1378 lines
47 KiB
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1378 lines
47 KiB
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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="#orge6954b3">1. Requirements PD200 Expected characteristics</a></li>
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<li><a href="#org83b63f6">2. Voltage Amplifier Model</a></li>
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<li><a href="#org607e21c">3. Transfer Function measurement</a>
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<ul>
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<li><a href="#orgce03501">3.1. Setup</a></li>
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<li><a href="#org685f229">3.2. Maximum Frequency/Voltage to not overload the amplifier</a></li>
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<li><a href="#org648d305">3.3. Small Signal Bandwidth</a></li>
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<li><a href="#orgd8b4beb">3.4. Model of the amplifier small signal dynamics</a></li>
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<li><a href="#org569c3b2">3.5. Large Signal Bandwidth</a></li>
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</ul>
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</li>
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<li><a href="#org1d6b724">4. Noise measurement</a>
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<ul>
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<li><a href="#orgd488faa">4.1. Measurement Setup</a></li>
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<li><a href="#orgb4062f5">4.2. Model of the setup</a></li>
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<li><a href="#org9ebdb8c">4.3. Quantization Noise of the ADC</a></li>
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<li><a href="#orgb22f8b9">4.4. EG&G - Amplifier noise measurement</a></li>
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<li><a href="#org9288e06">4.5. Femto - Amplifier noise measurement</a></li>
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<li><a href="#org5cafd0e">4.6. PD200 - Low frequency noise measurement</a></li>
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<li><a href="#orge3325ea">4.7. PD200 - High frequency noise measurement</a></li>
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<li><a href="#org84b301f">4.8. 16bits DAC noise measurement</a></li>
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<li><a href="#org9b88cef">4.9. Noise of the full setup with 16bits DAC</a></li>
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<li><a href="#orgdbba426">4.10. 20bits DAC noise measurement</a></li>
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<li><a href="#org130febd">4.11. Noise of the full setup with 20bits DAC</a></li>
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<li><a href="#org3cb50e3">4.12. PD200 Amplifier noise model</a></li>
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</ul>
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</li>
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<li><a href="#org1171b27">5. Comparison to other commercial amplifiers</a>
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<ul>
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<li><a href="#orgb368d4e">5.1. Introduction</a></li>
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<li><a href="#org4c15dc1">5.2. Transfer functions</a></li>
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<li><a href="#orgf6b59a0">5.3. Noise Characteristics</a></li>
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</ul>
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</li>
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<li><a href="#org0b600f7">6. Conclusion</a></li>
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</ul>
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</div>
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</div>
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<hr>
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<p>This report is also available as a <a href="./test-bench-pd200.pdf">pdf</a>.</p>
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<hr>
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<p>
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\clearpage
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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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</p>
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<p>
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This document is organized as follows:
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</p>
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<ul class="org-ul">
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<li>Section <a href="#orgf25ecff">1</a>: the requirements for the amplifiers and the characteristics of the PD200 amplifiers as advertise in the datasheet are listed.</li>
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<li>Section <a href="#org47bcaab">2</a>: a very simple amplifier model consisting of a transfer function and a noise source is described.</li>
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<li>Section <a href="#orgee7e444">3</a>: the transfer function from input voltage to output voltage is identified.</li>
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<li>Section <a href="#org34cbbb6">4</a>: the power spectral density of the amplifier’s noise is measured</li>
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<li>Section <a href="#orge72631c">5</a>: the characteristics of the PD200 amplifier are compared to the E.505 amplifier from PI and to the LA75 from cedrat</li>
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<li>Section <a href="#org127b80a">6</a>: the measured characteristics of the PD200 amplifier are compared with the requirements</li>
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</ul>
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<div id="outline-container-orge6954b3" class="outline-2">
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<h2 id="orge6954b3"><span class="section-number-2">1</span> Requirements PD200 Expected characteristics</h2>
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<div class="outline-text-2" id="text-1">
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<p>
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<a id="orgf25ecff"></a>
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</p>
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<p>
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A picture of the PD200 amplifier is shown in Figure <a href="#org90b6ed8">1</a>.
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</p>
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<div id="org90b6ed8" 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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<p>
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The specifications as well as the amplifier characteristics as shown in the datasheet are summarized in Table <a href="#org72844fa">1</a>.
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</p>
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<table id="org72844fa" 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> Characteristics of the PD200 compared with the specifications</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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The most important characteristics are the large (small signal) bandwidth > 5 [kHz] and the small noise (< 2 [mV RMS]).
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</p>
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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="#org530392d">2</a>) and the low frequency noise is \(650\,\mu V\,\text{rms}\) (Figure <a href="#org7985862">3</a>).
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</p>
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<p>
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These two characteristics are respectively measured in Section <a href="#orgee7e444">3</a> and Section <a href="#org34cbbb6">4</a>.
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</p>
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<div id="org530392d" 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="org7985862" 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-org83b63f6" class="outline-2">
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<h2 id="org83b63f6"><span class="section-number-2">2</span> Voltage Amplifier Model</h2>
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<div class="outline-text-2" id="text-2">
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<p>
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<a id="org47bcaab"></a>
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</p>
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<p>
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The Amplifier is characterized by its dynamics \(G_p(s)\) 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 <b>input</b> noise \(n\).
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</p>
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<p>
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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 input noise.
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</p>
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<p>
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As \(G_p\) depends on the load capacitance, it should be measured when loading the amplifier with a \(10\,\mu F\) capacitor.
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</p>
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<div id="orgd731a59" 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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<p>
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The input noise of the amplifier \(n\) can be further modeled by shaping a white noise with unitary PSD \(\tilde{n}\) with a transfer function \(G_n(s)\) as shown in Figure <a href="#orgca97d8f">6</a>.
