941 lines
30 KiB
HTML
941 lines
30 KiB
HTML
<?xml version="1.0" encoding="utf-8"?>
|
|
<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Strict//EN"
|
|
"http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd">
|
|
<html xmlns="http://www.w3.org/1999/xhtml" lang="en" xml:lang="en">
|
|
<head>
|
|
<!-- 2021-01-23 sam. 15:40 -->
|
|
<meta http-equiv="Content-Type" content="text/html;charset=utf-8" />
|
|
<title>Voltage Amplifier PD200 - Test Bench</title>
|
|
<meta name="generator" content="Org mode" />
|
|
<meta name="author" content="Dehaeze Thomas" />
|
|
<link rel="stylesheet" type="text/css" href="https://research.tdehaeze.xyz/css/style.css"/>
|
|
<script type="text/javascript" src="https://research.tdehaeze.xyz/js/script.js"></script>
|
|
<script>
|
|
MathJax = {
|
|
svg: {
|
|
scale: 1,
|
|
fontCache: "global"
|
|
},
|
|
tex: {
|
|
tags: "ams",
|
|
multlineWidth: "%MULTLINEWIDTH",
|
|
tagSide: "right",
|
|
macros: {bm: ["\\boldsymbol{#1}",1],},
|
|
tagIndent: ".8em"
|
|
}
|
|
};
|
|
</script>
|
|
<script id="MathJax-script" async
|
|
src="https://cdn.jsdelivr.net/npm/mathjax@3/es5/tex-svg.js"></script>
|
|
</head>
|
|
<body>
|
|
<div id="org-div-home-and-up">
|
|
<a accesskey="h" href="../index.html"> UP </a>
|
|
|
|
|
<a accesskey="H" href="../index.html"> HOME </a>
|
|
</div><div id="content">
|
|
<h1 class="title">Voltage Amplifier PD200 - Test Bench</h1>
|
|
<div id="table-of-contents">
|
|
<h2>Table of Contents</h2>
|
|
<div id="text-table-of-contents">
|
|
<ul>
|
|
<li><a href="#org8464676">1. Introduction</a></li>
|
|
<li><a href="#org377554e">2. Voltage Amplifier Requirements</a></li>
|
|
<li><a href="#orgb337f1e">3. PD200 Expected characteristics</a></li>
|
|
<li><a href="#orgb5bfcf0">4. Voltage Amplifier Model</a></li>
|
|
<li><a href="#orga876e4d">5. Noise measurement</a>
|
|
<ul>
|
|
<li><a href="#org2c9f60e">5.1. Setup</a></li>
|
|
<li><a href="#orgcf8ecc8">5.2. Model of the setup</a></li>
|
|
<li><a href="#org5f0cc17">5.3. Quantization Noise</a></li>
|
|
<li><a href="#org7c484b7">5.4. Pre Amplifier noise measurement</a></li>
|
|
<li><a href="#org4fcdc54">5.5. PD200 noise measurement</a></li>
|
|
<li><a href="#orga1b9697">5.6. DAC noise measurement</a></li>
|
|
<li><a href="#org6d8f9c2">5.7. Total noise measurement</a></li>
|
|
<li><a href="#org59c04f1">5.8. 20bits DAC noise measurement</a></li>
|
|
</ul>
|
|
</li>
|
|
<li><a href="#orga1cb3ef">6. Transfer Function measurement</a>
|
|
<ul>
|
|
<li><a href="#org2c3812b">6.1. Setup</a></li>
|
|
<li><a href="#orge1713a2">6.2. Maximum Frequency/Voltage to not overload the amplifier</a></li>
|
|
<li><a href="#org4ff0dfb">6.3. Obtained Transfer Functions</a></li>
|
|
</ul>
|
|
</li>
|
|
<li><a href="#org6becade">7. Conclusion</a></li>
|
|
</ul>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org8464676" class="outline-2">
|
|
<h2 id="org8464676"><span class="section-number-2">1</span> Introduction</h2>
|
|
<div class="outline-text-2" id="text-1">
|
|
<p>
|
|
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.
