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<title>Measurement of Piezoelectric Amplifiers</title>
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<div id="content">
<div id="org-div-home-and-up">
<a accesskey="h" href="../index.html"> UP </a>
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<h1 class="title">Measurement of Piezoelectric Amplifiers</h1>
<div id="table-of-contents">
<h2>Table of Contents</h2>
<div id="text-table-of-contents">
<ul>
<li><a href="#org2595d4f">1. Effect of a change of capacitance</a>
<li><a href="#org2765a72">1. Effect of a change of capacitance</a>
<ul>
<li><a href="#orgd8111a6">1.1. Cedrat Technology</a></li>
<li><a href="#org278fde7">1.2. PI</a></li>
<li><a href="#org0c5b019">1.1. Cedrat Technology</a></li>
<li><a href="#org452991d">1.2. PI</a></li>
</ul>
</li>
<li><a href="#org2c356cd">2. Effect of a change in Voltage level</a>
<li><a href="#org872b871">2. Effect of a change in Voltage level</a>
<ul>
<li><a href="#org26c0aa6">2.1. Cedrat Technology</a></li>
<li><a href="#org99f4366">2.2. PI</a></li>
<li><a href="#org99ab8fd">2.1. Cedrat Technology</a></li>
<li><a href="#org134abf4">2.2. PI</a></li>
</ul>
</li>
<li><a href="#orgaef7c1d">3. Comparison PI / Cedrat</a>
<li><a href="#orgd766270">3. Comparison PI / Cedrat</a>
<ul>
<li><a href="#orgb7b222e">3.1. Results</a></li>
<li><a href="#orgbec8ff4">3.1. Results</a></li>
</ul>
</li>
<li><a href="#org7cf90b4">4. Impedance Measurement</a>
<li><a href="#org2f91855">4. Impedance Measurement</a>
<ul>
<li><a href="#org2defd83">4.1. Cedrat Technology</a>
<li><a href="#orgebadc67">4.1. Cedrat Technology</a>
<ul>
<li><a href="#orgf66e83a">4.1.1. Compute Impedance</a></li>
<li><a href="#orgc7a6f64">4.1.2. Effect of Impedance on the phase drop</a></li>
<li><a href="#org947e6a7">4.1.1. Compute Impedance</a></li>
<li><a href="#org876a45b">4.1.2. Effect of Impedance on the phase drop</a></li>
</ul>
</li>
<li><a href="#orgfd9e37f">4.2. PI</a></li>
<li><a href="#org6c099fc">4.2. PI</a></li>
</ul>
</li>
<li><a href="#org943c8af">5. Effect of filters configuration on the PI-E505 dynamics</a>
<li><a href="#org67f8be8">5. Effect of filters configuration on the PI-E505 dynamics</a>
<ul>
<li><a href="#org86c1e48">5.1. PI</a></li>
<li><a href="#org35acfc7">5.2. Transfer function of the Voltage Amplifier</a></li>
<li><a href="#org1c608d2">5.3. With Load</a></li>
<li><a href="#orgf08c313">5.1. PI</a></li>
<li><a href="#orge828488">5.2. Transfer function of the Voltage Amplifier</a></li>
<li><a href="#orgd44e75c">5.3. With Load</a></li>
</ul>
</li>
</ul>
</div>
</div>
<div class="note" id="org6d2afbc">
<div class="note" id="org49fbae4">
<p>
The following two voltage amplifiers are tested:
</p>
@@ -89,22 +89,22 @@ It contains three stacks with a capacitance of \(5 \mu F\) each that can be conn
This document is divided into the following sections:
</p>
<ul class="org-ul">
<li>Section <a href="#org14b2007">1</a>: The effect of a change in load capacitance on the amplifier dynamics is studied</li>
<li>Section <a href="#org5952ed9">2</a>: The effect on the voltage level on the amplifier dynamics is studied</li>
<li>Section <a href="#org021167d">3</a>: The dynamics of the E-505 and LA75B are compared</li>
<li>Section <a href="#org3a61ea0">4</a>: The output impedance of both amplifiers are measured</li>
<li>Section <a href="#orgdc9f3a2">5</a>: The effect of the internal filters of the E-505 on its dynamics is studied</li>
<li>Section <a href="#org23aafd9">1</a>: The effect of a change in load capacitance on the amplifier dynamics is studied</li>
<li>Section <a href="#org2888e25">2</a>: The effect on the voltage level on the amplifier dynamics is studied</li>
<li>Section <a href="#org9834afb">3</a>: The dynamics of the E-505 and LA75B are compared</li>
<li>Section <a href="#org36e302c">4</a>: The output impedance of both amplifiers are measured</li>
<li>Section <a href="#org846f3ab">5</a>: The effect of the internal filters of the E-505 on its dynamics is studied</li>
</ul>
<div id="outline-container-org2595d4f" class="outline-2">
<h2 id="org2595d4f"><span class="section-number-2">1</span> Effect of a change of capacitance</h2>
<div id="outline-container-org2765a72" class="outline-2">