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</p>
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<p>
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The Amplitude Spectral Density \(\Gamma_n\) is then:
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</p>
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\begin{equation}
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\Gamma_n(\omega) = |G_n(j\omega)| \Gamma_{\tilde{n}}(\omega)
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\end{equation}
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<p>
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with \(\Gamma_{\tilde{n}}(\omega) = 1\).
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</p>
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<div id="orgfbf1dc4" class="figure">
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<p><img src="figs/pd200-model-schematic-normalized.png" alt="pd200-model-schematic-normalized.png" />
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</p>
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<p><span class="figure-number">Figure 5: </span>Model of the voltage amplifier with normalized noise input</p>
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</div>
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</div>
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</div>
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<div id="outline-container-org607e21c" class="outline-2">
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<h2 id="org607e21c"><span class="section-number-2">3</span> Transfer Function measurement</h2>
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<div class="outline-text-2" id="text-3">
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<p>
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<a id="orgee7e444"></a>
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</p>
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<p>
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In this section, the transfer function of the PD200 amplifier is measured:
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</p>
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<ul class="org-ul">
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<li>Section <a href="#org1837bc8">3.1</a>: the measurement setup is described</li>
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<li>Section <a href="#org75d58e2">3.2</a>: the maximum sinusoidal excitation frequency is estimated in order to not overload the amplifier</li>
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<li>Section <a href="#orgf98b9f7">3.3</a>: the small signal bandwidth measurement results are shown</li>
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<li>Section <a href="#orgbf0dd97">3.4</a>: a model of the small signal dynamics of the amplifier is obtained</li>
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<li>Section <a href="#org0adfae9">3.5</a>: the amplifier’s transfer function is estimated for several input amplitudes</li>
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</ul>
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</div>
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<div id="outline-container-orgce03501" class="outline-3">
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<h3 id="orgce03501"><span class="section-number-3">3.1</span> Setup</h3>
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<div class="outline-text-3" id="text-3-1">
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<p>
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<a id="org1837bc8"></a>
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</p>
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<p>
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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="#orgca97d8f">6</a> is used.
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</p>
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<div class="note" id="orgde4f5d7">
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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/KEM_F3040_C4G_AXIAL-1104248.pdf">Film Capacitors 600V 10uF 5%</a></li>
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<li>DAC/ADC: <a href="doc/IO131-OEM-Datasheet.pdf">IO313 Speedgoat Interface</a></li>
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</ul>
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</div>
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<p>
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For this measurement, the sampling frequency of the Speedgoat ADC should be as high as possible.
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</p>
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<div id="orgca97d8f" class="figure">
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<p><img src="figs/setup-dynamics-measurement.png" alt="setup-dynamics-measurement.png" />
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</p>
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<p><span class="figure-number">Figure 6: </span>Schematic of the test bench to estimate the dynamics from voltage input \(V_{in}\) to voltage output \(V_{out}\)</p>
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</div>
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</div>
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</div>
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<div id="outline-container-org685f229" class="outline-3">
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<h3 id="org685f229"><span class="section-number-3">3.2</span> Maximum Frequency/Voltage to not overload the amplifier</h3>
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<div class="outline-text-3" id="text-3-2">
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<p>
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<a id="org75d58e2"></a>
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</p>
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<p>
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Then the maximum output current of the amplifier is reached, the amplifier automatically shuts down itself.
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We should then make sure that the output current does not reach this maximum specified current.
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</p>
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<p>
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The maximum current is 1A [rms] which corresponds to 0.7A in amplitude of the sin wave.
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</p>
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<p>
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The impedance of the capacitance is:
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\[ Z_C(\omega) = \frac{1}{jC\omega} \]
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</p>
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<p>
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Therefore the relation between the output current amplitude and the output voltage amplitude for sinusoidal waves of frequency \(\omega\):
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\[ V_{out} = \frac{1}{C\omega} I_{out} \]
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</p>
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<p>
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Moreover, there is a gain of 20 between the input voltage and the output voltage:
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\[ 20 V_{in} = \frac{1}{C\omega} I_{out} \]
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</p>
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<p>
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For a specified voltage input amplitude \(V_{in}\), the maximum frequency at which the output current reaches its maximum value is:
|
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</p>
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\begin{equation}
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\boxed{\omega_{\text{max}} = \frac{1}{20 C V_{in}} I_{out,\text{max}}}
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\end{equation}
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<p>
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with:
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</p>
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<ul class="org-ul">
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<li>\(\omega_{\text{max}}\) the maximum input sinusoidal frequency in Radians per seconds</li>
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<li>\(C\) the load capacitance in Farads</li>
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<li>\(V_{in}\) the input voltage sinusoidal amplitude in Volts</li>
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<li>\(I_{out,\text{max}}\) the specified maximum output current in Amperes</li>
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</ul>
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<p>
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\(\omega_{\text{max}}/2\pi\) as a function of \(V_{in}\) is shown in Figure <a href="#org33f6506">7</a>.
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</p>
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<div id="org33f6506" class="figure">
|
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<p><img src="figs/max_frequency_voltage.png" alt="max_frequency_voltage.png" />
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</p>
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<p><span class="figure-number">Figure 7: </span>Maximum frequency as a function of the excitation voltage amplitude</p>
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</div>
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<p>
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When doing sweep sine excitation, we make sure not to reach this maximum excitation frequency.
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</p>
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</div>
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</div>
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|
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<div id="outline-container-org648d305" class="outline-3">
|
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<h3 id="org648d305"><span class="section-number-3">3.3</span> Small Signal Bandwidth</h3>
|
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<div class="outline-text-3" id="text-3-3">
|
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<p>
|
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<a id="orgf98b9f7"></a>
|
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</p>
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<p>
|
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Here the small signal dynamics of all the 7 PD200 amplifiers are identified.
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</p>
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<p>
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A (logarithmic) sweep sine excitation voltage is generated by the Speedgoat DAC with an amplitude of 0.1V and a frequency going from 1Hz up to 5kHz.
