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Add impedance test to the document

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Thomas Dehaeze 2020-08-13 17:11:21 +02:00
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@ -3,7 +3,7 @@
"http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd"> "http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd">
<html xmlns="http://www.w3.org/1999/xhtml" lang="en" xml:lang="en"> <html xmlns="http://www.w3.org/1999/xhtml" lang="en" xml:lang="en">
<head> <head>
<!-- 2020-08-13 jeu. 10:00 --> <!-- 2020-08-13 jeu. 17:11 -->
<meta http-equiv="Content-Type" content="text/html;charset=utf-8" /> <meta http-equiv="Content-Type" content="text/html;charset=utf-8" />
<title>Measurement of Piezoelectric Amplifiers</title> <title>Measurement of Piezoelectric Amplifiers</title>
<meta name="generator" content="Org mode" /> <meta name="generator" content="Org mode" />
@ -31,21 +31,27 @@
<h2>Table of Contents</h2> <h2>Table of Contents</h2>
<div id="text-table-of-contents"> <div id="text-table-of-contents">
<ul> <ul>
<li><a href="#orgf4c5526">1. Effect of a change of capacitance</a> <li><a href="#org1bbe59a">1. Effect of a change of capacitance</a>
<ul> <ul>
<li><a href="#org52f8a23">1.1. Cedrat Technology</a></li> <li><a href="#orgdb6f8ad">1.1. Cedrat Technology</a></li>
<li><a href="#org96f04ca">1.2. PI</a></li> <li><a href="#orgee41528">1.2. PI</a></li>
</ul> </ul>
</li> </li>
<li><a href="#orgcd4115f">2. Effect of a change in Voltage level</a> <li><a href="#orgd75b37d">2. Effect of a change in Voltage level</a>
<ul> <ul>
<li><a href="#orgacb19bc">2.1. Cedrat Technology</a></li> <li><a href="#orga6e0258">2.1. Cedrat Technology</a></li>
<li><a href="#org4012e58">2.2. PI</a></li> <li><a href="#orgd744290">2.2. PI</a></li>
</ul> </ul>
</li> </li>
<li><a href="#org6c9c30b">3. Comparison PI / Cedrat</a> <li><a href="#org4b79280">3. Comparison PI / Cedrat</a>
<ul> <ul>
<li><a href="#org05eec9b">3.1. Results</a></li> <li><a href="#org590829e">3.1. Results</a></li>
</ul>
</li>
<li><a href="#org2f30df2">4. Impedance Measurement</a>
<ul>
<li><a href="#org7ad403e">4.1. Cedrat Technology</a></li>
<li><a href="#org746e78c">4.2. PI</a></li>
</ul> </ul>
</li> </li>
</ul> </ul>
@ -65,12 +71,12 @@ The piezoelectric actuator under test is an APA95ML from Cedrat technology.
It contains three stacks with a capacitance of \(5 \mu F\) each that can be connected independently to the amplifier. It contains three stacks with a capacitance of \(5 \mu F\) each that can be connected independently to the amplifier.
