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540 lines
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<title>Measurement of Piezoelectric Amplifiers</title>
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<body>
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<div id="content">
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<h1 class="title">Measurement of Piezoelectric Amplifiers</h1>
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<div id="table-of-contents">
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<h2>Table of Contents</h2>
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<div id="text-table-of-contents">
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<ul>
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<li><a href="#org2595d4f">1. Effect of a change of capacitance</a>
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<ul>
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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="#org2c356cd">2. Effect of a change in Voltage level</a>
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<ul>
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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="#orgaef7c1d">3. Comparison PI / Cedrat</a>
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<ul>
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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="#org7cf90b4">4. Impedance Measurement</a>
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<ul>
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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="#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="#orgfd9e37f">4.2. PI</a></li>
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</ul>
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</li>
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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="#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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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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<li>Cedrat Technology LA75B (<a href="doc/LA75B.pdf">doc</a>)</li>
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</ul>
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<p>
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The piezoelectric actuator under test is an APA95ML from Cedrat technology (<a href="doc/APA95ML.pdf">doc</a>).
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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>
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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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</p>
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<div class="org-src-container">
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<pre class="src src-matlab">piezo1 = load(<span class="org-string">'cedrat_la75b_med_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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piezo2 = load(<span class="org-string">'cedrat_la75b_med_2_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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piezo3 = load(<span class="org-string">'cedrat_la75b_med_3_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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</pre>
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</div>
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<p>
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Compute Coherence and Transfer functions
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</p>
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<div class="org-src-container">
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<pre class="src src-matlab">Ts = 1e<span class="org-type">-</span>4;
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win = hann(ceil(0.1<span class="org-type">/</span>Ts));
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[tf_1, f] = tfestimate(piezo1.V_in, piezo1.V_out, win, [], [], 1<span class="org-type">/</span>Ts);
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[co_1, <span class="org-type">~</span>] = mscohere(piezo1.V_in, piezo1.V_out, win, [], [], 1<span class="org-type">/</span>Ts);
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[tf_2, <span class="org-type">~</span>] = tfestimate(piezo2.V_in, piezo2.V_out, win, [], [], 1<span class="org-type">/</span>Ts);
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[co_2, <span class="org-type">~</span>] = mscohere(piezo2.V_in, piezo2.V_out, win, [], [], 1<span class="org-type">/</span>Ts);
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[tf_3, <span class="org-type">~</span>] = tfestimate(piezo3.V_in, piezo3.V_out, win, [], [], 1<span class="org-type">/</span>Ts);
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[co_3, <span class="org-type">~</span>] = mscohere(piezo3.V_in, piezo3.V_out, win, [], [], 1<span class="org-type">/</span>Ts);
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</pre>
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</div>
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<p>
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We remove the phase delay due to the time delay of the ADC/DAC:
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</p>
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<div class="org-src-container">
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<pre class="src src-matlab">angle_delay = 180<span class="org-type">/</span><span class="org-constant">pi</span><span class="org-type">*</span>angle(squeeze(freqresp(exp(<span class="org-type">-</span>s<span class="org-type">*</span>Ts), f, <span class="org-string">'Hz'</span>)));
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</pre>
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</div>
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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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</div>
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</div>
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</div>
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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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piezo2 = load(<span class="org-string">'pi_505_high_2_stacks.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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piezo3 = load(<span class="org-string">'pi_505_high_3_stacks.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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</pre>
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</div>
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<div class="org-src-container">
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<pre class="src src-matlab">Ts = 1e<span class="org-type">-</span>4;
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win = hann(ceil(0.1<span class="org-type">/</span>Ts));
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[tf_1, f] = tfestimate(piezo1.V_in, piezo1.V_out, win, [], [], 1<span class="org-type">/</span>Ts);
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[co_1, <span class="org-type">~</span>] = mscohere(piezo1.V_in, piezo1.V_out, win, [], [], 1<span class="org-type">/</span>Ts);
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[tf_2, <span class="org-type">~</span>] = tfestimate(piezo2.V_in, piezo2.V_out, win, [], [], 1<span class="org-type">/</span>Ts);
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[co_2, <span class="org-type">~</span>] = mscohere(piezo2.V_in, piezo2.V_out, win, [], [], 1<span class="org-type">/</span>Ts);
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[tf_3, <span class="org-type">~</span>] = tfestimate(piezo3.V_in, piezo3.V_out, win, [], [], 1<span class="org-type">/</span>Ts);
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[co_3, <span class="org-type">~</span>] = mscohere(piezo3.V_in, piezo3.V_out, win, [], [], 1<span class="org-type">/</span>Ts);
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</pre>
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</div>
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<p>
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We remove the phase delay due to the time delay of the ADC/DAC:
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</p>
