Add impedance test to the document
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index.html
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index.html
@ -3,7 +3,7 @@
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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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<!-- 2020-08-13 jeu. 10:00 -->
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<!-- 2020-08-13 jeu. 17:11 -->
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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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@ -31,21 +31,27 @@
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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="#orgf4c5526">1. Effect of a change of capacitance</a>
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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="#org52f8a23">1.1. Cedrat Technology</a></li>
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<li><a href="#org96f04ca">1.2. PI</a></li>
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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="#orgcd4115f">2. Effect of a change in Voltage level</a>
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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="#orgacb19bc">2.1. Cedrat Technology</a></li>
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<li><a href="#org4012e58">2.2. PI</a></li>
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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="#org6c9c30b">3. Comparison PI / Cedrat</a>
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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="#org05eec9b">3.1. Results</a></li>
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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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@ -65,12 +71,12 @@ 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-orgf4c5526" class="outline-2">
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<h2 id="orgf4c5526"><span class="section-number-2">1</span> Effect of a change of capacitance</h2>
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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-org52f8a23" class="outline-3">
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<h3 id="org52f8a23"><span class="section-number-3">1.1</span> Cedrat Technology</h3>
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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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@ -103,7 +109,7 @@ win = hann(ceil(0.1/Ts));
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</div>
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<div id="org988e499" class="figure">
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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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@ -111,8 +117,8 @@ win = hann(ceil(0.1/Ts));
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</div>
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</div>
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<div id="outline-container-org96f04ca" class="outline-3">
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<h3 id="org96f04ca"><span class="section-number-3">1.2</span> PI</h3>
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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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@ -139,7 +145,7 @@ win = hann(ceil(0.1/Ts));
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</div>
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<div id="org9cf27f7" class="figure">
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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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@ -148,12 +154,12 @@ win = hann(ceil(0.1/Ts));
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</div>
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</div>
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<div id="outline-container-orgcd4115f" class="outline-2">
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<h2 id="orgcd4115f"><span class="section-number-2">2</span> Effect of a change in Voltage level</h2>
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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-orgacb19bc" class="outline-3">
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<h3 id="orgacb19bc"><span class="section-number-3">2.1</span> Cedrat Technology</h3>
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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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@ -178,7 +184,7 @@ win = hann(ceil(0.1/Ts));
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</div>
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<div id="orgbd8e672" class="figure">
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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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@ -186,8 +192,8 @@ win = hann(ceil(0.1/Ts));
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</div>
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</div>
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<div id="outline-container-org4012e58" class="outline-3">
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<h3 id="org4012e58"><span class="section-number-3">2.2</span> PI</h3>
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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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@ -208,7 +214,7 @@ win = hann(ceil(0.1/Ts));
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</div>
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<div id="orgaafc93d" class="figure">
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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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@ -217,12 +223,12 @@ win = hann(ceil(0.1/Ts));
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</div>
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</div>
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<div id="outline-container-org6c9c30b" class="outline-2">
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<h2 id="org6c9c30b"><span class="section-number-2">3</span> Comparison PI / Cedrat</h2>
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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-org05eec9b" class="outline-3">
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<h3 id="org05eec9b"><span class="section-number-3">3.1</span> Results</h3>
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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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@ -240,7 +246,7 @@ win = hann(ceil(0.1/Ts));
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</div>
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<div id="org1897cd3" class="figure">
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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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@ -248,10 +254,85 @@ win = hann(ceil(0.1/Ts));
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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. 10:00</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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82
index.org
82
index.org
@ -353,3 +353,85 @@ Compute Coherence and Transfer functions
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#+caption: Comparison of the two Amplifier transfer functions
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#+RESULTS:
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[[file:figs/tf_amplifiers_comp.png]]
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* Impedance Measurement
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** Introduction :ignore:
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The goal is to experimentally measure the output impedance of the voltage amplifiers.
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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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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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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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** Matlab Init :noexport:ignore:
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#+begin_src matlab :tangle no :exports none :results silent :noweb yes :var current_dir=(file-name-directory buffer-file-name)
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<<matlab-dir>>
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#+end_src
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#+begin_src matlab :exports none :results silent :noweb yes
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<<matlab-init>>
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#+end_src
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** Cedrat Technology
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#+begin_src matlab
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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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#+end_src
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#+begin_src matlab :results replace value
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R * (V - Vp)/Vp;
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#+end_src
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#+RESULTS:
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: 19.162
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#+begin_src matlab
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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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#+end_src
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#+begin_src matlab :exports none
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freqs = logspace(1, 4, 1000);
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figure;
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ax1 = subplot(2, 1, 1);
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hold on;
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plot(freqs, abs(squeeze(freqresp(G_ce, freqs, 'Hz'))));
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hold off;
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set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
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ylabel('Amplitude [m/N]'); set(gca, 'XTickLabel',[]);
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ax2 = subplot(2, 1, 2);
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hold on;
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plot(freqs, 180/pi*angle(squeeze(freqresp(G_ce, freqs, 'Hz'))));
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hold off;
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set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin');
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ylabel('Phase [deg]'); xlabel('Frequency [Hz]');
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ylim([-180, 180]);
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yticks([-180, -90, 0, 90, 180]);
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linkaxes([ax1,ax2],'x');
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#+end_src
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** PI
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#+begin_src matlab
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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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#+end_src
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#+begin_src matlab :results replace value
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R * (V - Vp)/Vp
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#+end_src
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#+RESULTS:
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: 15
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* Cedrat
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No charge
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V = 10.09
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10 Ohmn
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V = 3.46
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* PI
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No charge
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V = 10.35
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10 Ohm
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V = 4.14
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