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<title>Voltage Amplifier PD200 - Test Bench</title> <title>Voltage Amplifier PD200 - Test Bench</title>
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<body> <body>
<div id="org-div-home-and-up"> <div id="org-div-home-and-up">
@ -30,26 +39,34 @@
<h2>Table of Contents</h2> <h2>Table of Contents</h2>
<div id="text-table-of-contents"> <div id="text-table-of-contents">
<ul> <ul>
<li><a href="#orgeefbe5b">1. Voltage Amplifier Requirements</a></li> <li><a href="#org9fe8e60">1. Introduction</a></li>
<li><a href="#org2f6194f">2. PD200 Expected characteristics</a></li> <li><a href="#org83288a7">2. Voltage Amplifier Requirements</a></li>
<li><a href="#org12065bf">3. Voltage Amplifier Model</a></li> <li><a href="#org2725a7d">3. PD200 Expected characteristics</a></li>
<li><a href="#orgc5fc98e">4. Noise measurement</a> <li><a href="#org6748772">4. Voltage Amplifier Model</a></li>
<li><a href="#orgb0f1751">5. Noise measurement</a>
<ul> <ul>
<li><a href="#org72632dc">4.1. Setup</a></li> <li><a href="#org077faf1">5.1. Setup</a></li>
<li><a href="#org5fe0cf7">4.2. Results</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> </ul>
</li> </li>
<li><a href="#org0e85ab7">5. Transfer Function measurement</a>
<ul>
<li><a href="#org23bb14f">5.1. Setup</a></li>
<li><a href="#org58d7c48">5.2. Results</a></li>
</ul> </ul>
</li> </li>
<li><a href="#org351e02f">6. Conclusion</a></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> </ul>
</div> </div>
</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> <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. 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>
@ -59,16 +76,18 @@ The documentation of the PD200 is accessible <a href="doc/PD200-V7-R1.pdf">here<
</p> </p>
<div id="org97d8bc1" class="figure"> <div id="orga2cd341" class="figure">
<p><img src="figs/amplifier_PD200.png" alt="amplifier_PD200.png" /> <p><img src="figs/amplifier_PD200.png" alt="amplifier_PD200.png" />
</p> </p>
<p><span class="figure-number">Figure 1: </span>Picture of the PD200 Voltage Amplifier</p> <p><span class="figure-number">Figure 1: </span>Picture of the PD200 Voltage Amplifier</p>
</div> </div>
</div>
</div>
<div id="outline-container-orgeefbe5b" class="outline-2"> <div id="outline-container-org83288a7" class="outline-2">
<h2 id="orgeefbe5b"><span class="section-number-2">1</span> Voltage Amplifier Requirements</h2> <h2 id="org83288a7"><span class="section-number-2">2</span> Voltage Amplifier Requirements</h2>
<div class="outline-text-2" id="text-1"> <div class="outline-text-2" id="text-2">
<table id="orgcb23c6e" border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides"> <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> <caption class="t-above"><span class="table-number">Table 1:</span> Requirements for the Voltage Amplifier</caption>
<colgroup> <colgroup>
@ -112,10 +131,10 @@ The documentation of the PD200 is accessible <a href="doc/PD200-V7-R1.pdf">here<
</div> </div>
</div> </div>
<div id="outline-container-org2f6194f" class="outline-2"> <div id="outline-container-org2725a7d" class="outline-2">
<h2 id="org2f6194f"><span class="section-number-2">2</span> PD200 Expected characteristics</h2> <h2 id="org2725a7d"><span class="section-number-2">3</span> PD200 Expected characteristics</h2>
<div class="outline-text-2" id="text-2"> <div class="outline-text-2" id="text-3">
<table id="org37a9738" border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides"> <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> <caption class="t-above"><span class="table-number">Table 2:</span> Characteristics of the PD200</caption>
<colgroup> <colgroup>
@ -190,18 +209,18 @@ The documentation of the PD200 is accessible <a href="doc/PD200-V7-R1.pdf">here<
</table> </table>
<p> <p>
For a load capacitance of \(10\,\mu F\), the expected \(-3\,dB\) bandwidth is \(6.4\,kHz\) (Figure <a href="#org7cbbc0a">2</a>) and the low frequency noise is \(650\,\mu V\,\text{rms}\) (Figure <a href="#org99dc2f7">3</a>). 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> </p>
<div id="org7cbbc0a" class="figure"> <div id="orgf39e37f" class="figure">