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</p>
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<p>
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The output voltage of the PD200 amplifier is measured thanks to the monitor voltage of the PD200 amplifier.
|
|
The input voltage of the PD200 amplifier (the generated voltage by the DAC) is measured with another ADC of the Speedgoat.
|
|
This way, the time delay related to the ADC will not be apparent in the results.
|
|
</p>
|
|
|
|
<p>
|
|
The obtained transfer functions from \(V_{in}\) to \(V_{out}\) are shown in Figure <a href="#orgd92947a">8</a>.
|
|
</p>
|
|
|
|
<div id="orgd92947a" class="figure">
|
|
<p><img src="figs/pd200_small_signal_tf.png" alt="pd200_small_signal_tf.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 8: </span>Identified dynamics from input voltage to output voltage</p>
|
|
</div>
|
|
|
|
<p>
|
|
We can see the very well matching between all the 7 amplifiers.
|
|
The amplitude is constant over a wide frequency band and the phase drop is limited to less than 1 degree up to 500Hz.
|
|
</p>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-orgd8b4beb" class="outline-3">
|
|
<h3 id="orgd8b4beb"><span class="section-number-3">3.4</span> Model of the amplifier small signal dynamics</h3>
|
|
<div class="outline-text-3" id="text-3-4">
|
|
<p>
|
|
<a id="orgbf0dd97"></a>
|
|
</p>
|
|
|
|
<p>
|
|
The identified dynamics in Figure <a href="#orgd92947a">8</a> can very well be modeled this dynamics with a first order low pass filter (even a constant could work fine).
|
|
</p>
|
|
|
|
<p>
|
|
Below is the defined transfer function \(G_p(s)\).
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">Gp = 20<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>25e3);
|
|
</pre>
|
|
</div>
|
|
|
|
<p>
|
|
Comparison of the model with the identified dynamics is shown in Figure <a href="#orge725e7e">9</a>.
|
|
</p>
|
|
|
|
<div id="orge725e7e" class="figure">
|
|
<p><img src="figs/pd200_small_signal_tf_model.png" alt="pd200_small_signal_tf_model.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 9: </span>Bode plot of \(G_d(s)\) as well as the identified transfer functions of all 7 amplifiers</p>
|
|
</div>
|
|
|
|
<p>
|
|
And finally this model is saved.
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">save(<span class="org-string">'mat/pd200_model.mat'</span>, <span class="org-string">'Gp'</span>);
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org569c3b2" class="outline-3">
|
|
<h3 id="org569c3b2"><span class="section-number-3">3.5</span> Large Signal Bandwidth</h3>
|
|
<div class="outline-text-3" id="text-3-5">
|
|
<p>
|
|
<a id="org0adfae9"></a>
|
|
</p>
|
|
|
|
<p>
|
|
The PD200 amplifiers will most likely not be used for large signals, but it is still nice to see how the amplifier dynamics is changing with the input voltage amplitude.
|
|
</p>
|
|
|
|
<p>
|
|
Several identifications using sweep sin were performed with input voltage amplitude ranging from 0.1V to 4V.
|
|
The maximum excitation frequency for each amplitude was limited from the estimation in Section <a href="#org75d58e2">3.2</a>.
|
|
</p>
|
|
|
|
<p>
|
|
The obtained transfer functions for the different excitation amplitudes are shown in Figure <a href="#orgf601de5">10</a>.
|
|
It is shown that the input voltage amplitude does not affect that much the amplifier dynamics.
|
|
</p>
|
|
|
|
|
|
<div id="orgf601de5" class="figure">
|
|
<p><img src="figs/pd200_large_signal_tf.png" alt="pd200_large_signal_tf.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 10: </span>Amplifier dynamics for several input voltage amplitudes</p>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org1d6b724" class="outline-2">
|
|
<h2 id="org1d6b724"><span class="section-number-2">4</span> Noise measurement</h2>
|
|
<div class="outline-text-2" id="text-4">
|
|
<p>
|
|
<a id="org34cbbb6"></a>
|
|
</p>
|
|
<p>
|
|
In this part, the goal is to measure the noise of the PD200 voltage amplifier.
|
|
This noise can be separated into an input voltage noise and an input current noise.
|
|
However, the input voltage noise has much larger effects than the input current noise and we will only try to measure the input voltage noise.
|
|
</p>
|
|
|
|
|
|
<p>
|
|
In section <a href="#org01b36e2">4.1</a>, the measurement setup is described and a model (block diagram) of the setup is given in section <a href="#org2b73965">4.2</a>.
|
|
</p>
|
|
|
|
<p>
|
|
Then, the noise contribution of each element is measured:
|
|
</p>
|
|
<ul class="org-ul">
|
|
<li>Section <a href="#orga357b84">4.3</a>: the quantization noise of the ADC is estimated</li>
|
|
<li>Sections <a href="#orgbd7ef58">4.4</a> and <a href="#org35ce1b8">4.5</a>: the noise of the low-noise amplifiers are estimated</li>
|
|
<li>Sections <a href="#org866a734">4.6</a> and <a href="#org9016b5f">4.7</a>:: the input voltage noise of the PD200 amplifier is estimated</li>
|
|
<li>Section <a href="#org465fa3c">4.8</a>: the output noise of the DAC is measured</li>
|
|
<li>Section <a href="#org3004c04">4.9</a>: the noise of the full measurement chain (DAC to PD200 to pre-amplifier to ADC) is measured and it is found that the DAC is the main source of noise</li>
|
|
<li>Section <a href="#org3a5b9d6">4.10</a>: the noise of an 20bits DAC is measured</li>
|
|
<li>Section <a href="#orgae77708">4.11</a>: it is shown if using the 20bits DAC could lower the overall noise of the setup</li>
|
|
</ul>
|
|
|
|
<p>
|
|
Finally in section <a href="#org3a64053">4.12</a>, a model of the PD200 amplifier’s noise is developed.
