Add impedance test to the document
This commit is contained in:
parent
22886d014e
commit
4797a1d1ca
143
index.html
143
index.html
@ -3,7 +3,7 @@
|
||||
"http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd">
|
||||
<html xmlns="http://www.w3.org/1999/xhtml" lang="en" xml:lang="en">
|
||||
<head>
|
||||
<!-- 2020-08-13 jeu. 10:00 -->
|
||||
<!-- 2020-08-13 jeu. 17:11 -->
|
||||
<meta http-equiv="Content-Type" content="text/html;charset=utf-8" />
|
||||
<title>Measurement of Piezoelectric Amplifiers</title>
|
||||
<meta name="generator" content="Org mode" />
|
||||
@ -31,21 +31,27 @@
|
||||
<h2>Table of Contents</h2>
|
||||
<div id="text-table-of-contents">
|
||||
<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>
|
||||
<li><a href="#org52f8a23">1.1. Cedrat Technology</a></li>
|
||||
<li><a href="#org96f04ca">1.2. PI</a></li>
|
||||
<li><a href="#orgdb6f8ad">1.1. Cedrat Technology</a></li>
|
||||
<li><a href="#orgee41528">1.2. PI</a></li>
|
||||
</ul>
|
||||
</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>
|
||||
<li><a href="#orgacb19bc">2.1. Cedrat Technology</a></li>
|
||||
<li><a href="#org4012e58">2.2. PI</a></li>
|
||||
<li><a href="#orga6e0258">2.1. Cedrat Technology</a></li>
|
||||
<li><a href="#orgd744290">2.2. PI</a></li>
|
||||
</ul>
|
||||
</li>
|
||||
<li><a href="#org6c9c30b">3. Comparison PI / Cedrat</a>
|
||||
<li><a href="#org4b79280">3. Comparison PI / Cedrat</a>
|
||||
<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>
|
||||
</li>
|
||||
</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.
|
||||
</p>
|
||||
|
||||
<div id="outline-container-orgf4c5526" class="outline-2">
|
||||
<h2 id="orgf4c5526"><span class="section-number-2">1</span> Effect of a change of capacitance</h2>
|
||||
<div id="outline-container-org1bbe59a" class="outline-2">
|
||||
<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>
|
||||
<div id="outline-container-org52f8a23" class="outline-3">
|
||||
<h3 id="org52f8a23"><span class="section-number-3">1.1</span> Cedrat Technology</h3>
|
||||
<div id="outline-container-orgdb6f8ad" class="outline-3">
|
||||
<h3 id="orgdb6f8ad"><span class="section-number-3">1.1</span> Cedrat Technology</h3>
|
||||
<div class="outline-text-3" id="text-1-1">
|
||||
<p>
|
||||
Load Data
|
||||
@ -103,7 +109,7 @@ win = hann(ceil(0.1/Ts));
|
||||
</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>
|
||||
<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 id="outline-container-org96f04ca" class="outline-3">
|
||||
<h3 id="org96f04ca"><span class="section-number-3">1.2</span> PI</h3>
|
||||
<div id="outline-container-orgee41528" class="outline-3">
|
||||
<h3 id="orgee41528"><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('mat/pi_505_high.mat', 't', 'V_in', 'V_out');
|
||||
@ -139,7 +145,7 @@ win = hann(ceil(0.1/Ts));
|
||||
</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>
|
||||
<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 id="outline-container-orgcd4115f" class="outline-2">
|
||||
<h2 id="orgcd4115f"><span class="section-number-2">2</span> Effect of a change in Voltage level</h2>
|
||||
<div id="outline-container-orgd75b37d" class="outline-2">
|
||||
<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>
|
||||
<div id="outline-container-orgacb19bc" class="outline-3">
|
||||
<h3 id="orgacb19bc"><span class="section-number-3">2.1</span> Cedrat Technology</h3>
|
||||
<div id="outline-container-orga6e0258" class="outline-3">
|
||||
<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="org-src-container">
|
||||
<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 id="orgbd8e672" class="figure">
|
||||
<div id="org0ea5714" 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>
|
||||
@ -186,8 +192,8 @@ win = hann(ceil(0.1/Ts));
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org4012e58" class="outline-3">
|
||||
<h3 id="org4012e58"><span class="section-number-3">2.2</span> PI</h3>
|
||||
<div id="outline-container-orgd744290" class="outline-3">
|
||||
<h3 id="orgd744290"><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('mat/pi_505_high.mat', 't', 'V_in', 'V_out');
|
||||
@ -208,7 +214,7 @@ win = hann(ceil(0.1/Ts));
|
||||
</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>
|
||||
<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 id="outline-container-org6c9c30b" class="outline-2">
|
||||
<h2 id="org6c9c30b"><span class="section-number-2">3</span> Comparison PI / Cedrat</h2>
|
||||
<div id="outline-container-org4b79280" class="outline-2">
|
||||
<h2 id="org4b79280"><span class="section-number-2">3</span> Comparison PI / Cedrat</h2>
|
||||
<div class="outline-text-2" id="text-3">
|
||||
</div>
|
||||
<div id="outline-container-org05eec9b" class="outline-3">
|
||||
<h3 id="org05eec9b"><span class="section-number-3">3.1</span> Results</h3>
|
||||
<div id="outline-container-org590829e" class="outline-3">
|
||||
<h3 id="org590829e"><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('mat/cedrat_la75b_high_1_stack.mat', 't', 'V_in', 'V_out');
|
||||
@ -240,7 +246,7 @@ win = hann(ceil(0.1/Ts));
|
||||
</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>
|
||||
<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 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 id="postamble" class="status">
|
||||
<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>
|
||||
</body>
|
||||
</html>
|
||||
|
||||
82
index.org
82
index.org
@ -353,3 +353,85 @@ Compute Coherence and Transfer functions
|
||||
#+caption: Comparison of the two Amplifier transfer functions
|
||||
#+RESULTS:
|
||||
[[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
|
||||
|
||||
|
||||
@ -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
|
||||
|
||||
|
||||
|
||||
|
||||
Loading…
Reference in New Issue
Block a user