<p><img src="./figs/pd200_expected_small_signal_bandwidth.png" alt="pd200_expected_small_signal_bandwidth.png" /> <p><img src="./figs/pd200_expected_small_signal_bandwidth.png" alt="pd200_expected_small_signal_bandwidth.png" />
</p> </p>
<p><span class="figure-number">Figure 2: </span>Expected small signal bandwidth</p> <p><span class="figure-number">Figure 2: </span>Expected small signal bandwidth</p>
</div> </div>
<div id="org99dc2f7" class="figure"> <div id="org2267cad" class="figure">
<p><img src="figs/pd200_expected_noise.png" alt="pd200_expected_noise.png" /> <p><img src="figs/pd200_expected_noise.png" alt="pd200_expected_noise.png" />
</p> </p>
<p><span class="figure-number">Figure 3: </span>Expected Low frequency noise from 0.03Hz to 20Hz</p> <p><span class="figure-number">Figure 3: </span>Expected Low frequency noise from 0.03Hz to 20Hz</p>
@ -209,9 +228,9 @@ For a load capacitance of \(10\,\mu F\), the expected \(-3\,dB\) bandwidth is \(
</div> </div>
</div> </div>
<div id="outline-container-org12065bf" class="outline-2"> <div id="outline-container-org6748772" class="outline-2">
<h2 id="org12065bf"><span class="section-number-2">3</span> Voltage Amplifier Model</h2> <h2 id="org6748772"><span class="section-number-2">4</span> Voltage Amplifier Model</h2>
<div class="outline-text-2" id="text-3"> <div class="outline-text-2" id="text-4">
<p> <p>
The Amplifier is characterized by its dynamics \(G_a(s)\) from voltage inputs \(V_{in}\) to voltage output \(V_{out}\). 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. Ideally, the gain from \(V_{in}\) to \(V_{out}\) is constant over a wide frequency band with very small phase drop.
@ -222,8 +241,16 @@ It is also characterized by its output noise \(n\).
This noise is described by its Power Spectral Density. This noise is described by its Power Spectral Density.
</p> </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>
<div id="org5f2ad81" class="figure"> <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><img src="figs/pd200-model-schematic.png" alt="pd200-model-schematic.png" />
</p> </p>
<p><span class="figure-number">Figure 4: </span>Model of the voltage amplifier</p> <p><span class="figure-number">Figure 4: </span>Model of the voltage amplifier</p>
@ -231,20 +258,20 @@ This noise is described by its Power Spectral Density.
</div> </div>
</div> </div>
<div id="outline-container-orgc5fc98e" class="outline-2"> <div id="outline-container-orgb0f1751" class="outline-2">
<h2 id="orgc5fc98e"><span class="section-number-2">4</span> Noise measurement</h2> <h2 id="orgb0f1751"><span class="section-number-2">5</span> Noise measurement</h2>
<div class="outline-text-2" id="text-4"> <div class="outline-text-2" id="text-5">
</div> </div>
<div id="outline-container-org72632dc" class="outline-3"> <div id="outline-container-org077faf1" class="outline-3">
<h3 id="org72632dc"><span class="section-number-3">4.1</span> Setup</h3> <h3 id="org077faf1"><span class="section-number-3">5.1</span> Setup</h3>
<div class="outline-text-3" id="text-4-1"> <div class="outline-text-3" id="text-5-1">
<div class="note" id="orgdee7438"> <div class="note" id="org3d87176">
<p> <p>
Here are the documentation of the equipment used for this test bench: Here are the documentation of the equipment used for this test bench:
</p> </p>
<ul class="org-ul"> <ul class="org-ul">
<li>Voltage Amplifier <a href="doc/PD200-V7-R1.pdf">PD200</a></li> <li>Voltage Amplifier <a href="doc/PD200-V7-R1.pdf">PD200</a></li>
<li>Load Capacitor <a href="doc/0900766b815ea422.pdf">EPCOS 10μF Multilayer Ceramic Capacitor</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>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> <li>Speedgoat ADC <a href="doc/IO131-OEM-Datasheet.pdf">IO313</a></li>
</ul> </ul>
@ -262,7 +289,7 @@ If we suppose a white noise, this correspond to an amplitude spectral density:
<p> <p>
The RMS noise begin very small compare to the ADC resolution, we must amplify the noise before digitizing the signal. 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. 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 have a noise of \(\approx 4 nV/\sqrt{Hz}\) referred to its input which is much smaller than the noise induced by 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>
<p> <p>
@ -271,37 +298,165 @@ This gain should be around 1000.
