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<head>
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<meta http-equiv="Content-Type" content="text/html;charset=utf-8" />
<title>Measurements on the instrumentation</title>
<meta name="generator" content="Org mode" />
@@ -30,40 +30,40 @@
<h2>Table of Contents</h2>
<div id="text-table-of-contents">
<ul>
<li><a href="#org0b9c6e7">1. Measure of the noise of the Voltage Amplifier</a>
<li><a href="#org575a2ef">1. Measure of the noise of the Voltage Amplifier</a>
<ul>
<li><a href="#orgce5ef47">1.1. Measurement Description</a></li>
<li><a href="#org4658c5c">1.2. Load data</a></li>
<li><a href="#org5de2d60">1.3. Time Domain</a></li>
<li><a href="#org5fc539a">1.4. Frequency Domain</a></li>
<li><a href="#orgbc39043">1.5. Conclusion</a></li>
<li><a href="#orgf7d6556">1.1. Measurement Description</a></li>
<li><a href="#org355a7b5">1.2. Load data</a></li>
<li><a href="#orgdd9efc8">1.3. Time Domain</a></li>
<li><a href="#org2042f75">1.4. Frequency Domain</a></li>
<li><a href="#org58e87f6">1.5. Conclusion</a></li>
</ul>
</li>
<li><a href="#org182f3d2">2. Measure of the influence of the AC/DC option on the voltage amplifiers</a>
<li><a href="#org5837403">2. Measure of the influence of the AC/DC option on the voltage amplifiers</a>
<ul>
<li><a href="#orgc5cfc61">2.1. Measurement Description</a></li>
<li><a href="#org0c0a3f2">2.2. Load data</a></li>
<li><a href="#orgb381461">2.3. Time Domain</a></li>
<li><a href="#org831a8d7">2.4. Frequency Domain</a></li>
<li><a href="#org0f7903d">2.5. Conclusion</a></li>
<li><a href="#orgdbe55cf">2.1. Measurement Description</a></li>
<li><a href="#org7456e69">2.2. Load data</a></li>
<li><a href="#org25d2f84">2.3. Time Domain</a></li>
<li><a href="#org089c2d7">2.4. Frequency Domain</a></li>
<li><a href="#orgf774275">2.5. Conclusion</a></li>
</ul>
</li>
<li><a href="#orge486804">3. Transfer function of the Low Pass Filter</a>
<li><a href="#org53c2f0f">3. Transfer function of the Low Pass Filter</a>
<ul>
<li><a href="#org400e34d">3.1. First LPF with a Cut-off frequency of 160Hz</a>
<li><a href="#orge98780d">3.1. First LPF with a Cut-off frequency of 160Hz</a>
<ul>
<li><a href="#org8e6b3f9">3.1.1. Measurement Description</a></li>
<li><a href="#org3c2d014">3.1.2. Load data</a></li>
<li><a href="#orgddafe0a">3.1.3. Transfer function of the LPF</a></li>
<li><a href="#org7a0daf9">3.1.4. Conclusion</a></li>
<li><a href="#org96fa587">3.1.1. Measurement Description</a></li>
<li><a href="#orgf82e4ab">3.1.2. Load data</a></li>
<li><a href="#org9c9a07c">3.1.3. Transfer function of the LPF</a></li>
<li><a href="#orgb110f25">3.1.4. Conclusion</a></li>
</ul>
</li>
<li><a href="#org5504322">3.2. Second LPF with a Cut-off frequency of 1000Hz</a>
<li><a href="#org1edfecc">3.2. Second LPF with a Cut-off frequency of 1000Hz</a>
<ul>
<li><a href="#orge51e102">3.2.1. Measurement description</a></li>
<li><a href="#org609fd78">3.2.2. Load data</a></li>
<li><a href="#orgad7e872">3.2.3. Transfer function of the LPF</a></li>
<li><a href="#org73a58fb">3.2.4. Conclusion</a></li>
<li><a href="#org60fea06">3.2.1. Measurement description</a></li>
<li><a href="#org0ffd8a4">3.2.2. Load data</a></li>
<li><a href="#org39f2fc3">3.2.3. Transfer function of the LPF</a></li>
<li><a href="#org127ac21">3.2.4. Conclusion</a></li>
</ul>
</li>
</ul>
@@ -72,13 +72,13 @@
</div>
</div>
<div id="outline-container-org0b9c6e7" class="outline-2">
<h2 id="org0b9c6e7"><span class="section-number-2">1</span> Measure of the noise of the Voltage Amplifier</h2>
<div id="outline-container-org575a2ef" class="outline-2">
<h2 id="org575a2ef"><span class="section-number-2">1</span> Measure of the noise of the Voltage Amplifier</h2>
<div class="outline-text-2" id="text-1">
<p>
<a id="org6a52764"></a>
<a id="org87914f2"></a>
</p>
<div class="note" id="orge2ed99a">
<div class="note" id="orged55ddc">
<p>
All the files (data and Matlab scripts) are accessible <a href="data/meas_volt_amp.zip">here</a>.
