Analyze transfer function measurements
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@ -3,7 +3,7 @@
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"http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd">
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<html xmlns="http://www.w3.org/1999/xhtml" lang="en" xml:lang="en">
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<head>
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<!-- 2021-01-22 ven. 23:44 -->
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<!-- 2021-01-23 sam. 15:38 -->
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<meta http-equiv="Content-Type" content="text/html;charset=utf-8" />
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<title>Voltage Amplifier PD200 - Test Bench</title>
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<meta name="generator" content="Org mode" />
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@ -39,41 +39,36 @@
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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="#org8f2862b">1. Introduction</a></li>
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<li><a href="#org103c717">2. Voltage Amplifier Requirements</a></li>
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||||
<li><a href="#orgf22ce98">3. PD200 Expected characteristics</a></li>
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<li><a href="#orge04c2d5">4. Voltage Amplifier Model</a></li>
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<li><a href="#org5986efd">5. Noise measurement</a>
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<li><a href="#orge14df81">1. Introduction</a></li>
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<li><a href="#orgd794d0c">2. Voltage Amplifier Requirements</a></li>
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<li><a href="#org79cd976">3. PD200 Expected characteristics</a></li>
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<li><a href="#org3265b9b">4. Voltage Amplifier Model</a></li>
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<li><a href="#orgf27cdb1">5. Noise measurement</a>
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<ul>
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<li><a href="#org1515801">5.1. Setup</a></li>
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<li><a href="#orgf67652b">5.2. Model of the setup</a></li>
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<li><a href="#org109d4fe">5.3. Quantization Noise</a></li>
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<li><a href="#org3e7c8ba">5.4. Pre Amplifier noise measurement</a></li>
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<li><a href="#orgdd4cdcb">5.5. PD200 noise measurement</a></li>
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<li><a href="#org77f4d34">5.6. DAC noise measurement</a></li>
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<li><a href="#orgb297da3">5.7. Total noise measurement</a></li>
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<li><a href="#org41977eb">5.8. 20bits DAC noise measurement</a></li>
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<li><a href="#orgaaa2a30">5.1. Setup</a></li>
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<li><a href="#org959d7aa">5.2. Model of the setup</a></li>
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<li><a href="#org8283055">5.3. Quantization Noise</a></li>
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<li><a href="#orga8ab614">5.4. Pre Amplifier noise measurement</a></li>
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<li><a href="#orge67a27a">5.5. PD200 noise measurement</a></li>
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<li><a href="#orgc9e047f">5.6. DAC noise measurement</a></li>
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<li><a href="#orgd156ba1">5.7. Total noise measurement</a></li>
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<li><a href="#org802b093">5.8. 20bits DAC noise measurement</a></li>
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</ul>
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</li>
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<li><a href="#org311b8b4">6. Transfer Function measurement</a>
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<li><a href="#orga87a250">6. Transfer Function measurement</a>
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<ul>
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<li><a href="#org032d612">6.1. Setup</a></li>
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<li><a href="#orgcaa9498">6.2. Maximum Frequency/Voltage to not overload the amplifier</a></li>
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<li><a href="#org2323f70">6.3. Results</a>
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<ul>
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<li><a href="#orge73cc45">6.3.1. First test</a></li>
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<li><a href="#orgeb520e4">6.3.2. Results</a></li>
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<li><a href="#org2b82bca">6.1. Setup</a></li>
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<li><a href="#orgdf952ce">6.2. Maximum Frequency/Voltage to not overload the amplifier</a></li>
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<li><a href="#org05f8a88">6.3. Obtained Transfer Functions</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="#orgad3a328">7. Conclusion</a></li>
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<li><a href="#org5f03b6e">7. Conclusion</a></li>
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</ul>
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</div>
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</div>
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<div id="outline-container-org8f2862b" class="outline-2">
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<h2 id="org8f2862b"><span class="section-number-2">1</span> Introduction</h2>
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<div id="outline-container-orge14df81" class="outline-2">
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<h2 id="orge14df81"><span class="section-number-2">1</span> Introduction</h2>
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<div class="outline-text-2" id="text-1">
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<p>
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The goal of this test bench is to characterize the Voltage amplifier <a href="https://www.piezodrive.com/drivers/pd200-60-watt-voltage-amplifier/">PD200</a> from PiezoDrive.
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@ -84,7 +79,7 @@ The documentation of the PD200 is accessible <a href="doc/PD200-V7-R1.pdf">here<
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</p>
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<div id="org7aea75d" class="figure">
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<div id="orgea7d2e1" class="figure">
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<p><img src="figs/amplifier_PD200.png" alt="amplifier_PD200.png" />
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</p>
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<p><span class="figure-number">Figure 1: </span>Picture of the PD200 Voltage Amplifier</p>
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@ -92,10 +87,10 @@ The documentation of the PD200 is accessible <a href="doc/PD200-V7-R1.pdf">here<
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</div>
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</div>
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<div id="outline-container-org103c717" class="outline-2">
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<h2 id="org103c717"><span class="section-number-2">2</span> Voltage Amplifier Requirements</h2>
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<div id="outline-container-orgd794d0c" class="outline-2">
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<h2 id="orgd794d0c"><span class="section-number-2">2</span> Voltage Amplifier Requirements</h2>
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<div class="outline-text-2" id="text-2">
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<table id="orgf1fdf95" border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
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<table id="orgfc689c5" border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
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<caption class="t-above"><span class="table-number">Table 1:</span> Requirements for the Voltage Amplifier</caption>
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<colgroup>
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@ -139,10 +134,10 @@ The documentation of the PD200 is accessible <a href="doc/PD200-V7-R1.pdf">here<
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</div>
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</div>
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<div id="outline-container-orgf22ce98" class="outline-2">
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<h2 id="orgf22ce98"><span class="section-number-2">3</span> PD200 Expected characteristics</h2>
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<div id="outline-container-org79cd976" class="outline-2">
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<h2 id="org79cd976"><span class="section-number-2">3</span> PD200 Expected characteristics</h2>
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<div class="outline-text-2" id="text-3">
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<table id="org38f8e47" border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
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<table id="org6e26b68" border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
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<caption class="t-above"><span class="table-number">Table 2:</span> Characteristics of the PD200</caption>
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<colgroup>
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@ -217,18 +212,18 @@ The documentation of the PD200 is accessible <a href="doc/PD200-V7-R1.pdf">here<
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</table>
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<p>
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For a load capacitance of \(10\,\mu F\), the expected \(-3\,dB\) bandwidth is \(6.4\,kHz\) (Figure <a href="#org2190892">2</a>) and the low frequency noise is \(650\,\mu V\,\text{rms}\) (Figure <a href="#orgeaff484">3</a>).
