Analyze all noise meaurements
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<html xmlns="http://www.w3.org/1999/xhtml" lang="en" xml:lang="en">
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<!-- 2021-01-19 mar. 23:00 -->
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<!-- 2021-01-22 ven. 23:44 -->
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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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<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="#org9fe8e60">1. Introduction</a></li>
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<li><a href="#org83288a7">2. Voltage Amplifier Requirements</a></li>
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<li><a href="#org2725a7d">3. PD200 Expected characteristics</a></li>
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<li><a href="#org6748772">4. Voltage Amplifier Model</a></li>
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<li><a href="#orgb0f1751">5. Noise measurement</a>
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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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<ul>
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<li><a href="#org077faf1">5.1. Setup</a></li>
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<li><a href="#org8d11397">5.2. Results</a>
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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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</ul>
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</li>
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<li><a href="#org311b8b4">6. Transfer Function measurement</a>
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<ul>
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<li><a href="#org3e569c9">5.2.1. Noise when shunting the input (50 Ohms)</a></li>
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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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</ul>
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</li>
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</ul>
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</li>
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<li><a href="#orgaf96727">6. Transfer Function measurement</a>
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<ul>
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<li><a href="#org9868c43">6.1. Setup</a></li>
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<li><a href="#orgc5c49ee">6.2. Results</a></li>
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</ul>
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</li>
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<li><a href="#org516bcbb">7. Conclusion</a></li>
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<li><a href="#orgad3a328">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-org9fe8e60" class="outline-2">
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<h2 id="org9fe8e60"><span class="section-number-2">1</span> Introduction</h2>
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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 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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@@ -76,7 +84,7 @@ 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="orga2cd341" class="figure">
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<div id="org7aea75d" 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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@@ -84,10 +92,10 @@ 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-org83288a7" class="outline-2">
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<h2 id="org83288a7"><span class="section-number-2">2</span> Voltage Amplifier Requirements</h2>
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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 class="outline-text-2" id="text-2">
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<table id="org6825b69" border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
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<table id="orgf1fdf95" 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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@@ -131,10 +139,10 @@ 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-org2725a7d" class="outline-2">
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<h2 id="org2725a7d"><span class="section-number-2">3</span> PD200 Expected characteristics</h2>
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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 class="outline-text-2" id="text-3">
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<table id="orgf99d960" border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
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<table id="org38f8e47" 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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@@ -209,18 +217,18 @@ 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="#orgf39e37f">2</a>) and the low frequency noise is \(650\,\mu V\,\text{rms}\) (Figure <a href="#org2267cad">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="#org2190892">2</a>) and the low frequency noise is \(650\,\mu V\,\text{rms}\) (Figure <a href="#orgeaff484">3</a>).
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</p>
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<div id="orgf39e37f" class="figure">
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<div id="org2190892" 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="org2267cad" class="figure">
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<div id="orgeaff484" 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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@@ -228,8 +236,8 @@ 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-org6748772" class="outline-2">
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<h2 id="org6748772"><span class="section-number-2">4</span> Voltage Amplifier Model</h2>
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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 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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@@ -246,11 +254,11 @@ The objective is therefore to determine the transfer function \(G_a(s)\) from th
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</p>
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<p>
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As both \(G_a\) and \(S_n\) depends on the load capacitance, they should be measured when loading the amplifier with a \(\SI{10}{\micro\farad}\) capacitor.
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As both \(G_a\) and \(S_n\) depends on the load capacitance, they should be measured when loading the amplifier with a \(10\,\mu F\) capacitor.
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</p>
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<div id="org4313e25" class="figure">
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<div id="org5d4d3ab" 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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@@ -258,14 +266,29 @@ 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-orgb0f1751" class="outline-2">
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<h2 id="orgb0f1751"><span class="section-number-2">5</span> Noise measurement</h2>
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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 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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</ul>
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||||
</div>
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<div id="outline-container-org077faf1" class="outline-3">
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<h3 id="org077faf1"><span class="section-number-3">5.1</span> Setup</h3>
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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 class="outline-text-3" id="text-5-1">
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<div class="note" id="org3d87176">
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<p>
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<a id="org975f5ab"></a>
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</p>
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<div class="note" id="org0370347">
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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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@@ -298,7 +321,7 @@ This gain should be around 1000.