</p>
@@ -86,8 +86,8 @@ All the files (data and Matlab scripts) are accessible <a href="data/meas_volt_a
</div>
</div>
<div id="outline-container-orgce5ef47" class="outline-3">
<h3 id="orgce5ef47"><span class="section-number-3">1.1</span> Measurement Description</h3>
<div id="outline-container-orgf7d6556" class="outline-3">
<h3 id="orgf7d6556"><span class="section-number-3">1.1</span> Measurement Description</h3>
<div class="outline-text-3" id="text-1-1">
<p>
<b>Goal</b>:
@@ -118,8 +118,8 @@ All the files (data and Matlab scripts) are accessible <a href="data/meas_volt_a
</div>
</div>
<div id="outline-container-org4658c5c" class="outline-3">
<h3 id="org4658c5c"><span class="section-number-3">1.2</span> Load data</h3>
<div id="outline-container-org355a7b5" class="outline-3">
<h3 id="org355a7b5"><span class="section-number-3">1.2</span> Load data</h3>
<div class="outline-text-3" id="text-1-2">
<div class="org-src-container">
<pre class="src src-matlab">amp_off = load(<span class="org-string">'mat/data_003.mat'</span>, <span class="org-string">'data'</span>); amp_off = amp_off.data(<span class="org-type">:</span>, [1,3]);
@@ -131,15 +131,15 @@ amp_60d = load(<span class="org-string">'mat/data_006.mat'</span>, <span class="
</div>
</div>
<div id="outline-container-org5de2d60" class="outline-3">
<h3 id="org5de2d60"><span class="section-number-3">1.3</span> Time Domain</h3>
<div id="outline-container-orgdd9efc8" class="outline-3">
<h3 id="orgdd9efc8"><span class="section-number-3">1.3</span> Time Domain</h3>
<div class="outline-text-3" id="text-1-3">
<p>
The time domain signals are shown on figure <a href="#org2fccd36">1</a>.
The time domain signals are shown on figure <a href="#orgffaa33c">1</a>.
</p>
<div id="org2fccd36" class="figure">
<div id="orgffaa33c" class="figure">
<p><img src="figs/ampli_noise_time.png" alt="ampli_noise_time.png" />
</p>
<p><span class="figure-number">Figure 1: </span>Output of the amplifier</p>
@@ -147,8 +147,8 @@ The time domain signals are shown on figure <a href="#org2fccd36">1</a>.
</div>
</div>
<div id="outline-container-org5fc539a" class="outline-3">
<h3 id="org5fc539a"><span class="section-number-3">1.4</span> Frequency Domain</h3>
<div id="outline-container-org2042f75" class="outline-3">
<h3 id="org2042f75"><span class="section-number-3">1.4</span> Frequency Domain</h3>
<div class="outline-text-3" id="text-1-4">
<p>
We first compute some parameters that will be used for the PSD computation.