<h2 id="org2765a72"><span class="section-number-2">1</span> Effect of a change of capacitance</h2>
<div class="outline-text-2" id="text-1">
<p>
<a id="org14b2007"></a>
<a id="org23aafd9"></a>
</p>
</div>
<div id="outline-container-orgd8111a6" class="outline-3">
<h3 id="orgd8111a6"><span class="section-number-3">1.1</span> Cedrat Technology</h3>
<div id="outline-container-org0c5b019" class="outline-3">
<h3 id="org0c5b019"><span class="section-number-3">1.1</span> Cedrat Technology</h3>
<div class="outline-text-3" id="text-1-1">
<p>
Load Data
@@ -143,7 +143,7 @@ We remove the phase delay due to the time delay of the ADC/DAC:
</div>
<div id="org0f3ffec" class="figure">
<div id="org89f2a0e" class="figure">
<p><img src="figs/change_capa_cedrat.png" alt="change_capa_cedrat.png" />
</p>
<p><span class="figure-number">Figure 1: </span>Effect of a change of the piezo capacitance on the Amplifier transfer function</p>
@@ -151,8 +151,8 @@ We remove the phase delay due to the time delay of the ADC/DAC:
</div>
</div>
<div id="outline-container-org278fde7" class="outline-3">
<h3 id="org278fde7"><span class="section-number-3">1.2</span> PI</h3>
<div id="outline-container-org452991d" class="outline-3">
<h3 id="org452991d"><span class="section-number-3">1.2</span> PI</h3>
<div class="outline-text-3" id="text-1-2">
<div class="org-src-container">
<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>);
@@ -185,7 +185,7 @@ We remove the phase delay due to the time delay of the ADC/DAC:
</div>
<div id="org1f93710" class="figure">
<div id="org5607845" class="figure">
<p><img src="figs/change_capa_pi.png" alt="change_capa_pi.png" />
</p>
<p><span class="figure-number">Figure 2: </span>Effect of a change of the piezo capacitance on the Amplifier transfer function</p>
@@ -194,15 +194,15 @@ We remove the phase delay due to the time delay of the ADC/DAC:
</div>
</div>
<div id="outline-container-org2c356cd" class="outline-2">
<h2 id="org2c356cd"><span class="section-number-2">2</span> Effect of a change in Voltage level</h2>
<div id="outline-container-org872b871" class="outline-2">
<h2 id="org872b871"><span class="section-number-2">2</span> Effect of a change in Voltage level</h2>
<div class="outline-text-2" id="text-2">
<p>
<a id="org5952ed9"></a>
<a id="org2888e25"></a>
</p>
</div>
<div id="outline-container-org26c0aa6" class="outline-3">
<h3 id="org26c0aa6"><span class="section-number-3">2.1</span> Cedrat Technology</h3>
<div id="outline-container-org99ab8fd" class="outline-3">
<h3 id="org99ab8fd"><span class="section-number-3">2.1</span> Cedrat Technology</h3>
<div class="outline-text-3" id="text-2-1">
<div class="org-src-container">
<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>);
@@ -235,7 +235,7 @@ We remove the phase delay due to the time delay of the ADC/DAC:
</div>
<div id="org6fa5b64" class="figure">
<div id="org6cca8d0" class="figure">
<p><img src="figs/change_level_cedrat.png" alt="change_level_cedrat.png" />
</p>
<p><span class="figure-number">Figure 3: </span>Effect of a change of voltage level on the Amplifier transfer function</p>
@@ -243,8 +243,8 @@ We remove the phase delay due to the time delay of the ADC/DAC:
</div>
</div>
<div id="outline-container-org99f4366" class="outline-3">
<h3 id="org99f4366"><span class="section-number-3">2.2</span> PI</h3>
<div id="outline-container-org134abf4" class="outline-3">
<h3 id="org134abf4"><span class="section-number-3">2.2</span> PI</h3>
<div class="outline-text-3" id="text-2-2">
<div class="org-src-container">
<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>);
@@ -265,7 +265,7 @@ win = hann(ceil(0.1<span class="org-type">/</span>Ts));
</div>
<div id="org234ac05" class="figure">
<div id="orgdd3117a" class="figure">
<p><img src="figs/change_level_pi.png" alt="change_level_pi.png" />
</p>
<p><span class="figure-number">Figure 4: </span>Effect of a change of voltage level on the Amplifier transfer function</p>
@@ -274,15 +274,15 @@ win = hann(ceil(0.1<span class="org-type">/</span>Ts));
</div>
</div>
<div id="outline-container-orgaef7c1d" class="outline-2">
<h2 id="orgaef7c1d"><span class="section-number-2">3</span> Comparison PI / Cedrat</h2>
<div id="outline-container-orgd766270" class="outline-2">