|
|
</p>
|
|
|
|
<p>
|
|
The documentation of the PD200 is accessible <a href="doc/PD200-V7-R1.pdf">here</a>.
|
|
</p>
|
|
|
|
|
|
<div id="org6525f44" class="figure">
|
|
<p><img src="figs/amplifier_PD200.png" alt="amplifier_PD200.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 1: </span>Picture of the PD200 Voltage Amplifier</p>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org377554e" class="outline-2">
|
|
<h2 id="org377554e"><span class="section-number-2">2</span> Voltage Amplifier Requirements</h2>
|
|
<div class="outline-text-2" id="text-2">
|
|
<table id="orgf8783f3" border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
|
|
<caption class="t-above"><span class="table-number">Table 1:</span> Requirements for the Voltage Amplifier</caption>
|
|
|
|
<colgroup>
|
|
<col class="org-left" />
|
|
|
|
<col class="org-center" />
|
|
</colgroup>
|
|
<thead>
|
|
<tr>
|
|
<th scope="col" class="org-left"> </th>
|
|
<th scope="col" class="org-center"><b>Specification</b></th>
|
|
</tr>
|
|
</thead>
|
|
<tbody>
|
|
<tr>
|
|
<td class="org-left">Continuous Current</td>
|
|
<td class="org-center">> 50 [mA]</td>
|
|
</tr>
|
|
|
|
<tr>
|
|
<td class="org-left">Output Voltage Noise (1-200Hz)</td>
|
|
<td class="org-center">< 2 [mV rms]</td>
|
|
</tr>
|
|
|
|
<tr>
|
|
<td class="org-left">Voltage Input Range</td>
|
|
<td class="org-center">+/- 10 [V]</td>
|
|
</tr>
|
|
|
|
<tr>
|
|
<td class="org-left">Voltage Output Range</td>
|
|
<td class="org-center">-20 [V] to 150 [V]</td>
|
|
</tr>
|
|
|
|
<tr>
|
|
<td class="org-left">Small signal bandwidth (-3dB)</td>
|
|
<td class="org-center">> 5 [kHz]</td>
|
|
</tr>
|
|
</tbody>
|
|
</table>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-orgb337f1e" class="outline-2">
|
|
<h2 id="orgb337f1e"><span class="section-number-2">3</span> PD200 Expected characteristics</h2>
|
|
<div class="outline-text-2" id="text-3">
|
|
<table id="org6e09271" border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
|
|
<caption class="t-above"><span class="table-number">Table 2:</span> Characteristics of the PD200</caption>
|
|
|
|
<colgroup>
|
|
<col class="org-left" />
|
|
|
|
<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>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">+/- 10 [V]</td>
|
|
<td class="org-center">+/- 10 [V]</td>
|
|
</tr>
|
|
|
|
<tr>
|
|
<td class="org-left">Output Voltage Range</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">20 [V/V]</td>
|
|
<td class="org-center"> </td>
|
|
</tr>
|
|
|
|
<tr>
|
|
<td class="org-left">Maximum RMS current</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">10 [A]</td>
|
|
<td class="org-center"> </td>
|
|
</tr>
|
|
|
|
<tr>
|
|
<td class="org-left">Slew Rate</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">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">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">300 [Hz]</td>
|
|
<td class="org-center"> </td>
|
|
</tr>
|
|
</tbody>
|
|
</table>
|
|
|
|
<p>
|
|
For a load capacitance of \(10\,\mu F\), the expected \(-3\,dB\) bandwidth is \(6.4\,kHz\) (Figure <a href="#org407299e">2</a>) and the low frequency noise is \(650\,\mu V\,\text{rms}\) (Figure <a href="#org94560d5">3</a>).