@@ -183,10 +183,10 @@ Sq = q<span class="org-type">^</span>2<span class="org-type">/</span>12<span cla
</div>
<p>
Finally, the ASD is shown on figure <a href="#org46e6591">2</a>.
Finally, the ASD is shown on figure <a href="#org1514c56">2</a>.
</p>
<div id="org46e6591" class="figure">
<div id="org1514c56" class="figure">
<p><img src="figs/ampli_noise_psd.png" alt="ampli_noise_psd.png" />
</p>
<p><span class="figure-number">Figure 2: </span>Amplitude Spectral Density of the measured voltage at the output of the voltage amplifier</p>
@@ -194,10 +194,10 @@ Finally, the ASD is shown on figure <a href="#org46e6591">2</a>.
</div>
</div>
<div id="outline-container-orgbc39043" class="outline-3">
<h3 id="orgbc39043"><span class="section-number-3">1.5</span> Conclusion</h3>
<div id="outline-container-org58e87f6" class="outline-3">
<h3 id="org58e87f6"><span class="section-number-3">1.5</span> Conclusion</h3>
<div class="outline-text-3" id="text-1-5">
<div class="important" id="orgb8e9939">
<div class="important" id="org7198d4c">
<p>
<b>Questions</b>:
</p>
@@ -214,13 +214,13 @@ Noise induced by the voltage amplifiers seems not to be a limiting factor as we
</div>
</div>
<div id="outline-container-org182f3d2" class="outline-2">
<h2 id="org182f3d2"><span class="section-number-2">2</span> Measure of the influence of the AC/DC option on the voltage amplifiers</h2>
<div id="outline-container-org5837403" class="outline-2">
<h2 id="org5837403"><span class="section-number-2">2</span> Measure of the influence of the AC/DC option on the voltage amplifiers</h2>
<div class="outline-text-2" id="text-2">
<p>
<a id="org4bf4c36"></a>
<a id="org4e0bd48"></a>
</p>
<div class="note" id="org66d7fee">
<div class="note" id="org4311309">
<p>
All the files (data and Matlab scripts) are accessible <a href="data/meas_noise_ac_dc.zip">here</a>.
</p>
@@ -228,8 +228,8 @@ All the files (data and Matlab scripts) are accessible <a href="data/meas_noise_
</div>
</div>
<div id="outline-container-orgc5cfc61" class="outline-3">
<h3 id="orgc5cfc61"><span class="section-number-3">2.1</span> Measurement Description</h3>
<div id="outline-container-orgdbe55cf" class="outline-3">
<h3 id="orgdbe55cf"><span class="section-number-3">2.1</span> Measurement Description</h3>
<div class="outline-text-3" id="text-2-1">
<p>
<b>Goal</b>:
@@ -319,7 +319,7 @@ Second measurement (<code>mat/data_015.mat</code> file):
</table>
<div id="org52bc26f" class="figure">
<div id="org7c3455c" class="figure">
<p><img src="./img/IMG_20190503_170936.jpg" alt="IMG_20190503_170936.jpg" width="500px" />
</p>
<p><span class="figure-number">Figure 3: </span>Picture of the two voltages amplifiers</p>
@@ -327,8 +327,8 @@ Second measurement (<code>mat/data_015.mat</code> file):
</div>
</div>
<div id="outline-container-org0c0a3f2" class="outline-3">
<h3 id="org0c0a3f2"><span class="section-number-3">2.2</span> Load data</h3>
<div id="outline-container-org7456e69" class="outline-3">
<h3 id="org7456e69"><span class="section-number-3">2.2</span> Load data</h3>
<div class="outline-text-3" id="text-2-2">
<p>
We load the data of the z axis of two geophones.
@@ -341,14 +341,14 @@ meas15 = load(<span class="org-string">'mat/data_015.mat'</span>, <span class="o
</div>
</div>
<div id="outline-container-orgb381461" class="outline-3">
<h3 id="orgb381461"><span class="section-number-3">2.3</span> Time Domain</h3>
<div id="outline-container-org25d2f84" class="outline-3">
<h3 id="org25d2f84"><span class="section-number-3">2.3</span> Time Domain</h3>
<div class="outline-text-3" id="text-2-3">
<p>
The signals are shown on figure <a href="#org26ff108">4</a>.