</p> </p>
<div id="outline-container-orgf4c5526" class="outline-2"> <div id="outline-container-org1bbe59a" class="outline-2">
<h2 id="orgf4c5526"><span class="section-number-2">1</span> Effect of a change of capacitance</h2> <h2 id="org1bbe59a"><span class="section-number-2">1</span> Effect of a change of capacitance</h2>
<div class="outline-text-2" id="text-1"> <div class="outline-text-2" id="text-1">
</div> </div>
<div id="outline-container-org52f8a23" class="outline-3"> <div id="outline-container-orgdb6f8ad" class="outline-3">
<h3 id="org52f8a23"><span class="section-number-3">1.1</span> Cedrat Technology</h3> <h3 id="orgdb6f8ad"><span class="section-number-3">1.1</span> Cedrat Technology</h3>
<div class="outline-text-3" id="text-1-1"> <div class="outline-text-3" id="text-1-1">
<p> <p>
Load Data Load Data
@ -103,7 +109,7 @@ win = hann(ceil(0.1/Ts));
</div> </div>
<div id="org988e499" class="figure"> <div id="orga28400f" class="figure">
<p><img src="figs/change_capa_cedrat.png" alt="change_capa_cedrat.png" /> <p><img src="figs/change_capa_cedrat.png" alt="change_capa_cedrat.png" />
</p> </p>
<p><span class="figure-number">Figure 1: </span>Effect of a change of the piezo capacitance on the Amplifier transfer function</p> <p><span class="figure-number">Figure 1: </span>Effect of a change of the piezo capacitance on the Amplifier transfer function</p>
@ -111,8 +117,8 @@ win = hann(ceil(0.1/Ts));
</div> </div>
</div> </div>
<div id="outline-container-org96f04ca" class="outline-3"> <div id="outline-container-orgee41528" class="outline-3">
<h3 id="org96f04ca"><span class="section-number-3">1.2</span> PI</h3> <h3 id="orgee41528"><span class="section-number-3">1.2</span> PI</h3>
<div class="outline-text-3" id="text-1-2"> <div class="outline-text-3" id="text-1-2">
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab">piezo1 = load('mat/pi_505_high.mat', 't', 'V_in', 'V_out'); <pre class="src src-matlab">piezo1 = load('mat/pi_505_high.mat', 't', 'V_in', 'V_out');
@ -139,7 +145,7 @@ win = hann(ceil(0.1/Ts));
</div> </div>
<div id="org9cf27f7" class="figure"> <div id="org9cafd87" class="figure">
<p><img src="figs/change_capa_pi.png" alt="change_capa_pi.png" /> <p><img src="figs/change_capa_pi.png" alt="change_capa_pi.png" />
</p> </p>
<p><span class="figure-number">Figure 2: </span>Effect of a change of the piezo capacitance on the Amplifier transfer function</p> <p><span class="figure-number">Figure 2: </span>Effect of a change of the piezo capacitance on the Amplifier transfer function</p>
@ -148,12 +154,12 @@ win = hann(ceil(0.1/Ts));
</div> </div>
</div> </div>
<div id="outline-container-orgcd4115f" class="outline-2"> <div id="outline-container-orgd75b37d" class="outline-2">
<h2 id="orgcd4115f"><span class="section-number-2">2</span> Effect of a change in Voltage level</h2> <h2 id="orgd75b37d"><span class="section-number-2">2</span> Effect of a change in Voltage level</h2>
<div class="outline-text-2" id="text-2"> <div class="outline-text-2" id="text-2">
</div> </div>
<div id="outline-container-orgacb19bc" class="outline-3"> <div id="outline-container-orga6e0258" class="outline-3">
<h3 id="orgacb19bc"><span class="section-number-3">2.1</span> Cedrat Technology</h3> <h3 id="orga6e0258"><span class="section-number-3">2.1</span> Cedrat Technology</h3>
<div class="outline-text-3" id="text-2-1"> <div class="outline-text-3" id="text-2-1">
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab">hi = load('mat/cedrat_la75b_high_1_stack.mat', 't', 'V_in', 'V_out'); <pre class="src src-matlab">hi = load('mat/cedrat_la75b_high_1_stack.mat', 't', 'V_in', 'V_out');
@ -178,7 +184,7 @@ win = hann(ceil(0.1/Ts));
</div> </div>