|
|
</p>
|
|
|
|
<div class="note" id="org6137567">
|
|
<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/KEM_F3040_C4G_AXIAL-1104248.pdf">Film Capacitors 600V 10uF 5%</a></li>
|
|
<li>Low Noise Voltage Amplifiers <a href="doc/egg-5113-preamplifier.pdf">EG&G 5113</a> and <a href="doc/de-dlpva-100-b.pdf">Femto DLPVA</a></li>
|
|
<li>ADC: <a href="doc/IO131-OEM-Datasheet.pdf">IO313 Speedgoat card</a></li>
|
|
<li>16bits DAC: <a href="doc/IO131-OEM-Datasheet.pdf">IO313 Speedgoat card</a></li>
|
|
<li>20bits DAC: <a href="doc/SSI2V_Datasheet.pdf">SSI2V</a></li>
|
|
</ul>
|
|
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-orgd488faa" class="outline-3">
|
|
<h3 id="orgd488faa"><span class="section-number-3">4.1</span> Measurement Setup</h3>
|
|
<div class="outline-text-3" id="text-4-1">
|
|
<p>
|
|
<a id="org01b36e2"></a>
|
|
</p>
|
|
|
|
<p>
|
|
As the output noise of the PD200 voltage amplifier is foreseen to be around 1mV rms in a bandwidth from DC to 1MHz, it is not possible to directly measure it with an ADC.
|
|
We need to amplify the noise before digitizing the signal.
|
|
To do so, we need to use a low noise voltage amplifier with a noise density much smaller than the measured noise of the PD200 amplifier.
|
|
</p>
|
|
|
|
<p>
|
|
Let’s first estimate the noise density of the PD200 amplifier.
|
|
If we suppose a white noise, this correspond to an amplitude spectral density:
|
|
</p>
|
|
\begin{equation}
|
|
\Gamma_{n}(\omega) \approx \frac{1\,mV}{\sqrt{1\,MHz}} = 1 \frac{\mu V}{\sqrt{Hz}}
|
|
\end{equation}
|
|
|
|
<p>
|
|
The input noise of the instrumentation amplifier should be then much smaller than the output noise of the PD200.
|
|
We will use either the amplifier EG&G 5113 that has a noise of \(\approx 4 nV/\sqrt{Hz}\) referred to its input or the Femto DLPVA amplifier with an input noise of \(\approx 3nV/\sqrt{Hz}\).
|
|
</p>
|
|
|
|
<p>
|
|
The gain of the low-noise amplifier is then increased until the full range of the ADC is used.
|
|
This gain should be around 1000 (60dB).
|
|
</p>
|
|
|
|
<p>
|
|
A representation of the measurement bench is shown in Figure <a href="#org8223e35">11</a>.
|
|
</p>
|
|
|
|
<p>
|
|
Note that it is quite important to load the amplifier with the “Load Box” including a \(10\,\mu F\) capacitor as the (high frequency) noise of the amplifier depends on the actual load being used.
|
|
</p>
|
|
|
|
|
|
<div id="org8223e35" class="figure">
|
|
<p><img src="figs/setup-noise-measurement.png" alt="setup-noise-measurement.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 11: </span>Schematic of the test bench to measure the Power Spectral Density of the Voltage amplifier noise \(n\)</p>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-orgb4062f5" class="outline-3">
|
|
<h3 id="orgb4062f5"><span class="section-number-3">4.2</span> Model of the setup</h3>
|
|
<div class="outline-text-3" id="text-4-2">
|
|
<p>
|
|
<a id="org2b73965"></a>
|
|
</p>
|
|
|
|
<p>
|
|
As shown in Figure <a href="#org0e38e86">12</a>, there are 4 elements involved in the measurement:
|
|
</p>
|
|
<ul class="org-ul">
|
|
<li>a Digital to Analog Convert (DAC)</li>
|
|
<li>the Voltage amplifier to be measured with a gain of 20 (PD200)</li>
|
|
<li>a low noise voltage amplifier with a variable gain and integrated low pass filters and high pass filters</li>
|
|
<li>an Analog to Digital Converter (ADC)</li>
|
|
</ul>
|
|
|
|
<p>
|
|
Each of these equipment has some noise:
|
|
</p>
|
|
<ul class="org-ul">
|
|
<li>\(q_{da}\): quantization noise of the DAC</li>
|
|
<li>\(n_{da}\): output noise of the DAC</li>
|
|
<li>\(n_p\): input noise of the PD200 (what we wish to characterize)</li>
|
|
<li>\(n_a\): input noise of the pre-amplifier</li>
|
|
<li>\(q_{ad}\): quantization noise of the ADC</li>
|
|
</ul>
|
|
|
|
|
|
<div id="org0e38e86" class="figure">
|
|
<p><img src="figs/noise_meas_procedure.png" alt="noise_meas_procedure.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 12: </span>Sources of noise in the experimental setup</p>
|
|
</div>
|
|
|
|
<p>
|
|
In the next sections, we wish to measure all these sources of noise and make sure that we can effectively characterize the noise \(n_p\) of the PD200 amplifier.
|
|
</p>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org9ebdb8c" class="outline-3">
|
|
<h3 id="org9ebdb8c"><span class="section-number-3">4.3</span> Quantization Noise of the ADC</h3>
|
|
<div class="outline-text-3" id="text-4-3">
|
|
<p>
|
|
<a id="orga357b84"></a>
|
|
</p>
|
|
|
|
<p>
|
|
The quantization noise is something that can be predicted from the sampling frequency and the quantization of the ADC.
