1146 lines
37 KiB
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1146 lines
37 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="#orgc43f0fc">1. Requirements PD200 Expected characteristics</a></li>
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<li><a href="#org9e1f8da">2. Voltage Amplifier Model</a></li>
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<li><a href="#org58651b6">3. Transfer Function measurement</a>
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<ul>
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<li><a href="#org304a75d">3.1. Setup</a></li>
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<li><a href="#org02635e8">3.2. Maximum Frequency/Voltage to not overload the amplifier</a></li>
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<li><a href="#orgc7c2c23">3.3. Small Signal Bandwidth</a></li>
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<li><a href="#org1d1072a">3.4. Bandwidth for multiple excitation signals</a></li>
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</ul>
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</li>
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<li><a href="#orgff95d7c">4. Noise measurement</a>
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<ul>
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<li><a href="#orgc596a2b">4.1. Measurement Setup</a></li>
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<li><a href="#org09a7143">4.2. Model of the setup</a></li>
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<li><a href="#org38f7579">4.3. Quantization Noise</a></li>
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<li><a href="#orgc755c39">4.4. EG&G - Amplifier noise measurement</a></li>
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<li><a href="#orgc16dd7a">4.5. Femto - Amplifier noise measurement</a></li>
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<li><a href="#org32350ff">4.6. PD200 noise measurement</a></li>
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<li><a href="#orgea9aca9">4.7. DAC noise measurement</a></li>
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<li><a href="#org71ad511">4.8. Total noise measurement</a></li>
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<li><a href="#org8d4a13f">4.9. 20bits DAC noise measurement</a></li>
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<li><a href="#org8e194b0">4.10. PD200 Amplifier noise model</a></li>
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</ul>
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</li>
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<li><a href="#org63b40e4">5. Comparison to other commercial amplifiers</a>
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<ul>
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<li><a href="#orgb2b3b03">5.1. Transfer functions</a></li>
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<li><a href="#org3779171">5.2. Noise Characteristics</a></li>
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</ul>
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</li>
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<li><a href="#org61f0483">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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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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<div class="note" id="org51a8585">
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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>
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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="#org0690faf">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="#org2496dac">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="#org3f48045">3</a>: the transfer function from input voltage to output voltage is identified.</li>
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<li>Section <a href="#orgf21cb12">4</a>: the power spectral density of the amplifier’s noise is measured</li>
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<li>Section <a href="#org0768992">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="#org3f6c507">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-orgc43f0fc" class="outline-2">
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<h2 id="orgc43f0fc"><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="org0690faf"></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="#orgf059e11">1</a>.
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</p>
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<div id="orgf059e11" 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="#org53168ab">1</a>.
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</p>
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<table id="org53168ab" 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="#orgee79c85">2</a>) and the low frequency noise is \(650\,\mu V\,\text{rms}\) (Figure <a href="#org5bb9d30">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="#org3f48045">3</a> and Section <a href="#orgf21cb12">4</a>.
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</p>
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<div id="orgee79c85" 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="org5bb9d30" 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-org9e1f8da" class="outline-2">
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<h2 id="org9e1f8da"><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="org2496dac"></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="org3d926d5" 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="#org93c8310">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="org64a2245" 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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</div>
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</div>
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</div>
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<div id="outline-container-org58651b6" class="outline-2">
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<h2 id="org58651b6"><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="org3f48045"></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="#orgaa5a588">3.1</a>: the measurement setup is described</li>
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<li>Section <a href="#org04fcc9e">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="#org5972a0a">3.3</a>: the small signal bandwidth measurement results are shown</li>
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<li>Section <a href="#orgad0b3ab">3.4</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-org304a75d" class="outline-3">
|
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<h3 id="org304a75d"><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="orgaa5a588"></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="#org93c8310">6</a> is used.
