941 lines
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941 lines
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<title>Voltage Amplifier PD200 - Test Bench</title>
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<a accesskey="h" href="../index.html"> UP </a>
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<a accesskey="H" href="../index.html"> HOME </a>
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</div><div id="content">
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<h1 class="title">Voltage Amplifier PD200 - Test Bench</h1>
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<div id="table-of-contents">
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<h2>Table of Contents</h2>
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<div id="text-table-of-contents">
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<ul>
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<li><a href="#orge14df81">1. Introduction</a></li>
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<li><a href="#orgd794d0c">2. Voltage Amplifier Requirements</a></li>
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<li><a href="#org79cd976">3. PD200 Expected characteristics</a></li>
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<li><a href="#org3265b9b">4. Voltage Amplifier Model</a></li>
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<li><a href="#orgf27cdb1">5. Noise measurement</a>
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<ul>
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<li><a href="#orgaaa2a30">5.1. Setup</a></li>
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<li><a href="#org959d7aa">5.2. Model of the setup</a></li>
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<li><a href="#org8283055">5.3. Quantization Noise</a></li>
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<li><a href="#orga8ab614">5.4. Pre Amplifier noise measurement</a></li>
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<li><a href="#orge67a27a">5.5. PD200 noise measurement</a></li>
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<li><a href="#orgc9e047f">5.6. DAC noise measurement</a></li>
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<li><a href="#orgd156ba1">5.7. Total noise measurement</a></li>
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<li><a href="#org802b093">5.8. 20bits DAC noise measurement</a></li>
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</ul>
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</li>
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<li><a href="#orga87a250">6. Transfer Function measurement</a>
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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="#orgdf952ce">6.2. Maximum Frequency/Voltage to not overload the amplifier</a></li>
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<li><a href="#org05f8a88">6.3. Obtained Transfer Functions</a></li>
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</ul>
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</li>
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<li><a href="#org5f03b6e">7. Conclusion</a></li>
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</ul>
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</div>
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</div>
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<div id="outline-container-orge14df81" class="outline-2">
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<h2 id="orge14df81"><span class="section-number-2">1</span> Introduction</h2>
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<div class="outline-text-2" id="text-1">
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<p>
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The goal of this test bench is to characterize the Voltage amplifier <a href="https://www.piezodrive.com/drivers/pd200-60-watt-voltage-amplifier/">PD200</a> from PiezoDrive.
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</p>
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<p>
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The documentation of the PD200 is accessible <a href="doc/PD200-V7-R1.pdf">here</a>.
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</p>
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<div id="orgea7d2e1" class="figure">
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<p><img src="figs/amplifier_PD200.png" alt="amplifier_PD200.png" />
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</p>
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<p><span class="figure-number">Figure 1: </span>Picture of the PD200 Voltage Amplifier</p>
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</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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<h2 id="orgd794d0c"><span class="section-number-2">2</span> Voltage Amplifier Requirements</h2>
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<div class="outline-text-2" id="text-2">
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<table id="orgfc689c5" border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
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<caption class="t-above"><span class="table-number">Table 1:</span> Requirements for the Voltage Amplifier</caption>
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<colgroup>
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<col class="org-left" />
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<col class="org-center" />
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</colgroup>
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<thead>
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<tr>
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<th scope="col" class="org-left"> </th>
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<th scope="col" class="org-center"><b>Specification</b></th>
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</tr>
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</thead>
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<tbody>
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<tr>
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<td class="org-left">Continuous Current</td>
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<td class="org-center">> 50 [mA]</td>
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</tr>
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<tr>
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<td class="org-left">Output Voltage Noise (1-200Hz)</td>
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<td class="org-center">< 2 [mV rms]</td>
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</tr>
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<tr>
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<td class="org-left">Voltage Input Range</td>
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<td class="org-center">+/- 10 [V]</td>
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</tr>
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<tr>
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<td class="org-left">Voltage Output Range</td>
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<td class="org-center">-20 [V] to 150 [V]</td>
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</tr>
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<tr>
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<td class="org-left">Small signal bandwidth (-3dB)</td>
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<td class="org-center">> 5 [kHz]</td>
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</tr>
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</tbody>
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</table>
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</div>
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</div>
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<div id="outline-container-org79cd976" class="outline-2">
