339 lines
11 KiB
HTML
339 lines
11 KiB
HTML
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<!-- 2020-08-13 jeu. 17:11 -->
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<title>Measurement of Piezoelectric Amplifiers</title>
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<meta name="author" content="Dehaeze Thomas" />
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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="#org1bbe59a">1. Effect of a change of capacitance</a>
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<ul>
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<li><a href="#orgdb6f8ad">1.1. Cedrat Technology</a></li>
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<li><a href="#orgee41528">1.2. PI</a></li>
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</ul>
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</li>
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<li><a href="#orgd75b37d">2. Effect of a change in Voltage level</a>
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<ul>
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<li><a href="#orga6e0258">2.1. Cedrat Technology</a></li>
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<li><a href="#orgd744290">2.2. PI</a></li>
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</ul>
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</li>
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<li><a href="#org4b79280">3. Comparison PI / Cedrat</a>
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<ul>
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<li><a href="#org590829e">3.1. Results</a></li>
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</ul>
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</li>
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<li><a href="#org2f30df2">4. Impedance Measurement</a>
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<ul>
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<li><a href="#org7ad403e">4.1. Cedrat Technology</a></li>
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<li><a href="#org746e78c">4.2. PI</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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<p>
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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="https://www.pi-usa.us/en/products/controllers-drivers-motion-control-software/piezo-drivers-controllers-power-supplies-high-voltage-amplifiers/e-505-piezo-amplifier-module-602300/">link</a>)</li>
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<li>Cedrat Technology LA75B (<a href="https://www.cedrat-technologies.com/en/products/piezo-controllers/electronic-amplifier-boards.html">link</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.
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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-org1bbe59a" class="outline-2">
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<h2 id="org1bbe59a"><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-orgdb6f8ad" class="outline-3">
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<h3 id="orgdb6f8ad"><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('mat/cedrat_la75b_med_1_stack.mat', 't', 'V_in', 'V_out');
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piezo2 = load('mat/cedrat_la75b_med_2_stack.mat', 't', 'V_in', 'V_out');
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piezo3 = load('mat/cedrat_la75b_med_3_stack.mat', 't', 'V_in', 'V_out');
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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-4;
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win = hann(ceil(0.1/Ts));
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[tf_1, f_1] = tfestimate(piezo1.V_in, piezo1.V_out, win, [], [], 1/Ts);
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[co_1, ~] = mscohere(piezo1.V_in, piezo1.V_out, win, [], [], 1/Ts);
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[tf_2, f_2] = tfestimate(piezo2.V_in, piezo2.V_out, win, [], [], 1/Ts);
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[co_2, ~] = mscohere(piezo2.V_in, piezo2.V_out, win, [], [], 1/Ts);
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[tf_3, f_3] = tfestimate(piezo3.V_in, piezo3.V_out, win, [], [], 1/Ts);
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[co_3, ~] = mscohere(piezo3.V_in, piezo3.V_out, win, [], [], 1/Ts);
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</pre>
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</div>
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<div id="orga28400f" 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-orgee41528" class="outline-3">
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<h3 id="orgee41528"><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('mat/pi_505_high.mat', 't', 'V_in', 'V_out');
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piezo2 = load('mat/pi_505_high_2_stacks.mat', 't', 'V_in', 'V_out');
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piezo3 = load('mat/pi_505_high_3_stacks.mat', 't', 'V_in', 'V_out');
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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-4;
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win = hann(ceil(0.1/Ts));
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[tf_1, f_1] = tfestimate(piezo1.V_in, piezo1.V_out, win, [], [], 1/Ts);
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[co_1, ~] = mscohere(piezo1.V_in, piezo1.V_out, win, [], [], 1/Ts);
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[tf_2, f_2] = tfestimate(piezo2.V_in, piezo2.V_out, win, [], [], 1/Ts);
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[co_2, ~] = mscohere(piezo2.V_in, piezo2.V_out, win, [], [], 1/Ts);
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[tf_3, f_3] = tfestimate(piezo3.V_in, piezo3.V_out, win, [], [], 1/Ts);
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[co_3, ~] = mscohere(piezo3.V_in, piezo3.V_out, win, [], [], 1/Ts);
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</pre>
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</div>
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<div id="org9cafd87" 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-orgd75b37d" class="outline-2">
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<h2 id="orgd75b37d"><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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</div>
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<div id="outline-container-orga6e0258" class="outline-3">
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<h3 id="orga6e0258"><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('mat/cedrat_la75b_high_1_stack.mat', 't', 'V_in', 'V_out');
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me = load('mat/cedrat_la75b_med_1_stack.mat', 't', 'V_in', 'V_out');
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lo = load('mat/cedrat_la75b_low_1_stack.mat', 't', 'V_in', 'V_out');
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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-4;
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win = hann(ceil(0.1/Ts));
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[tf_hi, f_hi] = tfestimate(hi.V_in, hi.V_out, win, [], [], 1/Ts);
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[co_hi, ~] = mscohere(hi.V_in, hi.V_out, win, [], [], 1/Ts);
