Voltage Amplifier PD200 - Test Bench

In order to measure the transfer function from the input voltage \(V_{in}\) to the output voltage \(V_{out}\), the test bench shown in Figure 6 is used.

For this measurement, the sampling frequency of the Speedgoat ADC should be as high as possible.

Then the maximum output current of the amplifier is reached, the amplifier automatically shuts down itself. We should then make sure that the output current does not reach this maximum specified current.

The maximum current is 1A [rms] which corresponds to 0.7A in amplitude of the sin wave.

The impedance of the capacitance is: \[ Z_C(\omega) = \frac{1}{jC\omega} \]

Therefore the relation between the output current amplitude and the output voltage amplitude for sinusoidal waves of frequency \(\omega\): \[ V_{out} = \frac{1}{C\omega} I_{out} \]

Moreover, there is a gain of 20 between the input voltage and the output voltage: \[ 20 V_{in} = \frac{1}{C\omega} I_{out} \]

For a specified voltage input amplitude \(V_{in}\), the maximum frequency at which the output current reaches its maximum value is:

with:

• \(\omega_{\text{max}}\) the maximum input sinusoidal frequency in Radians per seconds
• \(C\) the load capacitance in Farads
• \(V_{in}\) the input voltage sinusoidal amplitude in Volts
• \(I_{out,\text{max}}\) the specified maximum output current in Amperes

\(\omega_{\text{max}}/2\pi\) as a function of \(V_{in}\) is shown in Figure 7.

When doing sweep sine excitation, we make sure not to reach this maximum excitation frequency.

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Several identifications using sweep sin were performed with input voltage amplitude ranging from 0.1V to 4V.

Iout_max = 0.57; % Maximum output current [A]
C = 10e-6; % Load Capacitance [F]

V_in = [0.1, 0.5, 1, 2, 4];
f_max = 0.8*Iout_max./(20*C*V_in/sqrt(2))/2/pi;
for i = 1:length(Vin_ampl)
    pd200{i}.notes.pd200.f_max = f_max(i);
    pd200{i}.notes.pd200.Vin = V_in(i);
end

The output noise of the voltage amplifier PD200 is foreseen to be around 1mV rms in a bandwidth from DC to 1MHz. If we suppose a white noise, this correspond to an amplitude spectral density:

The RMS noise being very small compare to the ADC resolution, we must amplify this noise before digitizing the signal.

The added noise of the instrumentation amplifier should be much smaller than the noise of the PD200. We use either the amplifier EG&G 5113 that has a noise of \(\approx 4 nV/\sqrt{Hz}\) referred to its input which is much smaller than the noise induced by the PD200.

The gain of the low-noise amplifier can be increased until the full range of the ADC is used. This gain should be around 1000 (60dB).

A low pass filter at 10kHz can be included in the EG&G amplifier in order to limit aliasing. An high pass filter at low frequency can be added if there is a problem of large offset.

As shown in Figure 9, there are 4 equipment involved in the measurement:

• a Digital to Analog Convert (DAC)
• the Voltage amplifier to be measured with a gain of 20 (PD200)
• a low noise voltage amplifier with a variable gain and integrated low pass filters and high pass filters
• an Analog to Digital Converter (ADC)

Each of these equipment has some noise:

• \(q_{da}\): quantization noise of the DAC
• \(n_{da}\): output noise of the DAC
• \(n_p\): input noise of the PD200 (what we wish to characterize)
• \(n_a\): input noise of the pre amplifier
• \(q_{ad}\): quantization noise of the ADC

The quantization noise is something that can be predicted. The Amplitude Spectral Density of the quantization noise of an ADC/DAC is equal to:

with:

• \(q = \frac{\Delta V}{2^n}\) the quantization in [V], which is the corresponding value in [V] of the least significant bit
• \(\Delta V\) is the full range of the ADC in [V]
• \(n\) is the number of bits
• \(f_s\) is the sample frequency in [Hz]

adc = struct();
adc.Delta_V = 20; % [V]
adc.n = 16; % number of bits
adc.Fs = 20e3; % [Hz]
adc.Gamma_q = adc.Delta_V/2^adc.n/sqrt(12*adc.Fs); % [V/sqrt(Hz)]

The obtained Amplitude Spectral Density is 6.2294e-07 \(V/\sqrt{Hz}\).