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</p>
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<div id="orgb37f1e6" class="figure">
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<div id="org451a2c9" 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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@@ -311,41 +334,192 @@ 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-org8d11397" class="outline-3">
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<h3 id="org8d11397"><span class="section-number-3">5.2</span> Results</h3>
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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 class="outline-text-3" id="text-5-2">
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</div>
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<div id="outline-container-org3e569c9" class="outline-4">
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<h4 id="org3e569c9"><span class="section-number-4">5.2.1</span> Noise when shunting the input (50 Ohms)</h4>
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<div class="outline-text-4" id="text-5-2-1">
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<p>
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The time domain measurements of the amplifier noise are shown in Figure <a href="#org6fb276a">6</a>.
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<a id="org58a7c02"></a>
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</p>
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<div id="org6fb276a" class="figure">
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<p><img src="figs/noise_shunt_time_3uF.png" alt="noise_shunt_time_3uF.png" />
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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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</p>
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<p><span class="figure-number">Figure 6: </span>Time domain measurement of the amplifier output noise</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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<li>the Voltage amplifier to be measured with a gain of 20 (PD200)</li>
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<li>a low noise voltage amplifier with a variable gain and integrated low pass filters and high pass filters</li>
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<li>an Analog to Digital Converter (ADC)</li>
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</ul>
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<p>
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Each of these equipment has some noise:
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</p>
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<ul class="org-ul">
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<li>\(q_{da}\): quantization noise of the DAC</li>
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<li>\(n_{da}\): output noise of the DAC</li>
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<li>\(n_p\): output noise of the PD200 (what we wish to characterize)</li>
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<li>\(n_a\): input noise of the pre amplifier</li>
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<li>\(q_{ad}\): quantization noise of the ADC</li>
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</ul>
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<div id="org8801056" 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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||||
</div>
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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 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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</p>
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<p>
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||||
The quantization noise is something that can be predicted.
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||||
The Amplitude Spectral Density of the quantization noise of an ADC/DAC is equal to:
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||||
</p>
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||||
\begin{equation}
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||||
\Gamma_q(\omega) = \frac{q}{\sqrt{12 f_s}}
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||||
\end{equation}
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||||
<p>
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||||
with:
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||||
</p>
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||||
<ul class="org-ul">
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||||
<li>\(q = \frac{\Delta V}{2^n}\) the quantization in [V], which is the corresponding value in [V] of the least significant bit</li>
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||||
<li>\(\Delta V\) is the full range of the ADC in [V]</li>
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||||
<li>\(n\) is the number of bits</li>
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||||
<li>\(f_s\) is the sample frequency in [Hz]</li>
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||||
</ul>
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||||
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||||
<div class="org-src-container">
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||||
<pre class="src src-matlab">adc = struct();
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||||
adc.Delta_V = 20; <span class="org-comment">% [V]</span>
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||||
adc.n = 16; <span class="org-comment">% number of bits</span>
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||||
adc.Fs = 20e3; <span class="org-comment">% [Hz]</span>
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||||
adc.Gamma_q = adc.Delta_V<span class="org-type">/</span>2<span class="org-type">^</span>adc.n<span class="org-type">/</span>sqrt(12<span class="org-type">*</span>adc.Fs); <span class="org-comment">% [V/sqrt(Hz)]</span>
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||||
</pre>
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||||
</div>
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||||
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||||
<p>
|
||||
Obtained low frequency (0.1Hz - 20Hz) noise is shown in Figure <a href="#orgaadf193">7</a> which is very similar to the noise shown in the documentation (Figure <a href="#org2267cad">3</a>).
|
||||
The obtained Amplitude Spectral Density is <code>6.2294e-07</code> \(V/\sqrt{Hz}\).