The signals are shown on figure <a href="#orgbb51b92">4</a>.
</p>
<div id="org26ff108" class="figure">
<div id="orgbb51b92" class="figure">
<p><img src="figs/ac_dc_option_time.png" alt="ac_dc_option_time.png" />
</p>
<p><span class="figure-number">Figure 4: </span>Comparison of the signals going through the Voltage amplifiers</p>
@@ -356,8 +356,8 @@ The signals are shown on figure <a href="#org26ff108">4</a>.
</div>
</div>
<div id="outline-container-org831a8d7" class="outline-3">
<h3 id="org831a8d7"><span class="section-number-3">2.4</span> Frequency Domain</h3>
<div id="outline-container-org089c2d7" class="outline-3">
<h3 id="org089c2d7"><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.
@@ -384,10 +384,10 @@ Then we compute the Power Spectral Density using <code>pwelch</code> function.
</div>
<p>
The ASD of the signals are compare on figure <a href="#org252ca9f">5</a>.
The ASD of the signals are compare on figure <a href="#orge363ddf">5</a>.
</p>
<div id="org252ca9f" class="figure">
<div id="orge363ddf" class="figure">
<p><img src="figs/ac_dc_option_asd.png" alt="ac_dc_option_asd.png" />
</p>
<p><span class="figure-number">Figure 5: </span>Amplitude Spectral Density of the measured signals</p>
@@ -395,10 +395,10 @@ The ASD of the signals are compare on figure <a href="#org252ca9f">5</a>.
</div>
</div>
<div id="outline-container-org0f7903d" class="outline-3">
<h3 id="org0f7903d"><span class="section-number-3">2.5</span> Conclusion</h3>
<div id="outline-container-orgf774275" class="outline-3">
<h3 id="orgf774275"><span class="section-number-3">2.5</span> Conclusion</h3>
<div class="outline-text-3" id="text-2-5">
<div class="important" id="orga7652b6">
<div class="important" id="org4302749">
<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>
@@ -409,23 +409,23 @@ The ASD of the signals are compare on figure <a href="#org252ca9f">5</a>.
</div>
</div>
<div id="outline-container-orge486804" class="outline-2">
<h2 id="orge486804"><span class="section-number-2">3</span> Transfer function of the Low Pass Filter</h2>
<div id="outline-container-org53c2f0f" class="outline-2">
<h2 id="org53c2f0f"><span class="section-number-2">3</span> Transfer function of the Low Pass Filter</h2>
<div class="outline-text-2" id="text-3">
<p>
<a id="orgae11ccf"></a>
<a id="org1dde479"></a>
</p>
<p>
The computation files for this section are accessible <a href="data/low_pass_filter_measurements.zip">here</a>.
</p>
</div>
<div id="outline-container-org400e34d" class="outline-3">
<h3 id="org400e34d"><span class="section-number-3">3.1</span> First LPF with a Cut-off frequency of 160Hz</h3>
<div id="outline-container-orge98780d" class="outline-3">
<h3 id="orge98780d"><span class="section-number-3">3.1</span> First LPF with a Cut-off frequency of 160Hz</h3>
<div class="outline-text-3" id="text-3-1">
</div>
<div id="outline-container-org8e6b3f9" class="outline-4">
<h4 id="org8e6b3f9"><span class="section-number-4">3.1.1</span> Measurement Description</h4>
<div id="outline-container-org96fa587" class="outline-4">
<h4 id="org96fa587"><span class="section-number-4">3.1.1</span> Measurement Description</h4>
<div class="outline-text-4" id="text-3-1-1">
<p>
<b>Goal</b>:
@@ -446,7 +446,7 @@ Which makes a cut-off frequency of \(f_c = \frac{1}{RC} = 1000 rad/s = 160Hz\).
