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Author SHA1 Message Date
Thomas Dehaeze
906a3c3cb9 Add Output impedance measurements 2021-03-12 14:59:01 +01:00
Thomas Dehaeze
6580a81f30 Analyze new measurements 2021-02-16 13:12:24 +01:00
Thomas Dehaeze
bbbe665505 measure again the LA75B 2021-02-16 10:40:37 +01:00
Thomas Dehaeze
f41058dd89 test all 6 DACs 2021-02-16 10:06:28 +01:00
Thomas Dehaeze
f7f6b10b2d measure DAC noise 2021-02-16 09:46:45 +01:00
Thomas Dehaeze
8f4ade29ac New Analysis 2021-02-12 14:59:36 +01:00
Thomas Dehaeze
41d420634f measure LA75 transfer function 2021-02-11 18:04:26 +01:00
Thomas Dehaeze
5ea367641b measure small signal bandwidth 2021-02-11 11:41:08 +01:00
Thomas Dehaeze
820f343169 Update the analysis + add noise model 2021-02-10 16:16:57 +01:00
Thomas Dehaeze
8d23c9e028 Measure TF with 10uF load 2021-02-04 17:56:07 +01:00
Thomas Dehaeze
a7a20f298e measure LA75 noise 2021-02-04 17:32:36 +01:00
Thomas Dehaeze
157f2fae7a Measure noise with 10uF load 2021-02-04 17:04:42 +01:00
Thomas Dehaeze
730fea5116 Rename files 2021-02-02 18:50:47 +01:00
Thomas Dehaeze
26239292ac Change notation 2021-01-23 15:40:31 +01:00
Thomas Dehaeze
47773665f5 Analyze transfer function measurements 2021-01-23 15:38:31 +01:00
Thomas Dehaeze
8f70c1588e Analyze all noise meaurements 2021-01-22 23:44:36 +01:00
Operator Cad
ea0b02a155 debug SSI2V and V2SSI - Measure V2SSI noise 2021-01-22 16:09:35 +01:00
Operator Cad
cebf629a50 measure PD200 TF for multiple voltages 2021-01-22 11:34:24 +01:00
Thomas Dehaeze
1bac507d7c Analyze: dac noise, pre-amp noise, amp bandwidth 2021-01-21 19:02:02 +01:00
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<title>Voltage Amplifier PD200 - Test Bench</title>
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</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="#org9fe8e60">1. Introduction</a></li>
<li><a href="#org83288a7">2. Voltage Amplifier Requirements</a></li>
<li><a href="#org2725a7d">3. PD200 Expected characteristics</a></li>
<li><a href="#org6748772">4. Voltage Amplifier Model</a></li>
<li><a href="#orgb0f1751">5. Noise measurement</a>
<ul>
<li><a href="#org077faf1">5.1. Setup</a></li>
<li><a href="#org8d11397">5.2. Results</a>
<ul>
<li><a href="#org3e569c9">5.2.1. Noise when shunting the input (50 Ohms)</a></li>
</ul>
</li>
</ul>
</li>
<li><a href="#orgaf96727">6. Transfer Function measurement</a>
<ul>
<li><a href="#org9868c43">6.1. Setup</a></li>
<li><a href="#orgc5c49ee">6.2. Results</a></li>
</ul>
</li>
<li><a href="#org516bcbb">7. Conclusion</a></li>
</ul>
</div>
</div>
<div id="outline-container-org9fe8e60" class="outline-2">
<h2 id="org9fe8e60"><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="orga2cd341" 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-org83288a7" class="outline-2">
<h2 id="org83288a7"><span class="section-number-2">2</span> Voltage Amplifier Requirements</h2>
<div class="outline-text-2" id="text-2">
<table id="org6825b69" 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">&#xa0;</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">&gt; 50 [mA]</td>
</tr>
<tr>
<td class="org-left">Output Voltage Noise (1-200Hz)</td>
<td class="org-center">&lt; 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">&gt; 5 [kHz]</td>
</tr>
</tbody>
</table>
</div>
</div>
<div id="outline-container-org2725a7d" class="outline-2">
<h2 id="org2725a7d"><span class="section-number-2">3</span> PD200 Expected characteristics</h2>
<div class="outline-text-2" id="text-3">
<table id="orgf99d960" 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">&#xa0;</td>
</tr>
<tr>
<td class="org-left">Maximum RMS current</td>
<td class="org-center">0.9 [A]</td>
<td class="org-center">&gt; 50 [mA]</td>
</tr>
<tr>
<td class="org-left">Maximum Pulse current</td>
<td class="org-center">10 [A]</td>
<td class="org-center">&#xa0;</td>
</tr>
<tr>
<td class="org-left">Slew Rate</td>
<td class="org-center">150 [V/us]</td>
<td class="org-center">&#xa0;</td>
</tr>
<tr>
<td class="org-left">Noise (10uF load)</td>
<td class="org-center">0.7 [mV RMS]</td>
<td class="org-center">&lt; 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">&gt; 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">&#xa0;</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="#orgf39e37f">2</a>) and the low frequency noise is \(650\,\mu V\,\text{rms}\) (Figure <a href="#org2267cad">3</a>).