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<h2 id="org79cd976"><span class="section-number-2">3</span> PD200 Expected characteristics</h2>
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<div class="outline-text-2" id="text-3">
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<table id="org6e26b68" border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
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<caption class="t-above"><span class="table-number">Table 2:</span> Characteristics of the PD200</caption>
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<colgroup>
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<col class="org-left" />
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<col class="org-center" />
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<col class="org-center" />
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</colgroup>
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<thead>
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<tr>
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<th scope="col" class="org-left"><b>Characteristics</b></th>
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<th scope="col" class="org-center"><b>Manual</b></th>
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<th scope="col" class="org-center"><b>Specification</b></th>
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</tr>
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</thead>
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<tbody>
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<tr>
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<td class="org-left">Input Voltage Range</td>
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<td class="org-center">+/- 10 [V]</td>
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<td class="org-center">+/- 10 [V]</td>
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</tr>
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<tr>
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<td class="org-left">Output Voltage Range</td>
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<td class="org-center">-50/150 [V]</td>
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<td class="org-center">-20/150 [V]</td>
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</tr>
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<tr>
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<td class="org-left">Gain</td>
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<td class="org-center">20 [V/V]</td>
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<td class="org-center"> </td>
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</tr>
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<tr>
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<td class="org-left">Maximum RMS current</td>
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<td class="org-center">0.9 [A]</td>
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<td class="org-center">> 50 [mA]</td>
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</tr>
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<tr>
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<td class="org-left">Maximum Pulse current</td>
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<td class="org-center">10 [A]</td>
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<td class="org-center"> </td>
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</tr>
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<tr>
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<td class="org-left">Slew Rate</td>
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<td class="org-center">150 [V/us]</td>
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<td class="org-center"> </td>
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</tr>
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<tr>
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<td class="org-left">Noise (10uF load)</td>
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<td class="org-center">0.7 [mV RMS]</td>
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<td class="org-center">< 2 [mV rms]</td>
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</tr>
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<tr>
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<td class="org-left">Small Signal Bandwidth (10uF load)</td>
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<td class="org-center">7.4 [kHz]</td>
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<td class="org-center">> 5 [kHz]</td>
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</tr>
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<tr>
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<td class="org-left">Large Signal Bandwidth (150V, 10uF)</td>
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<td class="org-center">300 [Hz]</td>
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<td class="org-center"> </td>
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</tr>
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</tbody>
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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="#orgaa88e71">2</a>) and the low frequency noise is \(650\,\mu V\,\text{rms}\) (Figure <a href="#orgdcb3bab">3</a>).
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</p>
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<div id="orgaa88e71" class="figure">
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<p><img src="./figs/pd200_expected_small_signal_bandwidth.png" alt="pd200_expected_small_signal_bandwidth.png" />
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</p>
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<p><span class="figure-number">Figure 2: </span>Expected small signal bandwidth</p>
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</div>
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<div id="orgdcb3bab" class="figure">
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<p><img src="figs/pd200_expected_noise.png" alt="pd200_expected_noise.png" />
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</p>
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<p><span class="figure-number">Figure 3: </span>Expected Low frequency noise from 0.03Hz to 20Hz</p>
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</div>
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</div>
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</div>
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<div id="outline-container-org3265b9b" class="outline-2">
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<h2 id="org3265b9b"><span class="section-number-2">4</span> Voltage Amplifier Model</h2>
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<div class="outline-text-2" id="text-4">
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<p>
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The Amplifier is characterized by its dynamics \(G_a(s)\) from voltage inputs \(V_{in}\) to voltage output \(V_{out}\).
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Ideally, the gain from \(V_{in}\) to \(V_{out}\) is constant over a wide frequency band with very small phase drop.
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</p>
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<p>
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It is also characterized by its output noise \(n\).
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This noise is described by its Power Spectral Density.
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</p>
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<p>
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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.
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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 \(10\,\mu F\) capacitor.
