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"http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd">
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<html xmlns="http://www.w3.org/1999/xhtml" lang="en" xml:lang="en">
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<head>
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<!-- 2020-11-10 mar. 12:34 -->
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<!-- 2020-11-10 mar. 12:44 -->
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<meta http-equiv="Content-Type" content="text/html;charset=utf-8" />
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<title>Measurement of Piezoelectric Amplifiers</title>
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<meta name="generator" content="Org mode" />
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@ -30,47 +30,48 @@
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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="#orgbf340db">1. Effect of a change of capacitance</a>
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<li><a href="#org2595d4f">1. Effect of a change of capacitance</a>
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<ul>
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<li><a href="#org641e8fa">1.1. Cedrat Technology</a></li>
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<li><a href="#org1418126">1.2. PI</a></li>
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<li><a href="#orgd8111a6">1.1. Cedrat Technology</a></li>
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<li><a href="#org278fde7">1.2. PI</a></li>
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</ul>
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</li>
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<li><a href="#org759da67">2. Effect of a change in Voltage level</a>
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<li><a href="#org2c356cd">2. Effect of a change in Voltage level</a>
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<ul>
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<li><a href="#org6a05198">2.1. Cedrat Technology</a></li>
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<li><a href="#orga82864e">2.2. PI</a></li>
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<li><a href="#org26c0aa6">2.1. Cedrat Technology</a></li>
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<li><a href="#org99f4366">2.2. PI</a></li>
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</ul>
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</li>
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<li><a href="#orgda5e46f">3. Comparison PI / Cedrat</a>
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<li><a href="#orgaef7c1d">3. Comparison PI / Cedrat</a>
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<ul>
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<li><a href="#orgf81af9e">3.1. Results</a></li>
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<li><a href="#orgb7b222e">3.1. Results</a></li>
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</ul>
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</li>
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<li><a href="#org2ac1966">4. Impedance Measurement</a>
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<li><a href="#org7cf90b4">4. Impedance Measurement</a>
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<ul>
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<li><a href="#orgabf5b9a">4.1. Cedrat Technology</a>
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<li><a href="#org2defd83">4.1. Cedrat Technology</a>
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<ul>
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<li><a href="#org373f123">4.1.1. Compute Impedance</a></li>
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<li><a href="#orgc9002d7">4.1.2. Effect of Impedance on the phase drop</a></li>
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<li><a href="#orgf66e83a">4.1.1. Compute Impedance</a></li>
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<li><a href="#orgc7a6f64">4.1.2. Effect of Impedance on the phase drop</a></li>
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</ul>
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</li>
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<li><a href="#org3134308">4.2. PI</a></li>
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<li><a href="#orgfd9e37f">4.2. PI</a></li>
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</ul>
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</li>
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<li><a href="#org84728eb">5. New PI amplifier measurements</a>
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<li><a href="#org943c8af">5. Effect of filters configuration on the PI-E505 dynamics</a>
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<ul>
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<li><a href="#org5ca1305">5.1. PI</a></li>
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<li><a href="#org091ce77">5.2. Transfer function of the Voltage Amplifier</a></li>
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<li><a href="#org78406e1">5.3. With Load</a></li>
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<li><a href="#org86c1e48">5.1. PI</a></li>
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<li><a href="#org35acfc7">5.2. Transfer function of the Voltage Amplifier</a></li>
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<li><a href="#org1c608d2">5.3. With Load</a></li>
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</ul>
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</li>
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</ul>
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</div>
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</div>
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<div class="note" id="org6d2afbc">
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<p>
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Two voltage amplifiers are tested:
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The following two voltage amplifiers are tested:
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</p>
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<ul class="org-ul">
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<li>PI E-505.00 (<a href="doc/E-505-Datasheet.pdf">doc</a>)</li>
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@ -82,12 +83,28 @@ The piezoelectric actuator under test is an APA95ML from Cedrat technology (<a h
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It contains three stacks with a capacitance of \(5 \mu F\) each that can be connected independently to the amplifier.
