delimiters-depth-1">]</span> = pwelch<span class="org-rainbow-delimiters-depth-1">(</span>amp_60d<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>,<span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, win, <span class="org-rainbow-delimiters-depth-2">[]</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, Fs<span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
</pre>
|
|
</div>
|
|
|
|
<p>
|
|
We compute the theoretical ADC noise.
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">q = <span class="org-highlight-numbers-number">20</span><span class="org-type">/</span><span class="org-highlight-numbers-number">2</span><span class="org-type">^</span><span class="org-highlight-numbers-number">16</span>; <span class="org-comment">% quantization</span>
|
|
Sq = q<span class="org-type">^</span><span class="org-highlight-numbers-number">2</span><span class="org-type">/</span><span class="org-highlight-numbers-number">12</span><span class="org-type">/</span><span class="org-highlight-numbers-number">1000</span>; <span class="org-comment">% PSD of the ADC noise</span>
|
|
</pre>
|
|
</div>
|
|
|
|
<p>
|
|
Finally, the ASD is shown on figure <a href="#orgc73d657">5</a>.
|
|
</p>
|
|
|
|
<div id="orgc73d657" class="figure">
|
|
<p><img src="figs/ampli_noise_psd.png" alt="ampli_noise_psd.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 5: </span>Amplitude Spectral Density of the measured voltage at the output of the voltage amplifier</p>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-orgf2d618a" class="outline-3">
|
|
<h3 id="orgf2d618a"><span class="section-number-3">2.5</span> Conclusion</h3>
|
|
<div class="outline-text-3" id="text-2-5">
|
|
<div class="important">
|
|
<p>
|
|
Noise induced by the voltage amplifiers is not a limiting factor.
|
|
</p>
|
|
|
|
</div>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-orga6037b5" class="outline-2">
|
|
<h2 id="orga6037b5"><span class="section-number-2">3</span> Measure of the noise induced by the Slip-Ring</h2>
|
|
<div class="outline-text-2" id="text-3">
|
|
<p>
|
|
The data and matlab files are accessible <a href="data/meas_slip_ring.zip">here</a>.
|
|
</p>
|
|
</div>
|
|
|
|
<div id="outline-container-org7a8e839" class="outline-3">
|
|
<h3 id="org7a8e839"><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="orgae8238c" class="figure">
|
|
<p><img src="./img/VID_20190503_160831.gif" alt="VID_20190503_160831.gif" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 6: </span>Slip-Ring rotating at 6rpm</p>
|
|
</div>
|
|
|
|
|
|
<div id="orga0ae65d" class="figure">
|
|
<p><img src="./img/VID_20190503_161401.gif" alt="VID_20190503_161401.gif" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 7: </span>Slip-Ring rotating at 60rpm</p>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-orgfd83860" class="outline-3">
|
|
<h3 id="orgfd83860"><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-orgd7f44ae" class="outline-3">
|
|
<h3 id="orgd7f44ae"><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="#orgd8a4939">8</a>) and for the signal going through the slip-ring (figure <a href="#orgb192b1f">9</a>);
|
|
</p>
|
|
|
|
|
|
<div id="orgd8a4939" class="figure">
|
|
<p><img src="figs/sr_direct_time.png" alt="sr_direct_time.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 8: </span>Direct measurement</p>
|
|
</div>
|
|
|
|
|
|
|
|
<div id="orgb192b1f" class="figure">
|
|
<p><img src="figs/sr_slipring_time.png" alt="sr_slipring_time.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 9: </span>Measurement of the signal going through the Slip-Ring</p>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org6d9481b" class="outline-3">
|
|
<h3 id="org6d9481b"><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="#org55f9c86">10</a>);
|
|
</p>
|
|
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab"><span class="org-type">figure</span>;
|
|
hold on;
|
|
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, sqrt<span class="org-rainbow-delimiters-depth-2">(</span>pxoff<span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'OFF'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, sqrt<span class="org-rainbow-delimiters-depth-2">(</span>pxon<span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'ON'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, sqrt<span class="org-rainbow-delimiters-depth-2">(</span>px6r<span class="org-rainbow-delimiters-depth-2">)</span>, 'DisplayName', '<span class="org-highlight-numbers-number">6rpm</span>'<span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, sqrt<span class="org-rainbow-delimiters-depth-2">(</span>px60r<span class="org-rainbow-delimiters-depth-2">)</span>, 'DisplayName', '<span class="org-highlight-numbers-number">60rpm</span>'<span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, sqrt<span class="org-rainbow-delimiters-depth-2">(</span>pxdir<span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'k-', 'DisplayName', 'Direct'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