</p>
<div id="orgf39e37f" 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="org2267cad" 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-org6748772" class="outline-2">
<h2 id="org6748772"><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 \(G_a(s)\) 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 \(G_a(s)\) from the input voltage to the output voltage as well as the Power Spectral Density \(S_n(\omega)\) of the amplifier output noise.
</p>
<p>
As both \(G_a\) and \(S_n\) depends on the load capacitance, they should be measured when loading the amplifier with a \(\SI{10}{\micro\farad}\) capacitor.
</p>
<div id="org4313e25" 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-orgb0f1751" class="outline-2">
<h2 id="orgb0f1751"><span class="section-number-2">5</span> Noise measurement</h2>
<div class="outline-text-2" id="text-5">
</div>
<div id="outline-container-org077faf1" class="outline-3">
<h3 id="org077faf1"><span class="section-number-3">5.1</span> Setup</h3>
<div class="outline-text-3" id="text-5-1">
<div class="note" id="org3d87176">
<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&amp;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&amp;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="orgb37f1e6" 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&amp;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-org8d11397" class="outline-3">
<h3 id="org8d11397"><span class="section-number-3">5.2</span> Results</h3>
<div class="outline-text-3" id="text-5-2">
</div>
<div id="outline-container-org3e569c9" class="outline-4">
<h4 id="org3e569c9"><span class="section-number-4">5.2.1</span> Noise when shunting the input (50 Ohms)</h4>
<div class="outline-text-4" id="text-5-2-1">
<p>
The time domain measurements of the amplifier noise are shown in Figure <a href="#org6fb276a">6</a>.
</p>
<div id="org6fb276a" class="figure">
<p><img src="figs/noise_shunt_time_3uF.png" alt="noise_shunt_time_3uF.png" />
</p>
<p><span class="figure-number">Figure 6: </span>Time domain measurement of the amplifier output noise</p>
</div>
<p>
Obtained low frequency (0.1Hz - 20Hz) noise is shown in Figure <a href="#orgaadf193">7</a> which is very similar to the noise shown in the documentation (Figure <a href="#org2267cad">3</a>).
</p>
<div id="orgaadf193" class="figure">
<p><img src="figs/low_noise_time_domain_3uF.png" alt="low_noise_time_domain_3uF.png" />
</p>
<p><span class="figure-number">Figure 7: </span>Low Frequency Noise (0.1Hz - 20Hz)</p>
</div>
<p>
The obtained RMS and peak to peak values of the measured noises are shown in Table <a href="#orgd174c39">3</a>.
