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<html xmlns="http://www.w3.org/1999/xhtml" lang="en" xml:lang="en">
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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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<head>
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<!-- 2021-01-23 sam. 15:38 -->
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<!-- 2021-01-23 sam. 15:40 -->
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<meta http-equiv="Content-Type" content="text/html;charset=utf-8" />
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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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<title>Voltage Amplifier PD200 - Test Bench</title>
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<meta name="generator" content="Org mode" />
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<meta name="generator" content="Org mode" />
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@ -39,36 +39,36 @@
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<h2>Table of Contents</h2>
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<h2>Table of Contents</h2>
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<div id="text-table-of-contents">
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<div id="text-table-of-contents">
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<ul>
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<ul>
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<li><a href="#orge14df81">1. Introduction</a></li>
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<li><a href="#org8464676">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="#org377554e">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="#orgb337f1e">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="#orgb5bfcf0">4. Voltage Amplifier Model</a></li>
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<li><a href="#orgf27cdb1">5. Noise measurement</a>
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<li><a href="#orga876e4d">5. Noise measurement</a>
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<ul>
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<ul>
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<li><a href="#orgaaa2a30">5.1. Setup</a></li>
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<li><a href="#org2c9f60e">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="#orgcf8ecc8">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="#org5f0cc17">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="#org7c484b7">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="#org4fcdc54">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="#orga1b9697">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="#org6d8f9c2">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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<li><a href="#org59c04f1">5.8. 20bits DAC noise measurement</a></li>
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</ul>
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</ul>
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</li>
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</li>
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<li><a href="#orga87a250">6. Transfer Function measurement</a>
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<li><a href="#orga1cb3ef">6. Transfer Function measurement</a>
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<ul>
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<ul>
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<li><a href="#org2b82bca">6.1. Setup</a></li>
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<li><a href="#org2c3812b">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="#orge1713a2">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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<li><a href="#org4ff0dfb">6.3. Obtained Transfer Functions</a></li>
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</ul>
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</ul>
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</li>
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</li>
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<li><a href="#org5f03b6e">7. Conclusion</a></li>
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<li><a href="#org6becade">7. Conclusion</a></li>
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</ul>
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</ul>
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</div>
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</div>
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</div>
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</div>
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<div id="outline-container-orge14df81" class="outline-2">
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<div id="outline-container-org8464676" class="outline-2">
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||||||
<h2 id="orge14df81"><span class="section-number-2">1</span> Introduction</h2>
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<h2 id="org8464676"><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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<div class="outline-text-2" id="text-1">
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<p>
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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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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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@ -79,7 +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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</p>
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<div id="orgea7d2e1" class="figure">
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<div id="org6525f44" class="figure">
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<p><img src="figs/amplifier_PD200.png" alt="amplifier_PD200.png" />
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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>
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<p><span class="figure-number">Figure 1: </span>Picture of the PD200 Voltage Amplifier</p>
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<p><span class="figure-number">Figure 1: </span>Picture of the PD200 Voltage Amplifier</p>
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@ -87,10 +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>
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</div>
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<div id="outline-container-orgd794d0c" class="outline-2">
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<div id="outline-container-org377554e" 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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<h2 id="org377554e"><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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<div class="outline-text-2" id="text-2">
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<table id="orgfc689c5" border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
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<table id="orgf8783f3" 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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<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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<colgroup>
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@ -134,10 +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>
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</div>
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<div id="outline-container-org79cd976" class="outline-2">
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<div id="outline-container-orgb337f1e" 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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<h2 id="orgb337f1e"><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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<div class="outline-text-2" id="text-3">
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<table id="org6e26b68" border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
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<table id="org6e09271" 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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<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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<colgroup>
|
||||||
@ -212,18 +212,18 @@ The documentation of the PD200 is accessible <a href="doc/PD200-V7-R1.pdf">here<
|
|||||||
</table>
|
</table>
|
||||||
|
|
||||||
<p>
|
<p>
|
||||||
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>).
|
For a load capacitance of \(10\,\mu F\), the expected \(-3\,dB\) bandwidth is \(6.4\,kHz\) (Figure <a href="#org407299e">2</a>) and the low frequency noise is \(650\,\mu V\,\text{rms}\) (Figure <a href="#org94560d5">3</a>).