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For a load capacitance of \(10\,\mu F\), the expected \(-3\,dB\) bandwidth is \(6.4\,kHz\) (Figure <a href="#orgaa88e71">2</a>) and the low frequency noise is \(650\,\mu V\,\text{rms}\) (Figure <a href="#orgdcb3bab">3</a>).
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</p>
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<div id="org2190892" class="figure">
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<div id="orgaa88e71" class="figure">
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<p><img src="./figs/pd200_expected_small_signal_bandwidth.png" alt="pd200_expected_small_signal_bandwidth.png" />
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</p>
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<p><span class="figure-number">Figure 2: </span>Expected small signal bandwidth</p>
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</div>
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<div id="orgeaff484" class="figure">
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<div id="orgdcb3bab" class="figure">
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<p><img src="figs/pd200_expected_noise.png" alt="pd200_expected_noise.png" />
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</p>
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<p><span class="figure-number">Figure 3: </span>Expected Low frequency noise from 0.03Hz to 20Hz</p>
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@ -236,8 +231,8 @@ For a load capacitance of \(10\,\mu F\), the expected \(-3\,dB\) bandwidth is \(
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</div>
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</div>
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<div id="outline-container-orge04c2d5" class="outline-2">
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<h2 id="orge04c2d5"><span class="section-number-2">4</span> Voltage Amplifier Model</h2>
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<div id="outline-container-org3265b9b" class="outline-2">
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<h2 id="org3265b9b"><span class="section-number-2">4</span> Voltage Amplifier Model</h2>
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<div class="outline-text-2" id="text-4">
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<p>
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The Amplifier is characterized by its dynamics \(G_a(s)\) from voltage inputs \(V_{in}\) to voltage output \(V_{out}\).
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@ -258,7 +253,7 @@ As both \(G_a\) and \(S_n\) depends on the load capacitance, they should be meas
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</p>
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<div id="org5d4d3ab" class="figure">
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<div id="orgbc3695d" class="figure">
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<p><img src="figs/pd200-model-schematic.png" alt="pd200-model-schematic.png" />
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</p>
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<p><span class="figure-number">Figure 4: </span>Model of the voltage amplifier</p>
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@ -266,29 +261,29 @@ As both \(G_a\) and \(S_n\) depends on the load capacitance, they should be meas
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</div>
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</div>
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<div id="outline-container-org5986efd" class="outline-2">
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<h2 id="org5986efd"><span class="section-number-2">5</span> Noise measurement</h2>
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<div id="outline-container-orgf27cdb1" class="outline-2">
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<h2 id="orgf27cdb1"><span class="section-number-2">5</span> Noise measurement</h2>
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<div class="outline-text-2" id="text-5">
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<ul class="org-ul">
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<li>Section <a href="#org975f5ab">5.1</a></li>
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<li>Section <a href="#org58a7c02">5.2</a></li>
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<li>Section <a href="#orgd6eb89a">5.3</a></li>
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<li>Section <a href="#orgd67c98a">5.4</a></li>
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<li>Section <a href="#orge02d748">5.5</a></li>
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<li>Section <a href="#org30c83b3">5.6</a></li>
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<li>Section <a href="#org0d900c3">5.7</a></li>
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<li>Section <a href="#org576bf2a">5.8</a></li>
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<li>Section <a href="#org9d21c0d">5.1</a></li>
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<li>Section <a href="#org6edf2e9">5.2</a></li>
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<li>Section <a href="#org7b5a20a">5.3</a></li>
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<li>Section <a href="#orge4eb592">5.4</a></li>
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<li>Section <a href="#org8909c5d">5.5</a></li>
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<li>Section <a href="#org7739514">5.6</a></li>
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<li>Section <a href="#org1920758">5.7</a></li>
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<li>Section <a href="#orgf336d8b">5.8</a></li>
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</ul>
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</div>
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<div id="outline-container-org1515801" class="outline-3">
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<h3 id="org1515801"><span class="section-number-3">5.1</span> Setup</h3>
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<div id="outline-container-orgaaa2a30" class="outline-3">
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<h3 id="orgaaa2a30"><span class="section-number-3">5.1</span> Setup</h3>
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<div class="outline-text-3" id="text-5-1">
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<p>
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<a id="org975f5ab"></a>
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<a id="org9d21c0d"></a>
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</p>
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<div class="note" id="org0370347">
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<div class="note" id="org4394587">
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<p>
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Here are the documentation of the equipment used for this test bench:
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</p>
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@ -321,7 +316,7 @@ This gain should be around 1000.