|
|
</p>
|
|
|
|
|
|
<div id="org407299e" class="figure">
|
|
<p><img src="./figs/pd200_expected_small_signal_bandwidth.png" alt="pd200_expected_small_signal_bandwidth.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 2: </span>Expected small signal bandwidth</p>
|
|
</div>
|
|
|
|
|
|
<div id="org94560d5" class="figure">
|
|
<p><img src="figs/pd200_expected_noise.png" alt="pd200_expected_noise.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 3: </span>Expected Low frequency noise from 0.03Hz to 20Hz</p>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-orgb5bfcf0" class="outline-2">
|
|
<h2 id="orgb5bfcf0"><span class="section-number-2">4</span> Voltage Amplifier Model</h2>
|
|
<div class="outline-text-2" id="text-4">
|
|
<p>
|
|
The Amplifier is characterized by its dynamics \(G_p(s)\) from voltage inputs \(V_{in}\) to voltage output \(V_{out}\).
|
|
Ideally, the gain from \(V_{in}\) to \(V_{out}\) is constant over a wide frequency band with very small phase drop.
|
|
</p>
|
|
|
|
<p>
|
|
It is also characterized by its output noise \(n\).
|
|
This noise is described by its Power Spectral Density.
|
|
</p>
|
|
|
|
<p>
|
|
The objective is therefore to determine the transfer function \(G_p(s)\) from the input voltage to the output voltage as well as the Power Spectral Density \(S_n(\omega)\) of the amplifier output noise.
|
|
</p>
|
|
|
|
<p>
|
|
As both \(G_p\) and \(S_n\) depends on the load capacitance, they should be measured when loading the amplifier with a \(10\,\mu F\) capacitor.
|
|
</p>
|
|
|
|
|
|
<div id="org388bf47" class="figure">
|
|
<p><img src="figs/pd200-model-schematic.png" alt="pd200-model-schematic.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 4: </span>Model of the voltage amplifier</p>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-orga876e4d" class="outline-2">
|
|
<h2 id="orga876e4d"><span class="section-number-2">5</span> Noise measurement</h2>
|
|
<div class="outline-text-2" id="text-5">
|
|
<ul class="org-ul">
|
|
<li>Section <a href="#org56bae9f">5.1</a></li>
|
|
<li>Section <a href="#orgc48d4f4">5.2</a></li>
|
|
<li>Section <a href="#org2a59e12">5.3</a></li>
|
|
<li>Section <a href="#orgff6c06d">5.4</a></li>
|
|
<li>Section <a href="#orgdb787b7">5.5</a></li>
|
|
<li>Section <a href="#org41a9b46">5.6</a></li>
|
|
<li>Section <a href="#org00954a7">5.7</a></li>
|
|
<li>Section <a href="#orgbe0f3de">5.8</a></li>
|
|
</ul>
|
|
</div>
|
|
|
|
<div id="outline-container-org2c9f60e" class="outline-3">
|
|
<h3 id="org2c9f60e"><span class="section-number-3">5.1</span> Setup</h3>
|
|
<div class="outline-text-3" id="text-5-1">
|
|
<p>
|
|
<a id="org56bae9f"></a>
|
|
</p>
|
|
|
|
<div class="note" id="org2bfae12">
|
|
<p>
|
|
Here are the documentation of the equipment used for this test bench:
|
|
</p>
|
|
<ul class="org-ul">
|
|
<li>Voltage Amplifier <a href="doc/PD200-V7-R1.pdf">PD200</a></li>
|
|
<li>Load Capacitor <a href="doc/0900766b815ea422.pdf">EPCOS 10uF Multilayer Ceramic Capacitor</a></li>
|
|
<li>Low Noise Voltage Amplifier <a href="doc/egg-5113-preamplifier.pdf">EG&G 5113</a></li>
|
|
<li>Speedgoat ADC <a href="doc/IO131-OEM-Datasheet.pdf">IO313</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}
|
|
\phi_{n} \approx \frac{1\,mV}{\sqrt{1\,MHz}} = 1 \frac{\mu V}{\sqrt{Hz}}
|
|
\end{equation}
|
|
|
|
<p>
|
|
The RMS noise begin very small compare to the ADC resolution, we must amplify the noise before digitizing the signal.