|
||||||
</p>
|
</p>
|
||||||
|
|
||||||
|
|
||||||
<div id="orgaa88e71" class="figure">
|
<div id="org407299e" class="figure">
|
||||||
<p><img src="./figs/pd200_expected_small_signal_bandwidth.png" alt="pd200_expected_small_signal_bandwidth.png" />
|
<p><img src="./figs/pd200_expected_small_signal_bandwidth.png" alt="pd200_expected_small_signal_bandwidth.png" />
|
||||||
</p>
|
</p>
|
||||||
<p><span class="figure-number">Figure 2: </span>Expected small signal bandwidth</p>
|
<p><span class="figure-number">Figure 2: </span>Expected small signal bandwidth</p>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
|
|
||||||
<div id="orgdcb3bab" class="figure">
|
<div id="org94560d5" class="figure">
|
||||||
<p><img src="figs/pd200_expected_noise.png" alt="pd200_expected_noise.png" />
|
<p><img src="figs/pd200_expected_noise.png" alt="pd200_expected_noise.png" />
|
||||||
</p>
|
</p>
|
||||||
<p><span class="figure-number">Figure 3: </span>Expected Low frequency noise from 0.03Hz to 20Hz</p>
|
<p><span class="figure-number">Figure 3: </span>Expected Low frequency noise from 0.03Hz to 20Hz</p>
|
||||||
@ -231,11 +231,11 @@ For a load capacitance of \(10\,\mu F\), the expected \(-3\,dB\) bandwidth is \(
|
|||||||
</div>
|
</div>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
<div id="outline-container-org3265b9b" class="outline-2">
|
<div id="outline-container-orgb5bfcf0" class="outline-2">
|
||||||
<h2 id="org3265b9b"><span class="section-number-2">4</span> Voltage Amplifier Model</h2>
|
<h2 id="orgb5bfcf0"><span class="section-number-2">4</span> Voltage Amplifier Model</h2>
|
||||||
<div class="outline-text-2" id="text-4">
|
<div class="outline-text-2" id="text-4">
|
||||||
<p>
|
<p>
|
||||||
The Amplifier is characterized by its dynamics \(G_a(s)\) from voltage inputs \(V_{in}\) to voltage output \(V_{out}\).
|
The Amplifier is characterized by its dynamics \(G_p(s)\) from voltage inputs \(V_{in}\) to voltage output \(V_{out}\).
|
||||||
Ideally, the gain from \(V_{in}\) to \(V_{out}\) is constant over a wide frequency band with very small phase drop.
|
Ideally, the gain from \(V_{in}\) to \(V_{out}\) is constant over a wide frequency band with very small phase drop.
|
||||||
</p>
|
</p>
|
||||||
|
|
||||||
@ -245,15 +245,15 @@ This noise is described by its Power Spectral Density.
|
|||||||
</p>
|
</p>
|
||||||
|
|
||||||
<p>
|
<p>
|
||||||
The objective is therefore to determine the transfer function \(G_a(s)\) from the input voltage to the output voltage as well as the Power Spectral Density \(S_n(\omega)\) of the amplifier output noise.
|
The objective is therefore to determine the transfer function \(G_p(s)\) from the input voltage to the output voltage as well as the Power Spectral Density \(S_n(\omega)\) of the amplifier output noise.
|
||||||
</p>
|
</p>
|
||||||
|
|
||||||
<p>
|
<p>
|
||||||
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.
|
As both \(G_p\) and \(S_n\) depends on the load capacitance, they should be measured when loading the amplifier with a \(10\,\mu F\) capacitor.
|
||||||
</p>
|
</p>
|
||||||
|
|
||||||
|
|
||||||
<div id="orgbc3695d" class="figure">
|
<div id="org388bf47" class="figure">
|
||||||
<p><img src="figs/pd200-model-schematic.png" alt="pd200-model-schematic.png" />
|
<p><img src="figs/pd200-model-schematic.png" alt="pd200-model-schematic.png" />
|
||||||
</p>
|
</p>
|
||||||
<p><span class="figure-number">Figure 4: </span>Model of the voltage amplifier</p>
|
<p><span class="figure-number">Figure 4: </span>Model of the voltage amplifier</p>
|
||||||
@ -261,29 +261,29 @@ As both \(G_a\) and \(S_n\) depends on the load capacitance, they should be meas
|
|||||||
</div>
|
</div>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
<div id="outline-container-orgf27cdb1" class="outline-2">
|
<div id="outline-container-orga876e4d" class="outline-2">
|
||||||
<h2 id="orgf27cdb1"><span class="section-number-2">5</span> Noise measurement</h2>
|
<h2 id="orga876e4d"><span class="section-number-2">5</span> Noise measurement</h2>
|
||||||
<div class="outline-text-2" id="text-5">
|
<div class="outline-text-2" id="text-5">
|
||||||
<ul class="org-ul">
|
<ul class="org-ul">
|
||||||
<li>Section <a href="#org9d21c0d">5.1</a></li>
|
<li>Section <a href="#org56bae9f">5.1</a></li>
|
||||||
<li>Section <a href="#org6edf2e9">5.2</a></li>
|
<li>Section <a href="#orgc48d4f4">5.2</a></li>
|
||||||
<li>Section <a href="#org7b5a20a">5.3</a></li>
|
<li>Section <a href="#org2a59e12">5.3</a></li>
|
||||||
<li>Section <a href="#orge4eb592">5.4</a></li>
|
<li>Section <a href="#orgff6c06d">5.4</a></li>
|
||||||
<li>Section <a href="#org8909c5d">5.5</a></li>
|
<li>Section <a href="#orgdb787b7">5.5</a></li>
|
||||||
<li>Section <a href="#org7739514">5.6</a></li>
|
<li>Section <a href="#org41a9b46">5.6</a></li>
|
||||||
<li>Section <a href="#org1920758">5.7</a></li>
|
<li>Section <a href="#org00954a7">5.7</a></li>
|
||||||
<li>Section <a href="#orgf336d8b">5.8</a></li>
|
<li>Section <a href="#orgbe0f3de">5.8</a></li>
|
||||||
</ul>
|
</ul>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
<div id="outline-container-orgaaa2a30" class="outline-3">
|
<div id="outline-container-org2c9f60e" class="outline-3">
|
||||||
<h3 id="orgaaa2a30"><span class="section-number-3">5.1</span> Setup</h3>
|
<h3 id="org2c9f60e"><span class="section-number-3">5.1</span> Setup</h3>
|
||||||
<div class="outline-text-3" id="text-5-1">
|
<div class="outline-text-3" id="text-5-1">
|
||||||
<p>
|
<p>
|
||||||
<a id="org9d21c0d"></a>
|
<a id="org56bae9f"></a>
|
||||||
</p>
|
</p>
|
||||||
|
|
||||||
<div class="note" id="org4394587">
|
<div class="note" id="org2bfae12">
|
||||||
<p>
|
<p>
|
||||||
Here are the documentation of the equipment used for this test bench:
|
Here are the documentation of the equipment used for this test bench:
|
||||||
</p>
|
</p>
|
||||||
@ -316,7 +316,7 @@ This gain should be around 1000.