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<div class="org-src-container">
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<pre class="src src-matlab">angle_delay = 180<span class="org-type">/</span><span class="org-constant">pi</span><span class="org-type">*</span>angle(squeeze(freqresp(exp(<span class="org-type">-</span>s<span class="org-type">*</span>Ts), f, <span class="org-string">'Hz'</span>)));
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</pre>
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</div>
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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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</div>
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</div>
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</div>
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</div>
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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-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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me = load(<span class="org-string">'cedrat_la75b_med_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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lo = load(<span class="org-string">'cedrat_la75b_low_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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</pre>
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</div>
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<div class="org-src-container">
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<pre class="src src-matlab">Ts = 1e<span class="org-type">-</span>4;
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win = hann(ceil(0.1<span class="org-type">/</span>Ts));
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[tf_hi, f] = tfestimate(hi.V_in, hi.V_out, win, [], [], 1<span class="org-type">/</span>Ts);
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[co_hi, <span class="org-type">~</span>] = mscohere(hi.V_in, hi.V_out, win, [], [], 1<span class="org-type">/</span>Ts);
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[tf_me, <span class="org-type">~</span>] = tfestimate(me.V_in, me.V_out, win, [], [], 1<span class="org-type">/</span>Ts);
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[co_me, <span class="org-type">~</span>] = mscohere(me.V_in, me.V_out, win, [], [], 1<span class="org-type">/</span>Ts);
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[tf_lo, <span class="org-type">~</span>] = tfestimate(lo.V_in, lo.V_out, win, [], [], 1<span class="org-type">/</span>Ts);
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[co_lo, <span class="org-type">~</span>] = mscohere(lo.V_in, lo.V_out, win, [], [], 1<span class="org-type">/</span>Ts);
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</pre>
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</div>
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<p>
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We remove the phase delay due to the time delay of the ADC/DAC:
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</p>
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<div class="org-src-container">
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<pre class="src src-matlab">angle_delay = 180<span class="org-type">/</span><span class="org-constant">pi</span><span class="org-type">*</span>angle(squeeze(freqresp(exp(<span class="org-type">-</span>s<span class="org-type">*</span>Ts), f, <span class="org-string">'Hz'</span>)));
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</pre>
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</div>
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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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</div>
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</div>
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</div>
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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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lo = load(<span class="org-string">'pi_505_low.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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</pre>
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</div>
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<div class="org-src-container">
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<pre class="src src-matlab">Ts = 1e<span class="org-type">-</span>4;
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win = hann(ceil(0.1<span class="org-type">/</span>Ts));
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[tf_hi, f] = tfestimate(hi.V_in, hi.V_out, win, [], [], 1<span class="org-type">/</span>Ts);
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[co_hi, <span class="org-type">~</span>] = mscohere(hi.V_in, hi.V_out, win, [], [], 1<span class="org-type">/</span>Ts);
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[tf_lo, <span class="org-type">~</span>] = tfestimate(lo.V_in, lo.V_out, win, [], [], 1<span class="org-type">/</span>Ts);
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[co_lo, <span class="org-type">~</span>] = mscohere(lo.V_in, lo.V_out, win, [], [], 1<span class="org-type">/</span>Ts);
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</pre>
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</div>
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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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</div>
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</div>
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</div>
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</div>
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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-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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pi_results = 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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</pre>
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</div>
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<div class="org-src-container">
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<pre class="src src-matlab">Ts = 1e<span class="org-type">-</span>4;
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win = hann(ceil(0.1<span class="org-type">/</span>Ts));
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[tf_ce, f] = tfestimate(ce_results.V_in, ce_results.V_out, win, [], [], 1<span class="org-type">/</span>Ts);
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[tf_pi, <span class="org-type">~</span>] = tfestimate(pi_results.V_in, pi_results.V_out, win, [], [], 1<span class="org-type">/</span>Ts);
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</pre>
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</div>
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<p>
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We remove the phase delay due to the time delay of the ADC/DAC:
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</p>
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<div class="org-src-container">
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<pre class="src src-matlab">angle_delay = 180<span class="org-type">/</span><span class="org-constant">pi</span><span class="org-type">*</span>angle(squeeze(freqresp(exp(<span class="org-type">-</span>s<span class="org-type">*</span>Ts), f, <span class="org-string">'Hz'</span>)));
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</pre>
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</div>
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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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</div>
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</div>
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</div>
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</div>
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|
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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>
|
|
<div class="outline-text-2" id="text-4">
|
|
<p>
|
|
<a id="org3a61ea0"></a>
|
|
</p>
|
|
<p>
|
|
The goal is to experimentally measure the output impedance of the voltage amplifiers.
|
|
</p>
|
|
|
|
<p>
|
|
To do so, the output voltage is first measure without any load (\(V\)).
|
|
It is then measure when a 10Ohm load is used (\(V^\prime\)).