hold off;
|
|
<span class="org-type">set</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-variable-name">gca</span>, <span class="org-string">'xscale', 'log'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
<span class="org-type">set</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-variable-name">gca</span>, <span class="org-string">'yscale', 'log'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
xlabel<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Frequency </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">Hz</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">)</span></span><span class="org-string">; ylabel</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">(</span></span><span class="org-string">'</span>ASD of the measured Voltage $<span class="org-type">\</span>left<span class="org-rainbow-delimiters-depth-2">[</span><span class="org-type">\</span>frac<span class="org-rainbow-delimiters-depth-3">{</span>V<span class="org-rainbow-delimiters-depth-3">}{</span><span class="org-type">\</span>sqrt<span class="org-rainbow-delimiters-depth-4">{</span>Hz<span class="org-rainbow-delimiters-depth-4">}</span><span class="org-rainbow-delimiters-depth-3">}</span><span class="org-type">\</span>right<span class="org-rainbow-delimiters-depth-2">]</span>$'<span class="org-rainbow-delimiters-depth-1">)</span>
|
|
legend<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Location', 'northeast'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
xlim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span><span class="org-highlight-numbers-number">0</span>.<span class="org-highlight-numbers-number">1</span>, <span class="org-highlight-numbers-number">500</span><span class="org-rainbow-delimiters-depth-2">]</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
</pre>
|
|
</div>
|
|
|
|
|
|
<div id="org55f9c86" class="figure">
|
|
<p><img src="figs/sr_psd_compare.png" alt="sr_psd_compare.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 10: </span>Comparison of the ASD of the measured signals when the slip-ring is ON, OFF and turning</p>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org492b214" class="outline-3">
|
|
<h3 id="org492b214"><span class="section-number-3">3.5</span> Conclusion</h3>
|
|
<div class="outline-text-3" id="text-3-5">
|
|
<div class="important">
|
|
<p>
|
|
|
|
</p>
|
|
|
|
</div>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-orga5361d8" class="outline-2">
|
|
<h2 id="orga5361d8"><span class="section-number-2">4</span> Measure of the noise induced by the slip ring when using a geophone</h2>
|
|
<div class="outline-text-2" id="text-4">
|
|
<p>
|
|
The data and matlab files are accessible <a href="data/meas_sr_geophone.zip">here</a>.
|
|
</p>
|
|
</div>
|
|
|
|
<div id="outline-container-orga2dfbe3" class="outline-3">
|
|
<h3 id="orga2dfbe3"><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-orgd13160a" class="outline-4">
|
|
<h4 id="orgd13160a"><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-org75b1cb2" class="outline-4">
|
|
<h4 id="org75b1cb2"><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-org6882137" class="outline-4">
|
|
<h4 id="org6882137"><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="#org7616103">11</a>) and when it is ON (figure <a href="#orga39cf4a">12</a>).
|
|
</p>
|
|
|
|
|
|
<div id="org7616103" class="figure">
|
|
<p><img src="figs/sr_geophone_time_off.png" alt="sr_geophone_time_off.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 11: </span>Comparison of the time domain signals when the slip-ring is OFF</p>
|
|
</div>
|
|
|
|
|
|
<div id="orga39cf4a" class="figure">
|
|
<p><img src="figs/sr_geophone_time_on.png" alt="sr_geophone_time_on.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 12: </span>Comparison of the time domain signals when the slip-ring is ON</p>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org0ecd16d" class="outline-4">
|
|
<h4 id="org0ecd16d"><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="#org594c556">13</a>);
|
|
</p>
|
|
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab"><span class="org-type">figure</span>;
|
|
hold on;
|
|
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, sqrt<span class="org-rainbow-delimiters-depth-2">(</span>pxdoff<span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'Direct - OFF'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, sqrt<span class="org-rainbow-delimiters-depth-2">(</span>pxsroff<span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'Slip-Ring - OFF'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, sqrt<span class="org-rainbow-delimiters-depth-2">(</span>pxdon<span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'Direct - ON'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, sqrt<span class="org-rainbow-delimiters-depth-2">(</span>pxsron<span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'Slip-Ring - ON'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