|
|||||||
</p>
|
</p>
|
||||||
|
|
||||||
|
|
||||||
<div id="org7800d75" class="figure">
|
<div id="org6c9024e" class="figure">
|
||||||
<p><img src="figs/setup-noise-measurement.png" alt="setup-noise-measurement.png" />
|
<p><img src="figs/setup-noise-measurement.png" alt="setup-noise-measurement.png" />
|
||||||
</p>
|
</p>
|
||||||
<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>
|
<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>
|
||||||
@ -329,15 +329,15 @@ An high pass filter at low frequency can be added if there is a problem of large
|
|||||||
</div>
|
</div>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
<div id="outline-container-org959d7aa" class="outline-3">
|
<div id="outline-container-orgcf8ecc8" class="outline-3">
|
||||||
<h3 id="org959d7aa"><span class="section-number-3">5.2</span> Model of the setup</h3>
|
<h3 id="orgcf8ecc8"><span class="section-number-3">5.2</span> Model of the setup</h3>
|
||||||
<div class="outline-text-3" id="text-5-2">
|
<div class="outline-text-3" id="text-5-2">
|
||||||
<p>
|
<p>
|
||||||
<a id="org6edf2e9"></a>
|
<a id="orgc48d4f4"></a>
|
||||||
</p>
|
</p>
|
||||||
|
|
||||||
<p>
|
<p>
|
||||||
As shown in Figure <a href="#orgb873ca1">6</a>, there are 4 equipment involved in the measurement:
|
As shown in Figure <a href="#org52225dc">6</a>, there are 4 equipment involved in the measurement:
|
||||||
</p>
|
</p>
|
||||||
<ul class="org-ul">
|
<ul class="org-ul">
|
||||||
<li>a Digital to Analog Convert (DAC)</li>
|
<li>a Digital to Analog Convert (DAC)</li>
|
||||||
@ -358,7 +358,7 @@ Each of these equipment has some noise:
|
|||||||
</ul>
|
</ul>
|
||||||
|
|
||||||
|
|
||||||
<div id="orgb873ca1" class="figure">
|
<div id="org52225dc" class="figure">
|
||||||
<p><img src="figs/noise_meas_procedure.png" alt="noise_meas_procedure.png" />
|
<p><img src="figs/noise_meas_procedure.png" alt="noise_meas_procedure.png" />
|
||||||
</p>
|
</p>
|
||||||
<p><span class="figure-number">Figure 6: </span>Sources of noise in the experimental setup</p>
|
<p><span class="figure-number">Figure 6: </span>Sources of noise in the experimental setup</p>
|
||||||
@ -366,11 +366,11 @@ Each of these equipment has some noise:
|
|||||||
</div>
|
</div>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
<div id="outline-container-org8283055" class="outline-3">
|
<div id="outline-container-org5f0cc17" class="outline-3">
|
||||||
<h3 id="org8283055"><span class="section-number-3">5.3</span> Quantization Noise</h3>
|
<h3 id="org5f0cc17"><span class="section-number-3">5.3</span> Quantization Noise</h3>
|
||||||
<div class="outline-text-3" id="text-5-3">
|
<div class="outline-text-3" id="text-5-3">
|
||||||
<p>
|
<p>
|
||||||
<a id="org7b5a20a"></a>
|
<a id="org2a59e12"></a>
|
||||||
</p>
|
</p>
|
||||||
|
|
||||||
<p>
|
<p>
|
||||||
@ -405,11 +405,11 @@ The obtained Amplitude Spectral Density is <code>6.2294e-07</code> \(V/\sqrt{Hz}
|
|||||||
</div>
|
</div>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
<div id="outline-container-orga8ab614" class="outline-3">
|
<div id="outline-container-org7c484b7" class="outline-3">
|
||||||
<h3 id="orga8ab614"><span class="section-number-3">5.4</span> Pre Amplifier noise measurement</h3>
|
<h3 id="org7c484b7"><span class="section-number-3">5.4</span> Pre Amplifier noise measurement</h3>
|
||||||
<div class="outline-text-3" id="text-5-4">
|
<div class="outline-text-3" id="text-5-4">
|
||||||
<p>
|
<p>
|
||||||
<a id="orge4eb592"></a>
|
<a id="orgff6c06d"></a>
|
||||||
</p>
|
</p>
|
||||||
|
|
||||||
<p>
|
<p>
|
||||||
@ -431,7 +431,7 @@ This is true if the quantization noise \(\Gamma_{q_{ad}}\) is negligible.