First, we wish to measure the noise of the pre-amplifier. To do so, the input of the pre-amplifier is shunted such that there is 0V at its inputs. Then, the gain of the amplifier is increase until the measured signal on the ADC is much larger than the quantization noise.

The Amplitude Spectral Density \(\Gamma_n(\omega)\) of the measured signal \(n\) is computed. Finally, the Amplitude Spectral Density of \(n_a\) can be computed taking into account the gain of the pre-amplifier:

This is true if the quantization noise \(\Gamma_{q_{ad}}\) is negligible.

The gain of the low noise amplifier is set to 50000.

The obtained Amplitude Spectral Density of the Low Noise Voltage Amplifier is shown in Figure 11. The obtained noise amplitude is very closed to the one specified in the documentation of \(4nV/\sqrt{Hz}\) at 1kHZ.

Similarly to Section 4.4, the noise of the Femto amplifier is identified.

% Hanning window
win = hanning(ceil(0.5/Ts));

% Power Spectral Density
[pxx, f] = pwelch(femto.Vout, win, [], [], Fs);

% Save the results inside the struct
femto.pxx = pxx;
femto.f = f;

The input of the PD200 amplifier is shunted with a 50 Ohm resistor. The gain of the pre-amplifier is increased in order to measure a signal much larger than the quantization noise of the ADC.

The Amplitude Spectral Density of the measured signal \(\Gamma_n(\omega)\) is computed. The Amplitude Spectral Density of \(n_p\) is then computed taking into account the gain of the pre-amplifier and the can of the PD200 amplifier:

And we verify that this is indeed the noise of the PD200 and not the noise of the pre-amplifier by checking that:

The measured low frequency output noise of one of the PD200 amplifiers is shown in Figure 14. It is very similar to the one specified in the datasheet in Figure 3.

The obtained RMS and peak to peak values of the measured output noise are shown in Table 2.

The Amplitude Spectral Density of the measured input noise is computed and shown in Figure 15.

The contribution of the PD200 noise is much larger than the contribution of the pre-amplifier noise of the quantization noise.

In order not to have any quantization noise, we impose the DAC to output a zero voltage. The gain of the low noise amplifier is adjusted in order to have sufficient voltage going to the ADC.

The Amplitude Spectral Density \(\Gamma_n(\omega)\) of the measured signal is computed. The Amplitude Spectral Density of \(n_{da}\) can be computed taking into account the gain of the pre-amplifier:

And it is verify that the Amplitude Spectral Density of \(n_{da}\) is much larger than the one of \(n_a\):

Let’s now analyze the measurement of the setup in Figure 18.

The PSD of the measured noise is computed and the ASD is shown in Figure 19.

win = hanning(ceil(0.5/Ts));

for i = 1:7
    [pxx, f] = pwelch(pd200dac{i}.Vn, win, [], [], Fs);
    pd200dac{i}.f = f;
    pd200dac{i}.pxx = pxx;
end

Let’s now measure the noise of another DAC called the “SSI2V” (doc). It is a 20bits DAC with an output of +/-10.48 V and a very low output noise.

The measurement setup is the same as the one in Figure 16.

win = hanning(ceil(0.5/Ts));

[pxx, f] = pwelch(ssi2v.Vn, win, [], [], Fs);
ssi2v.pxx = pxx;
ssi2v.f = f;

The obtained noise of the SSI2V DAC is shown in Figure 20 and compared with the noise of the 16bits DAC. It is shown to be much smaller (~1 order of magnitude).

Let’s design a transfer function whose norm represent the Amplitude Spectral Density of the input voltage noise of the PD200 amplifier.

Gn = 2.5e-5 * ((1 + s/2/pi/30)/(1 + s/2/pi/2))^2 /(1 + s/2/pi/5e3);

The comparison between the measured ASD of the modeled ASD is done in Figure

Let’s now compute the Cumulative Amplitude Spectrum corresponding to the measurement and the model and compare them.

The integration from low to high frequency and from high to low frequency are both shown in Figure

The obtained RMS noise of the model is 650.77 uV RMS which is the same as advertise.