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</p>
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<div id="outline-container-orgbf340db" class="outline-2">
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<h2 id="orgbf340db"><span class="section-number-2">1</span> Effect of a change of capacitance</h2>
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<div class="outline-text-2" id="text-1">
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</div>
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<div id="outline-container-org641e8fa" class="outline-3">
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<h3 id="org641e8fa"><span class="section-number-3">1.1</span> Cedrat Technology</h3>
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<p>
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This document is divided into the following sections:
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</p>
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<ul class="org-ul">
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<li>Section <a href="#org14b2007">1</a>: The effect of a change in load capacitance on the amplifier dynamics is studied</li>
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<li>Section <a href="#org5952ed9">2</a>: The effect on the voltage level on the amplifier dynamics is studied</li>
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<li>Section <a href="#org021167d">3</a>: The dynamics of the E-505 and LA75B are compared</li>
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<li>Section <a href="#org3a61ea0">4</a>: The output impedance of both amplifiers are measured</li>
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<li>Section <a href="#orgdc9f3a2">5</a>: The effect of the internal filters of the E-505 on its dynamics is studied</li>
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</ul>
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<div id="outline-container-org2595d4f" class="outline-2">
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<h2 id="org2595d4f"><span class="section-number-2">1</span> Effect of a change of capacitance</h2>
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<div class="outline-text-2" id="text-1">
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<p>
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<a id="org14b2007"></a>
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</p>
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</div>
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<div id="outline-container-orgd8111a6" class="outline-3">
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<h3 id="orgd8111a6"><span class="section-number-3">1.1</span> Cedrat Technology</h3>
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<div class="outline-text-3" id="text-1-1">
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<p>
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Load Data
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@ -126,7 +143,7 @@ We remove the phase delay due to the time delay of the ADC/DAC:
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</div>
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<div id="org51f0c1d" class="figure">
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<div id="org0f3ffec" class="figure">
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<p><img src="figs/change_capa_cedrat.png" alt="change_capa_cedrat.png" />
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</p>
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<p><span class="figure-number">Figure 1: </span>Effect of a change of the piezo capacitance on the Amplifier transfer function</p>
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@ -134,8 +151,8 @@ We remove the phase delay due to the time delay of the ADC/DAC:
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</div>
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</div>
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<div id="outline-container-org1418126" class="outline-3">
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<h3 id="org1418126"><span class="section-number-3">1.2</span> PI</h3>
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<div id="outline-container-org278fde7" class="outline-3">
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<h3 id="org278fde7"><span class="section-number-3">1.2</span> PI</h3>
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<div class="outline-text-3" id="text-1-2">
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<div class="org-src-container">
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<pre class="src src-matlab">piezo1 = load(<span class="org-string">'pi_505_high.mat'</span>, <span class="org-string">'t'</span>, <span class="org-string">'V_in'</span>, <span class="org-string">'V_out'</span>);
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@ -168,7 +185,7 @@ We remove the phase delay due to the time delay of the ADC/DAC:
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</div>
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<div id="org94c038d" class="figure">
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<div id="org1f93710" class="figure">
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<p><img src="figs/change_capa_pi.png" alt="change_capa_pi.png" />
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</p>
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<p><span class="figure-number">Figure 2: </span>Effect of a change of the piezo capacitance on the Amplifier transfer function</p>
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@ -177,12 +194,15 @@ We remove the phase delay due to the time delay of the ADC/DAC:
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</div>
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</div>
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<div id="outline-container-org759da67" class="outline-2">
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<h2 id="org759da67"><span class="section-number-2">2</span> Effect of a change in Voltage level</h2>
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<div id="outline-container-org2c356cd" class="outline-2">
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<h2 id="org2c356cd"><span class="section-number-2">2</span> Effect of a change in Voltage level</h2>
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<div class="outline-text-2" id="text-2">
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<p>
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<a id="org5952ed9"></a>
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</p>
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</div>
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<div id="outline-container-org6a05198" class="outline-3">
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<h3 id="org6a05198"><span class="section-number-3">2.1</span> Cedrat Technology</h3>
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<div id="outline-container-org26c0aa6" class="outline-3">