|
|||||||
</p>
|
</p>
|
||||||
|
|
||||||
|
|
||||||
<div id="org5debea0" class="figure">
|
<div id="org21a64c7" class="figure">
|
||||||
<p><img src="figs/noise_measure_setup_preamp.png" alt="noise_measure_setup_preamp.png" />
|
<p><img src="figs/noise_measure_setup_preamp.png" alt="noise_measure_setup_preamp.png" />
|
||||||
</p>
|
</p>
|
||||||
<p><span class="figure-number">Figure 7: </span>Sources of noise in the experimental setup</p>
|
<p><span class="figure-number">Figure 7: </span>Sources of noise in the experimental setup</p>
|
||||||
@ -455,12 +455,12 @@ preamp.f = f;
|
|||||||
</div>
|
</div>
|
||||||
|
|
||||||
<p>
|
<p>
|
||||||
The obtained Amplitude Spectral Density of the Low Noise Voltage Amplifier is shown in Figure <a href="#org865b855">8</a>.
|
The obtained Amplitude Spectral Density of the Low Noise Voltage Amplifier is shown in Figure <a href="#org0f7d698">8</a>.
|
||||||
The obtained noise amplitude is very closed to the one specified in the documentation of \(4nV/\sqrt{Hz}\) at 1kHZ.
|
The obtained noise amplitude is very closed to the one specified in the documentation of \(4nV/\sqrt{Hz}\) at 1kHZ.
|
||||||
</p>
|
</p>
|
||||||
|
|
||||||
|
|
||||||
<div id="org865b855" class="figure">
|
<div id="org0f7d698" class="figure">
|
||||||
<p><img src="figs/asd_preamp.png" alt="asd_preamp.png" />
|
<p><img src="figs/asd_preamp.png" alt="asd_preamp.png" />
|
||||||
</p>
|
</p>
|
||||||
<p><span class="figure-number">Figure 8: </span>Obtained Amplitude Spectral Density of the Low Noise Voltage Amplifier</p>
|
<p><span class="figure-number">Figure 8: </span>Obtained Amplitude Spectral Density of the Low Noise Voltage Amplifier</p>
|
||||||
@ -468,11 +468,11 @@ The obtained noise amplitude is very closed to the one specified in the document
|
|||||||
</div>
|
</div>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
<div id="outline-container-orge67a27a" class="outline-3">
|
<div id="outline-container-org4fcdc54" class="outline-3">
|
||||||
<h3 id="orge67a27a"><span class="section-number-3">5.5</span> PD200 noise measurement</h3>
|
<h3 id="org4fcdc54"><span class="section-number-3">5.5</span> PD200 noise measurement</h3>
|
||||||
<div class="outline-text-3" id="text-5-5">
|
<div class="outline-text-3" id="text-5-5">
|
||||||
<p>
|
<p>
|
||||||
<a id="org8909c5d"></a>
|
<a id="orgdb787b7"></a>
|
||||||
</p>
|
</p>
|
||||||
|
|
||||||
<p>
|
<p>
|
||||||
@ -493,27 +493,27 @@ And we verify that this is indeed the noise of the PD200 and not the noise of th
|
|||||||
\end{equation}
|
\end{equation}
|
||||||
|
|
||||||
|
|
||||||
<div id="orgcfcd12c" class="figure">
|
<div id="orged8fdf4" class="figure">
|
||||||
<p><img src="figs/noise_measure_setup_pd200.png" alt="noise_measure_setup_pd200.png" />
|
<p><img src="figs/noise_measure_setup_pd200.png" alt="noise_measure_setup_pd200.png" />
|
||||||
</p>
|
</p>
|
||||||
<p><span class="figure-number">Figure 9: </span>Sources of noise in the experimental setup</p>
|
<p><span class="figure-number">Figure 9: </span>Sources of noise in the experimental setup</p>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
<p>
|
<p>
|
||||||
The measured low frequency noise \(n_p\) of one of the amplifiers is shown in Figure <a href="#orgb61b700">10</a>.
|
The measured low frequency noise \(n_p\) of one of the amplifiers is shown in Figure <a href="#org9cb2c72">10</a>.
|
||||||
It is very similar to the one specified in the datasheet in Figure <a href="#orgdcb3bab">3</a>.
|
It is very similar to the one specified in the datasheet in Figure <a href="#org94560d5">3</a>.
|
||||||
</p>
|
</p>
|
||||||
|
|
||||||
<div id="orgb61b700" class="figure">
|
<div id="org9cb2c72" class="figure">
|
||||||
<p><img src="figs/pd200_noise_time_lpf.png" alt="pd200_noise_time_lpf.png" />
|
<p><img src="figs/pd200_noise_time_lpf.png" alt="pd200_noise_time_lpf.png" />
|
||||||
</p>
|
</p>
|
||||||
<p><span class="figure-number">Figure 10: </span>Measured low frequency noise of the PD200 from 0.01Hz to 20Hz</p>
|
<p><span class="figure-number">Figure 10: </span>Measured low frequency noise of the PD200 from 0.01Hz to 20Hz</p>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
<p>
|
<p>
|
||||||
The obtained RMS and peak to peak values of the measured noises are shown in Table <a href="#orgf452b35">3</a>.