|
|
The added noise of the instrumentation amplifier should be much smaller than the noise of the PD200.
|
|
We use the amplifier EG&G 5113 that has a noise of \(\approx 4 nV/\sqrt{Hz}\) referred to its input which is much smaller than the noise induced by the PD200.
|
|
</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.
|
|
</p>
|
|
|
|
|
|
<div id="org6c9024e" class="figure">
|
|
<p><img src="figs/setup-noise-measurement.png" alt="setup-noise-measurement.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 5: </span>Schematic of the test bench to measure the Power Spectral Density of the Voltage amplifier noise \(n\)</p>
|
|
</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-orgcf8ecc8" class="outline-3">
|
|
<h3 id="orgcf8ecc8"><span class="section-number-3">5.2</span> Model of the setup</h3>
|
|
<div class="outline-text-3" id="text-5-2">
|
|
<p>
|
|
<a id="orgc48d4f4"></a>
|
|
</p>
|
|
|
|
<p>
|
|
As shown in Figure <a href="#org52225dc">6</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>\(n_p\): output 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="org52225dc" class="figure">
|
|
<p><img src="figs/noise_meas_procedure.png" alt="noise_meas_procedure.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 6: </span>Sources of noise in the experimental setup</p>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org5f0cc17" class="outline-3">
|
|
<h3 id="org5f0cc17"><span class="section-number-3">5.3</span> Quantization Noise</h3>
|
|
<div class="outline-text-3" id="text-5-3">
|
|
<p>
|
|
<a id="org2a59e12"></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-org7c484b7" class="outline-3">
|
|
<h3 id="org7c484b7"><span class="section-number-3">5.4</span> Pre Amplifier noise measurement</h3>
|
|
<div class="outline-text-3" id="text-5-4">
|
|
<p>
|
|
<a id="orgff6c06d"></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="org21a64c7" class="figure">
|
|
<p><img src="figs/noise_measure_setup_preamp.png" alt="noise_measure_setup_preamp.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 7: </span>Sources of noise in the experimental setup</p>
|
|
</div>
|
|
|
|
<p>
|
|
The gain of the low noise amplifier is set to <code>50000</code>.
|
|
</p>
|
|
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab"><span class="org-comment">% Hanning window</span>
|
|
win = hanning(ceil(0.5<span class="org-type">/</span>Ts));
|
|
|
|
<span class="org-comment">% Power Spectral Density</span>
|
|
[pxx, f] = pwelch(preamp.Vn, win, [], [], Fs);
|
|
|
|
<span class="org-comment">% Save the results inside the struct</span>
|
|
preamp.pxx = pxx;
|
|
preamp.f = f;
|
|
</pre>
|
|
</div>
|
|
|
|
<p>
|
|
The obtained Amplitude Spectral Density of the Low Noise Voltage Amplifier is shown in Figure <a href="#org0f7d698">8</a>.
|
|
The obtained noise amplitude is very closed to the one specified in the documentation of \(4nV/\sqrt{Hz}\) at 1kHZ.
|
|
</p>
|
|
|
|
|
|
<div id="org0f7d698" class="figure">
|
|
<p><img src="figs/asd_preamp.png" alt="asd_preamp.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 8: </span>Obtained Amplitude Spectral Density of the Low Noise Voltage Amplifier</p>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org4fcdc54" class="outline-3">
|
|
<h3 id="org4fcdc54"><span class="section-number-3">5.5</span> PD200 noise measurement</h3>
|
|
<div class="outline-text-3" id="text-5-5">
|
|
<p>
|
|
<a id="orgdb787b7"></a>
|
|
</p>
|
|
|
|
<p>
|
|
The input of the PD200 amplifier is shunted such that there is 0V between its inputs.