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||||
</p>
|
||||
</div>
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||||
</div>
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||||
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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 class="outline-text-3" id="text-5-4">
|
||||
<p>
|
||||
<a id="orgd67c98a"></a>
|
||||
</p>
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||||
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||||
<p>
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||||
First, we wish to measure the noise of the pre-amplifier.
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||||
To do so, the input of the pre-amplifier is shunted such that there is 0V at its inputs.
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||||
Then, the gain of the amplifier is increase until the measured signal on the ADC is much larger than the quantization noise.
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||||
</p>
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||||
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||||
<p>
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||||
The Amplitude Spectral Density \(\Gamma_n(\omega)\) of the measured signal \(n\) is computed.
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||||
Finally, the Amplitude Spectral Density of \(n_a\) can be computed taking into account the gain of the pre-amplifier:
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||||
</p>
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||||
\begin{equation}
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||||
\Gamma_{n_a}(\omega) \approx \frac{\Gamma_n(\omega)}{|G_a(\omega)|}
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||||
\end{equation}
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||||
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||||
<p>
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||||
This is true if the quantization noise \(\Gamma_{q_{ad}}\) is negligible.
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||||
</p>
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||||
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||||
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||||
<div id="orgaadf193" class="figure">
|
||||
<p><img src="figs/low_noise_time_domain_3uF.png" alt="low_noise_time_domain_3uF.png" />
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||||
<div id="org0e8db56" class="figure">
|
||||
<p><img src="figs/noise_measure_setup_preamp.png" alt="noise_measure_setup_preamp.png" />
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||||
</p>
|
||||
<p><span class="figure-number">Figure 7: </span>Low Frequency Noise (0.1Hz - 20Hz)</p>
|
||||
<p><span class="figure-number">Figure 7: </span>Sources of noise in the experimental setup</p>
|
||||
</div>
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||||
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||||
<p>
|
||||
The obtained RMS and peak to peak values of the measured noises are shown in Table <a href="#orgd174c39">3</a>.
|
||||
The gain of the low noise amplifier is set to <code>50000</code>.
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||||
</p>
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||||
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||||
<table id="orgd174c39" 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 noise</caption>
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||||
<div class="org-src-container">
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||||
<pre class="src src-matlab"><span class="org-comment">% Hanning window</span>
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||||
win = hanning(ceil(0.5<span class="org-type">/</span>Ts));
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||||
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||||
<span class="org-comment">% Power Spectral Density</span>
|
||||
[pxx, f] = pwelch(preamp.Vn, win, [], [], Fs);
|
||||
|
||||
<span class="org-comment">% Save the results inside the struct</span>
|
||||
preamp.pxx = pxx;
|
||||
preamp.f = f;
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
<p>
|
||||
The obtained Amplitude Spectral Density of the Low Noise Voltage Amplifier is shown in Figure <a href="#org2880354">8</a>.
|
||||
The obtained noise amplitude is very closed to the one specified in the documentation of \(4nV/\sqrt{Hz}\) at 1kHZ.
|
||||
</p>
|
||||
|
||||
|
||||
<div id="org2880354" class="figure">
|
||||
<p><img src="figs/asd_preamp.png" alt="asd_preamp.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 8: </span>Obtained Amplitude Spectral Density of the Low Noise Voltage Amplifier</p>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-orgdd4cdcb" class="outline-3">
|
||||
<h3 id="orgdd4cdcb"><span class="section-number-3">5.5</span> PD200 noise measurement</h3>
|
||||
<div class="outline-text-3" id="text-5-5">
|
||||
<p>
|
||||
<a id="orge02d748"></a>
|
||||
</p>
|
||||
|
||||
<p>
|
||||
The input of the PD200 amplifier is shunted such that there is 0V between its inputs.
|
||||
Then the gain of the pre-amplifier is increased in order to measure a signal much larger than the quantization noise of the ADC.