</p>
<table id="orgd174c39" 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 noise</caption>
<colgroup>
<col class="org-left" />
<col class="org-right" />
<col class="org-right" />
</colgroup>
<thead>
<tr>
<th scope="col" class="org-left">&#xa0;</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">524.9</td>
<td class="org-right">4.5</td>
</tr>
<tr>
<td class="org-left">PD200_2</td>
<td class="org-right">807.7</td>
<td class="org-right">6.7</td>
</tr>
<tr>
<td class="org-left">PD200_3</td>
<td class="org-right">630.3</td>
<td class="org-right">5.4</td>
</tr>
<tr>
<td class="org-left">PD200_4</td>
<td class="org-right">619.7</td>
<td class="org-right">5.5</td>
</tr>
<tr>
<td class="org-left">PD200_5</td>
<td class="org-right">630.8</td>
<td class="org-right">5.6</td>
</tr>
<tr>
<td class="org-left">PD200_6</td>
<td class="org-right">517.3</td>
<td class="org-right">4.9</td>
</tr>
<tr>
<td class="org-left">PD200_7</td>
<td class="org-right">393.8</td>
<td class="org-right">3.7</td>
</tr>
</tbody>
</table>
<p>
The PSD of the measured noise is computed and the ASD is shown in Figure <a href="#org17a3769">8</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(pd200{1}.Vn, win, [], [], Fs);
pxx = zeros(length(pxx), 7);
<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(<span class="org-type">:</span>, <span class="org-constant">i</span>) = pwelch(pd200{<span class="org-constant">i</span>}.Vn, win, [], [], Fs);
<span class="org-keyword">end</span>
</pre>
</div>
<div id="org17a3769" class="figure">
<p><img src="figs/asd_noise_3uF.png" alt="asd_noise_3uF.png" />
</p>
<p><span class="figure-number">Figure 8: </span>Amplitude Spectral Density of the measured noise</p>
</div>
</div>
</div>
</div>
</div>
<div id="outline-container-orgaf96727" class="outline-2">
<h2 id="orgaf96727"><span class="section-number-2">6</span> Transfer Function measurement</h2>
<div class="outline-text-2" id="text-6">
</div>
<div id="outline-container-org9868c43" class="outline-3">
<h3 id="org9868c43"><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="#org472ad71">9</a> is used.
</p>
<div class="note" id="org5cbd7bf">
<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="org472ad71" class="figure">
<p><img src="figs/setup-dynamics-measurement.png" alt="setup-dynamics-measurement.png" />
</p>
<p><span class="figure-number">Figure 9: </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-orgc5c49ee" class="outline-3">
<h3 id="orgc5c49ee"><span class="section-number-3">6.2</span> Results</h3>
</div>
</div>
<div id="outline-container-org516bcbb" class="outline-2">
<h2 id="org516bcbb"><span class="section-number-2">7</span> Conclusion</h2>
<div class="outline-text-2" id="text-7">
<table id="orgcddfe96" 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">&#xa0;</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">&#xa0;</td>
<td class="org-center">0.9 [A]</td>
<td class="org-center">&gt; 50 [mA]</td>
</tr>
<tr>
<td class="org-left">Maximum Pulse current</td>
<td class="org-center">&#xa0;</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">&#xa0;</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">&#xa0;</td>
<td class="org-center">0.7 [mV RMS]</td>
<td class="org-center">&lt; 2 [mV rms]</td>
</tr>
<tr>
<td class="org-left">Small Signal Bandwidth (10uF load)</td>
<td class="org-center">&#xa0;</td>
<td class="org-center">7.4 [kHz]</td>
<td class="org-center">&gt; 5 [kHz]</td>
</tr>
<tr>
<td class="org-left">Large Signal Bandwidth (150V, 10uF)</td>
<td class="org-center">&#xa0;</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: 2021-01-19 mar. 23:00</p>
</div>
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#+TITLE: Voltage Amplifier PD200 - Test Bench
:DRAWER:
#+LANGUAGE: en
#+EMAIL: dehaeze.thomas@gmail.com
#+AUTHOR: Dehaeze Thomas
#+HTML_LINK_HOME: ../index.html
#+HTML_LINK_UP: ../index.html
#+HTML_HEAD: <link rel="stylesheet" type="text/css" href="https://research.tdehaeze.xyz/css/style.css"/>
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#+PROPERTY: header-args:latex+ :post pdf2svg(file=*this*, ext="png")
:END:
* Introduction
The goal of this test bench is to characterize the Voltage amplifier [[https://www.piezodrive.com/drivers/pd200-60-watt-voltage-amplifier/][PD200]] from PiezoDrive.
The documentation of the PD200 is accessible [[file:doc/PD200-V7-R1.pdf][here]].