<div id="orgbd8e672" class="figure"> <div id="org0ea5714" class="figure">
<p><img src="figs/change_level_cedrat.png" alt="change_level_cedrat.png" /> <p><img src="figs/change_level_cedrat.png" alt="change_level_cedrat.png" />
</p> </p>
<p><span class="figure-number">Figure 3: </span>Effect of a change of voltage level on the Amplifier transfer function</p> <p><span class="figure-number">Figure 3: </span>Effect of a change of voltage level on the Amplifier transfer function</p>
@ -186,8 +192,8 @@ win = hann(ceil(0.1/Ts));
</div> </div>
</div> </div>
<div id="outline-container-org4012e58" class="outline-3"> <div id="outline-container-orgd744290" class="outline-3">
<h3 id="org4012e58"><span class="section-number-3">2.2</span> PI</h3> <h3 id="orgd744290"><span class="section-number-3">2.2</span> PI</h3>
<div class="outline-text-3" id="text-2-2"> <div class="outline-text-3" id="text-2-2">
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab">hi = load('mat/pi_505_high.mat', 't', 'V_in', 'V_out'); <pre class="src src-matlab">hi = load('mat/pi_505_high.mat', 't', 'V_in', 'V_out');
@ -208,7 +214,7 @@ win = hann(ceil(0.1/Ts));
</div> </div>
<div id="orgaafc93d" class="figure"> <div id="orgb43e11f" class="figure">
<p><img src="figs/change_level_pi.png" alt="change_level_pi.png" /> <p><img src="figs/change_level_pi.png" alt="change_level_pi.png" />
</p> </p>
<p><span class="figure-number">Figure 4: </span>Effect of a change of voltage level on the Amplifier transfer function</p> <p><span class="figure-number">Figure 4: </span>Effect of a change of voltage level on the Amplifier transfer function</p>
@ -217,12 +223,12 @@ win = hann(ceil(0.1/Ts));
</div> </div>
</div> </div>
<div id="outline-container-org6c9c30b" class="outline-2"> <div id="outline-container-org4b79280" class="outline-2">
<h2 id="org6c9c30b"><span class="section-number-2">3</span> Comparison PI / Cedrat</h2> <h2 id="org4b79280"><span class="section-number-2">3</span> Comparison PI / Cedrat</h2>
<div class="outline-text-2" id="text-3"> <div class="outline-text-2" id="text-3">
</div> </div>
<div id="outline-container-org05eec9b" class="outline-3"> <div id="outline-container-org590829e" class="outline-3">
<h3 id="org05eec9b"><span class="section-number-3">3.1</span> Results</h3> <h3 id="org590829e"><span class="section-number-3">3.1</span> Results</h3>
<div class="outline-text-3" id="text-3-1"> <div class="outline-text-3" id="text-3-1">
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab">ce_results = load('mat/cedrat_la75b_high_1_stack.mat', 't', 'V_in', 'V_out'); <pre class="src src-matlab">ce_results = load('mat/cedrat_la75b_high_1_stack.mat', 't', 'V_in', 'V_out');
@ -240,7 +246,7 @@ win = hann(ceil(0.1/Ts));
</div> </div>
<div id="org1897cd3" class="figure"> <div id="orgbdf4de1" class="figure">
<p><img src="figs/tf_amplifiers_comp.png" alt="tf_amplifiers_comp.png" /> <p><img src="figs/tf_amplifiers_comp.png" alt="tf_amplifiers_comp.png" />
</p> </p>
<p><span class="figure-number">Figure 5: </span>Comparison of the two Amplifier transfer functions</p> <p><span class="figure-number">Figure 5: </span>Comparison of the two Amplifier transfer functions</p>
@ -248,10 +254,85 @@ win = hann(ceil(0.1/Ts));
</div> </div>
</div> </div>
</div> </div>
<div id="outline-container-org2f30df2" class="outline-2">
<h2 id="org2f30df2"><span class="section-number-2">4</span> Impedance Measurement</h2>
<div class="outline-text-2" id="text-4">
<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-org7ad403e" class="outline-3">
<h3 id="org7ad403e"><span class="section-number-3">4.1</span> Cedrat Technology</h3>
<div class="outline-text-3" id="text-4-1">
<div class="org-src-container">
<pre class="src src-matlab">R = 10; % Resistive Load used [Ohm]