|
||||
We compute the Amplitude Spectral Density of the measured signal \(\Gamma_n(\omega)\).
|
||||
The Amplitude Spectral Density of \(n_p\) can be computed taking into account the gain of the pre-amplifier:
|
||||
</p>
|
||||
\begin{equation}
|
||||
\Gamma_{n_p}(\omega) = \frac{\Gamma_n(\omega)}{|G_a(\omega)|}
|
||||
\end{equation}
|
||||
|
||||
<p>
|
||||
And we verify that this is indeed the noise of the PD200 and not the noise of the pre-amplifier by checking that:
|
||||
</p>
|
||||
\begin{equation}
|
||||
\Gamma_{n_p} \ll \Gamma_{n_a}
|
||||
\end{equation}
|
||||
|
||||
|
||||
<div id="org5660b1a" class="figure">
|
||||
<p><img src="figs/noise_measure_setup_pd200.png" alt="noise_measure_setup_pd200.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 9: </span>Sources of noise in the experimental setup</p>
|
||||
</div>
|
||||
|
||||
<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>.
|
||||
</p>
|
||||
|
||||
<div id="org99c1c8c" 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>.
|
||||
</p>
|
||||
<table id="org904c283" 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>
|
||||
<col class="org-left" />
|
||||
@@ -370,87 +544,202 @@ The obtained RMS and peak to peak values of the measured noises are shown in Tab
|
||||
|
||||
<tr>
|
||||
<td class="org-left">PD200_1</td>
|
||||
<td class="org-right">524.9</td>
|
||||
<td class="org-right">4.5</td>
|
||||
<td class="org-right">565.1</td>
|
||||
<td class="org-right">3.7</td>
|
||||
</tr>
|
||||
|
||||
<tr>
|
||||
<td class="org-left">PD200_2</td>
|
||||
<td class="org-right">807.7</td>
|
||||
<td class="org-right">6.7</td>
|
||||
<td class="org-right">767.6</td>
|
||||
<td class="org-right">3.5</td>
|
||||
</tr>
|
||||
|
||||
<tr>
|
||||
<td class="org-left">PD200_3</td>
|
||||
<td class="org-right">630.3</td>
|
||||
<td class="org-right">5.4</td>
|
||||
<td class="org-right">479.9</td>
|
||||
<td class="org-right">3.0</td>
|
||||
</tr>
|
||||
|
||||
<tr>
|
||||
<td class="org-left">PD200_4</td>
|
||||
<td class="org-right">619.7</td>
|
||||
<td class="org-right">5.5</td>
|
||||
<td class="org-right">615.7</td>
|
||||
<td class="org-right">3.5</td>
|
||||
</tr>
|
||||
|
||||
<tr>
|
||||
<td class="org-left">PD200_5</td>
|
||||
<td class="org-right">630.8</td>
|
||||
<td class="org-right">5.6</td>
|
||||
<td class="org-right">651.0</td>
|
||||
<td class="org-right">2.4</td>
|
||||
</tr>
|
||||
|
||||
<tr>
|
||||
<td class="org-left">PD200_6</td>
|
||||
<td class="org-right">517.3</td>
|
||||
<td class="org-right">4.9</td>
|
||||
<td class="org-right">473.2</td>
|
||||
<td class="org-right">2.7</td>
|
||||
</tr>
|
||||
|
||||
<tr>
|
||||
<td class="org-left">PD200_7</td>
|
||||
<td class="org-right">393.8</td>
|
||||
<td class="org-right">3.7</td>
|
||||
<td class="org-right">423.1</td>
|
||||
<td class="org-right">2.3</td>
|
||||
</tr>
|
||||
</tbody>
|
||||
</table>
|
||||
|
||||
<p>
|
||||
The PSD of the measured noise is computed and the ASD is shown in Figure <a href="#org17a3769">8</a>.
|
||||
The Amplitude Spectral Density of the measured noise is now computed and shown in Figure <a href="#org7bcb803">11</a>.