|
The obtained RMS and peak to peak values of the measured noises are shown in Table <a href="#orgec90acd">3</a>.
|
||||||
</p>
|
</p>
|
||||||
<table id="orgf452b35" border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
|
<table id="orgec90acd" 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>
|
<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>
|
<colgroup>
|
||||||
@ -582,10 +582,10 @@ The obtained RMS and peak to peak values of the measured noises are shown in Tab
|
|||||||
</table>
|
</table>
|
||||||
|
|
||||||
<p>
|
<p>
|
||||||
The Amplitude Spectral Density of the measured noise is now computed and shown in Figure <a href="#orgf1636b6">11</a>.
|
The Amplitude Spectral Density of the measured noise is now computed and shown in Figure <a href="#org177c379">11</a>.
|
||||||
</p>
|
</p>
|
||||||
|
|
||||||
<div id="orgf1636b6" class="figure">
|
<div id="org177c379" class="figure">
|
||||||
<p><img src="figs/asd_noise_3uF_warmup.png" alt="asd_noise_3uF_warmup.png" />
|
<p><img src="figs/asd_noise_3uF_warmup.png" alt="asd_noise_3uF_warmup.png" />
|
||||||
</p>
|
</p>
|
||||||
<p><span class="figure-number">Figure 11: </span>Amplitude Spectral Density of the measured noise</p>
|
<p><span class="figure-number">Figure 11: </span>Amplitude Spectral Density of the measured noise</p>
|
||||||
@ -593,11 +593,11 @@ The Amplitude Spectral Density of the measured noise is now computed and shown i
|
|||||||
</div>
|
</div>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
<div id="outline-container-orgc9e047f" class="outline-3">
|
<div id="outline-container-orga1b9697" class="outline-3">
|
||||||
<h3 id="orgc9e047f"><span class="section-number-3">5.6</span> DAC noise measurement</h3>
|
<h3 id="orga1b9697"><span class="section-number-3">5.6</span> DAC noise measurement</h3>
|
||||||
<div class="outline-text-3" id="text-5-6">
|
<div class="outline-text-3" id="text-5-6">
|
||||||
<p>
|
<p>
|
||||||
<a id="org7739514"></a>
|
<a id="org41a9b46"></a>
|
||||||
</p>
|
</p>
|
||||||
|
|
||||||
<p>
|
<p>
|
||||||
@ -621,33 +621,33 @@ And it is verify that the Amplitude Spectral Density of \(n_{da}\) is much large
|
|||||||
\end{equation}
|
\end{equation}
|
||||||
|
|
||||||
|
|
||||||
<div id="org0f39f6d" class="figure">
|
<div id="orga13ca97" class="figure">
|
||||||
<p><img src="figs/noise_measure_setup_dac.png" alt="noise_measure_setup_dac.png" />
|
<p><img src="figs/noise_measure_setup_dac.png" alt="noise_measure_setup_dac.png" />
|
||||||
</p>
|
</p>
|
||||||
<p><span class="figure-number">Figure 12: </span>Sources of noise in the experimental setup</p>
|
<p><span class="figure-number">Figure 12: </span>Sources of noise in the experimental setup</p>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
|
|
||||||
<div id="org531aca4" class="figure">
|
<div id="org428ef0b" class="figure">
|
||||||
<p><img src="figs/asd_noise_dac.png" alt="asd_noise_dac.png" />
|
<p><img src="figs/asd_noise_dac.png" alt="asd_noise_dac.png" />
|
||||||
</p>
|
</p>
|
||||||
</div>
|
</div>
|
||||||
</div>
|
</div>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
<div id="outline-container-orgd156ba1" class="outline-3">
|
<div id="outline-container-org6d8f9c2" class="outline-3">
|
||||||
<h3 id="orgd156ba1"><span class="section-number-3">5.7</span> Total noise measurement</h3>
|
<h3 id="org6d8f9c2"><span class="section-number-3">5.7</span> Total noise measurement</h3>
|
||||||
<div class="outline-text-3" id="text-5-7">
|
<div class="outline-text-3" id="text-5-7">
|
||||||
<p>
|
<p>
|
||||||
<a id="org1920758"></a>
|
<a id="org00954a7"></a>
|
||||||
</p>
|
</p>
|
||||||
|
|
||||||
<p>
|
<p>
|
||||||
Let’s now analyze the measurement of the setup in Figure <a href="#orgb873ca1">6</a>.
|
Let’s now analyze the measurement of the setup in Figure <a href="#org52225dc">6</a>.
|
||||||
</p>
|
</p>
|
||||||
|
|
||||||
<p>
|
<p>
|
||||||
The PSD of the measured noise is computed and the ASD is shown in Figure <a href="#orge63d88b">14</a>.
|
The PSD of the measured noise is computed and the ASD is shown in Figure <a href="#org18dbc81">14</a>.