hold off;
|
|
<span class="org-type">set</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-variable-name">gca</span>, <span class="org-string">'xscale', 'log'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
<span class="org-type">set</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-variable-name">gca</span>, <span class="org-string">'yscale', 'log'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
xlabel<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Frequency </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">Hz</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">)</span></span><span class="org-string">; ylabel</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">(</span></span><span class="org-string">'</span>ASD of the measured Voltage $<span class="org-type">\</span>left<span class="org-rainbow-delimiters-depth-2">[</span><span class="org-type">\</span>frac<span class="org-rainbow-delimiters-depth-3">{</span>V<span class="org-rainbow-delimiters-depth-3">}{</span><span class="org-type">\</span>sqrt<span class="org-rainbow-delimiters-depth-4">{</span>Hz<span class="org-rainbow-delimiters-depth-4">}</span><span class="org-rainbow-delimiters-depth-3">}</span><span class="org-type">\</span>right<span class="org-rainbow-delimiters-depth-2">]</span>$'<span class="org-rainbow-delimiters-depth-1">)</span>
|
|
legend<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Location', 'northeast'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
xlim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span><span class="org-highlight-numbers-number">0</span>.<span class="org-highlight-numbers-number">1</span>, <span class="org-highlight-numbers-number">500</span><span class="org-rainbow-delimiters-depth-2">]</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
</pre>
|
|
</div>
|
|
|
|
|
|
<div id="org594c556" class="figure">
|
|
<p><img src="figs/sr_geophone_asd.png" alt="sr_geophone_asd.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 13: </span>Comparison of the Amplitude Spectral Sensity</p>
|
|
</div>
|
|
|
|
|
|
<div id="orgf9abd35" class="figure">
|
|
<p><img src="figs/sr_geophone_asd_zoom.png" alt="sr_geophone_asd_zoom.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 14: </span>Comparison of the Amplitude Spectral Sensity - Zoom</p>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org1c6fc42" class="outline-4">
|
|
<h4 id="org1c6fc42"><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="#orgf9abd35">14</a> be due to the Aliasing?</li>
|
|
</ul>
|
|
|
|
</div>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org79131d0" class="outline-3">
|
|
<h3 id="org79131d0"><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-org08912ee" class="outline-4">
|
|
<h4 id="org08912ee"><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-org0f48206" class="outline-4">
|
|
<h4 id="org0f48206"><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="#org64c98bf">15</a>), we observe a signal at 40kHz with a peak-to-peak amplitude of 200mV for the direct measure and 100mV for the signal going through the Slip-Ring.
|
|
</p>
|
|
|
|
<p>
|
|
Then the Slip-Ring is OFF, we don't observe this 40kHz anymore (figure <a href="#org773a738">16</a>).
|
|
</p>
|
|
|
|
|
|
<div id="org64c98bf" class="figure">
|
|
<p><img src="./img/IMG_20190506_160420.jpg" alt="IMG_20190506_160420.jpg" width="500px" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 15: </span>Signals measured by the oscilloscope - Slip-Ring ON - Yellow: Direct measure - Blue: Through Slip-Ring</p>
|
|
</div>
|
|
|
|
|
|
<div id="org773a738" class="figure">
|
|
<p><img src="./img/IMG_20190506_160438.jpg" alt="IMG_20190506_160438.jpg" width="500px" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 16: </span>Signals measured by the oscilloscope - Slip-Ring OFF - Yellow: Direct measure - Blue: Through Slip-Ring</p>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org72426b5" class="outline-4">
|
|
<h4 id="org72426b5"><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 add a Low pass filter before the voltage amplifiers to not saturate them and filter the noise.</li>
|
|
</ul>
|
|
|
|
</div>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-orgdbbf506" class="outline-3">
|
|
<h3 id="orgdbbf506"><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-orga6a384e" class="outline-4">
|
|
<h4 id="orga6a384e"><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-org30f3214" class="outline-4">
|
|
<h4 id="org30f3214"><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-orgafee079" class="outline-4">
|
|
<h4 id="orgafee079"><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="#org9445bdb">17</a>) and when it is ON (figure <a href="#org47faa80">18</a>).