<h2 id="orgd766270"><span class="section-number-2">3</span> Comparison PI / Cedrat</h2>
<div class="outline-text-2" id="text-3">
<p>
<a id="org021167d"></a>
<a id="org9834afb"></a>
</p>
</div>
<div id="outline-container-orgb7b222e" class="outline-3">
<h3 id="orgb7b222e"><span class="section-number-3">3.1</span> Results</h3>
<div id="outline-container-orgbec8ff4" class="outline-3">
<h3 id="orgbec8ff4"><span class="section-number-3">3.1</span> Results</h3>
<div class="outline-text-3" id="text-3-1">
<div class="org-src-container">
<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>);
@@ -308,7 +308,7 @@ We remove the phase delay due to the time delay of the ADC/DAC:
</div>
<div id="orgd9445f5" class="figure">
<div id="orgc1176e8" class="figure">
<p><img src="figs/tf_amplifiers_comp.png" alt="tf_amplifiers_comp.png" />
</p>
<p><span class="figure-number">Figure 5: </span>Comparison of the two Amplifier transfer functions</p>
@@ -317,11 +317,11 @@ We remove the phase delay due to the time delay of the ADC/DAC:
</div>
</div>
<div id="outline-container-org7cf90b4" class="outline-2">
<h2 id="org7cf90b4"><span class="section-number-2">4</span> Impedance Measurement</h2>
<div id="outline-container-org2f91855" class="outline-2">
<h2 id="org2f91855"><span class="section-number-2">4</span> Impedance Measurement</h2>
<div class="outline-text-2" id="text-4">
<p>
<a id="org3a61ea0"></a>
<a id="org36e302c"></a>
</p>
<p>
The goal is to experimentally measure the output impedance of the voltage amplifiers.
@@ -342,12 +342,12 @@ 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 id="outline-container-orgebadc67" class="outline-3">
<h3 id="orgebadc67"><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 id="outline-container-org947e6a7" class="outline-4">
<h4 id="org947e6a7"><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>
@@ -384,8 +384,8 @@ Vp = 4.874; <span class="org-comment">% Output Voltage with resistice load [V]</
</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 id="outline-container-org876a45b" class="outline-4">
<h4 id="org876a45b"><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>
@@ -402,7 +402,7 @@ G_3 = G0<span class="org-type">/</span>(1<span class="org-type">+</span>Ri<span
</div>
<div id="org597c459" class="figure">
<div id="org9b2ba7f" 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>
@@ -411,8 +411,8 @@ G_3 = G0<span class="org-type">/</span>(1<span class="org-type">+</span>Ri<span
</div>
</div>
<div id="outline-container-orgfd9e37f" class="outline-3">
<h3 id="orgfd9e37f"><span class="section-number-3">4.2</span> PI</h3>
<div id="outline-container-org6c099fc" class="outline-3">
<h3 id="org6c099fc"><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>
@@ -450,15 +450,15 @@ Vp = 1.637; <span class="org-comment">% Output Voltage with resistice load [V]</
</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 id="outline-container-org67f8be8" class="outline-2">
<h2 id="org67f8be8"><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>
<a id="org846f3ab"></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 id="outline-container-orgf08c313" class="outline-3">
<h3 id="orgf08c313"><span class="section-number-3">5.1</span> PI</h3>
<div class="outline-text-3" id="text-5-1">
<p>
Three measurements are done:
@@ -494,7 +494,7 @@ win = hann(ceil(0.1<span class="org-type">/</span>Ts));
</div>
<div id="org85111b8" class="figure">
<div id="org5d55cf1" 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>
@@ -502,8 +502,8 @@ win = hann(ceil(0.1<span class="org-type">/</span>Ts));
</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 id="outline-container-orge828488" class="outline-3">
<h3 id="orge828488"><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.
@@ -517,8 +517,8 @@ G = 10.5<span class="org-type">*</span>(s<span class="org-type">^</span>2 <span
</div>
</div>
<div id="outline-container-org1c608d2" class="outline-3">
<h3 id="org1c608d2"><span class="section-number-3">5.3</span> With Load</h3>
<div id="outline-container-orgd44e75c" class="outline-3">
<h3 id="orgd44e75c"><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>
@@ -533,7 +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. 12:44</p>
<p class="date">Created: 2020-11-12 jeu. 10:11</p>
</div>
</body>
</html>