|
|
Indeed, 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}}
|
|
\end{equation}
|
|
<p>
|
|
with:
|
|
</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>
|
|
<li>\(\Delta V\) is the full range of the ADC in [V]</li>
|
|
<li>\(n\) is the number of bits</li>
|
|
<li>\(f_s\) is the sample frequency in [Hz]</li>
|
|
</ul>
|
|
|
|
<p>
|
|
Let’s estimate that with the ADC used for the measurements:
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab"><span class="org-matlab-cellbreak"><span class="org-comment">%% ADC Quantization noise</span></span>
|
|
adc = struct();
|
|
adc.Delta_V = 20; <span class="org-comment">% [V]</span>
|
|
adc.n = 16; <span class="org-comment">% number of bits</span>
|
|
adc.Fs = 20e3; <span class="org-comment">% [Hz]</span>
|
|
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>
|
|
</pre>
|
|
</div>
|
|
|
|
<p>
|
|
The obtained Amplitude Spectral Density is <code>6.2294e-07</code> \(V/\sqrt{Hz}\).
|
|
</p>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-orgb22f8b9" class="outline-3">
|
|
<h3 id="orgb22f8b9"><span class="section-number-3">4.4</span> EG&G - Amplifier noise measurement</h3>
|
|
<div class="outline-text-3" id="text-4-4">
|
|
<p>
|
|
<a id="orgbd7ef58"></a>
|
|
</p>
|
|
|
|
<p>
|
|
We now wish to measure the noise of the pre-amplifier.
|
|
To do so, the input of the pre-amplifier is shunted with a 50Ohms resistor such that the pre-amplifier input voltage is just its input noise.
|
|
Then, the gain of the amplifier is increased 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}
|
|
|
|
|
|
<div id="org95b8fc9" class="figure">
|
|
<p><img src="figs/noise_measure_setup_preamp.png" alt="noise_measure_setup_preamp.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 13: </span>Sources of noise in the experimental setup</p>
|
|
</div>
|
|
|
|
<p>
|
|
The gain of the low noise amplifier is set to <code>50000</code> for the measurement.
|
|
</p>
|
|
|
|
<p>
|
|
The obtained Amplitude Spectral Density of the Low Noise Voltage Amplifier is shown in Figure <a href="#orga0459d1">14</a>.
|
|
The obtained noise amplitude is very closed to the one specified in the documentation of \(4nV/\sqrt{Hz}\) at 1kHZ.
|
|
</p>
|
|
|
|
<p>
|
|
It is also verified that the quantization noise of the ADC is much smaller and what we are measuring is indeed the noise of the pre-amplifier.
|
|
</p>
|
|
|
|
|
|
<div id="orga0459d1" class="figure">
|
|
<p><img src="figs/asd_egg.png" alt="asd_egg.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 14: </span>Obtained Amplitude Spectral Density of the EG&G Low Noise Voltage Amplifier</p>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org9288e06" class="outline-3">
|
|
<h3 id="org9288e06"><span class="section-number-3">4.5</span> Femto - Amplifier noise measurement</h3>
|
|
<div class="outline-text-3" id="text-4-5">
|
|
<p>
|
|
<a id="org35ce1b8"></a>
|
|
</p>
|
|
|
|
<p>
|
|
Similarly to Section <a href="#orgbd7ef58">4.4</a>, the noise of the Femto amplifier is identified.
|
|
</p>
|
|
|
|
<p>
|
|
The obtained Amplitude spectral density is shown in Figure <a href="#orge81297b">15</a>.
|
|
</p>
|
|
|
|
|
|
<div id="orge81297b" class="figure">
|
|
<p><img src="figs/asd_femto.png" alt="asd_femto.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 15: </span>Obtained Amplitude Spectral Density of the Femto Low Noise Voltage Amplifier</p>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org5cafd0e" class="outline-3">
|
|
<h3 id="org5cafd0e"><span class="section-number-3">4.6</span> PD200 - Low frequency noise measurement</h3>
|
|
<div class="outline-text-3" id="text-4-6">
|
|
<p>
|
|
<a id="org866a734"></a>
|
|
</p>
|
|
|
|
<p>
|
|
The measurement setup is shown in Figure <a href="#orgca3b01d">16</a>.
|
|
The input of the PD200 amplifier is shunted with a 50 Ohm resistor such that there in no voltage input expected the PD200 input voltage noise.
|
|
The gain of the pre-amplifier is increased in order to measure a signal much larger than the quantization noise of the ADC.
|
|
</p>
|
|
|
|
|
|
<div id="orgca3b01d" class="figure">
|
|
<p><img src="figs/noise_measure_setup_pd200.png" alt="noise_measure_setup_pd200.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 16: </span>Sources of noise in the experimental setup</p>
|
|
</div>
|
|
|
|
<p>
|
|
The measured low frequency (<20Hz) <b>output</b> noise of one of the PD200 amplifiers is shown in Figure <a href="#org2485b87">17</a>.
|
|
It is very similar to the one specified in the datasheet in Figure <a href="#org7985862">3</a>.
|
|
</p>
|
|
|
|
|
|
<div id="org2485b87" class="figure">
|
|
<p><img src="figs/pd200_noise_time_lpf.png" alt="pd200_noise_time_lpf.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 17: </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 <b>output</b> noise are shown in Table <a href="#org6e0533c">2</a> and found to be very similar to the specified ones.
|
|
</p>
|
|
<table id="org6e0533c" border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
|
|
<caption class="t-above"><span class="table-number">Table 2:</span> RMS and Peak to Peak measured low frequency output 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 [\(\mu V\)]</b></th>
|
|
<th scope="col" class="org-right"><b>Peak to Peak [\(mV\)]</b></th>
|
|
</tr>
|
|
</thead>
|
|
<tbody>
|
|
<tr>
|
|
<td class="org-left">Specification [\(10\,\mu F\)]</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>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-orge3325ea" class="outline-3">
|
|
<h3 id="orge3325ea"><span class="section-number-3">4.7</span> PD200 - High frequency noise measurement</h3>
|
|
<div class="outline-text-3" id="text-4-7">
|
|
<p>
|
|
<a id="org9016b5f"></a>
|
|
</p>
|
|
|
|
<p>
|
|
The measurement setup is the same as in Figure <a href="#orgca3b01d">16</a>.