|
|
</p>
|
|
|
|
|
|
<div id="org9445bdb" class="figure">
|
|
<p><img src="figs/sr_lpf_geophone_time_off.png" alt="sr_lpf_geophone_time_off.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 17: </span>Comparison of the time domain signals when the slip-ring is OFF</p>
|
|
</div>
|
|
|
|
|
|
<div id="org47faa80" class="figure">
|
|
<p><img src="figs/sr_lpf_geophone_time_on.png" alt="sr_lpf_geophone_time_on.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 18: </span>Comparison of the time domain signals when the slip-ring is ON</p>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org21431fc" class="outline-4">
|
|
<h4 id="org21431fc"><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="#org7f3fe78">19</a>);
|
|
</p>
|
|
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab"><span class="org-type">figure</span>;
|
|
hold on;
|
|
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, sqrt<span class="org-rainbow-delimiters-depth-2">(</span>pxd_lpf_off<span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'Direct - OFF'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, sqrt<span class="org-rainbow-delimiters-depth-2">(</span>pxsr_lpf_off<span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'Slip-Ring - OFF'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, sqrt<span class="org-rainbow-delimiters-depth-2">(</span>pxd_lpf_on<span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'Direct - ON'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, sqrt<span class="org-rainbow-delimiters-depth-2">(</span>pxsr_lpf_on<span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'Slip-Ring - ON'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
hold off;
|
|
<span class="org-type">set</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-variable-name">gca</span>, <span class="org-string">'xscale', 'log'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
<span class="org-type">set</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-variable-name">gca</span>, <span class="org-string">'yscale', 'log'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
xlabel<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Frequency </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">Hz</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">)</span></span><span class="org-string">; ylabel</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">(</span></span><span class="org-string">'</span>ASD of the measured Voltage $<span class="org-type">\</span>left<span class="org-rainbow-delimiters-depth-2">[</span><span class="org-type">\</span>frac<span class="org-rainbow-delimiters-depth-3">{</span>V<span class="org-rainbow-delimiters-depth-3">}{</span><span class="org-type">\</span>sqrt<span class="org-rainbow-delimiters-depth-4">{</span>Hz<span class="org-rainbow-delimiters-depth-4">}</span><span class="org-rainbow-delimiters-depth-3">}</span><span class="org-type">\</span>right<span class="org-rainbow-delimiters-depth-2">]</span>$'<span class="org-rainbow-delimiters-depth-1">)</span>
|
|
legend<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Location', 'northeast'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
xlim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span><span class="org-highlight-numbers-number">0</span>.<span class="org-highlight-numbers-number">1</span>, <span class="org-highlight-numbers-number">500</span><span class="org-rainbow-delimiters-depth-2">]</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
</pre>
|
|
</div>
|
|
|
|
|
|
<div id="org7f3fe78" class="figure">
|
|
<p><img src="figs/sr_lpf_geophone_asd.png" alt="sr_lpf_geophone_asd.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 19: </span>Comparison of the Amplitude Spectral Sensity</p>
|
|
</div>
|
|
|
|
|
|
<div id="org205bf5a" class="figure">
|
|
<p><img src="figs/sr_lpf_geophone_asd_zoom.png" alt="sr_lpf_geophone_asd_zoom.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 20: </span>Comparison of the Amplitude Spectral Sensity - Zoom</p>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org56db2e6" class="outline-4">
|
|
<h4 id="org56db2e6"><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="orgb2cb8e7" class="figure">
|
|
<p><img src="figs/comp_with_without_lpf.png" alt="comp_with_without_lpf.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 21: </span>Comparison of the measured signals with and without LPF</p>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org2d768b8" class="outline-4">
|
|
<h4 id="org2d768b8"><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 will use a smaller value of the capacitor to have a cut-off frequency at \(1kHz\).</li>
|
|
</ul>
|
|
|
|
</div>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-orgd797cc0" class="outline-2">
|
|
<h2 id="orgd797cc0"><span class="section-number-2">5</span> Measure of the influence of the AC/DC option on the voltage amplifiers</h2>
|
|
<div class="outline-text-2" id="text-5">
|
|
<p>
|
|
The data and matlab files are accessible <a href="data/meas_noise_ac_dc.zip">here</a>.
