# Measurement of Piezoelectric Amplifiers
Author: Dehaeze Thomas

## Table of Contents

- 1. Effect of a change of capacitance
  - 1.1. Cedrat Technology
  - 1.2. PI
- 2. Effect of a change in Voltage level
  - 2.1. Cedrat Technology
  - 2.2. PI
- 3. Comparison PI / Cedrat
  - 3.1. Results

Two voltage amplifiers are tested:

- PI E-505.00 (link)
- Cedrat Technology LA75B (link)

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

### 1.1 Cedrat Technology

Load Data

    piezo1 = load('mat/cedrat_la75b_med_1_stack.mat', 't', 'V_in', 'V_out');
    piezo2 = load('mat/cedrat_la75b_med_2_stack.mat', 't', 'V_in', 'V_out');
    piezo3 = load('mat/cedrat_la75b_med_3_stack.mat', 't', 'V_in', 'V_out');

Compute Coherence and Transfer functions

    Ts = 1e-4;
    win = hann(ceil(0.1/Ts));

    [tf_1, f_1] = tfestimate(piezo1.V_in, piezo1.V_out, win, [], [], 1/Ts);
    [co_1, ~] = mscohere(piezo1.V_in, piezo1.V_out, win, [], [], 1/Ts);

    [tf_2, f_2] = tfestimate(piezo2.V_in, piezo2.V_out, win, [], [], 1/Ts);
    [co_2, ~] = mscohere(piezo2.V_in, piezo2.V_out, win, [], [], 1/Ts);

    [tf_3, f_3] = tfestimate(piezo3.V_in, piezo3.V_out, win, [], [], 1/Ts);
    [co_3, ~] = mscohere(piezo3.V_in, piezo3.V_out, win, [], [], 1/Ts);

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

### 1.2 PI

    piezo1 = load('mat/pi_505_high.mat', 't', 'V_in', 'V_out');
    piezo2 = load('mat/pi_505_high_2_stacks.mat', 't', 'V_in', 'V_out');
    piezo3 = load('mat/pi_505_high_3_stacks.mat', 't', 'V_in', 'V_out');

    Ts = 1e-4;
    win = hann(ceil(0.1/Ts));

    [tf_1, f_1] = tfestimate(piezo1.V_in, piezo1.V_out, win, [], [], 1/Ts);
    [co_1, ~] = mscohere(piezo1.V_in, piezo1.V_out, win, [], [], 1/Ts);

    [tf_2, f_2] = tfestimate(piezo2.V_in, piezo2.V_out, win, [], [], 1/Ts);
    [co_2, ~] = mscohere(piezo2.V_in, piezo2.V_out, win, [], [], 1/Ts);

    [tf_3, f_3] = tfestimate(piezo3.V_in, piezo3.V_out, win, [], [], 1/Ts);
    [co_3, ~] = mscohere(piezo3.V_in, piezo3.V_out, win, [], [], 1/Ts);

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

## 2 Effect of a change in Voltage level

### 2.1 Cedrat Technology

    hi = load('mat/cedrat_la75b_high_1_stack.mat', 't', 'V_in', 'V_out');
    me = load('mat/cedrat_la75b_med_1_stack.mat', 't', 'V_in', 'V_out');
    lo = load('mat/cedrat_la75b_low_1_stack.mat', 't', 'V_in', 'V_out');

    Ts = 1e-4;
    win = hann(ceil(0.1/Ts));

    [tf_hi, f_hi] = tfestimate(hi.V_in, hi.V_out, win, [], [], 1/Ts);
    [co_hi, ~] = mscohere(hi.V_in, hi.V_out, win, [], [], 1/Ts);

    [tf_me, f_me] = tfestimate(me.V_in, me.V_out, win, [], [], 1/Ts);
    [co_me, ~] = mscohere(me.V_in, me.V_out, win, [], [], 1/Ts);

    [tf_lo, f_lo] = tfestimate(lo.V_in, lo.V_out, win, [], [], 1/Ts);
    [co_lo, ~] = mscohere(lo.V_in, lo.V_out, win, [], [], 1/Ts);

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

### 2.2 PI

    hi = load('mat/pi_505_high.mat', 't', 'V_in', 'V_out');
    lo = load('mat/pi_505_low.mat', 't', 'V_in', 'V_out');

    Ts = 1e-4;
    win = hann(ceil(0.1/Ts));

    [tf_hi, f_hi] = tfestimate(hi.V_in, hi.V_out, win, [], [], 1/Ts);
    [co_hi, ~] = mscohere(hi.V_in, hi.V_out, win, [], [], 1/Ts);

    [tf_lo, f_lo] = tfestimate(lo.V_in, lo.V_out, win, [], [], 1/Ts);
    [co_lo, ~] = mscohere(lo.V_in, lo.V_out, win, [], [], 1/Ts);

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

## 3 Comparison PI / Cedrat

### 3.1 Results

    ce_results = load('mat/cedrat_la75b_high_1_stack.mat', 't', 'V_in', 'V_out');
    pi_results = load('mat/pi_505_high.mat', 't', 'V_in', 'V_out');

    Ts = 1e-4;
    win = hann(ceil(0.1/Ts));

    [tf_ce, f_ce] = tfestimate(ce_results.V_in, ce_results.V_out, win, [], [], 1/Ts);
    [tf_pi, f_pi] = tfestimate(pi_results.V_in, pi_results.V_out, win, [], [], 1/Ts);

Figure 5: Comparison of the two Amplifier transfer functions

Author: Dehaeze Thomas

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