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<h3 id="org26c0aa6"><span class="section-number-3">2.1</span> Cedrat Technology</h3>
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<div class="outline-text-3" id="text-2-1">
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<div class="org-src-container">
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<pre class="src src-matlab">hi = load(<span class="org-string">'cedrat_la75b_high_1_stack.mat'</span>, <span class="org-string">'t'</span>, <span class="org-string">'V_in'</span>, <span class="org-string">'V_out'</span>);
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@ -215,7 +235,7 @@ We remove the phase delay due to the time delay of the ADC/DAC:
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</div>
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<div id="org413319b" class="figure">
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<div id="org6fa5b64" class="figure">
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<p><img src="figs/change_level_cedrat.png" alt="change_level_cedrat.png" />
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</p>
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<p><span class="figure-number">Figure 3: </span>Effect of a change of voltage level on the Amplifier transfer function</p>
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@ -223,8 +243,8 @@ We remove the phase delay due to the time delay of the ADC/DAC:
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</div>
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</div>
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<div id="outline-container-orga82864e" class="outline-3">
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<h3 id="orga82864e"><span class="section-number-3">2.2</span> PI</h3>
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<div id="outline-container-org99f4366" class="outline-3">
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<h3 id="org99f4366"><span class="section-number-3">2.2</span> PI</h3>
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<div class="outline-text-3" id="text-2-2">
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<div class="org-src-container">
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<pre class="src src-matlab">hi = load(<span class="org-string">'pi_505_high.mat'</span>, <span class="org-string">'t'</span>, <span class="org-string">'V_in'</span>, <span class="org-string">'V_out'</span>);
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@ -245,7 +265,7 @@ win = hann(ceil(0.1<span class="org-type">/</span>Ts));
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</div>
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<div id="orgfdd759e" class="figure">
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<div id="org234ac05" class="figure">
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<p><img src="figs/change_level_pi.png" alt="change_level_pi.png" />
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</p>
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<p><span class="figure-number">Figure 4: </span>Effect of a change of voltage level on the Amplifier transfer function</p>
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@ -254,12 +274,15 @@ win = hann(ceil(0.1<span class="org-type">/</span>Ts));
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</div>
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</div>
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<div id="outline-container-orgda5e46f" class="outline-2">
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<h2 id="orgda5e46f"><span class="section-number-2">3</span> Comparison PI / Cedrat</h2>
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<div id="outline-container-orgaef7c1d" class="outline-2">
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<h2 id="orgaef7c1d"><span class="section-number-2">3</span> Comparison PI / Cedrat</h2>
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<div class="outline-text-2" id="text-3">
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<p>
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<a id="org021167d"></a>
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</p>
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</div>
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<div id="outline-container-orgf81af9e" class="outline-3">
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<h3 id="orgf81af9e"><span class="section-number-3">3.1</span> Results</h3>
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<div id="outline-container-orgb7b222e" class="outline-3">
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<h3 id="orgb7b222e"><span class="section-number-3">3.1</span> Results</h3>
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<div class="outline-text-3" id="text-3-1">
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<div class="org-src-container">
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<pre class="src src-matlab">ce_results = load(<span class="org-string">'cedrat_la75b_high_1_stack.mat'</span>, <span class="org-string">'t'</span>, <span class="org-string">'V_in'</span>, <span class="org-string">'V_out'</span>);
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@ -285,7 +308,7 @@ We remove the phase delay due to the time delay of the ADC/DAC:
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</div>
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<div id="orga60ef1b" class="figure">
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<div id="orgd9445f5" class="figure">
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<p><img src="figs/tf_amplifiers_comp.png" alt="tf_amplifiers_comp.png" />
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</p>
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<p><span class="figure-number">Figure 5: </span>Comparison of the two Amplifier transfer functions</p>
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@ -294,10 +317,13 @@ We remove the phase delay due to the time delay of the ADC/DAC:
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</div>
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</div>
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<div id="outline-container-org2ac1966" class="outline-2">
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<h2 id="org2ac1966"><span class="section-number-2">4</span> Impedance Measurement</h2>
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<div id="outline-container-org7cf90b4" class="outline-2">
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<h2 id="org7cf90b4"><span class="section-number-2">4</span> Impedance Measurement</h2>
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<div class="outline-text-2" id="text-4">
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<p>
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<a id="org3a61ea0"></a>
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</p>
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<p>
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The goal is to experimentally measure the output impedance of the voltage amplifiers.