|
||||
</p>
|
||||
|
||||
<div id="org7bcb803" 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>
|
||||
</div>
|
||||
</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 class="outline-text-3" id="text-5-6">
|
||||
<p>
|
||||
<a id="org30c83b3"></a>
|
||||
</p>
|
||||
|
||||
<p>
|
||||
In order not to have any quantization noise, we impose the DAC to output a zero voltage.
|
||||
The gain of the low noise amplifier is adjusted to
|
||||
</p>
|
||||
|
||||
<p>
|
||||
The Amplitude Spectral Density \(\Gamma_n(\omega)\) of the measured signal is computed.
|
||||
The Amplitude Spectral Density of \(n_{da}\) can be computed taking into account the gain of the pre-amplifier:
|
||||
</p>
|
||||
\begin{equation}
|
||||
\Gamma_{n_{da}}(\omega) = \frac{\Gamma_m(\omega)}{|G_a(\omega)|}
|
||||
\end{equation}
|
||||
|
||||
<p>
|
||||
And it is verify that the Amplitude Spectral Density of \(n_{da}\) is much larger than the one of \(n_a\):
|
||||
</p>
|
||||
\begin{equation}
|
||||
\Gamma_{n_{da}} \gg \Gamma_{n_a}
|
||||
\end{equation}
|
||||
|
||||
|
||||
<div id="org744e44a" 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">
|
||||
<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 class="outline-text-3" id="text-5-7">
|
||||
<p>
|
||||
<a id="org0d900c3"></a>
|
||||
</p>
|
||||
|
||||
<p>
|
||||
Let’s now analyze the measurement of the setup in Figure <a href="#org8801056">6</a>.
|
||||
</p>
|
||||
|
||||
<p>
|
||||
The PSD of the measured noise is computed and the ASD is shown in Figure <a href="#org929789a">14</a>.
|
||||
</p>
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab">win = hanning(ceil(0.5<span class="org-type">/</span>Ts));
|
||||
|
||||
[pxx, f] = pwelch(pd200{1}.Vn, win, [], [], Fs);
|
||||
|
||||
pxx = zeros(length(pxx), 7);
|
||||
|
||||
<span class="org-keyword">for</span> <span class="org-variable-name"><span class="org-constant">i</span></span> = <span class="org-constant">1:7</span>
|
||||
pxx(<span class="org-type">:</span>, <span class="org-constant">i</span>) = pwelch(pd200{<span class="org-constant">i</span>}.Vn, win, [], [], Fs);
|
||||
[pxx, f] = pwelch(pd200dac{<span class="org-constant">i</span>}.Vn, win, [], [], Fs);
|
||||
pd200dac{<span class="org-constant">i</span>}.f = f;
|
||||
pd200dac{<span class="org-constant">i</span>}.pxx = pxx;
|
||||
<span class="org-keyword">end</span>
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
|
||||
<div id="org17a3769" class="figure">
|
||||
<p><img src="figs/asd_noise_3uF.png" alt="asd_noise_3uF.png" />
|
||||
<div id="org929789a" class="figure">
|
||||
<p><img src="figs/asd_noise_tot.png" alt="asd_noise_tot.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 8: </span>Amplitude Spectral Density of the measured noise</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">
|
||||
<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.
|
||||
SSI2V DACs will be used to verify that.
|
||||
</p>
|
||||
|
||||
</div>
|
||||
</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 class="outline-text-3" id="text-5-8">
|
||||
<p>
|
||||
<a id="org576bf2a"></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>.
|
||||
</p>
|
||||
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab">win = hanning(ceil(0.5<span class="org-type">/</span>Ts));
|
||||
|
||||
[pxx, f] = pwelch(ssi2v.Vn, win, [], [], Fs);
|
||||
ssi2v.pxx = pxx;
|
||||
ssi2v.f = f;
|
||||
</pre>
|
||||
</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.
|
||||
It is shown to be much smaller (~1 order of magnitude).