|
||||||
</p>
|
</p>
|
||||||
<div class="org-src-container">
|
<div class="org-src-container">
|
||||||
<pre class="src src-matlab">win = hanning(ceil(0.5<span class="org-type">/</span>Ts));
|
<pre class="src src-matlab">win = hanning(ceil(0.5<span class="org-type">/</span>Ts));
|
||||||
@ -661,13 +661,13 @@ The PSD of the measured noise is computed and the ASD is shown in Figure <a href
|
|||||||
</div>
|
</div>
|
||||||
|
|
||||||
|
|
||||||
<div id="orge63d88b" class="figure">
|
<div id="org18dbc81" class="figure">
|
||||||
<p><img src="figs/asd_noise_tot.png" alt="asd_noise_tot.png" />
|
<p><img src="figs/asd_noise_tot.png" alt="asd_noise_tot.png" />
|
||||||
</p>
|
</p>
|
||||||
<p><span class="figure-number">Figure 14: </span>Amplitude Spectral Density of the measured noise and of the individual sources of 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>
|
||||||
|
|
||||||
<div class="important" id="orge883835">
|
<div class="important" id="org39d2c06">
|
||||||
<p>
|
<p>
|
||||||
The output noise of the PD200 amplifier is limited by the noise of the DAC.
|
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.
|
Having a DAC with lower noise could lower the output noise of the PD200.
|
||||||
@ -678,17 +678,17 @@ SSI2V DACs will be used to verify that.
|
|||||||
</div>
|
</div>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
<div id="outline-container-org802b093" class="outline-3">
|
<div id="outline-container-org59c04f1" class="outline-3">
|
||||||
<h3 id="org802b093"><span class="section-number-3">5.8</span> 20bits DAC noise measurement</h3>
|
<h3 id="org59c04f1"><span class="section-number-3">5.8</span> 20bits DAC noise measurement</h3>
|
||||||
<div class="outline-text-3" id="text-5-8">
|
<div class="outline-text-3" id="text-5-8">
|
||||||
<p>
|
<p>
|
||||||
<a id="orgf336d8b"></a>
|
<a id="orgbe0f3de"></a>
|
||||||
Let’s now measure the noise of another DAC called the “SSI2V” (<a href="doc/[SSI2V]Datasheet.pdf">doc</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.
|
It is a 20bits DAC with an output of +/-10.48 V and a very low noise.
|
||||||
</p>
|
</p>
|
||||||
|
|
||||||
<p>
|
<p>
|
||||||
The measurement setup is the same as the one in Figure <a href="#org0f39f6d">12</a>.
|
The measurement setup is the same as the one in Figure <a href="#orga13ca97">12</a>.
|
||||||
</p>
|
</p>
|
||||||
|
|
||||||
<div class="org-src-container">
|
<div class="org-src-container">
|
||||||
@ -701,18 +701,18 @@ ssi2v.f = f;
|
|||||||
</div>
|
</div>
|
||||||
|
|
||||||
<p>
|
<p>
|
||||||
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.
|
The obtained noise of the SSI2V DAC is shown in Figure <a href="#orge9f88e0">15</a> and compared with the noise of the 16bits DAC.
|
||||||
It is shown to be much smaller (~1 order of magnitude).
|
It is shown to be much smaller (~1 order of magnitude).
|
||||||
</p>
|
</p>
|
||||||
|
|
||||||
|
|
||||||
<div id="orge2b8a18" class="figure">
|
<div id="orge9f88e0" class="figure">
|
||||||
<p><img src="figs/asd_ssi2v_noise.png" alt="asd_ssi2v_noise.png" />
|
<p><img src="figs/asd_ssi2v_noise.png" alt="asd_ssi2v_noise.png" />
|
||||||
</p>
|
</p>
|
||||||
<p><span class="figure-number">Figure 15: </span>Amplitude Spectral Density of the SSI2V DAC’s noise</p>
|
<p><span class="figure-number">Figure 15: </span>Amplitude Spectral Density of the SSI2V DAC’s noise</p>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
<div class="important" id="org665f8e4">
|
<div class="important" id="org9ccd6d7">
|
||||||
<p>
|
<p>
|
||||||
Using the SSI2V as the DAC with the PD200 should give much better noise output than using the 16bits DAC.
|
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.
|
The limiting factor should then be the noise of the PD200 itself.
|
||||||
@ -723,18 +723,18 @@ The limiting factor should then be the noise of the PD200 itself.
|
|||||||
</div>
|
</div>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
<div id="outline-container-orga87a250" class="outline-2">
|
<div id="outline-container-orga1cb3ef" class="outline-2">
|
||||||
<h2 id="orga87a250"><span class="section-number-2">6</span> Transfer Function measurement</h2>
|
<h2 id="orga1cb3ef"><span class="section-number-2">6</span> Transfer Function measurement</h2>
|
||||||
<div class="outline-text-2" id="text-6">
|
<div class="outline-text-2" id="text-6">
|
||||||
</div>
|
</div>
|
||||||
<div id="outline-container-org2b82bca" class="outline-3">
|
<div id="outline-container-org2c3812b" class="outline-3">
|
||||||
<h3 id="org2b82bca"><span class="section-number-3">6.1</span> Setup</h3>
|
<h3 id="org2c3812b"><span class="section-number-3">6.1</span> Setup</h3>
|
||||||
<div class="outline-text-3" id="text-6-1">
|
<div class="outline-text-3" id="text-6-1">
|
||||||
<p>
|
<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="#org45f7f26">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="#org1a2018d">16</a> is used.