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</p>
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<div class="note" id="org3919fdc">
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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="org93c8310" 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-org02635e8" class="outline-3">
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<h3 id="org02635e8"><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="org04fcc9e"></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>
|
|
The impedance of the capacitance is:
|
|
\[ Z_C(\omega) = \frac{1}{jC\omega} \]
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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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|
\[ 20 V_{in} = \frac{1}{C\omega} I_{out} \]
|
|
</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:
|
|
</p>
|
|
\begin{equation}
|
|
\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>
|
|
with:
|
|
</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="#org3e7ecd4">7</a>.
|
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</p>
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<div id="org3e7ecd4" class="figure">
|
|
<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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<div id="outline-container-orgc7c2c23" class="outline-3">
|
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<h3 id="orgc7c2c23"><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>
|
|
<a id="org5972a0a"></a>
|
|
Load Data
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</p>
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<p>
|
|
Compute Transfer Functions
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</p>
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<p>
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Compare
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</p>
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<p>
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Model
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</p>
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<p>
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Save Model
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</p>
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</div>
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</div>
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<div id="outline-container-org1d1072a" class="outline-3">
|
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<h3 id="org1d1072a"><span class="section-number-3">3.4</span> Bandwidth for multiple excitation signals</h3>
|
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<div class="outline-text-3" id="text-3-4">
|
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<p>
|
|
<a id="orgad0b3ab"></a>
|
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</p>
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<p>
|
|
Several identifications using sweep sin were performed with input voltage amplitude ranging from 0.1V to 4V.
|
|
</p>
|
|
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">Iout_max = 0.57; <span class="org-comment">% Maximum output current [A]</span>
|
|
C = 10e<span class="org-type">-</span>6; <span class="org-comment">% Load Capacitance [F]</span>
|
|
|
|
V_in = [0.1, 0.5, 1, 2, 4];
|
|
f_max = 0.8<span class="org-type">*</span>Iout_max<span class="org-type">./</span>(20<span class="org-type">*</span>C<span class="org-type">*</span>V_in<span class="org-type">/</span>sqrt(2))<span class="org-type">/</span>2<span class="org-type">/</span><span class="org-constant">pi</span>;
|
|
<span class="org-keyword">for</span> <span class="org-variable-name"><span class="org-constant">i</span></span> = <span class="org-constant">1:length(Vin_ampl)</span>
|
|
pd200{<span class="org-constant">i</span>}.notes.pd200.f_max = f_max(<span class="org-constant">i</span>);
|
|
pd200{<span class="org-constant">i</span>}.notes.pd200.Vin = V_in(<span class="org-constant">i</span>);
|
|
<span class="org-keyword">end</span>
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-orgff95d7c" class="outline-2">
|
|
<h2 id="orgff95d7c"><span class="section-number-2">4</span> Noise measurement</h2>
|
|
<div class="outline-text-2" id="text-4">
|
|
<p>
|
|
<a id="orgf21cb12"></a>
|
|
</p>
|
|
<p>
|
|
In section <a href="#org22a9e3d">4.1</a>, the measurement setup is described and a model (block diagram) of the setup is given in section <a href="#org7b1d1b0">4.2</a>.
|
|
</p>
|
|
|
|
<p>
|
|
Then, the noise contribution of each element is measured:
|
|
</p>
|
|
<ul class="org-ul">
|
|
<li>Section <a href="#org118a1be">4.3</a>: the quantization noise of the ADC is estimated</li>
|
|
<li>Sections <a href="#org80f2aac">4.4</a> and <a href="#orgd77aed9">4.5</a>: the noise of the low-noise amplifiers are estimated</li>
|
|
<li>Section <a href="#org5f12bbc">4.6</a>: the input voltage noise of the PD200 amplifier is estimated</li>
|
|
<li>Section <a href="#org50df610">4.7</a>: the output noise of the DAC is measured</li>
|
|
<li>Section <a href="#orgd1ca5a0">4.8</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="#org6a7ec65">4.9</a>: the noise of an 20bits DAC is measured and it is shown if it could lowering the overall noise of the setup</li>
|
|
</ul>
|
|
|
|
<p>
|
|
Finally in section <a href="#org3c4edcc">4.10</a>, a model of the PD200 amplifier’s noise is developed.