#+name: fig:amplifier_PD200
#+caption: Picture of the PD200 Voltage Amplifier
#+attr_latex: :width 0.8\linewidth
[[file:figs/amplifier_PD200.png]]
* Voltage Amplifier Requirements
#+name: tab:voltage_amplifier_requirements
#+caption: Requirements for the Voltage Amplifier
#+attr_latex: :environment tabularx :width 0.5\linewidth :align lX
#+attr_latex: :center t :booktabs t :float t
| <l> | <c> |
| | *Specification* |
|--------------------------------+--------------------|
| Continuous Current | > 50 [mA] |
| Output Voltage Noise (1-200Hz) | < 2 [mV rms] |
| Voltage Input Range | +/- 10 [V] |
| Voltage Output Range | -20 [V] to 150 [V] |
| Small signal bandwidth (-3dB) | > 5 [kHz] |
* PD200 Expected characteristics
#+name: tab:pd200_characteristics
#+caption: Characteristics of the PD200
#+attr_latex: :environment tabularx :width \linewidth :align lXX
#+attr_latex: :center t :booktabs t :float t
| <l> | <c> | <c> |
| *Characteristics* | *Manual* | *Specification* |
|-------------------------------------+--------------+-----------------|
| Input Voltage Range | +/- 10 [V] | +/- 10 [V] |
| Output Voltage Range | -50/150 [V] | -20/150 [V] |
| Gain | 20 [V/V] | |
| Maximum RMS current | 0.9 [A] | > 50 [mA] |
| Maximum Pulse current | 10 [A] | |
| Slew Rate | 150 [V/us] | |
| Noise (10uF load) | 0.7 [mV RMS] | < 2 [mV rms] |
| Small Signal Bandwidth (10uF load) | 7.4 [kHz] | > 5 [kHz] |
| Large Signal Bandwidth (150V, 10uF) | 300 [Hz] | |
For a load capacitance of $10\,\mu F$, the expected $-3\,dB$ bandwidth is $6.4\,kHz$ (Figure [[fig:pd200_expected_small_signal_bandwidth]]) and the low frequency noise is $650\,\mu V\,\text{rms}$ (Figure [[fig:pd200_expected_noise]]).
#+name: fig:pd200_expected_small_signal_bandwidth
#+caption:Expected small signal bandwidth
#+attr_latex: :width 0.8\linewidth
[[file:./figs/pd200_expected_small_signal_bandwidth.png]]
#+name: fig:pd200_expected_noise
#+caption: Expected Low frequency noise from 0.03Hz to 20Hz
#+attr_latex: :width 0.8\linewidth
[[file:figs/pd200_expected_noise.png]]
* Voltage Amplifier Model
The Amplifier is characterized by its dynamics $G_a(s)$ 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.
It is also characterized by its output noise $n$.
This noise is described by its Power Spectral Density.
The objective is therefore to determine the transfer function $G_a(s)$ from the input voltage to the output voltage as well as the Power Spectral Density $S_n(\omega)$ of the amplifier output noise.
As both $G_a$ and $S_n$ depends on the load capacitance, they should be measured when loading the amplifier with a $\SI{10}{\micro\farad}$ capacitor.
#+begin_src latex :file pd200-model-schematic.pdf
\begin{tikzpicture}
\node[block] (G) at (0,0){$G_a(s)$};
\node[addb, right=0.8 of G] (add){};
\draw[<-] (G.west) -- ++(-1.2, 0) node[above right]{$V_{in}$};
\draw[->] (G.east) -- (add.west);
\draw[->] (add.east) -- ++(1.2, 0) node[above left]{$V_{out}$};
\draw[<-] (add.north) -- ++(0, 0.6) node[below right](n){$n$};
\begin{scope}[on background layer]
\node[fit={(G.south west) (n.north-|add.east)}, inner sep=8pt, draw, dashed, fill=black!20!white] (P) {};
\node[below] at (P.north) {PD-200};
\end{scope}
\end{tikzpicture}
#+end_src
#+name: fig:pd200-model-schematic
#+caption: Model of the voltage amplifier
#+RESULTS:
[[file:figs/pd200-model-schematic.png]]
* Noise measurement
** Setup
#+begin_note
Here are the documentation of the equipment used for this test bench:
- Voltage Amplifier [[file:doc/PD200-V7-R1.pdf][PD200]]
- Load Capacitor [[file:doc/0900766b815ea422.pdf][EPCOS 10uF Multilayer Ceramic Capacitor]]
- Low Noise Voltage Amplifier [[file:doc/egg-5113-preamplifier.pdf][EG&G 5113]]
- Speedgoat ADC [[file:doc/IO131-OEM-Datasheet.pdf][IO313]]
#+end_note
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:
\begin{equation}
\phi_{n} \approx \frac{1\,mV}{\sqrt{1\,MHz}} = 1 \frac{\mu V}{\sqrt{Hz}}
\end{equation}
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.