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</p>
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<div id="org451a2c9" class="figure">
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<div id="org7800d75" class="figure">
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<p><img src="figs/setup-noise-measurement.png" alt="setup-noise-measurement.png" />
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</p>
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<p><span class="figure-number">Figure 5: </span>Schematic of the test bench to measure the Power Spectral Density of the Voltage amplifier noise \(n\)</p>
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@ -334,15 +329,15 @@ An high pass filter at low frequency can be added if there is a problem of large
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</div>
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</div>
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<div id="outline-container-orgf67652b" class="outline-3">
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<h3 id="orgf67652b"><span class="section-number-3">5.2</span> Model of the setup</h3>
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<div id="outline-container-org959d7aa" class="outline-3">
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<h3 id="org959d7aa"><span class="section-number-3">5.2</span> Model of the setup</h3>
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<div class="outline-text-3" id="text-5-2">
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<p>
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<a id="org58a7c02"></a>
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<a id="org6edf2e9"></a>
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</p>
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<p>
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As shown in Figure <a href="#org8801056">6</a>, there are 4 equipment involved in the measurement:
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As shown in Figure <a href="#orgb873ca1">6</a>, there are 4 equipment involved in the measurement:
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</p>
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<ul class="org-ul">
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<li>a Digital to Analog Convert (DAC)</li>
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@ -363,7 +358,7 @@ Each of these equipment has some noise:
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</ul>
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<div id="org8801056" class="figure">
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<div id="orgb873ca1" class="figure">
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<p><img src="figs/noise_meas_procedure.png" alt="noise_meas_procedure.png" />
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</p>
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<p><span class="figure-number">Figure 6: </span>Sources of noise in the experimental setup</p>
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@ -371,11 +366,11 @@ Each of these equipment has some noise:
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</div>
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</div>
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<div id="outline-container-org109d4fe" class="outline-3">
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<h3 id="org109d4fe"><span class="section-number-3">5.3</span> Quantization Noise</h3>
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<div id="outline-container-org8283055" class="outline-3">
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<h3 id="org8283055"><span class="section-number-3">5.3</span> Quantization Noise</h3>
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<div class="outline-text-3" id="text-5-3">
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<p>
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<a id="orgd6eb89a"></a>
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<a id="org7b5a20a"></a>
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</p>
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<p>
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@ -410,11 +405,11 @@ The obtained Amplitude Spectral Density is <code>6.2294e-07</code> \(V/\sqrt{Hz}
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</div>
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</div>
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<div id="outline-container-org3e7c8ba" class="outline-3">
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<h3 id="org3e7c8ba"><span class="section-number-3">5.4</span> Pre Amplifier noise measurement</h3>
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<div id="outline-container-orga8ab614" class="outline-3">
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<h3 id="orga8ab614"><span class="section-number-3">5.4</span> Pre Amplifier noise measurement</h3>
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<div class="outline-text-3" id="text-5-4">
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<p>
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<a id="orgd67c98a"></a>
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<a id="orge4eb592"></a>
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||||
</p>
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<p>
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@ -436,7 +431,7 @@ This is true if the quantization noise \(\Gamma_{q_{ad}}\) is negligible.
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</p>
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<div id="org0e8db56" class="figure">
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<div id="org5debea0" class="figure">
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<p><img src="figs/noise_measure_setup_preamp.png" alt="noise_measure_setup_preamp.png" />
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</p>
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<p><span class="figure-number">Figure 7: </span>Sources of noise in the experimental setup</p>
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@ -460,12 +455,12 @@ preamp.f = f;
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</div>
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<p>
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||||
The obtained Amplitude Spectral Density of the Low Noise Voltage Amplifier is shown in Figure <a href="#org2880354">8</a>.
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||||
The obtained Amplitude Spectral Density of the Low Noise Voltage Amplifier is shown in Figure <a href="#org865b855">8</a>.
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||||
The obtained noise amplitude is very closed to the one specified in the documentation of \(4nV/\sqrt{Hz}\) at 1kHZ.
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</p>
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<div id="org2880354" class="figure">
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||||
<div id="org865b855" class="figure">
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<p><img src="figs/asd_preamp.png" alt="asd_preamp.png" />
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</p>
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<p><span class="figure-number">Figure 8: </span>Obtained Amplitude Spectral Density of the Low Noise Voltage Amplifier</p>
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@ -473,11 +468,11 @@ The obtained noise amplitude is very closed to the one specified in the document
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||||
</div>
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</div>
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<div id="outline-container-orgdd4cdcb" class="outline-3">
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<h3 id="orgdd4cdcb"><span class="section-number-3">5.5</span> PD200 noise measurement</h3>
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<div id="outline-container-orge67a27a" class="outline-3">
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||||
<h3 id="orge67a27a"><span class="section-number-3">5.5</span> PD200 noise measurement</h3>
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||||
<div class="outline-text-3" id="text-5-5">
|
||||
<p>
|
||||
<a id="orge02d748"></a>
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||||
<a id="org8909c5d"></a>
|
||||
</p>
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<p>
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@ -498,27 +493,27 @@ And we verify that this is indeed the noise of the PD200 and not the noise of th
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\end{equation}
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<div id="org5660b1a" class="figure">
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||||
<div id="orgcfcd12c" class="figure">
|
||||
<p><img src="figs/noise_measure_setup_pd200.png" alt="noise_measure_setup_pd200.png" />
|
||||
</p>
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||||
<p><span class="figure-number">Figure 9: </span>Sources of noise in the experimental setup</p>
|
||||
</div>
|
||||
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||||
<p>
|
||||
The measured low frequency noise \(n_p\) of one of the amplifiers is shown in Figure <a href="#org99c1c8c">10</a>.
|
||||
It is very similar to the one specified in the datasheet in Figure <a href="#orgeaff484">3</a>.
|
||||
The measured low frequency noise \(n_p\) of one of the amplifiers is shown in Figure <a href="#orgb61b700">10</a>.
|
||||
It is very similar to the one specified in the datasheet in Figure <a href="#orgdcb3bab">3</a>.
|
||||
</p>
|
||||
|
||||
<div id="org99c1c8c" class="figure">
|
||||
<div id="orgb61b700" class="figure">
|
||||
<p><img src="figs/pd200_noise_time_lpf.png" alt="pd200_noise_time_lpf.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 10: </span>Measured low frequency noise of the PD200 from 0.01Hz to 20Hz</p>
|
||||
</div>
|
||||
|
||||
<p>
|
||||
The obtained RMS and peak to peak values of the measured noises are shown in Table <a href="#org904c283">3</a>.
|
||||
The obtained RMS and peak to peak values of the measured noises are shown in Table <a href="#orgf452b35">3</a>.
|
||||
</p>
|
||||
<table id="org904c283" border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
|
||||
<table id="orgf452b35" border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
|
||||
<caption class="t-above"><span class="table-number">Table 3:</span> RMS and Peak to Peak measured low frequency noise (0.01Hz to 20Hz)</caption>
|
||||
|
||||
<colgroup>
|
||||
@ -587,10 +582,10 @@ The obtained RMS and peak to peak values of the measured noises are shown in Tab
|
||||
</table>
|
||||
|
||||
<p>
|
||||
The Amplitude Spectral Density of the measured noise is now computed and shown in Figure <a href="#org7bcb803">11</a>.
|
||||
The Amplitude Spectral Density of the measured noise is now computed and shown in Figure <a href="#orgf1636b6">11</a>.