|
|
</p>
|
|
</div>
|
|
|
|
<div id="outline-container-orgc596a2b" class="outline-3">
|
|
<h3 id="orgc596a2b"><span class="section-number-3">4.1</span> Measurement Setup</h3>
|
|
<div class="outline-text-3" id="text-4-1">
|
|
<p>
|
|
<a id="org22a9e3d"></a>
|
|
</p>
|
|
|
|
<div class="note" id="org6c9ffc6">
|
|
<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>
|
|
</ul>
|
|
|
|
</div>
|
|
|
|
<p>
|
|
The output noise of the voltage amplifier PD200 is foreseen to be around 1mV rms in a bandwidth from DC to 1MHz.
|
|
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 RMS noise being very small compare to the ADC resolution, we must amplify this noise before digitizing the signal.
|
|
</p>
|
|
|
|
<p>
|
|
The added noise of the instrumentation amplifier should be much smaller than the noise of the PD200.
|
|
We use either 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.
|
|
</p>
|
|
|
|
<p>
|
|
The gain of the low-noise amplifier can be increased until the full range of the ADC is used.
|
|
This gain should be around 1000 (60dB).
|
|
</p>
|
|
|
|
|
|
<div id="orgdae3c58" class="figure">
|
|
<p><img src="figs/setup-noise-measurement.png" alt="setup-noise-measurement.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 8: </span>Schematic of the test bench to measure the Power Spectral Density of the Voltage amplifier noise \(n\)</p>
|
|
</div>
|
|
|
|
<p>
|
|
A low pass filter at 10kHz can be included in the EG&G amplifier in order to limit aliasing.
|
|
An high pass filter at low frequency can be added if there is a problem of large offset.
|
|
</p>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org09a7143" class="outline-3">
|
|
<h3 id="org09a7143"><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="org7b1d1b0"></a>
|
|
</p>
|
|
|
|
<p>
|
|
As shown in Figure <a href="#org7a80897">9</a>, there are 4 equipment 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="org7a80897" class="figure">
|
|
<p><img src="figs/noise_meas_procedure.png" alt="noise_meas_procedure.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 9: </span>Sources of noise in the experimental setup</p>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org38f7579" class="outline-3">
|
|
<h3 id="org38f7579"><span class="section-number-3">4.3</span> Quantization Noise</h3>
|
|
<div class="outline-text-3" id="text-4-3">
|
|
<p>
|
|
<a id="org118a1be"></a>
|
|
</p>
|
|
|
|
<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}}
|
|
\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>
|
|
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">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-orgc755c39" class="outline-3">
|
|
<h3 id="orgc755c39"><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="org80f2aac"></a>
|
|
</p>
|
|
|
|
<p>
|
|
First, we wish to measure the noise of the pre-amplifier.
|
|
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="org04b4812" class="figure">
|
|
<p><img src="figs/noise_measure_setup_preamp.png" alt="noise_measure_setup_preamp.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 10: </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>
|
|
|
|
<p>
|
|
The obtained Amplitude Spectral Density of the Low Noise Voltage Amplifier is shown in Figure <a href="#org6a8e4a8">11</a>.
|
|
The obtained noise amplitude is very closed to the one specified in the documentation of \(4nV/\sqrt{Hz}\) at 1kHZ.
|
|
</p>
|
|
|
|
|
|
<div id="org6a8e4a8" class="figure">
|
|
<p><img src="figs/asd_egg.png" alt="asd_egg.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 11: </span>Obtained Amplitude Spectral Density of the EG&G Low Noise Voltage Amplifier</p>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-orgc16dd7a" class="outline-3">
|
|
<h3 id="orgc16dd7a"><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="orgd77aed9"></a>
|
|
</p>
|
|
|
|
<p>
|
|
Similarly to Section <a href="#org80f2aac">4.4</a>, the noise of the Femto amplifier is identified.