|
|
</p>
|
|
|
|
<p>
|
|
The load (\(R = 10\Omega\)) and the internal resistor (\(R_i\)) form a voltage divider, and thus:
|
|
\[ V^\prime = \frac{R}{R + R_i} V \]
|
|
</p>
|
|
|
|
<p>
|
|
From the two values of voltage, the internal resistor value can be computed:
|
|
\[ R_i = R \frac{V - V^\prime}{V^\prime} \]
|
|
</p>
|
|
</div>
|
|
<div id="outline-container-org2defd83" class="outline-3">
|
|
<h3 id="org2defd83"><span class="section-number-3">4.1</span> Cedrat Technology</h3>
|
|
<div class="outline-text-3" id="text-4-1">
|
|
</div>
|
|
<div id="outline-container-orgf66e83a" class="outline-4">
|
|
<h4 id="orgf66e83a"><span class="section-number-4">4.1.1</span> Compute Impedance</h4>
|
|
<div class="outline-text-4" id="text-4-1-1">
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">R = 10; <span class="org-comment">% Resistive Load used [Ohm]</span>
|
|
V = 0.998; <span class="org-comment">% Output Voltage without any load [V]</span>
|
|
Vp = 0.912; <span class="org-comment">% Output Voltage with resistice load [V]</span>
|
|
</pre>
|
|
</div>
|
|
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">R <span class="org-type">*</span> (V <span class="org-type">-</span> Vp)<span class="org-type">/</span>Vp;
|
|
</pre>
|
|
</div>
|
|
|
|
<pre class="example">
|
|
0.94298
|
|
</pre>
|
|
|
|
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">R = 47; <span class="org-comment">% Resistive Load used [Ohm]</span>
|
|
V = 4.960; <span class="org-comment">% Output Voltage without any load [V]</span>
|
|
Vp = 4.874; <span class="org-comment">% Output Voltage with resistice load [V]</span>
|
|
</pre>
|
|
</div>
|
|
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">R <span class="org-type">*</span> (V <span class="org-type">-</span> Vp)<span class="org-type">/</span>Vp;
|
|
</pre>
|
|
</div>
|
|
|
|
<pre class="example">
|
|
0.8293
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-orgc7a6f64" class="outline-4">
|
|
<h4 id="orgc7a6f64"><span class="section-number-4">4.1.2</span> Effect of Impedance on the phase drop</h4>
|
|
<div class="outline-text-4" id="text-4-1-2">
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">C_1 = 5e<span class="org-type">-</span>6; <span class="org-comment">% Capacitance in [F]</span>
|
|
C_2 = 10e<span class="org-type">-</span>6; <span class="org-comment">% Capacitance in [F]</span>
|
|
C_3 = 15e<span class="org-type">-</span>6; <span class="org-comment">% Capacitance in [F]</span>
|
|
|
|
Ri = R <span class="org-type">*</span> (V <span class="org-type">-</span> Vp)<span class="org-type">/</span>Vp; <span class="org-comment">% Internal resistance [Ohm]</span>
|
|
G0 = 20;
|
|
|
|
G_1 = G0<span class="org-type">/</span>(1<span class="org-type">+</span>Ri<span class="org-type">*</span>C_1<span class="org-type">*</span>s);
|
|
G_2 = G0<span class="org-type">/</span>(1<span class="org-type">+</span>Ri<span class="org-type">*</span>C_2<span class="org-type">*</span>s);
|
|
G_3 = G0<span class="org-type">/</span>(1<span class="org-type">+</span>Ri<span class="org-type">*</span>C_3<span class="org-type">*</span>s);
|
|
</pre>
|
|
</div>
|
|
|
|
|
|
<div id="org597c459" class="figure">
|
|
<p><img src="figs/change_capa_cedrat.png" alt="change_capa_cedrat.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 6: </span>Effect of a change of the piezo capacitance on the Amplifier transfer function</p>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-orgfd9e37f" class="outline-3">
|
|
<h3 id="orgfd9e37f"><span class="section-number-3">4.2</span> PI</h3>
|
|
<div class="outline-text-3" id="text-4-2">
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">R = 10; <span class="org-comment">% Resistive Load used [Ohm]</span>
|
|
V = 1.059; <span class="org-comment">% Output Voltage without any load [V]</span>
|
|
Vp = 0.828; <span class="org-comment">% Output Voltage with resistice load [V]</span>
|
|
</pre>
|
|
</div>
|
|
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">R <span class="org-type">*</span> (V <span class="org-type">-</span> Vp)<span class="org-type">/</span>Vp
|
|
</pre>
|
|
</div>
|
|
|
|
<pre class="example">
|
|
2.7899
|
|
</pre>
|
|
|
|
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">R = 10; <span class="org-comment">% Resistive Load used [Ohm]</span>
|
|