|
|
</p>
|
|
|
|
<p>
|
|
The Amplitude Spectral Density \(\Gamma_n(\omega)\) of the measured signal by the ADC is computed.
|
|
The Amplitude Spectral Density of the input voltage noise of the PD200 amplifier \(n_p\) is then computed taking into account the gain of the pre-amplifier and the gain of the PD200 amplifier:
|
|
</p>
|
|
\begin{equation}
|
|
\Gamma_{n_p}(\omega) = \frac{\Gamma_n(\omega)}{|G_p(j\omega) G_a(j\omega)|}
|
|
\end{equation}
|
|
|
|
<p>
|
|
And we verify that we are indeed measuring the noise of the PD200 and not the noise of the pre-amplifier by checking that:
|
|
</p>
|
|
\begin{equation}
|
|
\Gamma_{n_p}(\omega) |G_p(j\omega)| \ll \Gamma_{n_a}
|
|
\end{equation}
|
|
|
|
<p>
|
|
The Amplitude Spectral Density of the measured <b>input</b> noise is computed and shown in Figure <a href="#orgdf1f24c">18</a>.
|
|
</p>
|
|
|
|
<p>
|
|
It is verified that the contribution of the PD200 noise is much larger than the contribution of the pre-amplifier noise of the quantization noise.
|
|
</p>
|
|
|
|
<div id="orgdf1f24c" class="figure">
|
|
<p><img src="figs/asd_noise_pd200_10uF.png" alt="asd_noise_pd200_10uF.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 18: </span>Amplitude Spectral Density of the measured input voltage noise of the PD200 amplifiers</p>
|
|
</div>
|
|
|
|
<div class="note" id="org005fd13">
|
|
<p>
|
|
The Amplitude Spectral Density of the input noise of the PD200 amplifiers present sharp peaks.
|
|
It is not clear yet what causes such peaks and if these peaks have high influence on the total RMS noise of the amplifiers.
|
|
</p>
|
|
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org84b301f" class="outline-3">
|
|
<h3 id="org84b301f"><span class="section-number-3">4.8</span> 16bits DAC noise measurement</h3>
|
|
<div class="outline-text-3" id="text-4-8">
|
|
<p>
|
|
<a id="org465fa3c"></a>
|
|
</p>
|
|
|
|
<p>
|
|
In order not to have any quantization noise and only measure the output voltage noise of the DAC, we “ask” the DAC to output a zero voltage.
|
|
</p>
|
|
|
|
<p>
|
|
The measurement setup is schematically represented in Figure <a href="#orgb6a4427">19</a>.
|
|
The gain of the pre-amplifier is adjusted such that the measured amplified noise is much larger than the quantization noise of the ADC.
|
|
</p>
|
|
|
|
<p>
|
|
The Amplitude Spectral Density \(\Gamma_n(\omega)\) of the measured signal is computed.
|
|
The Amplitude Spectral Density of the DAC output voltage noise \(n_{da}\) 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 verified 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="orgb6a4427" class="figure">
|
|
<p><img src="figs/noise_measure_setup_dac.png" alt="noise_measure_setup_dac.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 19: </span>Sources of noise in the experimental setup</p>
|
|
</div>
|
|
|
|
<p>
|
|
The obtained Amplitude Spectral Density of the DAC’s output voltage is shown in Figure <a href="#orgaa163e6">20</a>.
|
|
</p>
|
|
|
|
|
|
<div id="orgaa163e6" class="figure">
|
|
<p><img src="figs/asd_noise_dac.png" alt="asd_noise_dac.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 20: </span>Amplitude Spectral Density of the measured output voltage noise of the 16bits DAC</p>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org9b88cef" class="outline-3">
|
|
<h3 id="org9b88cef"><span class="section-number-3">4.9</span> Noise of the full setup with 16bits DAC</h3>
|
|
<div class="outline-text-3" id="text-4-9">
|
|
<p>
|
|
<a id="org3004c04"></a>
|
|
</p>
|
|
|
|
<p>
|
|
Let’s now measure the noise of the full setup in Figure <a href="#orgfb24dda">21</a> and analyze the results.
|
|
</p>
|
|
|
|
|
|
<div id="orgfb24dda" class="figure">
|
|
<p><img src="figs/noise_meas_procedure.png" alt="noise_meas_procedure.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 21: </span>Sources of noise in the experimental setup</p>
|
|
</div>
|
|
|
|
<p>
|
|
The Amplitude Spectral Density of the measured noise is computed and the shown in Figure <a href="#org00930fe">22</a>.
|
|
</p>
|
|
|
|
<p>
|
|
We can very well see that to total measured noise is the sum of the DAC noise and the PD200 noise.
|
|
</p>
|
|
|
|
<div id="org00930fe" class="figure">
|
|
<p><img src="figs/asd_noise_tot.png" alt="asd_noise_tot.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 22: </span>Amplitude Spectral Density of the measured noise and of the individual sources of noise</p>
|
|
</div>
|
|
|
|
<div class="important" id="org44f6f14">
|
|
<p>
|
|
The input noise of the PD200 amplifier is limited by the output voltage noise of the DAC.
|
|
Having a DAC with lower output voltage noise could lower the overall noise of the setup.
|
|
SSI2V 20bits DACs are used in the next section to verify that.
|
|
</p>
|
|
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-orgdbba426" class="outline-3">
|
|
<h3 id="orgdbba426"><span class="section-number-3">4.10</span> 20bits DAC noise measurement</h3>
|
|
<div class="outline-text-3" id="text-4-10">
|
|
<p>
|
|
<a id="org3a5b9d6"></a>
|
|
</p>
|
|
|
|
<p>
|
|
Let’s now measure the output voltage noise of another DAC called the “SSI2V” (<a href="doc/[SSI2V]Datasheet.pdf">doc</a>).
|
|
It is a 20bits DAC with an output voltage range of +/-10.48 V and a very low output voltage noise.