|
||||
</p>
|
||||
|
||||
<div id="org7bcb803" class="figure">
|
||||
<div id="orgf1636b6" class="figure">
|
||||
<p><img src="figs/asd_noise_3uF_warmup.png" alt="asd_noise_3uF_warmup.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 11: </span>Amplitude Spectral Density of the measured noise</p>
|
||||
@ -598,11 +593,11 @@ The Amplitude Spectral Density of the measured noise is now computed and shown i
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org77f4d34" class="outline-3">
|
||||
<h3 id="org77f4d34"><span class="section-number-3">5.6</span> DAC noise measurement</h3>
|
||||
<div id="outline-container-orgc9e047f" class="outline-3">
|
||||
<h3 id="orgc9e047f"><span class="section-number-3">5.6</span> DAC noise measurement</h3>
|
||||
<div class="outline-text-3" id="text-5-6">
|
||||
<p>
|
||||
<a id="org30c83b3"></a>
|
||||
<a id="org7739514"></a>
|
||||
</p>
|
||||
|
||||
<p>
|
||||
@ -626,33 +621,33 @@ And it is verify that the Amplitude Spectral Density of \(n_{da}\) is much large
|
||||
\end{equation}
|
||||
|
||||
|
||||
<div id="org744e44a" class="figure">
|
||||
<div id="org0f39f6d" class="figure">
|
||||
<p><img src="figs/noise_measure_setup_dac.png" alt="noise_measure_setup_dac.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 12: </span>Sources of noise in the experimental setup</p>
|
||||
</div>
|
||||
|
||||
|
||||
<div id="orgc0933a7" class="figure">
|
||||
<div id="org531aca4" class="figure">
|
||||
<p><img src="figs/asd_noise_dac.png" alt="asd_noise_dac.png" />
|
||||
</p>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-orgb297da3" class="outline-3">
|
||||
<h3 id="orgb297da3"><span class="section-number-3">5.7</span> Total noise measurement</h3>
|
||||
<div id="outline-container-orgd156ba1" class="outline-3">
|
||||
<h3 id="orgd156ba1"><span class="section-number-3">5.7</span> Total noise measurement</h3>
|
||||
<div class="outline-text-3" id="text-5-7">
|
||||
<p>
|
||||
<a id="org0d900c3"></a>
|
||||
<a id="org1920758"></a>
|
||||
</p>
|
||||
|
||||
<p>
|
||||
Let’s now analyze the measurement of the setup in Figure <a href="#org8801056">6</a>.
|
||||
Let’s now analyze the measurement of the setup in Figure <a href="#orgb873ca1">6</a>.
|
||||
</p>
|
||||
|
||||
<p>
|
||||
The PSD of the measured noise is computed and the ASD is shown in Figure <a href="#org929789a">14</a>.
|
||||
The PSD of the measured noise is computed and the ASD is shown in Figure <a href="#orge63d88b">14</a>.
|
||||
</p>
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab">win = hanning(ceil(0.5<span class="org-type">/</span>Ts));
|
||||
@ -666,13 +661,13 @@ The PSD of the measured noise is computed and the ASD is shown in Figure <a href
|
||||
</div>
|
||||
|
||||
|
||||
<div id="org929789a" class="figure">
|
||||
<div id="orge63d88b" class="figure">
|
||||
<p><img src="figs/asd_noise_tot.png" alt="asd_noise_tot.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 14: </span>Amplitude Spectral Density of the measured noise and of the individual sources of noise</p>
|
||||
</div>
|
||||
|
||||
<div class="important" id="org623c3d1">
|
||||
<div class="important" id="orge883835">
|
||||
<p>
|
||||
The output noise of the PD200 amplifier is limited by the noise of the DAC.
|
||||
Having a DAC with lower noise could lower the output noise of the PD200.
|
||||
@ -683,17 +678,17 @@ SSI2V DACs will be used to verify that.
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org41977eb" class="outline-3">
|
||||
<h3 id="org41977eb"><span class="section-number-3">5.8</span> 20bits DAC noise measurement</h3>
|
||||
<div id="outline-container-org802b093" class="outline-3">
|
||||
<h3 id="org802b093"><span class="section-number-3">5.8</span> 20bits DAC noise measurement</h3>
|
||||
<div class="outline-text-3" id="text-5-8">
|
||||
<p>
|
||||
<a id="org576bf2a"></a>
|
||||
<a id="orgf336d8b"></a>
|
||||
Let’s now measure the noise of another DAC called the “SSI2V” (<a href="doc/[SSI2V]Datasheet.pdf">doc</a>).
|
||||
It is a 20bits DAC with an output of +/-10.48 V and a very low noise.
|
||||
</p>
|
||||
|
||||
<p>
|
||||
The measurement setup is the same as the one in Figure <a href="#org744e44a">12</a>.
|
||||
The measurement setup is the same as the one in Figure <a href="#org0f39f6d">12</a>.
|
||||
</p>
|
||||
|
||||
<div class="org-src-container">
|
||||
@ -706,18 +701,18 @@ ssi2v.f = f;
|
||||
</div>
|
||||
|
||||
<p>
|
||||
The obtained noise of the SSI2V DAC is shown in Figure <a href="#orgd5ecb95">15</a> and compared with the noise of the 16bits DAC.
|
||||
The obtained noise of the SSI2V DAC is shown in Figure <a href="#orge2b8a18">15</a> and compared with the noise of the 16bits DAC.
|
||||
It is shown to be much smaller (~1 order of magnitude).
|
||||
</p>
|
||||
|
||||
|
||||
<div id="orgd5ecb95" class="figure">
|
||||
<div id="orge2b8a18" class="figure">
|
||||
<p><img src="figs/asd_ssi2v_noise.png" alt="asd_ssi2v_noise.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 15: </span>Amplitude Spectral Density of the SSI2V DAC’s noise</p>
|
||||
</div>
|
||||
|
||||
<div class="important" id="org3ec30db">
|
||||
<div class="important" id="org665f8e4">
|
||||
<p>
|
||||
Using the SSI2V as the DAC with the PD200 should give much better noise output than using the 16bits DAC.
|
||||
The limiting factor should then be the noise of the PD200 itself.
|
||||
@ -728,18 +723,18 @@ The limiting factor should then be the noise of the PD200 itself.