|
||||||
</p>
|
</p>
|
||||||
|
|
||||||
<div class="note" id="orgaa21e8d">
|
<div class="note" id="orgb90f0e1">
|
||||||
<p>
|
<p>
|
||||||
Here are the documentation of the equipment used for this test bench:
|
Here are the documentation of the equipment used for this test bench:
|
||||||
</p>
|
</p>
|
||||||
@ -751,7 +751,7 @@ For this measurement, the sampling frequency of the Speedgoat ADC should be as h
|
|||||||
</p>
|
</p>
|
||||||
|
|
||||||
|
|
||||||
<div id="org45f7f26" class="figure">
|
<div id="org1a2018d" class="figure">
|
||||||
<p><img src="figs/setup-dynamics-measurement.png" alt="setup-dynamics-measurement.png" />
|
<p><img src="figs/setup-dynamics-measurement.png" alt="setup-dynamics-measurement.png" />
|
||||||
</p>
|
</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>
|
<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>
|
||||||
@ -759,8 +759,8 @@ For this measurement, the sampling frequency of the Speedgoat ADC should be as h
|
|||||||
</div>
|
</div>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
<div id="outline-container-orgdf952ce" class="outline-3">
|
<div id="outline-container-orge1713a2" class="outline-3">
|
||||||
<h3 id="orgdf952ce"><span class="section-number-3">6.2</span> Maximum Frequency/Voltage to not overload the amplifier</h3>
|
<h3 id="orge1713a2"><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">
|
<div class="outline-text-3" id="text-6-2">
|
||||||
<p>
|
<p>
|
||||||
The maximum current is 1A [rms] which corresponds to 0.7A in amplitude of the sin wave.
|
The maximum current is 1A [rms] which corresponds to 0.7A in amplitude of the sin wave.
|
||||||
@ -787,11 +787,11 @@ For a specified voltage input amplitude \(V_{in}\), the maximum frequency at whi
|
|||||||
</p>
|
</p>
|
||||||
|
|
||||||
<p>
|
<p>
|
||||||
\(\omega_max\) as a function of \(V_{in}\) is shown in Figure <a href="#orga03c37f">17</a>.
|
\(\omega_max\) as a function of \(V_{in}\) is shown in Figure <a href="#orgfadee8c">17</a>.
|
||||||
</p>
|
</p>
|
||||||
|
|
||||||
|
|
||||||
<div id="orga03c37f" class="figure">
|
<div id="orgfadee8c" class="figure">
|
||||||
<p><img src="figs/max_frequency_voltage.png" alt="max_frequency_voltage.png" />
|
<p><img src="figs/max_frequency_voltage.png" alt="max_frequency_voltage.png" />
|
||||||
</p>
|
</p>
|
||||||
<p><span class="figure-number">Figure 17: </span>Maximum frequency as a function of the excitation voltage amplitude</p>
|
<p><span class="figure-number">Figure 17: </span>Maximum frequency as a function of the excitation voltage amplitude</p>
|
||||||
@ -799,20 +799,20 @@ For a specified voltage input amplitude \(V_{in}\), the maximum frequency at whi
|
|||||||
</div>
|
</div>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
<div id="outline-container-org05f8a88" class="outline-3">
|
<div id="outline-container-org4ff0dfb" class="outline-3">
|
||||||
<h3 id="org05f8a88"><span class="section-number-3">6.3</span> Obtained Transfer Functions</h3>
|
<h3 id="org4ff0dfb"><span class="section-number-3">6.3</span> Obtained Transfer Functions</h3>
|
||||||
<div class="outline-text-3" id="text-6-3">
|
<div class="outline-text-3" id="text-6-3">
|
||||||
<p>
|
<p>
|
||||||
Several identifications using sweep sin were performed with input voltage amplitude ranging from 0.1V to 4V.
|
Several identifications using sweep sin were performed with input voltage amplitude ranging from 0.1V to 4V.
|
||||||
</p>
|
</p>
|
||||||
|
|
||||||
<p>
|
<p>
|
||||||
The obtained frequency response functions are shown in Figure <a href="#org16bc426">18</a>.
|
The obtained frequency response functions are shown in Figure <a href="#orgf2c5d27">18</a>.
|
||||||
As the input voltage increases, the voltage drop is increasing.
|
As the input voltage increases, the voltage drop is increasing.
|
||||||
</p>
|
</p>
|
||||||
|
|
||||||
|
|
||||||
<div id="org16bc426" class="figure">
|
<div id="orgf2c5d27" class="figure">
|
||||||
<p><img src="figs/pd200_tf_voltage.png" alt="pd200_tf_voltage.png" />
|
<p><img src="figs/pd200_tf_voltage.png" alt="pd200_tf_voltage.png" />
|
||||||
</p>
|
</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>
|
<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>
|
||||||
@ -828,11 +828,11 @@ The small signal transfer function of the amplifier can be approximated by a fir
|
|||||||
</div>
|
</div>
|
||||||
|
|
||||||
<p>
|
<p>
|
||||||
The comparison from the model and measurements are shown in Figure <a href="#org1ae50fe">19</a>.