V = 10.09; % Output Voltage without any load [V]
Vp = 3.46; % Output Voltage with resistice load [V]
</pre>
</div>
<div class="org-src-container">
<pre class="src src-matlab">R * (V - Vp)/Vp;
</pre>
</div>
<pre class="example">
19.162
</pre>
<div class="org-src-container">
<pre class="src src-matlab">C = 5e-6; % Capacitance in [F]
Ri = R * (V - Vp)/Vp; % Internal resistance [Ohm]
G_ce = 1/(1+Ri*C*s);
</pre>
</div>
</div>
</div>
<div id="outline-container-org746e78c" class="outline-3">
<h3 id="org746e78c"><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; % Resistive Load used [Ohm]
V = 10.35; % Output Voltage without any load [V]
Vp = 4.14; % Output Voltage with resistice load [V]
</pre>
</div>
<div class="org-src-container">
<pre class="src src-matlab">R * (V - Vp)/Vp
</pre>
</div>
<pre class="example">
15
</pre>
</div>
</div>
</div>
</div> </div>
<div id="postamble" class="status"> <div id="postamble" class="status">
<p class="author">Author: Dehaeze Thomas</p> <p class="author">Author: Dehaeze Thomas</p>
<p class="date">Created: 2020-08-13 jeu. 10:00</p> <p class="date">Created: 2020-08-13 jeu. 17:11</p>
</div> </div>
</body> </body>
</html> </html>

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@ -353,3 +353,85 @@ Compute Coherence and Transfer functions
#+caption: Comparison of the two Amplifier transfer functions #+caption: Comparison of the two Amplifier transfer functions
#+RESULTS: #+RESULTS:
[[file:figs/tf_amplifiers_comp.png]] [[file:figs/tf_amplifiers_comp.png]]
* Impedance Measurement
** Introduction :ignore:
The goal is to experimentally measure the output impedance of the voltage amplifiers.
To do so, the output voltage is first measure without any load ($V$).
It is then measure when a 10Ohm load is used ($V^\prime$).
The load ($R = 10\Omega$) and the internal resistor ($R_i$) form a voltage divider, and thus:
\[ V^\prime = \frac{R}{R + R_i} V \]
From the two values of voltage, the internal resistor value can be computed:
\[ R_i = R \frac{V - V^\prime}{V^\prime} \]
** Matlab Init :noexport:ignore:
#+begin_src matlab :tangle no :exports none :results silent :noweb yes :var current_dir=(file-name-directory buffer-file-name)
<<matlab-dir>>
#+end_src
#+begin_src matlab :exports none :results silent :noweb yes
<<matlab-init>>
#+end_src
** Cedrat Technology
#+begin_src matlab
R = 10; % Resistive Load used [Ohm]
V = 10.09; % Output Voltage without any load [V]
Vp = 3.46; % Output Voltage with resistice load [V]
#+end_src
#+begin_src matlab :results replace value
R * (V - Vp)/Vp;
#+end_src
#+RESULTS:
: 19.162
#+begin_src matlab
C = 5e-6; % Capacitance in [F]
Ri = R * (V - Vp)/Vp; % Internal resistance [Ohm]
G_ce = 1/(1+Ri*C*s);
#+end_src
#+begin_src matlab :exports none
freqs = logspace(1, 4, 1000);
figure;
ax1 = subplot(2, 1, 1);
hold on;
plot(freqs, abs(squeeze(freqresp(G_ce, freqs, 'Hz'))));
hold off;
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
ylabel('Amplitude [m/N]'); set(gca, 'XTickLabel',[]);
ax2 = subplot(2, 1, 2);
hold on;
plot(freqs, 180/pi*angle(squeeze(freqresp(G_ce, freqs, 'Hz'))));
hold off;
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin');
ylabel('Phase [deg]'); xlabel('Frequency [Hz]');
ylim([-180, 180]);
yticks([-180, -90, 0, 90, 180]);
linkaxes([ax1,ax2],'x');
#+end_src
** PI
#+begin_src matlab
R = 10; % Resistive Load used [Ohm]
V = 10.35; % Output Voltage without any load [V]
Vp = 4.14; % Output Voltage with resistice load [V]
#+end_src
#+begin_src matlab :results replace value
R * (V - Vp)/Vp
#+end_src
#+RESULTS:
: 15

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@ -1,18 +0,0 @@
* Cedrat
No charge
V = 10.09
10 Ohmn
V = 3.46
* PI
No charge
V = 10.35
10 Ohm
V = 4.14