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org311b8b4" class="outline-2">
|
||||
<h2 id="org311b8b4"><span class="section-number-2">6</span> Transfer Function measurement</h2>
|
||||
<div id="outline-container-orga87a250" class="outline-2">
|
||||
<h2 id="orga87a250"><span class="section-number-2">6</span> Transfer Function measurement</h2>
|
||||
<div class="outline-text-2" id="text-6">
|
||||
</div>
|
||||
<div id="outline-container-org032d612" class="outline-3">
|
||||
<h3 id="org032d612"><span class="section-number-3">6.1</span> Setup</h3>
|
||||
<div id="outline-container-org2b82bca" class="outline-3">
|
||||
<h3 id="org2b82bca"><span class="section-number-3">6.1</span> Setup</h3>
|
||||
<div class="outline-text-3" id="text-6-1">
|
||||
<p>
|
||||
In order to measure the transfer function from the input voltage \(V_{in}\) to the output voltage \(V_{out}\), the test bench shown in Figure <a href="#orga5c58e5">16</a> is used.
|
||||
In order to measure the transfer function from the input voltage \(V_{in}\) to the output voltage \(V_{out}\), the test bench shown in Figure <a href="#org45f7f26">16</a> is used.
|
||||
</p>
|
||||
|
||||
<div class="note" id="org44386ba">
|
||||
<div class="note" id="orgaa21e8d">
|
||||
<p>
|
||||
Here are the documentation of the equipment used for this test bench:
|
||||
</p>
|
||||
@ -756,7 +751,7 @@ For this measurement, the sampling frequency of the Speedgoat ADC should be as h
|
||||
</p>
|
||||
|
||||
|
||||
<div id="orga5c58e5" class="figure">
|
||||
<div id="org45f7f26" class="figure">
|
||||
<p><img src="figs/setup-dynamics-measurement.png" alt="setup-dynamics-measurement.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 16: </span>Schematic of the test bench to estimate the dynamics from voltage input \(V_{in}\) to voltage output \(V_{out}\)</p>
|
||||
@ -764,8 +759,8 @@ For this measurement, the sampling frequency of the Speedgoat ADC should be as h
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-orgcaa9498" class="outline-3">
|
||||
<h3 id="orgcaa9498"><span class="section-number-3">6.2</span> Maximum Frequency/Voltage to not overload the amplifier</h3>
|
||||
<div id="outline-container-orgdf952ce" class="outline-3">
|
||||
<h3 id="orgdf952ce"><span class="section-number-3">6.2</span> Maximum Frequency/Voltage to not overload the amplifier</h3>
|
||||
<div class="outline-text-3" id="text-6-2">
|
||||
<p>
|
||||
The maximum current is 1A [rms] which corresponds to 0.7A in amplitude of the sin wave.
|
||||
@ -777,145 +772,79 @@ The impedance of the capacitance is:
|
||||
</p>
|
||||
|
||||
<p>
|
||||
Therefore the relation between the output current and the output voltage is (in amplitude):
|
||||
Therefore the relation between the output current amplitude and the output voltage amplitude for sinusoidal waves of frequency \(\omega\):
|
||||
\[ V_{out} = \frac{1}{C\omega} I_{out} \]
|
||||
</p>
|
||||
|
||||
<p>
|
||||
There is a gain of 20 between the input voltage and the output voltage:
|
||||
Moreover, there is a gain of 20 between the input voltage and the output voltage:
|
||||
\[ 20 V_{in} = \frac{1}{C\omega} I_{out} \]
|
||||
</p>
|
||||
|
||||
<p>
|
||||
For a specified voltage input amplitude \(V_{in}\), the maximum frequency is then:
|
||||
For a specified voltage input amplitude \(V_{in}\), the maximum frequency at which the output current reaches its maximum value is:
|
||||
\[ \omega_{\text{max}} = \frac{1}{20 C V_{in}} I_{out,\text{max}} \]
|
||||
</p>
|
||||
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab">Iout_max = 0.57; <span class="org-comment">% Maximum output current [A]</span>
|
||||
C = 2.7e<span class="org-type">-</span>6; <span class="org-comment">% Load Capacitance [F]</span>
|
||||
<p>
|
||||
\(\omega_max\) as a function of \(V_{in}\) is shown in Figure <a href="#orga03c37f">17</a>.
|
||||
</p>
|
||||
|
||||
V_in = linspace(0, 5, 100); <span class="org-comment">% Input Voltage [V]</span>
|
||||
|
||||
w_max = 1<span class="org-type">./</span>(20<span class="org-type">*</span>C<span class="org-type">*</span>V_in) <span class="org-type">*</span> Iout_max; <span class="org-comment">% [rad/s]</span>
|
||||
|
||||
<span class="org-type">figure</span>;
|
||||
plot(V_in, w_max<span class="org-type">/</span>2<span class="org-type">/</span><span class="org-constant">pi</span>);
|
||||
xlabel(<span class="org-string">'Input Voltage Amplitude [V]'</span>);
|
||||
ylabel(<span class="org-string">'Maximum Frequency [Hz]'</span>);
|
||||
<span class="org-type">set</span>(<span class="org-variable-name">gca</span>, <span class="org-string">'yscale'</span>, <span class="org-string">'log'</span>);
|
||||
</pre>
|
||||
<div id="orga03c37f" class="figure">
|
||||
<p><img src="figs/max_frequency_voltage.png" alt="max_frequency_voltage.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 17: </span>Maximum frequency as a function of the excitation voltage amplitude</p>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org2323f70" class="outline-3">
|
||||
<h3 id="org2323f70"><span class="section-number-3">6.3</span> Results</h3>
|
||||
<div id="outline-container-org05f8a88" class="outline-3">
|
||||
<h3 id="org05f8a88"><span class="section-number-3">6.3</span> Obtained Transfer Functions</h3>
|
||||
<div class="outline-text-3" id="text-6-3">
|
||||
<p>
|
||||
Several identifications using sweep sin were performed with input voltage amplitude ranging from 0.1V to 4V.
|
||||
</p>
|
||||
|
||||
<p>
|
||||
The obtained frequency response functions are shown in Figure <a href="#org16bc426">18</a>.
|
||||
As the input voltage increases, the voltage drop is increasing.
|
||||
</p>
|
||||
|
||||
|
||||
<div id="org16bc426" class="figure">
|
||||
<p><img src="figs/pd200_tf_voltage.png" alt="pd200_tf_voltage.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 18: </span>Transfer function for the PD200 amplitude between \(V_{in}\) and \(V_{out}\) for multiple voltage amplitudes</p>
|
||||
</div>
|
||||
<div id="outline-container-orge73cc45" class="outline-4">
|
||||
<h4 id="orge73cc45"><span class="section-number-4">6.3.1</span> First test</h4>
|
||||
<div class="outline-text-4" id="text-6-3-1">
|
||||
|
||||
<p>
|
||||
The small signal transfer function of the amplifier can be approximated by a first order low pass filter.
