Measurement of Piezoelectric Amplifiers

Table of Contents

Two voltage amplifiers are tested:

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

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

We remove the phase delay due to the time delay of the ADC/DAC: 

angle_delay = 180/pi*angle(squeeze(freqresp(exp(-s*Ts), f, 'Hz')));

change_capa_cedrat.png

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

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

We remove the phase delay due to the time delay of the ADC/DAC: 

angle_delay = 180/pi*angle(squeeze(freqresp(exp(-s*Ts), f, 'Hz')));

change_capa_pi.png

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

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

We remove the phase delay due to the time delay of the ADC/DAC: 

angle_delay = 180/pi*angle(squeeze(freqresp(exp(-s*Ts), f, 'Hz')));

change_level_cedrat.png

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

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

change_level_pi.png

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

We remove the phase delay due to the time delay of the ADC/DAC: 

angle_delay = 180/pi*angle(squeeze(freqresp(exp(-s*Ts), f, 'Hz')));

tf_amplifiers_comp.png

Figure 5: Comparison of the two Amplifier transfer functions

4 Impedance Measurement

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

4.1.1 Compute Impedance

R = 10;    % Resistive Load used [Ohm]
V = 0.998; % Output Voltage without any load [V]
Vp = 0.912; % Output Voltage with resistice load [V]

R * (V - Vp)/Vp;

0.94298

R = 47;    % Resistive Load used [Ohm]
V = 4.960; % Output Voltage without any load [V]
Vp = 4.874; % Output Voltage with resistice load [V]

R * (V - Vp)/Vp;

0.8293

4.1.2 Effect of Impedance on the phase drop

C_1 = 5e-6; % Capacitance in [F]
C_2 = 10e-6; % Capacitance in [F]
C_3 = 15e-6; % Capacitance in [F]

Ri = R * (V - Vp)/Vp; % Internal resistance [Ohm]
G0 = 20;

G_1 = G0/(1+Ri*C_1*s);
G_2 = G0/(1+Ri*C_2*s);
G_3 = G0/(1+Ri*C_3*s);

change_capa_cedrat.png

Figure 6: Effect of a change of the piezo capacitance on the Amplifier transfer function

4.2 PI

R = 10;    % Resistive Load used [Ohm]
V = 1.059; % Output Voltage without any load [V]
Vp = 0.828; % Output Voltage with resistice load [V]

R * (V - Vp)/Vp

2.7899

R = 10;    % Resistive Load used [Ohm]
V = 2.092; % Output Voltage without any load [V]
Vp = 1.637; % Output Voltage with resistice load [V]

R * (V - Vp)/Vp

2.7795

5 New PI amplifier measurements

5.1 PI

Three measurements are done:

  • Slew Rate limitation at maximum
  • Slew Rate limitation at minimum
  • Notch Filter at maximum frequency
pi_sr_min = load('mat/pi_slew_rate_min.mat');
pi_sr_max = load('mat/pi_slew_rate_max.mat');
pi_sr_max_notch = load('mat/pi_slew_rate_max_notch_high.mat');

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

[tf_sr_min, f] = tfestimate(pi_sr_min.V_in, pi_sr_min.V_out, win, [], [], 1/Ts);
[tf_sr_max, ~] = tfestimate(pi_sr_max.V_in, pi_sr_max.V_out, win, [], [], 1/Ts);
[tf_sr_max_notch, ~] = tfestimate(pi_sr_max_notch.V_in, pi_sr_max_notch.V_out, win, [], [], 1/Ts);

angle_delay = 180/pi*angle(squeeze(freqresp(exp(-s*Ts), f, 'Hz')));

pi_slew_rate_notch.png

Figure 7: Effect of a change in the slew rate limitation and notch filter

5.2 Transfer function of the Voltage Amplifier

The identified transfer function still seems to match the one of a notch filter at 5kHz. 

w_nf = 2*pi*5e3; % Notch Filter Frequency [rad/s]
G = 10.5*(s^2 + 2*w_nf*0.12*s + w_nf^2)/(s^2 + 2*w_nf*s + w_nf^2);

Author: Dehaeze Thomas

Created: 2020-09-03 jeu. 14:08