From 4797a1d1ca85605f0a08ea480b582c00fe220f3e Mon Sep 17 00:00:00 2001 From: Thomas Dehaeze Date: Thu, 13 Aug 2020 17:11:21 +0200 Subject: [PATCH] Add impedance test to the document --- index.html | 143 ++++++++++++++++++++++++++++++++++---------- index.org | 82 +++++++++++++++++++++++++ test_impdedance.org | 18 ------ 3 files changed, 194 insertions(+), 49 deletions(-) delete mode 100644 test_impdedance.org diff --git a/index.html b/index.html index 7ac2dcb..c525ca7 100644 --- a/index.html +++ b/index.html @@ -3,7 +3,7 @@ "http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd"> - + Measurement of Piezoelectric Amplifiers @@ -31,21 +31,27 @@

Table of Contents

@@ -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.

-
-

1 Effect of a change of capacitance

+
+

1 Effect of a change of capacitance

-
-

1.1 Cedrat Technology

+
+

1.1 Cedrat Technology

Load Data @@ -103,7 +109,7 @@ win = hann(ceil(0.1/Ts));

-
+

change_capa_cedrat.png

Figure 1: Effect of a change of the piezo capacitance on the Amplifier transfer function

@@ -111,8 +117,8 @@ win = hann(ceil(0.1/Ts));
-
-

1.2 PI

+
+

1.2 PI

piezo1 = load('mat/pi_505_high.mat', 't', 'V_in', 'V_out');
@@ -139,7 +145,7 @@ win = hann(ceil(0.1/Ts));
-
+

change_capa_pi.png

Figure 2: Effect of a change of the piezo capacitance on the Amplifier transfer function

@@ -148,12 +154,12 @@ win = hann(ceil(0.1/Ts));
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2 Effect of a change in Voltage level

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+

2 Effect of a change in Voltage level

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2.1 Cedrat Technology

+
+

2.1 Cedrat Technology

hi = load('mat/cedrat_la75b_high_1_stack.mat', 't', 'V_in', 'V_out');
@@ -178,7 +184,7 @@ win = hann(ceil(0.1/Ts));
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+

change_level_cedrat.png

Figure 3: Effect of a change of voltage level on the Amplifier transfer function

@@ -186,8 +192,8 @@ win = hann(ceil(0.1/Ts));
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2.2 PI

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+

2.2 PI

hi = load('mat/pi_505_high.mat', 't', 'V_in', 'V_out');
@@ -208,7 +214,7 @@ win = hann(ceil(0.1/Ts));
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+

change_level_pi.png

Figure 4: Effect of a change of voltage level on the Amplifier transfer function

@@ -217,12 +223,12 @@ win = hann(ceil(0.1/Ts));
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3 Comparison PI / Cedrat

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+

3 Comparison PI / Cedrat

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3.1 Results

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+

3.1 Results

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));
-
+

tf_amplifiers_comp.png

Figure 5: Comparison of the two Amplifier transfer functions

@@ -248,10 +254,85 @@ win = hann(ceil(0.1/Ts));
+ +
+

4 Impedance Measurement

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+

+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: +\[ R_i = R \frac{V - V^\prime}{V^\prime} \] +

+
+ +
+

4.1 Cedrat Technology

+
+
+
R = 10;    % Resistive Load used [Ohm]
+V = 10.09; % Output Voltage without any load [V]
+Vp = 3.46; % Output Voltage with resistice load [V]
+
+
+ +
+
R * (V - Vp)/Vp;
+
+
+ +
+19.162
+
+ + +
+
C = 5e-6; % Capacitance in [F]
+Ri = R * (V - Vp)/Vp; % Internal resistance [Ohm]
+
+G_ce = 1/(1+Ri*C*s);
+
+
+
+
+ +
+

4.2 PI

+
+
+
R = 10;    % Resistive Load used [Ohm]
+V = 10.35; % Output Voltage without any load [V]
+Vp = 4.14; % Output Voltage with resistice load [V]
+
+
+ +
+
R * (V - Vp)/Vp
+
+
+ +
+15
+
+
+
+

Author: Dehaeze Thomas

-

Created: 2020-08-13 jeu. 10:00

+

Created: 2020-08-13 jeu. 17:11

diff --git a/index.org b/index.org index 3ff9977..aeb4889 100644 --- a/index.org +++ b/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) + <> +#+end_src + +#+begin_src matlab :exports none :results silent :noweb yes + <> +#+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 + diff --git a/test_impdedance.org b/test_impdedance.org deleted file mode 100644 index 91629ac..0000000 --- a/test_impdedance.org +++ /dev/null @@ -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 - - - -