|
||||
</p>
|
||||
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab">pd200_1V_1 = load(<span class="org-string">'mat/tf_pd200_7_1V.mat'</span>, <span class="org-string">'t'</span>, <span class="org-string">'Vin'</span>, <span class="org-string">'Vout'</span>, <span class="org-string">'Iout'</span>);
|
||||
<pre class="src src-matlab">Gp = 19.95<span class="org-type">/</span>(1 <span class="org-type">+</span> s<span class="org-type">/</span>2<span class="org-type">/</span><span class="org-constant">pi</span><span class="org-type">/</span>35e3);
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab">Ts = (pd200_1V_1.t(end) <span class="org-type">-</span> pd200_1V_1.t(1))<span class="org-type">/</span>(length(pd200_1V_1.t)<span class="org-type">-</span>1);
|
||||
Fs = 1<span class="org-type">/</span>Ts;
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab">win = hanning(ceil(1<span class="org-type">*</span>Fs));
|
||||
|
||||
[tf_1, f] = tfestimate(pd200_1V_1.Vin, pd200_1V_1.Vout, win, [], [], 1<span class="org-type">/</span>Ts);
|
||||
</pre>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-orgeb520e4" class="outline-4">
|
||||
<h4 id="orgeb520e4"><span class="section-number-4">6.3.2</span> Results</h4>
|
||||
<div class="outline-text-4" id="text-6-3-2">
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab">Ts = (pd200{1}.t(end) <span class="org-type">-</span> pd200{1}.t(1))<span class="org-type">/</span>(length(pd200{1}.t)<span class="org-type">-</span>1);
|
||||
Fs = 1<span class="org-type">/</span>Ts;
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab">win = hanning(ceil(0.5<span class="org-type">*</span>Fs));
|
||||
|
||||
<span class="org-keyword">for</span> <span class="org-variable-name"><span class="org-constant">i</span></span> = <span class="org-constant">1:length(pd200)</span>
|
||||
[tf_est, f] = tfestimate(pd200{<span class="org-constant">i</span>}.Vin, 20<span class="org-type">*</span>pd200{<span class="org-constant">i</span>}.Vout, win, [], [], 1<span class="org-type">/</span>Ts);
|
||||
pd200{<span class="org-constant">i</span>}.tf = tf_est(f <span class="org-type"><</span> 0.99<span class="org-type">*</span>pd200{<span class="org-constant">i</span>}.notes.pd200.f_max);
|
||||
pd200{<span class="org-constant">i</span>}.f = f(f <span class="org-type"><</span> 0.99<span class="org-type">*</span>pd200{<span class="org-constant">i</span>}.notes.pd200.f_max);
|
||||
<span class="org-keyword">end</span>
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab">f_max = zeros(1, length(pd200));
|
||||
Vin_ampl = zeros(1, length(pd200));
|
||||
<span class="org-keyword">for</span> <span class="org-variable-name"><span class="org-constant">i</span></span> = <span class="org-constant">1:length(pd200)</span>
|
||||
f_max(<span class="org-constant">i</span>) = pd200{<span class="org-constant">i</span>}.notes.pd200.f_max;
|
||||
Vin_ampl(<span class="org-constant">i</span>) = pd200{<span class="org-constant">i</span>}.notes.pd200.Vin;
|
||||
<span class="org-keyword">end</span>
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
<table border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
|
||||
<p>
|
||||
The comparison from the model and measurements are shown in Figure <a href="#org1ae50fe">19</a>.
|
||||
</p>
|
||||
|
||||
|
||||
<colgroup>
|
||||
<col class="org-right" />
|
||||
|
||||
<col class="org-right" />
|
||||
</colgroup>
|
||||
<thead>
|
||||
<tr>
|
||||
<th scope="col" class="org-right">Vin</th>
|
||||
<th scope="col" class="org-right">Fmax</th>
|
||||
</tr>
|
||||
</thead>
|
||||
<tbody>
|
||||
<tr>
|
||||
<td class="org-right">0.1</td>
|
||||
<td class="org-right">5000.0</td>
|
||||
</tr>
|
||||
|
||||
<tr>
|
||||
<td class="org-right">0.5</td>
|
||||
<td class="org-right">3801.3</td>
|
||||
</tr>
|
||||
|
||||
<tr>
|
||||
<td class="org-right">1.0</td>
|
||||
<td class="org-right">1900.7</td>
|
||||
</tr>
|
||||
|
||||
<tr>
|
||||
<td class="org-right">2.0</td>
|
||||
<td class="org-right">950.3</td>
|
||||
</tr>
|
||||
|
||||
<tr>
|
||||
<td class="org-right">4.0</td>
|
||||
<td class="org-right">475.2</td>
|
||||
</tr>
|
||||
</tbody>
|
||||
</table>
|
||||
<div id="org1ae50fe" class="figure">
|
||||
<p><img src="figs/tf_pd200_model.png" alt="tf_pd200_model.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 19: </span>Comparison of the model transfer function and the measured frequency response function</p>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-orgad3a328" class="outline-2">
|
||||
<h2 id="orgad3a328"><span class="section-number-2">7</span> Conclusion</h2>
|
||||
<div id="outline-container-org5f03b6e" class="outline-2">
|
||||
<h2 id="org5f03b6e"><span class="section-number-2">7</span> Conclusion</h2>
|
||||
<div class="outline-text-2" id="text-7">
|
||||
<table id="org4bb2717" border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
|
||||
<table id="org039c233" border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
|
||||
<caption class="t-above"><span class="table-number">Table 4:</span> Measured characteristics, Manual characterstics and specified ones</caption>
|
||||
|
||||
<colgroup>
|
||||
@ -1005,7 +934,7 @@ Vin_ampl = zeros(1, length(pd200));
|
||||
</div>
|
||||
<div id="postamble" class="status">
|
||||
<p class="author">Author: Dehaeze Thomas</p>
|
||||
<p class="date">Created: 2021-01-22 ven. 23:44</p>
|
||||
<p class="date">Created: 2021-01-23 sam. 15:38</p>
|
||||
</div>
|
||||
</body>
|
||||
</html>
|
||||
|
||||
190
index.org
190
index.org
@ -1397,39 +1397,7 @@ For this measurement, the sampling frequency of the Speedgoat ADC should be as h
|
||||
#+caption: Schematic of the test bench to estimate the dynamics from voltage input $V_{in}$ to voltage output $V_{out}$
|
||||
[[file:figs/setup-dynamics-measurement.png]]
|
||||
|
||||
** Maximum Frequency/Voltage to not overload the amplifier
|
||||
|
||||
The maximum current is 1A [rms] which corresponds to 0.7A in amplitude of the sin wave.