|
|
</p>
|
|
</div>
|
|
|
|
<div id="outline-container-orgc085afb" class="outline-3">
|
|
<h3 id="orgc085afb"><span class="section-number-3">5.1</span> Measurement Description</h3>
|
|
<div class="outline-text-3" id="text-5-1">
|
|
<p>
|
|
<b>Goal</b>:
|
|
</p>
|
|
<ul class="org-ul">
|
|
<li>Measure the influence of the high-pass filter option of the voltage amplifiers</li>
|
|
</ul>
|
|
|
|
<p>
|
|
<b>Setup</b>:
|
|
</p>
|
|
<ul class="org-ul">
|
|
<li>One geophone is located on the marble.</li>
|
|
<li>It's signal goes to two voltage amplifiers with a gain of 60dB.</li>
|
|
<li>One voltage amplifier is on the AC option, the other is on the DC option.</li>
|
|
</ul>
|
|
|
|
<p>
|
|
<b>Measurements</b>:
|
|
First measurement (<code>mat/data_014.mat</code> file):
|
|
</p>
|
|
<table border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
|
|
|
|
|
|
<colgroup>
|
|
<col class="org-right" />
|
|
|
|
<col class="org-left" />
|
|
</colgroup>
|
|
<thead>
|
|
<tr>
|
|
<th scope="col" class="org-right">Column</th>
|
|
<th scope="col" class="org-left">Signal</th>
|
|
</tr>
|
|
</thead>
|
|
<tbody>
|
|
<tr>
|
|
<td class="org-right">1</td>
|
|
<td class="org-left">Amplifier 1 with AC option</td>
|
|
</tr>
|
|
|
|
<tr>
|
|
<td class="org-right">2</td>
|
|
<td class="org-left">Amplifier 2 with DC option</td>
|
|
</tr>
|
|
|
|
<tr>
|
|
<td class="org-right">3</td>
|
|
<td class="org-left">Time</td>
|
|
</tr>
|
|
</tbody>
|
|
</table>
|
|
|
|
<p>
|
|
Second measurement (<code>mat/data_015.mat</code> file):
|
|
</p>
|
|
<table border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
|
|
|
|
|
|
<colgroup>
|
|
<col class="org-right" />
|
|
|
|
<col class="org-left" />
|
|
</colgroup>
|
|
<thead>
|
|
<tr>
|
|
<th scope="col" class="org-right">Column</th>
|
|
<th scope="col" class="org-left">Signal</th>
|
|
</tr>
|
|
</thead>
|
|
<tbody>
|
|
<tr>
|
|
<td class="org-right">1</td>
|
|
<td class="org-left">Amplifier 1 with DC option</td>
|
|
</tr>
|
|
|
|
<tr>
|
|
<td class="org-right">2</td>
|
|
<td class="org-left">Amplifier 2 with AC option</td>
|
|
</tr>
|
|
|
|
<tr>
|
|
<td class="org-right">3</td>
|
|
<td class="org-left">Time</td>
|
|
</tr>
|
|
</tbody>
|
|
</table>
|
|
|
|
|
|
<div id="org89d8f1d" class="figure">
|
|
<p><img src="./img/IMG_20190503_170936.jpg" alt="IMG_20190503_170936.jpg" width="500px" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 22: </span>Picture of the two voltages amplifiers</p>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-orgfc17680" class="outline-3">
|
|
<h3 id="orgfc17680"><span class="section-number-3">5.2</span> Load data</h3>
|
|
<div class="outline-text-3" id="text-5-2">
|
|
<p>
|
|
We load the data of the z axis of two geophones.
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">meas14 = load<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'mat/data_014.mat', 'data'</span><span class="org-rainbow-delimiters-depth-1">)</span>; meas14 = meas14.data;
|
|
meas15 = load<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'mat/data_015.mat', 'data'</span><span class="org-rainbow-delimiters-depth-1">)</span>; meas15 = meas15.data;
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org343469a" class="outline-3">
|
|
<h3 id="org343469a"><span class="section-number-3">5.3</span> Time Domain</h3>
|
|
<div class="outline-text-3" id="text-5-3">
|
|
<p>
|
|
The signals are shown on figure <a href="#orgd09e0dc">23</a>.
|
|
</p>
|
|
|
|
<div id="orgd09e0dc" class="figure">
|
|
<p><img src="figs/ac_dc_option_time.png" alt="ac_dc_option_time.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 23: </span>Comparison of the signals going through the Voltage amplifiers</p>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-orge3b762c" class="outline-3">
|
|
<h3 id="orge3b762c"><span class="section-number-3">5.4</span> Frequency Domain</h3>
|
|
<div class="outline-text-3" id="text-5-4">
|
|
<p>
|
|
We first compute some parameters that will be used for the PSD computation.
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">dt = meas14<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">2</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-1">)</span><span class="org-type">-</span>meas14<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">1</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
|
|
Fs = <span class="org-highlight-numbers-number">1</span><span class="org-type">/</span>dt; <span class="org-comment">% [Hz]</span>
|
|
|
|
win = hanning<span class="org-rainbow-delimiters-depth-1">(</span>ceil<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-highlight-numbers-number">10</span><span class="org-type">*</span>Fs<span class="org-rainbow-delimiters-depth-2">)</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
</pre>
|
|
</div>
|
|
|
|
<p>
|
|
Then we compute the Power Spectral Density using <code>pwelch</code> function.