</p>
<div class="org-src-container">
<pre class="src src-latex" id="orgebabef7"><span class="org-font-latex-sedate"><span class="org-keyword">\begin</span></span>{<span class="org-function-name">tikzpicture</span>}
<pre class="src src-latex" id="orgedba10d"><span class="org-font-latex-sedate"><span class="org-keyword">\begin</span></span>{<span class="org-function-name">tikzpicture</span>}
<span class="org-font-latex-sedate">\draw</span> (0,2)
to [R=<span class="org-font-latex-sedate"><span class="org-font-latex-math">\(R\)</span></span>] ++(2,0) node[circ]
to ++(2,0)
@@ -460,7 +460,7 @@ Which makes a cut-off frequency of \(f_c = \frac{1}{RC} = 1000 rad/s = 160Hz\).
</div>
<div id="org19a615d" class="figure">
<div id="org75b8ca4" class="figure">
<p><img src="figs/lpf.png" alt="lpf.png" />
</p>
<p><span class="figure-number">Figure 6: </span>Schematic of the Low Pass Filter used</p>
@@ -513,7 +513,7 @@ Which makes a cut-off frequency of \(f_c = \frac{1}{RC} = 1000 rad/s = 160Hz\).
</table>
<div id="org91c0742" class="figure">
<div id="org1f2ff7e" class="figure">
<p><img src="./img/IMG_20190507_102756.jpg" alt="IMG_20190507_102756.jpg" width="500px" />
</p>
<p><span class="figure-number">Figure 7: </span>Picture of the low pass filter used</p>
@@ -521,8 +521,8 @@ Which makes a cut-off frequency of \(f_c = \frac{1}{RC} = 1000 rad/s = 160Hz\).
</div>
</div>
<div id="outline-container-org3c2d014" class="outline-4">
<h4 id="org3c2d014"><span class="section-number-4">3.1.2</span> Load data</h4>
<div id="outline-container-orgf82e4ab" class="outline-4">
<h4 id="orgf82e4ab"><span class="section-number-4">3.1.2</span> Load data</h4>
<div class="outline-text-4" id="text-3-1-2">
<p>
We load the data of the z axis of two geophones.
@@ -534,8 +534,8 @@ We load the data of the z axis of two geophones.
</div>
</div>
<div id="outline-container-orgddafe0a" class="outline-4">
<h4 id="orgddafe0a"><span class="section-number-4">3.1.3</span> Transfer function of the LPF</h4>
<div id="outline-container-org9c9a07c" class="outline-4">
<h4 id="org9c9a07c"><span class="section-number-4">3.1.3</span> Transfer function of the LPF</h4>
<div class="outline-text-4" id="text-3-1-3">
<p>
We compute the transfer function from the signal without the LPF to the signal measured with the LPF.
@@ -556,7 +556,7 @@ win = hanning(ceil(10<span class="org-type">*</span>Fs));
<p>
We compare this transfer function with a transfer function corresponding to an ideal first order LPF with a cut-off frequency of \(1000rad/s\).
We obtain the result on figure <a href="#orgb174301">8</a>.
We obtain the result on figure <a href="#orga5b8e9e">8</a>.