|
The comparison from the model and measurements are shown in Figure <a href="#orga34bca3">19</a>.
|
||||||
</p>
|
</p>
|
||||||
|
|
||||||
|
|
||||||
<div id="org1ae50fe" class="figure">
|
<div id="orga34bca3" class="figure">
|
||||||
<p><img src="figs/tf_pd200_model.png" alt="tf_pd200_model.png" />
|
<p><img src="figs/tf_pd200_model.png" alt="tf_pd200_model.png" />
|
||||||
</p>
|
</p>
|
||||||
<p><span class="figure-number">Figure 19: </span>Comparison of the model transfer function and the measured frequency response function</p>
|
<p><span class="figure-number">Figure 19: </span>Comparison of the model transfer function and the measured frequency response function</p>
|
||||||
@ -841,10 +841,10 @@ The comparison from the model and measurements are shown in Figure <a href="#org
|
|||||||
</div>
|
</div>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
<div id="outline-container-org5f03b6e" class="outline-2">
|
<div id="outline-container-org6becade" class="outline-2">
|
||||||
<h2 id="org5f03b6e"><span class="section-number-2">7</span> Conclusion</h2>
|
<h2 id="org6becade"><span class="section-number-2">7</span> Conclusion</h2>
|
||||||
<div class="outline-text-2" id="text-7">
|
<div class="outline-text-2" id="text-7">
|
||||||
<table id="org039c233" border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
|
<table id="org9961e87" 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>
|
<caption class="t-above"><span class="table-number">Table 4:</span> Measured characteristics, Manual characterstics and specified ones</caption>
|
||||||
|
|
||||||
<colgroup>
|
<colgroup>
|
||||||
@ -934,7 +934,7 @@ The comparison from the model and measurements are shown in Figure <a href="#org
|
|||||||
</div>
|
</div>
|
||||||
<div id="postamble" class="status">
|
<div id="postamble" class="status">
|
||||||
<p class="author">Author: Dehaeze Thomas</p>
|
<p class="author">Author: Dehaeze Thomas</p>
|
||||||
<p class="date">Created: 2021-01-23 sam. 15:38</p>
|
<p class="date">Created: 2021-01-23 sam. 15:40</p>
|
||||||
</div>
|
</div>
|
||||||
</body>
|
</body>
|
||||||
</html>
|
</html>
|
||||||
|
|||||||
@ -97,19 +97,19 @@ For a load capacitance of $10\,\mu F$, the expected $-3\,dB$ bandwidth is $6.4\,
|
|||||||
[[file:figs/pd200_expected_noise.png]]
|
[[file:figs/pd200_expected_noise.png]]
|
||||||
|
|
||||||
* Voltage Amplifier Model
|
* Voltage Amplifier Model
|
||||||
The Amplifier is characterized by its dynamics $G_a(s)$ from voltage inputs $V_{in}$ to voltage output $V_{out}$.
|
The Amplifier is characterized by its dynamics $G_p(s)$ from voltage inputs $V_{in}$ to voltage output $V_{out}$.
|
||||||
Ideally, the gain from $V_{in}$ to $V_{out}$ is constant over a wide frequency band with very small phase drop.
|
Ideally, the gain from $V_{in}$ to $V_{out}$ is constant over a wide frequency band with very small phase drop.
|
||||||
|
|
||||||
It is also characterized by its output noise $n$.
|
It is also characterized by its output noise $n$.
|
||||||
This noise is described by its Power Spectral Density.
|
This noise is described by its Power Spectral Density.
|
||||||
|
|
||||||
The objective is therefore to determine the transfer function $G_a(s)$ from the input voltage to the output voltage as well as the Power Spectral Density $S_n(\omega)$ of the amplifier output noise.
|
The objective is therefore to determine the transfer function $G_p(s)$ from the input voltage to the output voltage as well as the Power Spectral Density $S_n(\omega)$ of the amplifier output noise.
|
||||||
|
|
||||||
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.
|
As both $G_p$ and $S_n$ depends on the load capacitance, they should be measured when loading the amplifier with a $10\,\mu F$ capacitor.
|
||||||
|
|
||||||
#+begin_src latex :file pd200-model-schematic.pdf
|
#+begin_src latex :file pd200-model-schematic.pdf
|
||||||
\begin{tikzpicture}
|
\begin{tikzpicture}
|
||||||
\node[block] (G) at (0,0){$G_a(s)$};
|
\node[block] (G) at (0,0){$G_p(s)$};
|
||||||
\node[addb, right=0.8 of G] (add){};
|
\node[addb, right=0.8 of G] (add){};
|
||||||
|
|
||||||
\draw[<-] (G.west) -- ++(-1.2, 0) node[above right]{$V_{in}$};
|
\draw[<-] (G.west) -- ++(-1.2, 0) node[above right]{$V_{in}$};
|
||||||
|
|||||||
Loading…
Reference in New Issue
Block a user