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</p>
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<div id="orgbc3695d" class="figure">
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<p><img src="figs/pd200-model-schematic.png" alt="pd200-model-schematic.png" />
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</p>
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<p><span class="figure-number">Figure 4: </span>Model of the voltage amplifier</p>
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</div>
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</div>
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</div>
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<div id="outline-container-orgf27cdb1" class="outline-2">
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<h2 id="orgf27cdb1"><span class="section-number-2">5</span> Noise measurement</h2>
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<div class="outline-text-2" id="text-5">
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<ul class="org-ul">
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<li>Section <a href="#org9d21c0d">5.1</a></li>
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<li>Section <a href="#org6edf2e9">5.2</a></li>
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<li>Section <a href="#org7b5a20a">5.3</a></li>
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<li>Section <a href="#orge4eb592">5.4</a></li>
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<li>Section <a href="#org8909c5d">5.5</a></li>
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<li>Section <a href="#org7739514">5.6</a></li>
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<li>Section <a href="#org1920758">5.7</a></li>
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<li>Section <a href="#orgf336d8b">5.8</a></li>
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</ul>
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</div>
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<div id="outline-container-orgaaa2a30" class="outline-3">
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<h3 id="orgaaa2a30"><span class="section-number-3">5.1</span> Setup</h3>
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<div class="outline-text-3" id="text-5-1">
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<p>
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<a id="org9d21c0d"></a>
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</p>
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<div class="note" id="org4394587">
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<p>
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Here are the documentation of the equipment used for this test bench:
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</p>
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<ul class="org-ul">
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<li>Voltage Amplifier <a href="doc/PD200-V7-R1.pdf">PD200</a></li>
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<li>Load Capacitor <a href="doc/0900766b815ea422.pdf">EPCOS 10uF Multilayer Ceramic Capacitor</a></li>
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<li>Low Noise Voltage Amplifier <a href="doc/egg-5113-preamplifier.pdf">EG&G 5113</a></li>
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<li>Speedgoat ADC <a href="doc/IO131-OEM-Datasheet.pdf">IO313</a></li>
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</ul>
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</div>
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<p>
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The output noise of the voltage amplifier PD200 is foreseen to be around 1mV rms in a bandwidth from DC to 1MHz.
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If we suppose a white noise, this correspond to an amplitude spectral density:
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</p>
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\begin{equation}
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|
\phi_{n} \approx \frac{1\,mV}{\sqrt{1\,MHz}} = 1 \frac{\mu V}{\sqrt{Hz}}
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\end{equation}
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<p>
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The RMS noise begin very small compare to the ADC resolution, we must amplify the noise before digitizing the signal.
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The added noise of the instrumentation amplifier should be much smaller than the noise of the PD200.
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We use the amplifier EG&G 5113 that has a noise of \(\approx 4 nV/\sqrt{Hz}\) referred to its input which is much smaller than the noise induced by the PD200.
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</p>
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<p>
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The gain of the low-noise amplifier can be increased until the full range of the ADC is used.
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This gain should be around 1000.
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</p>
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<div id="org7800d75" class="figure">
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<p><img src="figs/setup-noise-measurement.png" alt="setup-noise-measurement.png" />
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</p>
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<p><span class="figure-number">Figure 5: </span>Schematic of the test bench to measure the Power Spectral Density of the Voltage amplifier noise \(n\)</p>
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</div>
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<p>
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A low pass filter at 10kHz can be included in the EG&G amplifier in order to limit aliasing.
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An high pass filter at low frequency can be added if there is a problem of large offset.
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</p>
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</div>
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</div>
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<div id="outline-container-org959d7aa" class="outline-3">
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<h3 id="org959d7aa"><span class="section-number-3">5.2</span> Model of the setup</h3>
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<div class="outline-text-3" id="text-5-2">
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<p>
|
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<a id="org6edf2e9"></a>
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</p>
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|
|
<p>
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As shown in Figure <a href="#orgb873ca1">6</a>, there are 4 equipment involved in the measurement:
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</p>
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<ul class="org-ul">
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|
<li>a Digital to Analog Convert (DAC)</li>
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<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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|
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<div id="orgb873ca1" class="figure">
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<p><img src="figs/noise_meas_procedure.png" alt="noise_meas_procedure.png" />
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|
</p>
|
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<p><span class="figure-number">Figure 6: </span>Sources of noise in the experimental setup</p>
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</div>
|
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</div>
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</div>
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<div id="outline-container-org8283055" class="outline-3">
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<h3 id="org8283055"><span class="section-number-3">5.3</span> Quantization Noise</h3>
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<div class="outline-text-3" id="text-5-3">
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<p>
|
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<a id="org7b5a20a"></a>
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</p>
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<p>
|
|
The quantization noise is something that can be predicted.
|
|
The Amplitude Spectral Density of the quantization noise of an ADC/DAC is equal to:
|
|
</p>
|
|
\begin{equation}
|
|
\Gamma_q(\omega) = \frac{q}{\sqrt{12 f_s}}
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\end{equation}
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<p>
|
|
with:
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|
</p>
|
|
<ul class="org-ul">
|
|
<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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<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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<p>
|
|
The obtained Amplitude Spectral Density is <code>6.2294e-07</code> \(V/\sqrt{Hz}\).