|
|
</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(femto.Vout, win, [], [], Fs);
|
|
|
|
<span class="org-comment">% Save the results inside the struct</span>
|
|
femto.pxx = pxx;
|
|
femto.f = f;
|
|
</pre>
|
|
</div>
|
|
|
|
|
|
<div id="orgd6ec0a3" class="figure">
|
|
<p><img src="figs/asd_femto.png" alt="asd_femto.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 12: </span>Obtained Amplitude Spectral Density of the Femto Low Noise Voltage Amplifier</p>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org32350ff" class="outline-3">
|
|
<h3 id="org32350ff"><span class="section-number-3">4.6</span> PD200 noise measurement</h3>
|
|
<div class="outline-text-3" id="text-4-6">
|
|
<p>
|
|
<a id="org5f12bbc"></a>
|
|
</p>
|
|
|
|
<p>
|
|
The input of the PD200 amplifier is shunted with a 50 Ohm resistor.
|
|
The gain of the pre-amplifier is increased in order to measure a signal much larger than the quantization noise of the ADC.
|
|
</p>
|
|
|
|
<p>
|
|
The Amplitude Spectral Density of the measured signal \(\Gamma_n(\omega)\) is computed.
|
|
The Amplitude Spectral Density of \(n_p\) is then computed taking into account the gain of the pre-amplifier and the can 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 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}(\omega) |G_p(j\omega)| \ll \Gamma_{n_a}
|
|
\end{equation}
|
|
|
|
|
|
<div id="orgef32d0c" class="figure">
|
|
<p><img src="figs/noise_measure_setup_pd200.png" alt="noise_measure_setup_pd200.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 13: </span>Sources of noise in the experimental setup</p>
|
|
</div>
|
|
|
|
<p>
|
|
The measured low frequency <b>output</b> noise of one of the PD200 amplifiers is shown in Figure <a href="#org37538d1">14</a>.
|
|
It is very similar to the one specified in the datasheet in Figure <a href="#org5bb9d30">3</a>.
|
|
</p>
|
|
|
|
<div id="org37538d1" class="figure">
|
|
<p><img src="figs/pd200_noise_time_lpf.png" alt="pd200_noise_time_lpf.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 14: </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="#orgbddbe0f">2</a>.
|
|
</p>
|
|
<table id="orgbddbe0f" 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 [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 <b>input</b> noise is computed and shown in Figure <a href="#org8143da2">15</a>.
|
|
</p>
|
|
|
|
<p>
|
|
The contribution of the PD200 noise is much larger than the contribution of the pre-amplifier noise of the quantization noise.
|
|
</p>
|
|
|
|
<div id="org8143da2" class="figure">
|
|
<p><img src="figs/asd_noise_3uF_warmup.png" alt="asd_noise_3uF_warmup.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 15: </span>Amplitude Spectral Density of the measured noise</p>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-orgea9aca9" class="outline-3">
|
|
<h3 id="orgea9aca9"><span class="section-number-3">4.7</span> DAC noise measurement</h3>
|
|
<div class="outline-text-3" id="text-4-7">
|
|
<p>
|
|
<a id="org50df610"></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 in order to have sufficient voltage going to the ADC.
|
|
</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="orgf6bcfdf" class="figure">
|
|
<p><img src="figs/noise_measure_setup_dac.png" alt="noise_measure_setup_dac.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 16: </span>Sources of noise in the experimental setup</p>
|
|
</div>
|
|
|
|
|
|
<div id="org5bf4a01" class="figure">
|
|
<p><img src="figs/asd_noise_dac.png" alt="asd_noise_dac.png" />
|
|
</p>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org71ad511" class="outline-3">
|
|
<h3 id="org71ad511"><span class="section-number-3">4.8</span> Total noise measurement</h3>
|
|
<div class="outline-text-3" id="text-4-8">
|
|
<p>
|
|
<a id="orgd1ca5a0"></a>
|
|
</p>
|
|
|
|
<p>
|
|
Let’s now analyze the measurement of the setup in Figure <a href="#org1480d92">18</a>.