</p> </p>
<div id="orgcafa4d8" class="figure"> <div id="orgb37f1e6" class="figure">
<p><img src="figs/setup-noise-measurement.png" alt="setup-noise-measurement.png" /> <p><img src="figs/setup-noise-measurement.png" alt="setup-noise-measurement.png" />
</p> </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> <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> </div>
</div>
</div>
<div id="outline-container-org5fe0cf7" class="outline-3">
<h3 id="org5fe0cf7"><span class="section-number-3">4.2</span> Results</h3>
</div>
</div>
<div id="outline-container-org0e85ab7" class="outline-2">
<h2 id="org0e85ab7"><span class="section-number-2">5</span> Transfer Function measurement</h2>
<div class="outline-text-2" id="text-5">
</div>
<div id="outline-container-org23bb14f" class="outline-3">
<h3 id="org23bb14f"><span class="section-number-3">5.1</span> Setup</h3>
<div class="outline-text-3" id="text-5-1">
<p> <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="#orgab136cf">6</a> is used. 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> </p>
<div class="note" id="org6dbb8f7">
<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> <p>
Here are the documentation of the equipment used for this test bench: Here are the documentation of the equipment used for this test bench:
</p> </p>
<ul class="org-ul"> <ul class="org-ul">
<li>Voltage Amplifier <a href="doc/PD200-V7-R1.pdf">PD200</a></li> <li>Voltage Amplifier <a href="doc/PD200-V7-R1.pdf">PD200</a></li>
<li>Load Capacitor <a href="doc/0900766b815ea422.pdf">EPCOS 10μF Multilayer Ceramic Capacitor</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> <li>Speedgoat DAC/ADC <a href="doc/IO131-OEM-Datasheet.pdf">IO313</a></li>
</ul> </ul>
@ -312,23 +467,23 @@ For this measurement, the sampling frequency of the Speedgoat ADC should be as h
</p> </p>
<div id="orgab136cf" class="figure"> <div id="org472ad71" class="figure">
<p><img src="figs/setup-dynamics-measurement.png" alt="setup-dynamics-measurement.png" /> <p><img src="figs/setup-dynamics-measurement.png" alt="setup-dynamics-measurement.png" />
</p> </p>
<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> <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>
</div> </div>
<div id="outline-container-org58d7c48" class="outline-3"> <div id="outline-container-orgc5c49ee" class="outline-3">
<h3 id="org58d7c48"><span class="section-number-3">5.2</span> Results</h3> <h3 id="orgc5c49ee"><span class="section-number-3">6.2</span> Results</h3>
</div> </div>
</div> </div>
<div id="outline-container-org351e02f" class="outline-2"> <div id="outline-container-org516bcbb" class="outline-2">
<h2 id="org351e02f"><span class="section-number-2">6</span> Conclusion</h2> <h2 id="org516bcbb"><span class="section-number-2">7</span> Conclusion</h2>
<div class="outline-text-2" id="text-6"> <div class="outline-text-2" id="text-7">
<table id="org920ccdb" border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides"> <table id="orgcddfe96" 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> <caption class="t-above"><span class="table-number">Table 4:</span> Measured characteristics, Manual characterstics and specified ones</caption>
<colgroup> <colgroup>
<col class="org-left" /> <col class="org-left" />
@ -417,7 +572,7 @@ For this measurement, the sampling frequency of the Speedgoat ADC should be as h
</div> </div>
<div id="postamble" class="status"> <div id="postamble" class="status">
<p class="author">Author: Dehaeze Thomas</p> <p class="author">Author: Dehaeze Thomas</p>
<p class="date">Created: 2021-01-04 lun. 11:09</p> <p class="date">Created: 2021-01-19 mar. 23:00</p>
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@ -161,6 +161,154 @@ A low pass filter at 10kHz can be included in the EG&G amplifier in order to lim
An high pass filter at low frequency can be added if there is a problem of large offset. An high pass filter at low frequency can be added if there is a problem of large offset.
** Results ** 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 * Transfer Function measurement
** Setup ** Setup