|
||||
|
||||
The impedance of the capacitance is:
|
||||
\[ Z_C(\omega) = \frac{1}{jC\omega} \]
|
||||
|
||||
Therefore the relation between the output current and the output voltage is (in amplitude):
|
||||
\[ V_{out} = \frac{1}{C\omega} I_{out} \]
|
||||
|
||||
There is a gain of 20 between the input voltage and the output voltage:
|
||||
\[ 20 V_{in} = \frac{1}{C\omega} I_{out} \]
|
||||
|
||||
For a specified voltage input amplitude $V_{in}$, the maximum frequency is then:
|
||||
\[ \omega_{\text{max}} = \frac{1}{20 C V_{in}} I_{out,\text{max}} \]
|
||||
|
||||
#+begin_src matlab
|
||||
Iout_max = 0.57; % Maximum output current [A]
|
||||
C = 2.7e-6; % Load Capacitance [F]
|
||||
|
||||
V_in = linspace(0, 5, 100); % Input Voltage [V]
|
||||
|
||||
w_max = 1./(20*C*V_in) * Iout_max; % [rad/s]
|
||||
|
||||
figure;
|
||||
plot(V_in, w_max/2/pi);
|
||||
xlabel('Input Voltage Amplitude [V]');
|
||||
ylabel('Maximum Frequency [Hz]');
|
||||
set(gca, 'yscale', 'log');
|
||||
#+end_src
|
||||
|
||||
** Results
|
||||
*** Matlab Init :noexport:ignore:
|
||||
** Matlab Init :noexport:ignore:
|
||||
#+begin_src matlab :tangle no :exports none :results silent :noweb yes :var current_dir=(file-name-directory buffer-file-name)
|
||||
<<matlab-dir>>
|
||||
#+end_src
|
||||
@ -1447,49 +1415,51 @@ addpath('./matlab/');
|
||||
addpath('./mat/');
|
||||
#+end_src
|
||||
|
||||
*** First test
|
||||
#+begin_src matlab
|
||||
pd200_1V_1 = load('mat/tf_pd200_7_1V.mat', 't', 'Vin', 'Vout', 'Iout');
|
||||
#+end_src
|
||||
** Maximum Frequency/Voltage to not overload the amplifier
|
||||
|
||||
#+begin_src matlab
|
||||
Ts = (pd200_1V_1.t(end) - pd200_1V_1.t(1))/(length(pd200_1V_1.t)-1);
|
||||
Fs = 1/Ts;
|
||||
#+end_src
|
||||
The maximum current is 1A [rms] which corresponds to 0.7A in amplitude of the sin wave.
|
||||
|
||||
#+begin_src matlab
|
||||
win = hanning(ceil(1*Fs));
|
||||
The impedance of the capacitance is:
|
||||
\[ Z_C(\omega) = \frac{1}{jC\omega} \]
|
||||
|
||||
[tf_1, f] = tfestimate(pd200_1V_1.Vin, pd200_1V_1.Vout, win, [], [], 1/Ts);
|
||||
#+end_src
|
||||
Therefore the relation between the output current amplitude and the output voltage amplitude for sinusoidal waves of frequency $\omega$:
|
||||
\[ V_{out} = \frac{1}{C\omega} I_{out} \]
|
||||
|
||||
Moreover, there is a gain of 20 between the input voltage and the output voltage:
|
||||
\[ 20 V_{in} = \frac{1}{C\omega} I_{out} \]
|
||||
|
||||
For a specified voltage input amplitude $V_{in}$, the maximum frequency at which the output current reaches its maximum value is:
|
||||
\[ \omega_{\text{max}} = \frac{1}{20 C V_{in}} I_{out,\text{max}} \]
|
||||
|
||||
$\omega_max$ as a function of $V_{in}$ is shown in Figure [[fig:max_frequency_voltage]].
|
||||
|
||||
#+begin_src matlab :exports none
|
||||
Iout_max = 0.57; % Maximum output current [A]
|
||||
C = 2.7e-6; % Load Capacitance [F]
|
||||
|
||||
V_in = linspace(0, 5, 100); % Input Voltage [V]
|
||||
|
||||
w_max = 1./(20*C*V_in) * Iout_max; % [rad/s]
|
||||
|
||||
figure;
|
||||
tiledlayout(3, 1, 'TileSpacing', 'None', 'Padding', 'None');
|
||||
|
||||
ax1 = nexttile([2,1]);
|
||||
hold on;
|
||||
plot(f, abs(tf_1));
|
||||
hold off;
|
||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
||||
ylabel('Amplitude $V_{out}/V_{in}$ [V/V]'); set(gca, 'XTickLabel',[]);
|
||||
hold off;
|
||||
ylim([1e-1, 1e1]);
|
||||
|
||||
ax2 = nexttile;
|
||||
hold on;
|
||||
plot(f, 180/pi*angle(tf_1));
|
||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin');
|
||||
yticks(-360:15:360);
|
||||
xlabel('Frequency [Hz]'); ylabel('Phase [deg]');
|
||||
hold off;
|
||||
ylim([-45, 15]);
|
||||
|
||||
linkaxes([ax1,ax2],'x');
|
||||
xlim([1, 2e3]);
|
||||
plot(V_in, w_max/2/pi);
|
||||
xlabel('Input Voltage Amplitude [V]');
|
||||
ylabel('Maximum Frequency [Hz]');
|
||||
set(gca, 'yscale', 'log');
|
||||
#+end_src
|
||||
|
||||
*** Results
|
||||
#+begin_src matlab :tangle no :exports results :results file replace
|
||||
exportFig('figs/max_frequency_voltage.pdf', 'width', 'wide', 'height', 'normal');
|
||||
#+end_src
|
||||
|
||||
#+name: fig:max_frequency_voltage
|
||||
#+caption: Maximum frequency as a function of the excitation voltage amplitude
|
||||
#+RESULTS:
|
||||
[[file:figs/max_frequency_voltage.png]]
|
||||
|
||||
** Obtained Transfer Functions
|
||||
Several identifications using sweep sin were performed with input voltage amplitude ranging from 0.1V to 4V.