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[tf_me, f_me] = tfestimate(me.V_in, me.V_out, win, [], [], 1/Ts);
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[co_me, ~] = mscohere(me.V_in, me.V_out, win, [], [], 1/Ts);
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[tf_lo, f_lo] = tfestimate(lo.V_in, lo.V_out, win, [], [], 1/Ts);
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[co_lo, ~] = mscohere(lo.V_in, lo.V_out, win, [], [], 1/Ts);
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</pre>
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</div>
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<div id="org0ea5714" 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-orgd744290" class="outline-3">
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<h3 id="orgd744290"><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('mat/pi_505_high.mat', 't', 'V_in', 'V_out');
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lo = load('mat/pi_505_low.mat', 't', 'V_in', 'V_out');
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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-4;
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win = hann(ceil(0.1/Ts));
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[tf_hi, f_hi] = tfestimate(hi.V_in, hi.V_out, win, [], [], 1/Ts);
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[co_hi, ~] = mscohere(hi.V_in, hi.V_out, win, [], [], 1/Ts);
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[tf_lo, f_lo] = tfestimate(lo.V_in, lo.V_out, win, [], [], 1/Ts);
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[co_lo, ~] = mscohere(lo.V_in, lo.V_out, win, [], [], 1/Ts);
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</pre>
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</div>
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<div id="orgb43e11f" 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-org4b79280" class="outline-2">
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<h2 id="org4b79280"><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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</div>
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<div id="outline-container-org590829e" class="outline-3">
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<h3 id="org590829e"><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('mat/cedrat_la75b_high_1_stack.mat', 't', 'V_in', 'V_out');
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pi_results = load('mat/pi_505_high.mat', 't', 'V_in', 'V_out');
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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-4;
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win = hann(ceil(0.1/Ts));
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[tf_ce, f_ce] = tfestimate(ce_results.V_in, ce_results.V_out, win, [], [], 1/Ts);
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[tf_pi, f_pi] = tfestimate(pi_results.V_in, pi_results.V_out, win, [], [], 1/Ts);
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</pre>
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</div>
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<div id="orgbdf4de1" 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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<div id="outline-container-org2f30df2" class="outline-2">
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<h2 id="org2f30df2"><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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The goal is to experimentally measure the output impedance of the voltage amplifiers.
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</p>
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<p>
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To do so, the output voltage is first measure without any load (\(V\)).
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It is then measure when a 10Ohm load is used (\(V^\prime\)).
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</p>
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<p>
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The load (\(R = 10\Omega\)) and the internal resistor (\(R_i\)) form a voltage divider, and thus:
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\[ V^\prime = \frac{R}{R + R_i} V \]
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</p>
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<p>
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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-org7ad403e" class="outline-3">
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<h3 id="org7ad403e"><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 class="org-src-container">
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<pre class="src src-matlab">R = 10; % Resistive Load used [Ohm]
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V = 10.09; % Output Voltage without any load [V]
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Vp = 3.46; % Output Voltage with resistice load [V]
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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">R * (V - Vp)/Vp;
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</pre>
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</div>
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<pre class="example">
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19.162
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</pre>
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<div class="org-src-container">
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<pre class="src src-matlab">C = 5e-6; % Capacitance in [F]
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Ri = R * (V - Vp)/Vp; % Internal resistance [Ohm]
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G_ce = 1/(1+Ri*C*s);
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</pre>
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</div>
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</div>
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</div>
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<div id="outline-container-org746e78c" class="outline-3">
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<h3 id="org746e78c"><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; % Resistive Load used [Ohm]
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V = 10.35; % Output Voltage without any load [V]
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Vp = 4.14; % Output Voltage with resistice load [V]
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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">R * (V - Vp)/Vp
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</pre>
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</div>
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<pre class="example">
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15
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</pre>
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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="postamble" class="status">
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<p class="author">Author: Dehaeze Thomas</p>
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<p class="date">Created: 2020-08-13 jeu. 17:11</p>
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</div>
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</body>
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</html>
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