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.
#+name: fig:setup-noise-measurement
#+caption: Schematic of the test bench to measure the Power Spectral Density of the Voltage amplifier noise $n$
#+attr_latex: :width \linewidth
[[file:figs/setup-noise-measurement.png]]
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.
** Results
*** Matlab Init :noexport:ignore:
#+begin_src matlab :tangle no :exports none :results silent :noweb yes :var current_dir=(file-name-directory buffer-file-name)
<<matlab-dir>>
#+end_src
#+begin_src matlab :exports none :results silent :noweb yes
<<matlab-init>>
#+end_src
#+begin_src matlab :tangle no
addpath('./matlab/mat/');
addpath('./matlab/');
#+end_src
#+begin_src matlab :eval no
addpath('./mat/');
#+end_src
*** Noise when shunting the input (50 Ohms)
#+begin_src matlab :exports none
%% Load all the measurements
pd200 = {};
for i = 1:7
pd200(i) = {load(['mat/noise_PD200_' num2str(i) '.mat'], 't', 'Vn', 'notes')};
end
%% Take into account the pre-amplifier gain
for i = 1:7
pd200{i}.Vn = pd200{i}.Vn/pd200{i}.notes.pre_amp.gain;
end
#+end_src
The time domain measurements of the amplifier noise are shown in Figure [[fig:noise_shunt_time_3uF]].
#+begin_src matlab :exports none
figure;
hold on;
for i = 1:7
plot(pd200{i}.t, 1e3*pd200{i}.Vn)
end
hold off;
xlabel('Time [s]');
ylabel('Voltage [mV]');
#+end_src
#+begin_src matlab :tangle no :exports results :results file replace
exportFig('figs/noise_shunt_time_3uF.pdf', 'width', 'wide', 'height', 'normal');
#+end_src
#+name: fig:noise_shunt_time_3uF
#+caption: Time domain measurement of the amplifier output noise
#+RESULTS:
[[file:figs/noise_shunt_time_3uF.png]]
Obtained low frequency (0.1Hz - 20Hz) noise is shown in Figure [[fig:low_noise_time_domain_3uF]] which is very similar to the noise shown in the documentation (Figure [[fig:pd200_expected_noise]]).
#+begin_src matlab :exports none
figure;
hold on;
plot(pd200{1}.t, lsim(1/(1 + s/2/pi/20), 1e3*pd200{1}.Vn, pd200{1}.t))
hold off;
xlabel('Time [s]');
ylabel('Voltage [mV]');
xlim([0, 40]); ylim([-3, 3]);
#+end_src
#+begin_src matlab :tangle no :exports results :results file replace
exportFig('figs/low_noise_time_domain_3uF.pdf', 'width', 'wide', 'height', 'normal');
#+end_src
#+name: fig:low_noise_time_domain_3uF
#+caption: Low Frequency Noise (0.1Hz - 20Hz)
#+RESULTS:
[[file:figs/low_noise_time_domain_3uF.png]]
The obtained RMS and peak to peak values of the measured noises are shown in Table [[tab:rms_pkp_noise]].