|
|
</p>
|
|
|
|
<p>
|
|
The measurement setup is the same as the one in Figure <a href="#orgb6a4427">19</a>.
|
|
</p>
|
|
|
|
<p>
|
|
The obtained Amplitude Spectral Density of the output voltage noise of the SSI2V DAC is shown in Figure <a href="#orgbfd6428">23</a> and compared with the output voltage noise of the 16bits DAC.
|
|
It is shown to be much smaller (~1 order of magnitude).
|
|
</p>
|
|
|
|
|
|
<div id="orgbfd6428" class="figure">
|
|
<p><img src="figs/asd_ssi2v_noise.png" alt="asd_ssi2v_noise.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 23: </span>Amplitude Spectral Density of the SSI2V DAC’s noise</p>
|
|
</div>
|
|
|
|
<div class="important" id="org5b2d09c">
|
|
<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 id="outline-container-org130febd" class="outline-3">
|
|
<h3 id="org130febd"><span class="section-number-3">4.11</span> Noise of the full setup with 20bits DAC</h3>
|
|
<div class="outline-text-3" id="text-4-11">
|
|
<p>
|
|
<a id="orgae77708"></a>
|
|
</p>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org3cb50e3" class="outline-3">
|
|
<h3 id="org3cb50e3"><span class="section-number-3">4.12</span> PD200 Amplifier noise model</h3>
|
|
<div class="outline-text-3" id="text-4-12">
|
|
<p>
|
|
<a id="org3a64053"></a>
|
|
</p>
|
|
|
|
<p>
|
|
Let’s design a transfer function \(G_n(s)\) whose norm represent the Amplitude Spectral Density of the input voltage noise of the PD200 amplifier as shown in Figure <a href="#orgfc59efa">24</a>.
|
|
</p>
|
|
|
|
|
|
<div id="orgfc59efa" class="figure">
|
|
<p><img src="figs/pd200-model-schematic-normalized.png" alt="pd200-model-schematic-normalized.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 24: </span>Model of the voltage amplifier with normalized noise input</p>
|
|
</div>
|
|
|
|
|
|
<p>
|
|
A simple transfer function that allows to obtain a good fit is defined below.
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab"><span class="org-matlab-cellbreak"><span class="org-comment">%% Model of the PD200 Input Voltage Noise</span></span>
|
|
Gn = 1e<span class="org-type">-</span>5 <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>20)<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>2))<span class="org-type">^</span>2 <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>5e3);
|
|
</pre>
|
|
</div>
|
|
|
|
<p>
|
|
The comparison between the measured ASD of the modeled ASD is done in Figure <a href="#orge174258">25</a>.
|
|
</p>
|
|
|
|
<div id="orge174258" class="figure">
|
|
<p><img src="figs/pd200_asd_noise_model.png" alt="pd200_asd_noise_model.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 25: </span>ASD of the measured input voltage noise and modeled noise using \(G_n(s)\)</p>
|
|
</div>
|
|
|
|
<p>
|
|
Let’s now compute the Cumulative Amplitude Spectrum corresponding to the measurement and the model and compare them.
|
|
</p>
|
|
|
|
<p>
|
|
The integration from low to high frequency and from high to low frequency are both shown in Figure <a href="#org3b37b33">26</a>.
|
|
</p>
|
|
|
|
<p>
|
|
The fit between the model and the measurements is rather good considering the complex shape of the measured ASD and the simple model used.
|
|
</p>
|
|
|
|
<div id="org3b37b33" class="figure">
|
|
<p><img src="figs/pd200_cas_noise_model.png" alt="pd200_cas_noise_model.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 26: </span>Cumulative Amplitude Spectrum of the measured input voltage noise and modeled noise using \(G_n(s)\)</p>
|
|
</div>
|
|
|
|
<p>
|
|
The obtained RMS noise of the model is <code>286.74</code> uV RMS which is not that far from the specifications.
|
|
</p>
|
|
|
|
<p>
|
|
Finally the model of the amplifier noise is saved.
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">save(<span class="org-string">'mat/pd200_model.mat'</span>, <span class="org-string">'Gn'</span>, <span class="org-string">'-append'</span>);
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org1171b27" class="outline-2">
|
|
<h2 id="org1171b27"><span class="section-number-2">5</span> Comparison to other commercial amplifiers</h2>
|
|
<div class="outline-text-2" id="text-5">
|
|
<p>
|
|
<a id="orge72631c"></a>
|
|
</p>
|
|
</div>
|
|
<div id="outline-container-orgb368d4e" class="outline-3">
|
|
<h3 id="orgb368d4e"><span class="section-number-3">5.1</span> Introduction</h3>
|
|
<div class="outline-text-3" id="text-5-1">
|
|
<p>
|
|
In this section, three similar voltage amplifiers are compared:
|
|
</p>
|
|
<ul class="org-ul">
|
|
<li>the <a href="doc/PD200-V7-R1.pdf">PD200</a> from PiezoDrive</li>
|
|
<li>the <a href="doc/LA75B.pdf">LA75B</a> from CedratTechnologies</li>
|
|
<li>the <a href="doc/E-505-Datasheet.pdf">E-505.00</a> from PI</li>
|
|
</ul>
|
|
|
|
<p>
|
|
These are compared in term of dynamic from input voltage to output voltage for a load of \(10\,\mu F\) in Section <a href="#orgd6f010c">5.2</a> and then in term of input voltage noise in Section <a href="#org5c6ce12">5.3</a>.
|
|
</p>
|
|
|
|
<p>
|
|
The characteristics that I could find for the three amplifiers are summarized in Table <a href="#orgeb1ecfc">3</a>.