V = 2.092; <span class="org-comment">% Output Voltage without any load [V]</span>
|
|
Vp = 1.637; <span class="org-comment">% Output Voltage with resistice load [V]</span>
|
|
</pre>
|
|
</div>
|
|
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">R <span class="org-type">*</span> (V <span class="org-type">-</span> Vp)<span class="org-type">/</span>Vp
|
|
</pre>
|
|
</div>
|
|
|
|
<pre class="example">
|
|
2.7795
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org943c8af" class="outline-2">
|
|
<h2 id="org943c8af"><span class="section-number-2">5</span> Effect of filters configuration on the PI-E505 dynamics</h2>
|
|
<div class="outline-text-2" id="text-5">
|
|
<p>
|
|
<a id="orgdc9f3a2"></a>
|
|
</p>
|
|
</div>
|
|
<div id="outline-container-org86c1e48" class="outline-3">
|
|
<h3 id="org86c1e48"><span class="section-number-3">5.1</span> PI</h3>
|
|
<div class="outline-text-3" id="text-5-1">
|
|
<p>
|
|
Three measurements are done:
|
|
</p>
|
|
<ul class="org-ul">
|
|
<li>Slew Rate limitation at maximum</li>
|
|
<li>Slew Rate limitation at minimum</li>
|
|
<li>Notch Filter at maximum frequency</li>
|
|
</ul>
|
|
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">pi_sr_min = load(<span class="org-string">'pi_slew_rate_min.mat'</span>);
|
|
pi_sr_max = load(<span class="org-string">'pi_slew_rate_max.mat'</span>);
|
|
pi_sr_max_notch = load(<span class="org-string">'pi_slew_rate_max_notch_high.mat'</span>);
|
|
pi_sr_load = load(<span class="org-string">'pi_slew_rate_max_notch_high_2stacks.mat'</span>);
|
|
</pre>
|
|
</div>
|
|
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">Ts = 1e<span class="org-type">-</span>4;
|
|
win = hann(ceil(0.1<span class="org-type">/</span>Ts));
|
|
|
|
[tf_sr_min, f] = tfestimate(pi_sr_min.V_in, pi_sr_min.V_out, win, [], [], 1<span class="org-type">/</span>Ts);
|
|
[tf_sr_max, <span class="org-type">~</span>] = tfestimate(pi_sr_max.V_in, pi_sr_max.V_out, win, [], [], 1<span class="org-type">/</span>Ts);
|
|
[tf_sr_max_notch, <span class="org-type">~</span>] = tfestimate(pi_sr_max_notch.V_in, pi_sr_max_notch.V_out, win, [], [], 1<span class="org-type">/</span>Ts);
|
|
[tf_sr_load, <span class="org-type">~</span>] = tfestimate(pi_sr_load.V_in, pi_sr_load.V_out, win, [], [], 1<span class="org-type">/</span>Ts);
|
|
</pre>
|
|
</div>
|
|
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">angle_delay = 180<span class="org-type">/</span><span class="org-constant">pi</span><span class="org-type">*</span>angle(squeeze(freqresp(exp(<span class="org-type">-</span>s<span class="org-type">*</span>Ts), f, <span class="org-string">'Hz'</span>)));
|
|
</pre>
|
|
</div>
|
|
|
|
|
|
<div id="org85111b8" class="figure">
|
|
<p><img src="figs/pi_slew_rate_notch.png" alt="pi_slew_rate_notch.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 7: </span>Effect of a change in the slew rate limitation and notch filter</p>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<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.
|
|
</p>
|
|
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">w_nf = 2<span class="org-type">*</span><span class="org-constant">pi</span><span class="org-type">*</span>5e3; <span class="org-comment">% Notch Filter Frequency [rad/s]</span>
|
|
G = 10.5<span class="org-type">*</span>(s<span class="org-type">^</span>2 <span class="org-type">+</span> 2<span class="org-type">*</span>w_nf<span class="org-type">*</span>0.12<span class="org-type">*</span>s <span class="org-type">+</span> w_nf<span class="org-type">^</span>2)<span class="org-type">/</span>(s<span class="org-type">^</span>2 <span class="org-type">+</span> 2<span class="org-type">*</span>w_nf<span class="org-type">*</span>s <span class="org-type">+</span> w_nf<span class="org-type">^</span>2);
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<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>
|
|
C = 9e<span class="org-type">-</span>6; <span class="org-comment">% Load capacitance [F]</span>
|
|
|
|
G_amp = 10<span class="org-type">/</span>(1 <span class="org-type">+</span> s<span class="org-type">*</span>R<span class="org-type">*</span>C);
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
<div id="postamble" class="status">
|
|
<p class="author">Author: Dehaeze Thomas</p>
|
|
<p class="date">Created: 2020-11-10 mar. 12:44</p>
|
|
</div>
|
|
</body>
|
|
</html>
|