|
|
Then the gain of the pre-amplifier is increased in order to measure a signal much larger than the quantization noise of the ADC.
|
|
We compute the Amplitude Spectral Density of the measured signal \(\Gamma_n(\omega)\).
|
|
The Amplitude Spectral Density of \(n_p\) can be computed taking into account the gain of the pre-amplifier:
|
|
</p>
|
|
\begin{equation}
|
|
\Gamma_{n_p}(\omega) = \frac{\Gamma_n(\omega)}{|G_a(\omega)|}
|
|
\end{equation}
|
|
|
|
<p>
|
|
And we verify that this is indeed the noise of the PD200 and not the noise of the pre-amplifier by checking that:
|
|
</p>
|
|
\begin{equation}
|
|
\Gamma_{n_p} \ll \Gamma_{n_a}
|
|
\end{equation}
|
|
|
|
|
|
<div id="orged8fdf4" class="figure">
|
|
<p><img src="figs/noise_measure_setup_pd200.png" alt="noise_measure_setup_pd200.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 9: </span>Sources of noise in the experimental setup</p>
|
|
</div>
|
|
|
|
<p>
|
|
The measured low frequency noise \(n_p\) of one of the amplifiers is shown in Figure <a href="#org9cb2c72">10</a>.
|
|
It is very similar to the one specified in the datasheet in Figure <a href="#org94560d5">3</a>.
|
|
</p>
|
|
|
|
<div id="org9cb2c72" class="figure">
|
|
<p><img src="figs/pd200_noise_time_lpf.png" alt="pd200_noise_time_lpf.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 10: </span>Measured low frequency noise of the PD200 from 0.01Hz to 20Hz</p>
|
|
</div>
|
|
|
|
<p>
|
|
The obtained RMS and peak to peak values of the measured noises are shown in Table <a href="#orgec90acd">3</a>.
|
|
</p>
|
|
<table id="orgec90acd" border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
|
|
<caption class="t-above"><span class="table-number">Table 3:</span> RMS and Peak to Peak measured low frequency noise (0.01Hz to 20Hz)</caption>
|
|
|
|
<colgroup>
|
|
<col class="org-left" />
|
|
|
|
<col class="org-right" />
|
|
|
|
<col class="org-right" />
|
|
</colgroup>
|
|
<thead>
|
|
<tr>
|
|
<th scope="col" class="org-left"> </th>
|
|
<th scope="col" class="org-right"><b>RMS [uV]</b></th>
|
|
<th scope="col" class="org-right"><b>Peak to Peak [mV]</b></th>
|
|
</tr>
|
|
</thead>
|
|
<tbody>
|
|
<tr>
|
|
<td class="org-left">Specification [10uF]</td>
|
|
<td class="org-right">714.0</td>
|
|
<td class="org-right">4.3</td>
|
|
</tr>
|
|
|
|
<tr>
|
|
<td class="org-left">PD200_1</td>
|
|
<td class="org-right">565.1</td>
|
|
<td class="org-right">3.7</td>
|
|
</tr>
|
|
|
|
<tr>
|
|
<td class="org-left">PD200_2</td>
|
|
<td class="org-right">767.6</td>
|
|
<td class="org-right">3.5</td>
|
|
</tr>
|
|
|
|
<tr>
|
|
<td class="org-left">PD200_3</td>
|
|
<td class="org-right">479.9</td>
|
|
<td class="org-right">3.0</td>
|
|
</tr>
|
|
|
|
<tr>
|
|
<td class="org-left">PD200_4</td>
|
|
<td class="org-right">615.7</td>
|
|
<td class="org-right">3.5</td>
|
|
</tr>
|
|
|
|
<tr>
|
|
<td class="org-left">PD200_5</td>
|
|
<td class="org-right">651.0</td>
|
|
<td class="org-right">2.4</td>
|
|
</tr>
|
|
|
|
<tr>
|
|
<td class="org-left">PD200_6</td>
|
|
<td class="org-right">473.2</td>
|
|
<td class="org-right">2.7</td>
|
|
</tr>
|
|
|
|
<tr>
|
|
<td class="org-left">PD200_7</td>
|
|
<td class="org-right">423.1</td>
|
|
<td class="org-right">2.3</td>
|
|
</tr>
|
|
</tbody>
|
|
</table>
|
|
|
|
<p>
|
|
The Amplitude Spectral Density of the measured noise is now computed and shown in Figure <a href="#org177c379">11</a>.