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab"><span class="org-rainbow-delimiters-depth-1">[</span>pxamp1ac, f<span class="org-rainbow-delimiters-depth-1">]</span> = pwelch<span class="org-rainbow-delimiters-depth-1">(</span>meas14<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, win, <span class="org-rainbow-delimiters-depth-2">[]</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, Fs<span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
<span class="org-rainbow-delimiters-depth-1">[</span>pxamp2dc, <span class="org-type">~</span><span class="org-rainbow-delimiters-depth-1">]</span> = pwelch<span class="org-rainbow-delimiters-depth-1">(</span>meas14<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span>, win, <span class="org-rainbow-delimiters-depth-2">[]</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, Fs<span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
|
|
<span class="org-rainbow-delimiters-depth-1">[</span>pxamp1dc, <span class="org-type">~</span><span class="org-rainbow-delimiters-depth-1">]</span> = pwelch<span class="org-rainbow-delimiters-depth-1">(</span>meas15<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, win, <span class="org-rainbow-delimiters-depth-2">[]</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, Fs<span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
<span class="org-rainbow-delimiters-depth-1">[</span>pxamp2ac, <span class="org-type">~</span><span class="org-rainbow-delimiters-depth-1">]</span> = pwelch<span class="org-rainbow-delimiters-depth-1">(</span>meas15<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span>, win, <span class="org-rainbow-delimiters-depth-2">[]</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, Fs<span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
</pre>
|
|
</div>
|
|
|
|
<p>
|
|
The ASD of the signals are compare on figure <a href="#orgd978dff">24</a>.
|
|
</p>
|
|
|
|
<div id="orgd978dff" class="figure">
|
|
<p><img src="figs/ac_dc_option_asd.png" alt="ac_dc_option_asd.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 24: </span>Amplitude Spectral Density of the measured signals</p>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org329c1e0" class="outline-3">
|
|
<h3 id="org329c1e0"><span class="section-number-3">5.5</span> Conclusion</h3>
|
|
<div class="outline-text-3" id="text-5-5">
|
|
<div class="important">
|
|
<ul class="org-ul">
|
|
<li>The voltage amplifiers include some very sharp high pass filters at 1.5Hz (maybe 4th order)</li>
|
|
<li>There is a DC offset on the time domain signal because the DC-offset knob was not set to zero</li>
|
|
</ul>
|
|
|
|
<p>
|
|
<b>Questions</b>:
|
|
</p>
|
|
<ul class="org-ul">
|
|
<li>What option should be used for the measurements?</li>
|
|
</ul>
|
|
|
|
</div>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org30ed796" class="outline-2">
|
|
<h2 id="org30ed796"><span class="section-number-2">6</span> Measure of the Low Pass Filter</h2>
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<div class="outline-text-2" id="text-6">
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</div>
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<div id="outline-container-org25394a2" class="outline-3">
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<h3 id="org25394a2"><span class="section-number-3">6.1</span> Measurement Description</h3>
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<div class="outline-text-3" id="text-6-1">
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<p>
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<b>Goal</b>:
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</p>
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<ul class="org-ul">
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<li>Measure the Low Pass Filter Transfer Function</li>
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</ul>
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<p>
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The values of the components are:
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</p>
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\begin{aligned}
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R &= 1k\Omega \\
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C &= 1\mu F
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\end{aligned}
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<p>
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Which makes a cut-off frequency of \(f_c = \frac{1}{RC} = 1000 rad/s = 160Hz\).
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</p>
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<div class="org-src-container">
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<pre class="src src-latex" id="org8c8e857"><span class="org-font-latex-sedate"><span class="org-keyword">\begin</span></span>{<span class="org-function-name">tikzpicture</span>}
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<span class="org-font-latex-sedate">\draw</span> (0,2) node[circ]
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to [R=<span class="org-font-latex-sedate"><span class="org-font-latex-math">\(R\)</span></span>] ++(2,0)
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to ++(2,0) node[circ]
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++(-2,0) node[circ]
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to [C=<span class="org-font-latex-sedate"><span class="org-font-latex-math">\(C\)</span></span>] ++(0,-2)
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++(-2,0) node[circ]
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to ++(2,0) node[circ]
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to ++(2,0) node[circ];
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<span class="org-font-latex-sedate"><span class="org-keyword">\end</span></span>{<span class="org-function-name">tikzpicture</span>}
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</pre>
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</div>
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<div id="org960847c" class="figure">
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<p><img src="figs/lpf.png" alt="lpf.png" />
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</p>
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<p><span class="figure-number">Figure 25: </span>Schematic of the Low Pass Filter used</p>
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</div>
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<p>
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<b>Setup</b>:
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</p>
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<ul class="org-ul">
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<li>We are measuring the signal from from Geophone with a BNC T</li>
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<li>On part goes to column 1 through the LPF</li>
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<li>The other part goes to column 2 without the LPF</li>
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</ul>
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<p>
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<b>Measurements</b>:
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<code>mat/data_018.mat</code>:
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</p>
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<table border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
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<colgroup>
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<col class="org-right" />
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<col class="org-left" />
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</colgroup>
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<thead>
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<tr>
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<th scope="col" class="org-right">Column</th>
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<th scope="col" class="org-left">Signal</th>
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</tr>
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</thead>
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<tbody>
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<tr>
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<td class="org-right">1</td>
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<td class="org-left">Amplifier 1 with LPF</td>
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</tr>
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<tr>
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<td class="org-right">2</td>
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<td class="org-left">Amplifier 2</td>
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</tr>
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<tr>
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<td class="org-right">3</td>
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<td class="org-left">Time</td>
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</tr>
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</tbody>
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</table>
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</div>
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</div>
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<div id="outline-container-org603ee8b" class="outline-3">
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<h3 id="org603ee8b"><span class="section-number-3">6.2</span> Load data</h3>
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<div class="outline-text-3" id="text-6-2">
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<p>
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We load the data of the z axis of two geophones.
