test-bench-piezo-amplifiers/index.org

Measurement of Piezoelectric Amplifiers

• Introduction
• Effect of a change of capacitance
  • Cedrat Technology
  • PI
• Effect of a change in Voltage level
  • Cedrat Technology
  • PI
• Comparison PI / Cedrat
  • Results
• Impedance Measurement
  • Introduction
  • Cedrat Technology
  • PI

Introduction   ignore

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.

Effect of a change of capacitance

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);

Effect of a change of the piezo capacitance on the Amplifier transfer function

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);

Effect of a change of the piezo capacitance on the Amplifier transfer function

Effect of a change in Voltage level

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);

Effect of a change of voltage level on the Amplifier transfer function

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);

Effect of a change of voltage level on the Amplifier transfer function

Comparison PI / Cedrat

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')));

Comparison of the two Amplifier transfer functions

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

Cedrat Technology

  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

  C = 5e-6; % Capacitance in [F]
  Ri = R * (V - Vp)/Vp; % Internal resistance [Ohm]

  G_ce = 1/(1+Ri*C*s);

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