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</p>
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</div>
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</div>
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<div id="outline-container-orga8ab614" class="outline-3">
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<h3 id="orga8ab614"><span class="section-number-3">5.4</span> Pre Amplifier noise measurement</h3>
|
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<div class="outline-text-3" id="text-5-4">
|
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<p>
|
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<a id="orge4eb592"></a>
|
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</p>
|
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<p>
|
|
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.
|
|
Then, the gain of the amplifier is increase until the measured signal on the ADC is much larger than the quantization noise.
|
|
</p>
|
|
|
|
<p>
|
|
The Amplitude Spectral Density \(\Gamma_n(\omega)\) of the measured signal \(n\) is computed.
|
|
Finally, the Amplitude Spectral Density of \(n_a\) can be computed taking into account the gain of the pre-amplifier:
|
|
</p>
|
|
\begin{equation}
|
|
\Gamma_{n_a}(\omega) \approx \frac{\Gamma_n(\omega)}{|G_a(\omega)|}
|
|
\end{equation}
|
|
|
|
<p>
|
|
This is true if the quantization noise \(\Gamma_{q_{ad}}\) is negligible.
|
|
</p>
|
|
|
|
|
|
<div id="org5debea0" class="figure">
|
|
<p><img src="figs/noise_measure_setup_preamp.png" alt="noise_measure_setup_preamp.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 7: </span>Sources of noise in the experimental setup</p>
|
|
</div>
|
|
|
|
<p>
|
|
The gain of the low noise amplifier is set to <code>50000</code>.
|
|
</p>
|
|
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab"><span class="org-comment">% Hanning window</span>
|
|
win = hanning(ceil(0.5<span class="org-type">/</span>Ts));
|
|
|
|
<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="#org865b855">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="org865b855" 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-orge67a27a" class="outline-3">
|
|
<h3 id="orge67a27a"><span class="section-number-3">5.5</span> PD200 noise measurement</h3>
|
|
<div class="outline-text-3" id="text-5-5">
|
|
<p>
|
|
<a id="org8909c5d"></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="orgcfcd12c" 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="#orgb61b700">10</a>.
|
|
It is very similar to the one specified in the datasheet in Figure <a href="#orgdcb3bab">3</a>.
|
|
</p>
|
|
|
|
<div id="orgb61b700" class="figure">
|
|
<p><img src="figs/pd200_noise_time_lpf.png" alt="pd200_noise_time_lpf.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 10: </span>Measured low frequency noise of the PD200 from 0.01Hz to 20Hz</p>
|
|
</div>
|
|
|
|
<p>
|
|
The obtained RMS and peak to peak values of the measured noises are shown in Table <a href="#orgf452b35">3</a>.
|
|
</p>
|
|
<table id="orgf452b35" border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
|
|
<caption class="t-above"><span class="table-number">Table 3:</span> RMS and Peak to Peak measured low frequency noise (0.01Hz to 20Hz)</caption>
|
|
|
|
<colgroup>
|
|
<col class="org-left" />
|
|
|
|
<col class="org-right" />
|
|
|
|
<col class="org-right" />
|
|
</colgroup>
|
|
<thead>
|
|
<tr>
|
|
<th scope="col" class="org-left"> </th>
|
|
<th scope="col" class="org-right"><b>RMS [uV]</b></th>
|
|
<th scope="col" class="org-right"><b>Peak to Peak [mV]</b></th>
|
|
</tr>
|
|
</thead>
|
|
<tbody>
|
|
<tr>
|
|
<td class="org-left">Specification [10uF]</td>
|
|
<td class="org-right">714.0</td>
|
|
<td class="org-right">4.3</td>
|
|
</tr>
|
|
|
|
<tr>
|
|
<td class="org-left">PD200_1</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">767.6</td>
|
|
<td class="org-right">3.5</td>
|
|
</tr>
|
|
|
|
<tr>
|
|
<td class="org-left">PD200_3</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">615.7</td>
|
|
<td class="org-right">3.5</td>
|
|
</tr>
|
|
|
|
<tr>
|
|
<td class="org-left">PD200_5</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">473.2</td>
|
|
<td class="org-right">2.7</td>
|
|
</tr>
|
|
|
|
<tr>
|
|
<td class="org-left">PD200_7</td>
|
|
<td class="org-right">423.1</td>
|
|
<td class="org-right">2.3</td>
|
|
</tr>
|
|
</tbody>
|
|
</table>
|
|
|
|
<p>
|
|
The Amplitude Spectral Density of the measured noise is now computed and shown in Figure <a href="#orgf1636b6">11</a>.