|
|
</p>
|
|
|
|
<div id="org177c379" class="figure">
|
|
<p><img src="figs/asd_noise_3uF_warmup.png" alt="asd_noise_3uF_warmup.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 11: </span>Amplitude Spectral Density of the measured noise</p>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-orga1b9697" class="outline-3">
|
|
<h3 id="orga1b9697"><span class="section-number-3">5.6</span> DAC noise measurement</h3>
|
|
<div class="outline-text-3" id="text-5-6">
|
|
<p>
|
|
<a id="org41a9b46"></a>
|
|
</p>
|
|
|
|
<p>
|
|
In order not to have any quantization noise, we impose the DAC to output a zero voltage.
|
|
The gain of the low noise amplifier is adjusted to
|
|
</p>
|
|
|
|
<p>
|
|
The Amplitude Spectral Density \(\Gamma_n(\omega)\) of the measured signal is computed.
|
|
The Amplitude Spectral Density of \(n_{da}\) can be computed taking into account the gain of the pre-amplifier:
|
|
</p>
|
|
\begin{equation}
|
|
\Gamma_{n_{da}}(\omega) = \frac{\Gamma_m(\omega)}{|G_a(\omega)|}
|
|
\end{equation}
|
|
|
|
<p>
|
|
And it is verify that the Amplitude Spectral Density of \(n_{da}\) is much larger than the one of \(n_a\):
|
|
</p>
|
|
\begin{equation}
|
|
\Gamma_{n_{da}} \gg \Gamma_{n_a}
|
|
\end{equation}
|
|
|
|
|
|
<div id="orga13ca97" class="figure">
|
|
<p><img src="figs/noise_measure_setup_dac.png" alt="noise_measure_setup_dac.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 12: </span>Sources of noise in the experimental setup</p>
|
|
</div>
|
|
|
|
|
|
<div id="org428ef0b" class="figure">
|
|
<p><img src="figs/asd_noise_dac.png" alt="asd_noise_dac.png" />
|
|
</p>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org6d8f9c2" class="outline-3">
|
|
<h3 id="org6d8f9c2"><span class="section-number-3">5.7</span> Total noise measurement</h3>
|
|
<div class="outline-text-3" id="text-5-7">
|
|
<p>
|
|
<a id="org00954a7"></a>
|
|
</p>
|
|
|
|
<p>
|
|
Let’s now analyze the measurement of the setup in Figure <a href="#org52225dc">6</a>.
|
|
</p>
|
|
|
|
<p>
|
|
The PSD of the measured noise is computed and the ASD is shown in Figure <a href="#org18dbc81">14</a>.
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">win = hanning(ceil(0.5<span class="org-type">/</span>Ts));
|
|
|
|
<span class="org-keyword">for</span> <span class="org-variable-name"><span class="org-constant">i</span></span> = <span class="org-constant">1:7</span>
|
|
[pxx, f] = pwelch(pd200dac{<span class="org-constant">i</span>}.Vn, win, [], [], Fs);
|
|
pd200dac{<span class="org-constant">i</span>}.f = f;
|
|
pd200dac{<span class="org-constant">i</span>}.pxx = pxx;
|
|
<span class="org-keyword">end</span>
|
|
</pre>
|
|
</div>
|
|
|
|
|
|
<div id="org18dbc81" class="figure">
|
|
<p><img src="figs/asd_noise_tot.png" alt="asd_noise_tot.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 14: </span>Amplitude Spectral Density of the measured noise and of the individual sources of noise</p>
|
|
</div>
|
|
|
|
<div class="important" id="org39d2c06">
|
|
<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-org59c04f1" class="outline-3">
|
|
<h3 id="org59c04f1"><span class="section-number-3">5.8</span> 20bits DAC noise measurement</h3>
|
|
<div class="outline-text-3" id="text-5-8">
|
|
<p>
|
|
<a id="orgbe0f3de"></a>
|
|
Let’s now measure the noise of another DAC called the “SSI2V” (<a href="doc/[SSI2V]Datasheet.pdf">doc</a>).