|
||||
</p>
|
||||
|
||||
|
||||
<div id="orgd5ecb95" 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">
|
||||
<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.
|
||||
</p>
|
||||
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-orgaf96727" class="outline-2">
|
||||
<h2 id="orgaf96727"><span class="section-number-2">6</span> Transfer Function measurement</h2>
|
||||
<div id="outline-container-org311b8b4" class="outline-2">
|
||||
<h2 id="org311b8b4"><span class="section-number-2">6</span> Transfer Function measurement</h2>
|
||||
<div class="outline-text-2" id="text-6">
|
||||
</div>
|
||||
<div id="outline-container-org9868c43" class="outline-3">
|
||||
<h3 id="org9868c43"><span class="section-number-3">6.1</span> Setup</h3>
|
||||
<div id="outline-container-org032d612" class="outline-3">
|
||||
<h3 id="org032d612"><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="#org472ad71">9</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="#orga5c58e5">16</a> is used.
|
||||
</p>
|
||||
|
||||
<div class="note" id="org5cbd7bf">
|
||||
<div class="note" id="org44386ba">
|
||||
<p>
|
||||
Here are the documentation of the equipment used for this test bench:
|
||||
</p>
|
||||
@@ -467,22 +756,166 @@ For this measurement, the sampling frequency of the Speedgoat ADC should be as h
|
||||
</p>
|
||||
|
||||
|
||||
<div id="org472ad71" class="figure">
|
||||
<div id="orga5c58e5" class="figure">
|
||||
<p><img src="figs/setup-dynamics-measurement.png" alt="setup-dynamics-measurement.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 9: </span>Schematic of the test bench to estimate the dynamics from voltage input \(V_{in}\) to voltage output \(V_{out}\)</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>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-orgc5c49ee" class="outline-3">
|
||||
<h3 id="orgc5c49ee"><span class="section-number-3">6.2</span> Results</h3>
|
||||
<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 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.
|
||||
</p>
|
||||
|
||||
<p>
|
||||
The impedance of the capacitance is:
|
||||
\[ Z_C(\omega) = \frac{1}{jC\omega} \]
|
||||
</p>
|
||||
|
||||
<p>
|
||||
Therefore the relation between the output current and the output voltage is (in amplitude):
|
||||
\[ V_{out} = \frac{1}{C\omega} I_{out} \]
|
||||
</p>
|
||||
|
||||
<p>
|
||||
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:
|
||||
\[ \omega_{\text{max}} = \frac{1}{20 C V_{in}} I_{out,\text{max}} \]
|
||||
</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>
|
||||
|
||||
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>
|
||||
</div>
|
||||
<div id="outline-container-org516bcbb" class="outline-2">
|
||||
<h2 id="org516bcbb"><span class="section-number-2">7</span> Conclusion</h2>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org2323f70" class="outline-3">
|
||||
<h3 id="org2323f70"><span class="section-number-3">6.3</span> Results</h3>
|
||||
<div class="outline-text-3" id="text-6-3">
|
||||
</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">
|
||||
<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>
|
||||
</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">
|
||||
|
||||
|
||||
<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>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-orgad3a328" class="outline-2">
|
||||
<h2 id="orgad3a328"><span class="section-number-2">7</span> Conclusion</h2>
|
||||
<div class="outline-text-2" id="text-7">
|
||||
<table id="orgcddfe96" border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
|
||||
<table id="org4bb2717" 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>
|
||||
@@ -572,7 +1005,7 @@ For this measurement, the sampling frequency of the Speedgoat ADC should be as h
|
||||
</div>
|
||||
<div id="postamble" class="status">
|
||||
<p class="author">Author: Dehaeze Thomas</p>
|
||||
<p class="date">Created: 2021-01-19 mar. 23:00</p>
|
||||
<p class="date">Created: 2021-01-22 ven. 23:44</p>
|
||||
</div>
|
||||
</body>
|
||||
</html>
|
||||
|
||||
Reference in New Issue
Block a user