|
|
</p>
|
|
|
|
<div id="orgf1636b6" class="figure">
|
|
<p><img src="figs/asd_noise_3uF_warmup.png" alt="asd_noise_3uF_warmup.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 11: </span>Amplitude Spectral Density of the measured noise</p>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-orgc9e047f" class="outline-3">
|
|
<h3 id="orgc9e047f"><span class="section-number-3">5.6</span> DAC noise measurement</h3>
|
|
<div class="outline-text-3" id="text-5-6">
|
|
<p>
|
|
<a id="org7739514"></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="org0f39f6d" class="figure">
|
|
<p><img src="figs/noise_measure_setup_dac.png" alt="noise_measure_setup_dac.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 12: </span>Sources of noise in the experimental setup</p>
|
|
</div>
|
|
|
|
|
|
<div id="org531aca4" class="figure">
|
|
<p><img src="figs/asd_noise_dac.png" alt="asd_noise_dac.png" />
|
|
</p>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-orgd156ba1" class="outline-3">
|
|
<h3 id="orgd156ba1"><span class="section-number-3">5.7</span> Total noise measurement</h3>
|
|
<div class="outline-text-3" id="text-5-7">
|
|
<p>
|
|
<a id="org1920758"></a>
|
|
</p>
|
|
|
|
<p>
|
|
Let’s now analyze the measurement of the setup in Figure <a href="#orgb873ca1">6</a>.
|
|
</p>
|
|
|
|
<p>
|
|
The PSD of the measured noise is computed and the ASD is shown in Figure <a href="#orge63d88b">14</a>.
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">win = hanning(ceil(0.5<span class="org-type">/</span>Ts));
|
|
|
|
<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, 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="orge63d88b" class="figure">
|
|
<p><img src="figs/asd_noise_tot.png" alt="asd_noise_tot.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 14: </span>Amplitude Spectral Density of the measured noise and of the individual sources of noise</p>
|
|
</div>
|
|
|
|
<div class="important" id="orge883835">
|
|
<p>
|
|
The output noise of the PD200 amplifier is limited by the noise of the DAC.
|
|
Having a DAC with lower noise could lower the output noise of the PD200.
|
|
SSI2V DACs will be used to verify that.
|
|
</p>
|
|
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org802b093" class="outline-3">
|
|
<h3 id="org802b093"><span class="section-number-3">5.8</span> 20bits DAC noise measurement</h3>
|
|
<div class="outline-text-3" id="text-5-8">
|
|
<p>
|
|
<a id="orgf336d8b"></a>
|
|
Let’s now measure the noise of another DAC called the “SSI2V” (<a href="doc/[SSI2V]Datasheet.pdf">doc</a>).
|
|
It is a 20bits DAC with an output of +/-10.48 V and a very low noise.
|
|
</p>
|
|
|
|
<p>
|
|
The measurement setup is the same as the one in Figure <a href="#org0f39f6d">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="#orge2b8a18">15</a> and compared with the noise of the 16bits DAC.
|
|
It is shown to be much smaller (~1 order of magnitude).
|
|
</p>
|
|
|
|
|
|
<div id="orge2b8a18" class="figure">
|
|
<p><img src="figs/asd_ssi2v_noise.png" alt="asd_ssi2v_noise.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 15: </span>Amplitude Spectral Density of the SSI2V DAC’s noise</p>
|
|
</div>
|
|
|
|
<div class="important" id="org665f8e4">
|
|
<p>
|
|
Using the SSI2V as the DAC with the PD200 should give much better noise output than using the 16bits DAC.
|
|
The limiting factor should then be the noise of the PD200 itself.