|
|
It is a 20bits DAC with an output of +/-10.48 V and a very low noise.
|
|
</p>
|
|
|
|
<p>
|
|
The measurement setup is the same as the one in Figure <a href="#orga13ca97">12</a>.
|
|
</p>
|
|
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">win = hanning(ceil(0.5<span class="org-type">/</span>Ts));
|
|
|
|
[pxx, f] = pwelch(ssi2v.Vn, win, [], [], Fs);
|
|
ssi2v.pxx = pxx;
|
|
ssi2v.f = f;
|
|
</pre>
|
|
</div>
|
|
|
|
<p>
|
|
The obtained noise of the SSI2V DAC is shown in Figure <a href="#orge9f88e0">15</a> and compared with the noise of the 16bits DAC.
|
|
It is shown to be much smaller (~1 order of magnitude).
|
|
</p>
|
|
|
|
|
|
<div id="orge9f88e0" class="figure">
|
|
<p><img src="figs/asd_ssi2v_noise.png" alt="asd_ssi2v_noise.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 15: </span>Amplitude Spectral Density of the SSI2V DAC’s noise</p>
|
|
</div>
|
|
|
|
<div class="important" id="org9ccd6d7">
|
|
<p>
|
|
Using the SSI2V as the DAC with the PD200 should give much better noise output than using the 16bits DAC.
|
|
The limiting factor should then be the noise of the PD200 itself.
|
|
</p>
|
|
|
|
</div>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-orga1cb3ef" class="outline-2">
|
|
<h2 id="orga1cb3ef"><span class="section-number-2">6</span> Transfer Function measurement</h2>
|
|
<div class="outline-text-2" id="text-6">
|
|
</div>
|
|
<div id="outline-container-org2c3812b" class="outline-3">
|
|
<h3 id="org2c3812b"><span class="section-number-3">6.1</span> Setup</h3>
|
|
<div class="outline-text-3" id="text-6-1">
|
|
<p>
|
|
In order to measure the transfer function from the input voltage \(V_{in}\) to the output voltage \(V_{out}\), the test bench shown in Figure <a href="#org1a2018d">16</a> is used.
|
|
</p>
|
|
|
|
<div class="note" id="orgb90f0e1">
|
|
<p>
|
|
Here are the documentation of the equipment used for this test bench:
|
|
</p>
|
|
<ul class="org-ul">
|
|
<li>Voltage Amplifier <a href="doc/PD200-V7-R1.pdf">PD200</a></li>
|
|
<li>Load Capacitor <a href="doc/0900766b815ea422.pdf">EPCOS 10uF Multilayer Ceramic Capacitor</a></li>
|
|
<li>Speedgoat DAC/ADC <a href="doc/IO131-OEM-Datasheet.pdf">IO313</a></li>
|
|
</ul>
|
|
|
|
</div>
|
|
|
|
<p>
|
|
For this measurement, the sampling frequency of the Speedgoat ADC should be as high as possible.
|
|
</p>
|
|
|
|
|
|
<div id="org1a2018d" class="figure">
|
|
<p><img src="figs/setup-dynamics-measurement.png" alt="setup-dynamics-measurement.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 16: </span>Schematic of the test bench to estimate the dynamics from voltage input \(V_{in}\) to voltage output \(V_{out}\)</p>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-orge1713a2" class="outline-3">
|
|
<h3 id="orge1713a2"><span class="section-number-3">6.2</span> Maximum Frequency/Voltage to not overload the amplifier</h3>
|
|
<div class="outline-text-3" id="text-6-2">
|
|
<p>
|
|
The maximum current is 1A [rms] which corresponds to 0.7A in amplitude of the sin wave.