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</p>
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<div class="org-src-container">
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<pre class="src src-matlab">data = load<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'mat/data_018.mat', 'data'</span><span class="org-rainbow-delimiters-depth-1">)</span>; data = data.data;
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</pre>
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</div>
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</div>
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</div>
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<div id="outline-container-org23355c0" class="outline-3">
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<h3 id="org23355c0"><span class="section-number-3">6.3</span> Transfer function of the LPF</h3>
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<div class="outline-text-3" id="text-6-3">
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<p>
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We compute the transfer function from the signal without the LPF to the signal measured with the LPF.
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</p>
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<div class="org-src-container">
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<pre class="src src-matlab">dt = data<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">2</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-1">)</span><span class="org-type">-</span>data<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">1</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-1">)</span>;
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Fs = <span class="org-highlight-numbers-number">1</span><span class="org-type">/</span>dt; <span class="org-comment">% [Hz]</span>
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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>;
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</pre>
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</div>
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<div class="org-src-container">
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<pre class="src src-matlab"><span class="org-rainbow-delimiters-depth-1">[</span>Glpf, f<span class="org-rainbow-delimiters-depth-1">]</span> = tfestimate<span class="org-rainbow-delimiters-depth-1">(</span>data<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span>, data<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, win, <span class="org-rainbow-delimiters-depth-2">[]</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, Fs<span class="org-rainbow-delimiters-depth-1">)</span>;
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</pre>
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</div>
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<p>
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We compare this transfer function with a transfer function corresponding to an ideal first order LPF with a cut-off frequency of \(1000rad/s\).
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We obtain the result on figure <a href="#orgf6faf5b">26</a>.
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</p>
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<div class="org-src-container">
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<pre class="src src-matlab">Gth = <span class="org-highlight-numbers-number">1</span><span class="org-type">/</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">1</span><span class="org-type">+</span>s<span class="org-type">/</span><span class="org-highlight-numbers-number">1000</span><span class="org-rainbow-delimiters-depth-1">)</span>
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</pre>
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</div>
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<div class="org-src-container">
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<pre class="src src-matlab"><span class="org-type">figure</span>;
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|
ax1 = subplot<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">2</span>, <span class="org-highlight-numbers-number">1</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-1">)</span>;
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|
hold on;
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|
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, abs<span class="org-rainbow-delimiters-depth-2">(</span>Glpf<span class="org-rainbow-delimiters-depth-2">)</span><span class="org-rainbow-delimiters-depth-1">)</span>;
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|
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, abs<span class="org-rainbow-delimiters-depth-2">(</span>squeeze<span class="org-rainbow-delimiters-depth-3">(</span>freqresp<span class="org-rainbow-delimiters-depth-4">(</span>Gth, f, <span class="org-string">'Hz'</span><span class="org-rainbow-delimiters-depth-4">)</span><span class="org-rainbow-delimiters-depth-3">)</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-rainbow-delimiters-depth-1">)</span>;
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hold off;
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|
<span class="org-type">set</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-variable-name">gca</span>, <span class="org-string">'xscale', 'log'</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">)</span></span><span class="org-string">; set</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">(</span></span><span class="org-string">gca, 'yscale', 'log'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
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|
<span class="org-type">set</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-variable-name">gca</span>, <span class="org-string">'XTickLabel'</span>,<span class="org-rainbow-delimiters-depth-2">[]</span><span class="org-rainbow-delimiters-depth-1">)</span>;