|
|
</p>
|
|
|
|
</div>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-orga87a250" class="outline-2">
|
|
<h2 id="orga87a250"><span class="section-number-2">6</span> Transfer Function measurement</h2>
|
|
<div class="outline-text-2" id="text-6">
|
|
</div>
|
|
<div id="outline-container-org2b82bca" class="outline-3">
|
|
<h3 id="org2b82bca"><span class="section-number-3">6.1</span> Setup</h3>
|
|
<div class="outline-text-3" id="text-6-1">
|
|
<p>
|
|
In order to measure the transfer function from the input voltage \(V_{in}\) to the output voltage \(V_{out}\), the test bench shown in Figure <a href="#org45f7f26">16</a> is used.
|
|
</p>
|
|
|
|
<div class="note" id="orgaa21e8d">
|
|
<p>
|
|
Here are the documentation of the equipment used for this test bench:
|
|
</p>
|
|
<ul class="org-ul">
|
|
<li>Voltage Amplifier <a href="doc/PD200-V7-R1.pdf">PD200</a></li>
|
|
<li>Load Capacitor <a href="doc/0900766b815ea422.pdf">EPCOS 10uF Multilayer Ceramic Capacitor</a></li>
|
|
<li>Speedgoat DAC/ADC <a href="doc/IO131-OEM-Datasheet.pdf">IO313</a></li>
|
|
</ul>
|
|
|
|
</div>
|
|
|
|
<p>
|
|
For this measurement, the sampling frequency of the Speedgoat ADC should be as high as possible.
|
|
</p>
|
|
|
|
|
|
<div id="org45f7f26" class="figure">
|
|
<p><img src="figs/setup-dynamics-measurement.png" alt="setup-dynamics-measurement.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 16: </span>Schematic of the test bench to estimate the dynamics from voltage input \(V_{in}\) to voltage output \(V_{out}\)</p>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-orgdf952ce" class="outline-3">
|
|
<h3 id="orgdf952ce"><span class="section-number-3">6.2</span> Maximum Frequency/Voltage to not overload the amplifier</h3>
|
|
<div class="outline-text-3" id="text-6-2">
|
|
<p>
|
|
The maximum current is 1A [rms] which corresponds to 0.7A in amplitude of the sin wave.
|
|
</p>
|
|
|
|
<p>
|
|
The impedance of the capacitance is:
|
|
\[ Z_C(\omega) = \frac{1}{jC\omega} \]
|
|
</p>
|
|
|
|
<p>
|
|
Therefore the relation between the output current amplitude and the output voltage amplitude for sinusoidal waves of frequency \(\omega\):
|
|
\[ V_{out} = \frac{1}{C\omega} I_{out} \]
|
|
</p>
|
|
|
|
<p>
|
|
Moreover, there is a gain of 20 between the input voltage and the output voltage:
|
|
\[ 20 V_{in} = \frac{1}{C\omega} I_{out} \]
|
|
</p>
|
|
|
|
<p>
|
|
For a specified voltage input amplitude \(V_{in}\), the maximum frequency at which the output current reaches its maximum value is:
|
|
\[ \omega_{\text{max}} = \frac{1}{20 C V_{in}} I_{out,\text{max}} \]
|
|
</p>
|
|
|
|
<p>
|
|
\(\omega_max\) as a function of \(V_{in}\) is shown in Figure <a href="#orga03c37f">17</a>.
|
|
</p>
|
|
|
|
|
|
<div id="orga03c37f" class="figure">
|
|
<p><img src="figs/max_frequency_voltage.png" alt="max_frequency_voltage.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 17: </span>Maximum frequency as a function of the excitation voltage amplitude</p>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org05f8a88" class="outline-3">
|
|
<h3 id="org05f8a88"><span class="section-number-3">6.3</span> Obtained Transfer Functions</h3>
|
|
<div class="outline-text-3" id="text-6-3">
|
|
<p>
|
|
Several identifications using sweep sin were performed with input voltage amplitude ranging from 0.1V to 4V.
|
|
</p>
|
|
|
|
<p>
|
|
The obtained frequency response functions are shown in Figure <a href="#org16bc426">18</a>.
|
|
As the input voltage increases, the voltage drop is increasing.
|
|
</p>
|
|
|
|
|
|
<div id="org16bc426" class="figure">
|
|
<p><img src="figs/pd200_tf_voltage.png" alt="pd200_tf_voltage.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 18: </span>Transfer function for the PD200 amplitude between \(V_{in}\) and \(V_{out}\) for multiple voltage amplitudes</p>
|
|
</div>
|
|
|
|
<p>
|
|
The small signal transfer function of the amplifier can be approximated by a first order low pass filter.