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</p>
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@ -316,13 +342,12 @@ From the two values of voltage, the internal resistor value can be computed:
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\[ R_i = R \frac{V - V^\prime}{V^\prime} \]
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</p>
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</div>
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<div id="outline-container-orgabf5b9a" class="outline-3">
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<h3 id="orgabf5b9a"><span class="section-number-3">4.1</span> Cedrat Technology</h3>
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<div id="outline-container-org2defd83" class="outline-3">
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<h3 id="org2defd83"><span class="section-number-3">4.1</span> Cedrat Technology</h3>
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<div class="outline-text-3" id="text-4-1">
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</div>
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<div id="outline-container-org373f123" class="outline-4">
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<h4 id="org373f123"><span class="section-number-4">4.1.1</span> Compute Impedance</h4>
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<div id="outline-container-orgf66e83a" class="outline-4">
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<h4 id="orgf66e83a"><span class="section-number-4">4.1.1</span> Compute Impedance</h4>
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<div class="outline-text-4" id="text-4-1-1">
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<div class="org-src-container">
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<pre class="src src-matlab">R = 10; <span class="org-comment">% Resistive Load used [Ohm]</span>
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@ -359,8 +384,8 @@ Vp = 4.874; <span class="org-comment">% Output Voltage with resistice load [V]</
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</div>
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</div>
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<div id="outline-container-orgc9002d7" class="outline-4">
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<h4 id="orgc9002d7"><span class="section-number-4">4.1.2</span> Effect of Impedance on the phase drop</h4>
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<div id="outline-container-orgc7a6f64" class="outline-4">
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<h4 id="orgc7a6f64"><span class="section-number-4">4.1.2</span> Effect of Impedance on the phase drop</h4>
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<div class="outline-text-4" id="text-4-1-2">
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<div class="org-src-container">
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<pre class="src src-matlab">C_1 = 5e<span class="org-type">-</span>6; <span class="org-comment">% Capacitance in [F]</span>
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@ -377,7 +402,7 @@ G_3 = G0<span class="org-type">/</span>(1<span class="org-type">+</span>Ri<span
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</div>
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<div id="orgcbac798" class="figure">
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<div id="org597c459" class="figure">
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<p><img src="figs/change_capa_cedrat.png" alt="change_capa_cedrat.png" />
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</p>
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<p><span class="figure-number">Figure 6: </span>Effect of a change of the piezo capacitance on the Amplifier transfer function</p>
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@ -386,8 +411,8 @@ G_3 = G0<span class="org-type">/</span>(1<span class="org-type">+</span>Ri<span
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</div>
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</div>
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<div id="outline-container-org3134308" class="outline-3">
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<h3 id="org3134308"><span class="section-number-3">4.2</span> PI</h3>
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<div id="outline-container-orgfd9e37f" class="outline-3">
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<h3 id="orgfd9e37f"><span class="section-number-3">4.2</span> PI</h3>
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<div class="outline-text-3" id="text-4-2">
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<div class="org-src-container">
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<pre class="src src-matlab">R = 10; <span class="org-comment">% Resistive Load used [Ohm]</span>
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@ -425,12 +450,15 @@ Vp = 1.637; <span class="org-comment">% Output Voltage with resistice load [V]</
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</div>
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</div>
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<div id="outline-container-org84728eb" class="outline-2">
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<h2 id="org84728eb"><span class="section-number-2">5</span> New PI amplifier measurements</h2>
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<div id="outline-container-org943c8af" class="outline-2">
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<h2 id="org943c8af"><span class="section-number-2">5</span> Effect of filters configuration on the PI-E505 dynamics</h2>
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<div class="outline-text-2" id="text-5">
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<p>
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<a id="orgdc9f3a2"></a>
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</p>
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</div>
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<div id="outline-container-org5ca1305" class="outline-3">
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<h3 id="org5ca1305"><span class="section-number-3">5.1</span> PI</h3>
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<div id="outline-container-org86c1e48" class="outline-3">
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<h3 id="org86c1e48"><span class="section-number-3">5.1</span> PI</h3>
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<div class="outline-text-3" id="text-5-1">
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<p>
|
||||
Three measurements are done:
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@ -466,7 +494,7 @@ win = hann(ceil(0.1<span class="org-type">/</span>Ts));
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</div>
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<div id="org431d6ed" class="figure">
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<div id="org85111b8" class="figure">
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<p><img src="figs/pi_slew_rate_notch.png" alt="pi_slew_rate_notch.png" />
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</p>
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<p><span class="figure-number">Figure 7: </span>Effect of a change in the slew rate limitation and notch filter</p>
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@ -474,8 +502,8 @@ win = hann(ceil(0.1<span class="org-type">/</span>Ts));
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</div>
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</div>
|
||||
|
||||
<div id="outline-container-org091ce77" class="outline-3">
|
||||
<h3 id="org091ce77"><span class="section-number-3">5.2</span> Transfer function of the Voltage Amplifier</h3>
|
||||
<div id="outline-container-org35acfc7" class="outline-3">
|
||||
<h3 id="org35acfc7"><span class="section-number-3">5.2</span> Transfer function of the Voltage Amplifier</h3>
|
||||
<div class="outline-text-3" id="text-5-2">
|
||||
<p>
|
||||
The identified transfer function still seems to match the one of a notch filter at 5kHz.