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ylabel<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Magnitude'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
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|
|
ax2 = subplot<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">2</span>, <span class="org-highlight-numbers-number">1</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-1">)</span>;
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|
hold on;
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|
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, mod<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-highlight-numbers-number">180</span><span class="org-type">+</span><span class="org-highlight-numbers-number">180</span><span class="org-type">/</span><span class="org-constant">pi</span><span class="org-type">*</span>phase<span class="org-rainbow-delimiters-depth-3">(</span>Glpf<span class="org-rainbow-delimiters-depth-3">)</span>, <span class="org-highlight-numbers-number">360</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-type">-</span><span class="org-highlight-numbers-number">180</span><span class="org-rainbow-delimiters-depth-1">)</span>;
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plot<span class="org-rainbow-delimiters-depth-1">(</span>f, <span class="org-highlight-numbers-number">180</span><span class="org-type">/</span><span class="org-constant">pi</span><span class="org-type">*</span>unwrap<span class="org-rainbow-delimiters-depth-2">(</span>angle<span class="org-rainbow-delimiters-depth-3">(</span>squeeze<span class="org-rainbow-delimiters-depth-4">(</span>freqresp<span class="org-rainbow-delimiters-depth-5">(</span>Gth, f, <span class="org-string">'Hz'</span><span class="org-rainbow-delimiters-depth-5">)</span><span class="org-rainbow-delimiters-depth-4">)</span><span class="org-rainbow-delimiters-depth-3">)</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-rainbow-delimiters-depth-1">)</span>;
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|
hold off;
|
|
<span class="org-type">set</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-variable-name">gca</span>, <span class="org-string">'xscale', 'log'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
ylim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span><span class="org-type">-</span><span class="org-highlight-numbers-number">180</span>, <span class="org-highlight-numbers-number">180</span><span class="org-rainbow-delimiters-depth-2">]</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
yticks<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span><span class="org-type">-</span><span class="org-highlight-numbers-number">180</span>, <span class="org-type">-</span><span class="org-highlight-numbers-number">90</span>, <span class="org-highlight-numbers-number">0</span>, <span class="org-highlight-numbers-number">90</span>, <span class="org-highlight-numbers-number">180</span><span class="org-rainbow-delimiters-depth-2">]</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
xlabel<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Frequency </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">Hz</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">)</span></span><span class="org-string">; ylabel</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">(</span></span><span class="org-string">'Phase'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
|
|
linkaxes<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span>ax1,ax2<span class="org-rainbow-delimiters-depth-2">]</span>,<span class="org-string">'x'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
xlim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span><span class="org-highlight-numbers-number">1</span>, <span class="org-highlight-numbers-number">500</span><span class="org-rainbow-delimiters-depth-2">]</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
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</pre>
|
|
</div>
|
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|
|
|
|
<div id="orgf6faf5b" class="figure">
|
|
<p><img src="figs/Glpf_bode.png" alt="Glpf_bode.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 26: </span>Bode Diagram of the measured Low Pass filter and the theoritical one</p>
|
|
</div>
|
|
</div>
|
|
</div>
|
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<div id="outline-container-org461899b" class="outline-3">
|
|
<h3 id="org461899b"><span class="section-number-3">6.4</span> Conclusion</h3>
|
|
<div class="outline-text-3" id="text-6-4">
|
|
<div class="important">
|
|
<p>
|
|
As we want to measure things up to \(500Hz\), we chose to change the value of the capacitor to obtain a cut-off frequency of \(1kHz\).
|
|
</p>
|
|
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org25a2b36" class="outline-3">
|
|
<h3 id="org25a2b36"><span class="section-number-3">6.5</span> <span class="todo TODO">TODO</span> Low Pass Filter with a cut-off frequency of 1kHz</h3>
|
|
<div class="outline-text-3" id="text-6-5">
|
|
<p>
|
|
This time, the value are
|
|
</p>
|
|
\begin{aligned}
|
|
R &= 1k\Omega \\
|
|
C &= 150nF
|
|
\end{aligned}
|
|
|
|
<p>
|
|
Which makes a low pass filter with a cut-off frequency of \(f_c = 1060Hz\).
|
|
</p>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
<div id="postamble" class="status">
|
|
<p class="author">Author: Thomas Dehaeze</p>
|
|
<p class="date">Created: 2019-05-07 mar. 13:49</p>
|
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<p class="validation"><a href="http://validator.w3.org/check?uri=referer">Validate</a></p>
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</div>
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</body>
|
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</html>
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