Measurement of Piezoelectric Amplifiers

Table of ContentsClose

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
4. Impedance Measurement
- 4.1. Cedrat Technology
  - 4.1.1. Compute Impedance
  - 4.1.2. Effect of Impedance on the phase drop
- 4.2. PI
5. Effect of filters configuration on the PI-E505 dynamics

Note

The following two voltage amplifiers are tested:

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

The piezoelectric actuator under test is an APA95ML from Cedrat technology (doc). It contains three stacks with a capacitance of $5 μ F$ each that can be connected independently to the amplifier.

This document is divided into the following sections:

Section 1: The effect of a change in load capacitance on the amplifier dynamics is studied
Section 2: The effect on the voltage level on the amplifier dynamics is studied
Section 3: The dynamics of the E-505 and LA75B are compared
Section 4: The output impedance of both amplifiers are measured
Section 5: The effect of the internal filters of the E-505 on its dynamics is studied

1 Effect of a change of capacitance

1.1 Cedrat Technology

Load Data

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

Compute Coherence and Transfer functions

Copy
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:

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

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

1.2 PI

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

Copy
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:

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

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

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

Copy
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:

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

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

2.2 PI

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

Copy
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);

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

3 Comparison PI / Cedrat

3.1 Results

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

Copy
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:

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

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 ( $V^{'}$ ).

The load ( $R = 10 Ω$ ) and the internal resistor ( $R_{i}$ ) form a voltage divider, and thus: $V^{'} = \frac{R}{R + R_{i}} V$

From the two values of voltage, the internal resistor value can be computed: $R_{i} = R \frac{V - V^{'}}{V^{'}}$

4.1 Cedrat Technology

4.1.1 Compute Impedance

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

Copy
R * (V - Vp)/Vp;

0.94298

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

Copy
R * (V - Vp)/Vp;

0.8293

4.1.2 Effect of Impedance on the phase drop

Copy
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);

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

4.2 PI

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

Copy
R * (V - Vp)/Vp

2.7899

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

Copy
R * (V - Vp)/Vp

2.7795

5 Effect of filters configuration on the PI-E505 dynamics

5.1 PI

Three measurements are done:

Slew Rate limitation at maximum
Slew Rate limitation at minimum
Notch Filter at maximum frequency

Copy
pi_sr_min       = load('pi_slew_rate_min.mat');
pi_sr_max       = load('pi_slew_rate_max.mat');
pi_sr_max_notch = load('pi_slew_rate_max_notch_high.mat');
pi_sr_load      = load('pi_slew_rate_max_notch_high_2stacks.mat');

Copy
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);
[tf_sr_load, ~] = tfestimate(pi_sr_load.V_in, pi_sr_load.V_out, win, [], [], 1/Ts);

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

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.

Copy
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);

5.3 With Load

Copy
R = 2.78; % Output Impedance [Ohm]
C = 9e-6; % Load capacitance [F]

G_amp = 10/(1 + s*R*C);