#+begin_src matlab :exports none
%% Compute the RMS and Peak to Peak noise
Vn_rms = zeros(7,1); % RMS value [uV rms]
Vn_pkp = zeros(7,1); % Peak to Peak Value [mV]
for i = 1:7
Vn_rms(i) = 1e6*rms(pd200{i}.Vn);
Vn_pkp(i) = 1e3*(max(pd200{i}.Vn)-min(pd200{i}.Vn));
end
#+end_src
#+begin_src matlab :exports results :results value table replace :tangle no :post addhdr(*this*)
data2orgtable([[714; Vn_rms], [4.3; Vn_pkp]], {'Specification [10uF]', 'PD200_1', 'PD200_2', 'PD200_3', 'PD200_4', 'PD200_5', 'PD200_6', 'PD200_7'}, {'*RMS [uV]*', '*Peak to Peak [mV]*'}, ' %.1f ');
#+end_src
#+name: tab:rms_pkp_noise
#+caption: RMS and Peak to Peak measured noise
#+attr_latex: :environment tabularx :width \linewidth :align lXX
#+attr_latex: :center t :booktabs t :float t
#+RESULTS:
| | *RMS [uV]* | *Peak to Peak [mV]* |
|----------------------+------------+---------------------|
| Specification [10uF] | 714.0 | 4.3 |
| PD200_1 | 524.9 | 4.5 |
| PD200_2 | 807.7 | 6.7 |
| PD200_3 | 630.3 | 5.4 |
| PD200_4 | 619.7 | 5.5 |
| PD200_5 | 630.8 | 5.6 |
| PD200_6 | 517.3 | 4.9 |
| PD200_7 | 393.8 | 3.7 |
#+begin_src matlab :exports none
% Sampling time / frequency
Ts = (pd200{1}.t(end) - pd200{1}.t(1))/(length(pd200{1}.t) - 1);
Fs = 1/Ts;
#+end_src
The PSD of the measured noise is computed and the ASD is shown in Figure [[fig:asd_noise_3uF]].
#+begin_src matlab
win = hanning(ceil(0.5/Ts));
[pxx, f] = pwelch(pd200{1}.Vn, win, [], [], Fs);
pxx = zeros(length(pxx), 7);
for i = 1:7
pxx(:, i) = pwelch(pd200{i}.Vn, win, [], [], Fs);
end
#+end_src
#+begin_src matlab :exports none
figure;
hold on;
for i = 1:7
plot(f, sqrt(pxx(:, i)), 'DisplayName', sprintf('PD200-%i', i));
end
hold off;
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
xlabel('Frequency [Hz]'); ylabel('ASD [$V/\sqrt{Hz}$]');
legend('location', 'southwest');
xlim([1, Fs/2]);
#+end_src
#+begin_src matlab :tangle no :exports results :results file replace
exportFig('figs/asd_noise_3uF.pdf', 'width', 'wide', 'height', 'tall');
#+end_src
#+name: fig:asd_noise_3uF
#+caption: Amplitude Spectral Density of the measured noise
#+RESULTS:
[[file:figs/asd_noise_3uF.png]]
* Transfer Function measurement
** Setup
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 [[fig:setup-dynamics-measurement]] is used.
#+begin_note
Here are the documentation of the equipment used for this test bench:
- Voltage Amplifier [[file:doc/PD200-V7-R1.pdf][PD200]]
- Load Capacitor [[file:doc/0900766b815ea422.pdf][EPCOS 10uF Multilayer Ceramic Capacitor]]
- Speedgoat DAC/ADC [[file:doc/IO131-OEM-Datasheet.pdf][IO313]]
#+end_note
For this measurement, the sampling frequency of the Speedgoat ADC should be as high as possible.
#+name: fig:setup-dynamics-measurement
#+caption: Schematic of the test bench to estimate the dynamics from voltage input $V_{in}$ to voltage output $V_{out}$
[[file:figs/setup-dynamics-measurement.png]]
** Results
* Conclusion
#+name: tab:table_name
#+caption: Measured characteristics, Manual characterstics and specified ones
#+attr_latex: :environment tabularx :width \linewidth :align lXXX
#+attr_latex: :center t :booktabs t :float t
| <l> | <c> | <c> | <c> |
| *Characteristics* | *Measurement* | *Manual* | *Specification* |
|-------------------------------------+---------------+--------------+-----------------|
| Input Voltage Range | - | +/- 10 [V] | +/- 10 [V] |
| Output Voltage Range | - | -50/150 [V] | -20/150 [V] |
| Gain | | 20 [V/V] | - |
| Maximum RMS current | | 0.9 [A] | > 50 [mA] |
| Maximum Pulse current | | 10 [A] | - |
| Slew Rate | | 150 [V/us] | - |
| Noise (10uF load) | | 0.7 [mV RMS] | < 2 [mV rms] |
| Small Signal Bandwidth (10uF load) | | 7.4 [kHz] | > 5 [kHz] |
| Large Signal Bandwidth (150V, 10uF) | | 300 [Hz] | - |

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