|
||||
@ -489,8 +517,8 @@ G = 10.5<span class="org-type">*</span>(s<span class="org-type">^</span>2 <span
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org78406e1" class="outline-3">
|
||||
<h3 id="org78406e1"><span class="section-number-3">5.3</span> With Load</h3>
|
||||
<div id="outline-container-org1c608d2" class="outline-3">
|
||||
<h3 id="org1c608d2"><span class="section-number-3">5.3</span> With Load</h3>
|
||||
<div class="outline-text-3" id="text-5-3">
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab">R = 2.78; <span class="org-comment">% Output Impedance [Ohm]</span>
|
||||
@ -505,7 +533,7 @@ G_amp = 10<span class="org-type">/</span>(1 <span class="org-type">+</span> s<sp
|
||||
</div>
|
||||
<div id="postamble" class="status">
|
||||
<p class="author">Author: Dehaeze Thomas</p>
|
||||
<p class="date">Created: 2020-11-10 mar. 12:34</p>
|
||||
<p class="date">Created: 2020-11-10 mar. 12:44</p>
|
||||
</div>
|
||||
</body>
|
||||
</html>
|
||||
|
||||
18
index.org
18
index.org
@ -34,17 +34,27 @@
|
||||
|
||||
* Introduction :ignore:
|
||||
|
||||
Two voltage amplifiers are tested:
|
||||
#+begin_note
|
||||
The following two voltage amplifiers are tested:
|
||||
- PI E-505.00 ([[file:doc/E-505-Datasheet.pdf][doc]])
|
||||
- Cedrat Technology LA75B ([[file:doc/LA75B.pdf][doc]])
|
||||
|
||||
The piezoelectric actuator under test is an APA95ML from Cedrat technology ([[file:doc/APA95ML.pdf][doc]]).
|
||||
It contains three stacks with a capacitance of $5 \mu F$ each that can be connected independently to the amplifier.
|
||||
#+end_note
|
||||
|
||||
This document is divided into the following sections:
|
||||
- Section [[sec:effect_change_capacitance]]: The effect of a change in load capacitance on the amplifier dynamics is studied
|
||||
- Section [[sec:effect_change_voltage]]: The effect on the voltage level on the amplifier dynamics is studied
|
||||
- Section [[sec:comp_pi_cedrat]]: The dynamics of the E-505 and LA75B are compared
|
||||
- Section [[sec:impedance_meas]]: The output impedance of both amplifiers are measured
|
||||
- Section [[sec:pi_e505_filters]]: The effect of the internal filters of the E-505 on its dynamics is studied
|
||||
|
||||
* Effect of a change of capacitance
|
||||
:PROPERTIES:
|
||||
:header-args:matlab+: :tangle src/effect_change_capacitance.m
|
||||
:END:
|
||||
<<sec:effect_change_capacitance>>
|
||||
** 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>>
|
||||
@ -194,6 +204,7 @@ We remove the phase delay due to the time delay of the ADC/DAC:
|
||||
:PROPERTIES:
|
||||
:header-args:matlab+: :tangle src/effect_change_voltage.m
|
||||
:END:
|
||||
<<sec:effect_change_voltage>>
|
||||
** 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>>
|
||||
@ -330,6 +341,7 @@ We remove the phase delay due to the time delay of the ADC/DAC:
|
||||
:PROPERTIES:
|
||||
:header-args:matlab+: :tangle src/comp_pi_cedrat.m
|
||||
:END:
|
||||
<<sec:comp_pi_cedrat>>
|
||||
** 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>>
|
||||
@ -405,6 +417,7 @@ We remove the phase delay due to the time delay of the ADC/DAC:
|
||||
:PROPERTIES:
|
||||
:header-args:matlab+: :tangle src/impedance_meas.m
|
||||
:END:
|
||||
<<sec:impedance_meas>>
|
||||
** Introduction :ignore:
|
||||
The goal is to experimentally measure the output impedance of the voltage amplifiers.
|
||||
|
||||
@ -569,10 +582,11 @@ From the two values of voltage, the internal resistor value can be computed:
|
||||
#+RESULTS:
|
||||
: 2.7795
|
||||
|
||||
* New PI amplifier measurements
|
||||
* Effect of filters configuration on the PI-E505 dynamics
|
||||
:PROPERTIES:
|
||||
:header-args:matlab+: :tangle src/pi_e505_filters.m
|
||||
:END:
|
||||
<<sec:pi_e505_filters>>
|
||||
** 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>>
|
||||
|
||||
Loading…
Reference in New Issue
Block a user