|
|
</p>
|
|
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">Gp = 19.95<span class="org-type">/</span>(1 <span class="org-type">+</span> s<span class="org-type">/</span>2<span class="org-type">/</span><span class="org-constant">pi</span><span class="org-type">/</span>35e3);
|
|
</pre>
|
|
</div>
|
|
|
|
<p>
|
|
The comparison from the model and measurements are shown in Figure <a href="#org1ae50fe">19</a>.
|
|
</p>
|
|
|
|
|
|
<div id="org1ae50fe" class="figure">
|
|
<p><img src="figs/tf_pd200_model.png" alt="tf_pd200_model.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 19: </span>Comparison of the model transfer function and the measured frequency response function</p>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org5f03b6e" class="outline-2">
|
|
<h2 id="org5f03b6e"><span class="section-number-2">7</span> Conclusion</h2>
|
|
<div class="outline-text-2" id="text-7">
|
|
<table id="org039c233" border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
|
|
<caption class="t-above"><span class="table-number">Table 4:</span> Measured characteristics, Manual characterstics and specified ones</caption>
|
|
|
|
<colgroup>
|
|
<col class="org-left" />
|
|
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<col class="org-center" />
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<col class="org-center" />
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|
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<col class="org-center" />
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</colgroup>
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<thead>
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<tr>
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<th scope="col" class="org-left"><b>Characteristics</b></th>
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<th scope="col" class="org-center"><b>Measurement</b></th>
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<th scope="col" class="org-center"><b>Manual</b></th>
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<th scope="col" class="org-center"><b>Specification</b></th>
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</tr>
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</thead>
|
|
<tbody>
|
|
<tr>
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|
<td class="org-left">Input Voltage Range</td>
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|
<td class="org-center">-</td>
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|
<td class="org-center">+/- 10 [V]</td>
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|
<td class="org-center">+/- 10 [V]</td>
|
|
</tr>
|
|
|
|
<tr>
|
|
<td class="org-left">Output Voltage Range</td>
|
|
<td class="org-center">-</td>
|
|
<td class="org-center">-50/150 [V]</td>
|
|
<td class="org-center">-20/150 [V]</td>
|
|
</tr>
|
|
|
|
<tr>
|
|
<td class="org-left">Gain</td>
|
|
<td class="org-center"> </td>
|
|
<td class="org-center">20 [V/V]</td>
|
|
<td class="org-center">-</td>
|
|
</tr>
|
|
|
|
<tr>
|
|
<td class="org-left">Maximum RMS current</td>
|
|
<td class="org-center"> </td>
|
|
<td class="org-center">0.9 [A]</td>
|
|
<td class="org-center">> 50 [mA]</td>
|
|
</tr>
|
|
|
|
<tr>
|
|
<td class="org-left">Maximum Pulse current</td>
|
|
<td class="org-center"> </td>
|
|
<td class="org-center">10 [A]</td>
|
|
<td class="org-center">-</td>
|
|
</tr>
|
|
|
|
<tr>
|
|
<td class="org-left">Slew Rate</td>
|
|
<td class="org-center"> </td>
|
|
<td class="org-center">150 [V/us]</td>
|
|
<td class="org-center">-</td>
|
|
</tr>
|
|
|
|
<tr>
|
|
<td class="org-left">Noise (10uF load)</td>
|
|
<td class="org-center"> </td>
|
|
<td class="org-center">0.7 [mV RMS]</td>
|
|
<td class="org-center">< 2 [mV rms]</td>
|
|
</tr>
|
|
|
|
<tr>
|
|
<td class="org-left">Small Signal Bandwidth (10uF load)</td>
|
|
<td class="org-center"> </td>
|
|
<td class="org-center">7.4 [kHz]</td>
|
|
<td class="org-center">> 5 [kHz]</td>
|
|
</tr>
|
|
|
|
<tr>
|
|
<td class="org-left">Large Signal Bandwidth (150V, 10uF)</td>
|
|
<td class="org-center"> </td>
|
|
<td class="org-center">300 [Hz]</td>
|
|
<td class="org-center">-</td>
|
|
</tr>
|
|
</tbody>
|
|
</table>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
<div id="postamble" class="status">
|
|
<p class="author">Author: Dehaeze Thomas</p>
|
|
<p class="date">Created: 2021-01-23 sam. 15:38</p>
|
|
</div>
|
|
</body>
|
|
</html>
|