|
|
</p>
|
|
|
|
|
|
<div id="org1480d92" class="figure">
|
|
<p><img src="figs/noise_meas_procedure.png" alt="noise_meas_procedure.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 18: </span>Sources of noise in the experimental setup</p>
|
|
</div>
|
|
|
|
<p>
|
|
The PSD of the measured noise is computed and the ASD is shown in Figure <a href="#orgc059f95">19</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="orgc059f95" class="figure">
|
|
<p><img src="figs/asd_noise_tot.png" alt="asd_noise_tot.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 19: </span>Amplitude Spectral Density of the measured noise and of the individual sources of noise</p>
|
|
</div>
|
|
|
|
<div class="important" id="orgd4a443e">
|
|
<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-org8d4a13f" class="outline-3">
|
|
<h3 id="org8d4a13f"><span class="section-number-3">4.9</span> 20bits DAC noise measurement</h3>
|
|
<div class="outline-text-3" id="text-4-9">
|
|
<p>
|
|
<a id="org6a7ec65"></a>
|
|
</p>
|
|
|
|
<p>
|
|
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 output noise.
|
|
</p>
|
|
|
|
<p>
|
|
The measurement setup is the same as the one in Figure <a href="#orgf6bcfdf">16</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="#orge8679e1">20</a> and compared with the noise of the 16bits DAC.
|
|
It is shown to be much smaller (~1 order of magnitude).
|
|
</p>
|
|
|
|
|
|
<div id="orge8679e1" class="figure">
|
|
<p><img src="figs/asd_ssi2v_noise.png" alt="asd_ssi2v_noise.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 20: </span>Amplitude Spectral Density of the SSI2V DAC’s noise</p>
|
|
</div>
|
|
|
|
<div class="important" id="org83f9d60">
|
|
<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-org8e194b0" class="outline-3">
|
|
<h3 id="org8e194b0"><span class="section-number-3">4.10</span> PD200 Amplifier noise model</h3>
|
|
<div class="outline-text-3" id="text-4-10">
|
|
<p>
|
|
<a id="org3c4edcc"></a>
|
|
</p>
|
|
|
|
<p>
|
|
Let’s design a transfer function whose norm represent the Amplitude Spectral Density of the input voltage noise of the PD200 amplifier.
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">Gn = 2.5e<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>30)<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
|
|
</p>
|
|
|
|
<div id="org046b04a" class="figure">
|
|
<p><img src="figs/pd200_asd_noise_model.png" alt="pd200_asd_noise_model.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 21: </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
|
|
</p>
|
|
|
|
<div id="orgf7b2ac4" class="figure">
|
|
<p><img src="figs/pd200_cas_noise_model.png" alt="pd200_cas_noise_model.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 22: </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>650.77</code> uV RMS which is the same as advertise.
|
|
</p>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org63b40e4" class="outline-2">
|
|
<h2 id="org63b40e4"><span class="section-number-2">5</span> Comparison to other commercial amplifiers</h2>
|
|
<div class="outline-text-2" id="text-5">
|
|
<p>
|
|
<a id="org0768992"></a>
|
|
</p>
|
|
</div>
|
|
<div id="outline-container-orgb2b3b03" class="outline-3">
|
|
<h3 id="orgb2b3b03"><span class="section-number-3">5.1</span> Transfer functions</h3>
|
|
</div>
|
|
<div id="outline-container-org3779171" class="outline-3">
|
|
<h3 id="org3779171"><span class="section-number-3">5.2</span> Noise Characteristics</h3>
|
|
<div class="outline-text-3" id="text-5-2">
|
|
<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-org61f0483" class="outline-2">
|
|
<h2 id="org61f0483"><span class="section-number-2">6</span> Conclusion</h2>
|
|
<div class="outline-text-2" id="text-6">
|
|
<p>
|
|
<a id="org3f6c507"></a>
|
|
</p>
|
|
|
|
<table id="orgca48cbf" border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
|
|
<caption class="t-above"><span class="table-number">Table 3:</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: 2021-02-10 mer. 16:16</p>
|
|
</div>
|
|
</body>
|
|
</html>
|