</p>
<div class="org-src-container">
<pre class="src src-matlab">Gth = 1<span class="org-type">/</span>(1<span class="org-type">+</span>s<span class="org-type">/</span>1000)
@@ -590,17 +590,17 @@ xlim([1, 500]);
</div>
<div id="orgb174301" class="figure">
<div id="orga5b8e9e" class="figure">
<p><img src="figs/Glpf_bode.png" alt="Glpf_bode.png" />
</p>
<p><span class="figure-number">Figure 8: </span>Bode Diagram of the measured Low Pass filter and the theoritical one</p>
</div>
</div>
</div>
<div id="outline-container-org7a0daf9" class="outline-4">
<h4 id="org7a0daf9"><span class="section-number-4">3.1.4</span> Conclusion</h4>
<div id="outline-container-orgb110f25" class="outline-4">
<h4 id="orgb110f25"><span class="section-number-4">3.1.4</span> Conclusion</h4>
<div class="outline-text-4" id="text-3-1-4">
<div class="important" id="org84503a8">
<div class="important" id="orgdd53898">
<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>
@@ -610,12 +610,12 @@ As we want to measure things up to \(500Hz\), we chose to change the value of th
</div>
</div>
<div id="outline-container-org5504322" class="outline-3">
<h3 id="org5504322"><span class="section-number-3">3.2</span> Second LPF with a Cut-off frequency of 1000Hz</h3>
<div id="outline-container-org1edfecc" class="outline-3">
<h3 id="org1edfecc"><span class="section-number-3">3.2</span> Second LPF with a Cut-off frequency of 1000Hz</h3>
<div class="outline-text-3" id="text-3-2">
</div>
<div id="outline-container-orge51e102" class="outline-4">
<h4 id="orge51e102"><span class="section-number-4">3.2.1</span> Measurement description</h4>
<div id="outline-container-org60fea06" class="outline-4">
<h4 id="org60fea06"><span class="section-number-4">3.2.1</span> Measurement description</h4>
<div class="outline-text-4" id="text-3-2-1">
<p>
This time, the value are
@@ -630,8 +630,8 @@ Which makes a low pass filter with a cut-off frequency of \(f_c = 1060Hz\).
</div>
</div>
<div id="outline-container-org609fd78" class="outline-4">
<h4 id="org609fd78"><span class="section-number-4">3.2.2</span> Load data</h4>
<div id="outline-container-org0ffd8a4" class="outline-4">
<h4 id="org0ffd8a4"><span class="section-number-4">3.2.2</span> Load data</h4>
<div class="outline-text-4" id="text-3-2-2">
<p>
We load the data of the z axis of two geophones.
@@ -643,8 +643,8 @@ We load the data of the z axis of two geophones.
</div>
</div>
<div id="outline-container-orgad7e872" class="outline-4">
<h4 id="orgad7e872"><span class="section-number-4">3.2.3</span> Transfer function of the LPF</h4>
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<h4 id="org39f2fc3"><span class="section-number-4">3.2.3</span> Transfer function of the LPF</h4>
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<p>
We compute the transfer function from the signal without the LPF to the signal measured with the LPF.
@@ -665,7 +665,7 @@ win = hanning(ceil(10<span class="org-type">*</span>Fs));
<p>
We compare this transfer function with a transfer function corresponding to an ideal first order LPF with a cut-off frequency of \(1060Hz\).
We obtain the result on figure <a href="#org9707219">9</a>.
We obtain the result on figure <a href="#org16c9122">9</a>.
</p>
<div class="org-src-container">
<pre class="src src-matlab">Gth = 1<span class="org-type">/</span>(1<span class="org-type">+</span>s<span class="org-type">/</span>1060<span class="org-type">/</span>2<span class="org-type">/</span><span class="org-constant">pi</span>);
@@ -699,17 +699,17 @@ xlim([1, 500]);
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<div id="org9707219" class="figure">
<div id="org16c9122" class="figure">
<p><img src="figs/Glpf_bode_bis.png" alt="Glpf_bode_bis.png" />
</p>
<p><span class="figure-number">Figure 9: </span>Bode Diagram of the measured Low Pass filter and the theoritical one</p>
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<h4 id="org73a58fb"><span class="section-number-4">3.2.4</span> Conclusion</h4>
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<h4 id="org127ac21"><span class="section-number-4">3.2.4</span> Conclusion</h4>
<div class="outline-text-4" id="text-3-2-4">
<div class="important" id="org1fede99">
<div class="important" id="orgd954ff9">
<p>
The added LPF has the expected behavior.
</p>
@@ -722,7 +722,7 @@ The added LPF has the expected behavior.
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<div id="postamble" class="status">
<p class="author">Author: Dehaeze Thomas</p>
<p class="date">Created: 2020-11-12 jeu. 10:28</p>
<p class="date">Created: 2020-11-12 jeu. 16:39</p>
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