|
|
</p>
|
|
|
|
<p>
|
|
The impedance of the capacitance is:
|
|
\[ Z_C(\omega) = \frac{1}{jC\omega} \]
|
|
</p>
|
|
|
|
<p>
|
|
Therefore the relation between the output current amplitude and the output voltage amplitude for sinusoidal waves of frequency \(\omega\):
|
|
\[ V_{out} = \frac{1}{C\omega} I_{out} \]
|
|
</p>
|
|
|
|
<p>
|
|
Moreover, there is a gain of 20 between the input voltage and the output voltage:
|
|
\[ 20 V_{in} = \frac{1}{C\omega} I_{out} \]
|
|
</p>
|
|
|
|
<p>
|
|
For a specified voltage input amplitude \(V_{in}\), the maximum frequency at which the output current reaches its maximum value is:
|
|
\[ \omega_{\text{max}} = \frac{1}{20 C V_{in}} I_{out,\text{max}} \]
|
|
</p>
|
|
|
|
<p>
|
|
\(\omega_max\) as a function of \(V_{in}\) is shown in Figure <a href="#orgfadee8c">17</a>.
|
|
</p>
|
|
|
|
|
|
<div id="orgfadee8c" class="figure">
|
|
<p><img src="figs/max_frequency_voltage.png" alt="max_frequency_voltage.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 17: </span>Maximum frequency as a function of the excitation voltage amplitude</p>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org4ff0dfb" class="outline-3">
|
|
<h3 id="org4ff0dfb"><span class="section-number-3">6.3</span> Obtained Transfer Functions</h3>
|
|
<div class="outline-text-3" id="text-6-3">
|
|
<p>
|
|
Several identifications using sweep sin were performed with input voltage amplitude ranging from 0.1V to 4V.
|
|
</p>
|
|
|
|
<p>
|
|
The obtained frequency response functions are shown in Figure <a href="#orgf2c5d27">18</a>.
|
|
As the input voltage increases, the voltage drop is increasing.
|
|
</p>
|
|
|
|
|
|
<div id="orgf2c5d27" class="figure">
|
|
<p><img src="figs/pd200_tf_voltage.png" alt="pd200_tf_voltage.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 18: </span>Transfer function for the PD200 amplitude between \(V_{in}\) and \(V_{out}\) for multiple voltage amplitudes</p>
|
|
</div>
|
|
|
|
<p>
|
|
The small signal transfer function of the amplifier can be approximated by a first order low pass filter.
|
|
</p>
|
|
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">Gp = 19.95<span class="org-type">/</span>(1 <span class="org-type">+</span> s<span class="org-type">/</span>2<span class="org-type">/</span><span class="org-constant">pi</span><span class="org-type">/</span>35e3);
|
|
</pre>
|
|
</div>
|
|
|
|
<p>
|
|
The comparison from the model and measurements are shown in Figure <a href="#orga34bca3">19</a>.
|
|
</p>
|
|
|
|
|
|
<div id="orga34bca3" class="figure">
|
|
<p><img src="figs/tf_pd200_model.png" alt="tf_pd200_model.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 19: </span>Comparison of the model transfer function and the measured frequency response function</p>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org6becade" class="outline-2">
|
|
<h2 id="org6becade"><span class="section-number-2">7</span> Conclusion</h2>
|
|
<div class="outline-text-2" id="text-7">
|
|
<table id="org9961e87" border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
|
|
<caption class="t-above"><span class="table-number">Table 4:</span> Measured characteristics, Manual characterstics and specified ones</caption>
|
|
|
|
<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: 2021-01-23 sam. 15:40</p>
|
|
</div>
|
|
</body>
|
|
</html>
|