|
||||
|
||||
#+begin_src matlab :exports none
|
||||
%% Load all the measurements
|
||||
Vin_ampl = {'0_1', '0_5', '1', '2', '4'};
|
||||
@ -1500,14 +1470,17 @@ for i = 1:length(Vin_ampl)
|
||||
end
|
||||
#+end_src
|
||||
|
||||
#+begin_src matlab
|
||||
#+begin_src matlab :exports none
|
||||
% Compute sampling Frequency
|
||||
Ts = (pd200{1}.t(end) - pd200{1}.t(1))/(length(pd200{1}.t)-1);
|
||||
Fs = 1/Ts;
|
||||
#+end_src
|
||||
|
||||
#+begin_src matlab
|
||||
#+begin_src matlab :exports none
|
||||
% Hannning Windows
|
||||
win = hanning(ceil(0.5*Fs));
|
||||
|
||||
% Compute all the transfer functions
|
||||
for i = 1:length(pd200)
|
||||
[tf_est, f] = tfestimate(pd200{i}.Vin, 20*pd200{i}.Vout, win, [], [], 1/Ts);
|
||||
pd200{i}.tf = tf_est(f < 0.99*pd200{i}.notes.pd200.f_max);
|
||||
@ -1515,6 +1488,9 @@ for i = 1:length(pd200)
|
||||
end
|
||||
#+end_src
|
||||
|
||||
The obtained frequency response functions are shown in Figure [[fig:pd200_tf_voltage]].
|
||||
As the input voltage increases, the voltage drop is increasing.
|
||||
|
||||
#+begin_src matlab :exports none
|
||||
figure;
|
||||
tiledlayout(2, 1, 'TileSpacing', 'None', 'Padding', 'None');
|
||||
@ -1546,27 +1522,65 @@ linkaxes([ax1,ax2],'x');
|
||||
xlim([10, 5e3]);
|
||||
#+end_src
|
||||
|
||||
#+begin_src matlab
|
||||
f_max = zeros(1, length(pd200));
|
||||
Vin_ampl = zeros(1, length(pd200));
|
||||
for i = 1:length(pd200)
|
||||
f_max(i) = pd200{i}.notes.pd200.f_max;
|
||||
Vin_ampl(i) = pd200{i}.notes.pd200.Vin;
|
||||
end
|
||||
#+end_src
|
||||
|
||||
#+begin_src matlab :exports results :results value table replace :tangle no :post addhdr(*this*)
|
||||
data2orgtable([Vin_ampl; f_max]', {}, {'Vin', 'Fmax'}, ' %.1f ');
|
||||
#+begin_src matlab :tangle no :exports results :results file replace
|
||||
exportFig('figs/pd200_tf_voltage.pdf', 'width', 'wide', 'height', 'tall');
|
||||
#+end_src
|
||||
|
||||
#+name: fig:pd200_tf_voltage
|
||||
#+caption: Transfer function for the PD200 amplitude between $V_{in}$ and $V_{out}$ for multiple voltage amplitudes
|
||||
#+RESULTS:
|
||||
| Vin | Fmax |
|
||||
|-----+--------|
|
||||
| 0.1 | 5000.0 |
|
||||
| 0.5 | 3801.3 |
|
||||
| 1.0 | 1900.7 |
|
||||
| 2.0 | 950.3 |
|
||||
| 4.0 | 475.2 |
|
||||
[[file:figs/pd200_tf_voltage.png]]
|
||||
|
||||
The small signal transfer function of the amplifier can be approximated by a first order low pass filter.
|
||||
|
||||
#+begin_src matlab
|
||||
Gp = 19.95/(1 + s/2/pi/35e3);
|
||||
#+end_src
|
||||
|
||||
The comparison from the model and measurements are shown in Figure [[fig:tf_pd200_model]].
|
||||
|
||||
#+begin_src matlab :exports none
|
||||
freqs = logspace(1, 4, 1000);
|
||||
figure;
|
||||
tiledlayout(2, 1, 'TileSpacing', 'None', 'Padding', 'None');
|
||||
|
||||
ax1 = nexttile;
|
||||
hold on;
|
||||
for i = 1:length(pd200)
|
||||
plot(pd200{i}.f, abs(pd200{i}.tf))
|
||||
end
|
||||
plot(freqs, abs(squeeze(freqresp(Gp, freqs, 'Hz'))), 'k--');
|
||||
hold off;
|
||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
||||
ylabel('Amplitude $V_{out}/V_{in}$ [V/V]'); set(gca, 'XTickLabel',[]);
|
||||
hold off;
|
||||
ylim([19, 21]);
|
||||
|
||||
ax2 = nexttile;
|
||||
hold on;
|
||||
for i = 1:length(pd200)
|
||||
plot(pd200{i}.f, 180/pi*angle(pd200{i}.tf), 'DisplayName', sprintf('$V_{in} = %.1f [V]$', pd200{i}.notes.pd200.Vin))
|
||||
end
|
||||
plot(freqs, 180/pi*angle(squeeze(freqresp(Gp, freqs, 'Hz'))), 'k--', 'DisplayName', '$G_p(j\omega)$');
|
||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin');
|
||||
yticks(-5:1:5);
|
||||
xlabel('Frequency [Hz]'); ylabel('Phase [deg]');
|
||||
hold off;
|
||||
ylim([-3, 1]);
|
||||
legend('location', 'southwest');
|
||||
|
||||
linkaxes([ax1,ax2],'x');
|
||||
xlim([10, 1e3]);
|
||||
#+end_src
|
||||
|
||||
#+begin_src matlab :tangle no :exports results :results file replace
|
||||
exportFig('figs/tf_pd200_model.pdf', 'width', 'wide', 'height', 'tall');
|
||||
#+end_src
|
||||
|
||||
#+name: fig:tf_pd200_model
|
||||
#+caption: Comparison of the model transfer function and the measured frequency response function
|
||||
#+RESULTS:
|
||||
[[file:figs/tf_pd200_model.png]]
|
||||
|
||||
* Conclusion
|
||||
|
||||
|
||||
Loading…
Reference in New Issue
Block a user