|
|
</p>
|
|
|
|
<table id="orgeb1ecfc" border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
|
|
<caption class="t-above"><span class="table-number">Table 3:</span> Characteristics of the three tested voltage amplifiers</caption>
|
|
|
|
<colgroup>
|
|
<col class="org-left" />
|
|
|
|
<col class="org-center" />
|
|
|
|
<col class="org-center" />
|
|
|
|
<col class="org-center" />
|
|
</colgroup>
|
|
<thead>
|
|
<tr>
|
|
<th scope="col" class="org-left"><b>Characteristics</b></th>
|
|
<th scope="col" class="org-center"><b>PD200</b></th>
|
|
<th scope="col" class="org-center"><b>LA75B</b></th>
|
|
<th scope="col" class="org-center"><b>E-505</b></th>
|
|
</tr>
|
|
</thead>
|
|
<tbody>
|
|
<tr>
|
|
<td class="org-left">Gain</td>
|
|
<td class="org-center">20 [V/V]</td>
|
|
<td class="org-center">20 [V/V]</td>
|
|
<td class="org-center">10 [V/V]</td>
|
|
</tr>
|
|
|
|
<tr>
|
|
<td class="org-left">Maximum RMS current</td>
|
|
<td class="org-center">0.9 [A]</td>
|
|
<td class="org-center">0.4 [A]</td>
|
|
<td class="org-center"> </td>
|
|
</tr>
|
|
|
|
<tr>
|
|
<td class="org-left">Maximum Pulse current</td>
|
|
<td class="org-center">10 [A]</td>
|
|
<td class="org-center">1 [A]</td>
|
|
<td class="org-center">2 [A]</td>
|
|
</tr>
|
|
|
|
<tr>
|
|
<td class="org-left">Slew Rate</td>
|
|
<td class="org-center">150 [V/us]</td>
|
|
<td class="org-center"> </td>
|
|
<td class="org-center"> </td>
|
|
</tr>
|
|
|
|
<tr>
|
|
<td class="org-left">Noise (10uF load)</td>
|
|
<td class="org-center">0.7 [mV RMS]</td>
|
|
<td class="org-center">3.4 [mV RMS]</td>
|
|
<td class="org-center">0.6 [mV RMS]</td>
|
|
</tr>
|
|
|
|
<tr>
|
|
<td class="org-left">Small Signal Bandwidth</td>
|
|
<td class="org-center">7.4 [kHz] (10uF)</td>
|
|
<td class="org-center">30 [kHz] (unloaded)</td>
|
|
<td class="org-center"> </td>
|
|
</tr>
|
|
</tbody>
|
|
</table>
|
|
|
|
<div class="note" id="org44ba4f1">
|
|
<p>
|
|
The documentation for the three amplifiers can be found here: <a href="doc/PD200-V7-R1.pdf">PD200</a>, <a href="doc/LA75B.pdf">LA75B</a>, <a href="doc/E-505-Datasheet.pdf">E-505.00</a>.
|
|
</p>
|
|
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org4c15dc1" class="outline-3">
|
|
<h3 id="org4c15dc1"><span class="section-number-3">5.2</span> Transfer functions</h3>
|
|
<div class="outline-text-3" id="text-5-2">
|
|
<p>
|
|
<a id="orgd6f010c"></a>
|
|
</p>
|
|
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">la75 = load(<span class="org-string">'tf_la75_10uF_small_signal.mat'</span>, <span class="org-string">'t'</span>, <span class="org-string">'Vin'</span>, <span class="org-string">'Vout'</span>);
|
|
pd200 = load(<span class="org-string">'tf_pd200_1_10uF_small_signal.mat'</span>, <span class="org-string">'t'</span>, <span class="org-string">'Vin'</span>, <span class="org-string">'Vout'</span>, <span class="org-string">'notes'</span>);
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-orgf6b59a0" class="outline-3">
|
|
<h3 id="orgf6b59a0"><span class="section-number-3">5.3</span> Noise Characteristics</h3>
|
|
<div class="outline-text-3" id="text-5-3">
|
|
<p>
|
|
<a id="org5c6ce12"></a>
|
|
</p>
|
|
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">pd200.Vout = pd200.Vout<span class="org-type">/</span>pd200.notes.pre_amp.gain;
|
|
la75.Vout = la75.Vout<span class="org-type">/</span>la75.notes.pre_amp.gain;
|
|
</pre>
|
|
</div>
|
|
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab"><span class="org-type">figure</span>;
|
|
hold on;
|
|
plot(pd200.t, 1e3<span class="org-type">*</span>pd200.Vout)
|
|
plot(la75.t, 1e3<span class="org-type">*</span>la75.Vout)
|
|
hold off;
|
|
xlabel(<span class="org-string">'Time [s]'</span>);
|
|
ylabel(<span class="org-string">'Voltage [mV]'</span>);
|
|
<span class="org-comment">% ylim([-3, 3]);</span>
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org0b600f7" class="outline-2">
|
|
<h2 id="org0b600f7"><span class="section-number-2">6</span> Conclusion</h2>
|
|
<div class="outline-text-2" id="text-6">
|
|
<p>
|
|
<a id="org127b80a"></a>
|
|
</p>
|
|
|
|
<table id="org1c85c04" 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" />
|
|
|
|
<col class="org-center" />
|
|
|
|
<col class="org-center" />
|
|
|
|
<col class="org-center" />
|
|
</colgroup>
|
|
<thead>
|
|
<tr>
|
|
<th scope="col" class="org-left"><b>Characteristics</b></th>
|
|
<th scope="col" class="org-center"><b>Measurement</b></th>
|
|
<th scope="col" class="org-center"><b>Manual</b></th>
|
|
<th scope="col" class="org-center"><b>Specification</b></th>
|
|
</tr>
|
|
</thead>
|
|
<tbody>
|
|
<tr>
|
|
<td class="org-left">Input Voltage Range</td>
|
|
<td class="org-center">-</td>
|
|
<td class="org-center">+/- 10 [V]</td>
|
|
<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: 2021-02-12 ven. 14:59</p>
|
|
</div>
|
|
</body>
|
|
</html>
|