Measurements on the instrumentation

Table of Contents

1 Measure of the noise of the Voltage Amplifier

The data and matlab files are accessible here.

1.1 Measurement Description

Goal:

  • Determine the Voltage Amplifier noise

Setup:

  • The two inputs (differential) of the voltage amplifier are shunted with 50Ohms
  • The AC/DC option of the Voltage amplifier is on AC
  • The low pass filter is set to 1hHz
  • We measure the output of the voltage amplifier with a 16bits ADC of the Speedgoat

Measurements:

  • data_003: Ampli OFF
  • data_004: Ampli ON set to 20dB
  • data_005: Ampli ON set to 40dB
  • data_006: Ampli ON set to 60dB

1.2 Load data

amp_off = load('mat/data_003.mat', 'data'); amp_off = amp_off.data(:, [1,3]);
amp_20d = load('mat/data_004.mat', 'data'); amp_20d = amp_20d.data(:, [1,3]);
amp_40d = load('mat/data_005.mat', 'data'); amp_40d = amp_40d.data(:, [1,3]);
amp_60d = load('mat/data_006.mat', 'data'); amp_60d = amp_60d.data(:, [1,3]);

1.3 Time Domain

The time domain signals are shown on figure 1.

ampli_noise_time.png

Figure 1: Output of the amplifier

1.4 Frequency Domain

We first compute some parameters that will be used for the PSD computation. 

dt = amp_off(2, 2)-amp_off(1, 2);

Fs = 1/dt; % [Hz]

win = hanning(ceil(10*Fs));

Then we compute the Power Spectral Density using pwelch function. 

[pxoff, f] = pwelch(amp_off(:,1), win, [], [], Fs);
[px20d, ~] = pwelch(amp_20d(:,1), win, [], [], Fs);
[px40d, ~] = pwelch(amp_40d(:,1), win, [], [], Fs);
[px60d, ~] = pwelch(amp_60d(:,1), win, [], [], Fs);

We compute the theoretical ADC noise. 

q = 20/2^16; % quantization
Sq = q^2/12/1000; % PSD of the ADC noise

Finally, the ASD is shown on figure 2.

ampli_noise_psd.png

Figure 2: Amplitude Spectral Density of the measured voltage at the output of the voltage amplifier

1.5 Conclusion

Questions:

  • Where does those sharp peaks comes from? Can this be due to aliasing?

Noise induced by the voltage amplifiers seems not to be a limiting factor as we have the same noise when they are OFF and ON.

2 Measure of the influence of the AC/DC option on the voltage amplifiers

The data and matlab files are accessible here.

2.1 Measurement Description

Goal:

  • Measure the influence of the high-pass filter option of the voltage amplifiers

Setup:

  • One geophone is located on the marble.
  • It's signal goes to two voltage amplifiers with a gain of 60dB.
  • One voltage amplifier is on the AC option, the other is on the DC option.

Measurements: First measurement (mat/data_014.mat file):

Column Signal
1 Amplifier 1 with AC option
2 Amplifier 2 with DC option
3 Time

Second measurement (mat/data_015.mat file):

Column Signal
1 Amplifier 1 with DC option
2 Amplifier 2 with AC option
3 Time

IMG_20190503_170936.jpg

Figure 3: Picture of the two voltages amplifiers

2.2 Load data

We load the data of the z axis of two geophones. 

meas14 = load('mat/data_014.mat', 'data'); meas14 = meas14.data;
meas15 = load('mat/data_015.mat', 'data'); meas15 = meas15.data;

2.3 Time Domain

The signals are shown on figure 4.

ac_dc_option_time.png

Figure 4: Comparison of the signals going through the Voltage amplifiers

2.4 Frequency Domain

We first compute some parameters that will be used for the PSD computation. 

dt = meas14(2, 3)-meas14(1, 3);

Fs = 1/dt; % [Hz]

win = hanning(ceil(10*Fs));

Then we compute the Power Spectral Density using pwelch function. 

[pxamp1ac, f] = pwelch(meas14(:, 1), win, [], [], Fs);
[pxamp2dc, ~] = pwelch(meas14(:, 2), win, [], [], Fs);

[pxamp1dc, ~] = pwelch(meas15(:, 1), win, [], [], Fs);
[pxamp2ac, ~] = pwelch(meas15(:, 2), win, [], [], Fs);

The ASD of the signals are compare on figure 5.

ac_dc_option_asd.png

Figure 5: Amplitude Spectral Density of the measured signals

2.5 Conclusion

  • The voltage amplifiers include some very sharp high pass filters at 1.5Hz (maybe 4th order)
  • There is a DC offset on the time domain signal because the DC-offset knob was not set to zero

3 Transfer function of the Low Pass Filter

The computation files for this section are accessible here.

3.1 First LPF with a Cut-off frequency of 160Hz

3.1.1 Measurement Description

Goal:

  • Measure the Low Pass Filter Transfer Function

The values of the components are:

\begin{aligned} R &= 1k\Omega \\ C &= 1\mu F \end{aligned}

Which makes a cut-off frequency of \(f_c = \frac{1}{RC} = 1000 rad/s = 160Hz\). 

\begin{tikzpicture}
  \draw (0,2)
        to [R=\(R\)] ++(2,0) node[circ]
        to ++(2,0)
        ++(-2,0)
        to [C=\(C\)] ++(0,-2) node[circ]
        ++(-2,0)
        to ++(2,0)
        to ++(2,0)
\end{tikzpicture}

lpf.png

Figure 6: Schematic of the Low Pass Filter used

Setup:

  • We are measuring the signal from from Geophone with a BNC T
  • On part goes to column 1 through the LPF
  • The other part goes to column 2 without the LPF

Measurements: mat/data_018.mat:

Column Signal
1 Amplifier 1 with LPF
2 Amplifier 2
3 Time

IMG_20190507_102756.jpg

Figure 7: Picture of the low pass filter used

3.1.2 Load data

We load the data of the z axis of two geophones. 

data = load('mat/data_018.mat', 'data'); data = data.data;

3.1.3 Transfer function of the LPF

We compute the transfer function from the signal without the LPF to the signal measured with the LPF. 

dt = data(2, 3)-data(1, 3);

Fs = 1/dt; % [Hz]

win = hanning(ceil(10*Fs));

[Glpf, f] = tfestimate(data(:, 2), data(:, 1), win, [], [], Fs);

We compare this transfer function with a transfer function corresponding to an ideal first order LPF with a cut-off frequency of \(1000rad/s\). We obtain the result on figure 8. 

Gth = 1/(1+s/1000)

figure;
ax1 = subplot(2, 1, 1);
hold on;
plot(f, abs(Glpf));
plot(f, abs(squeeze(freqresp(Gth, f, 'Hz'))));
hold off;
set(gca, 'xscale', 'log'); set(gca, 'yscale', 'log');
set(gca, 'XTickLabel',[]);
ylabel('Magnitude');

ax2 = subplot(2, 1, 2);
hold on;
plot(f, mod(180+180/pi*phase(Glpf), 360)-180);
plot(f, 180/pi*unwrap(angle(squeeze(freqresp(Gth, f, 'Hz')))));
hold off;
set(gca, 'xscale', 'log');
ylim([-180, 180]);
yticks([-180, -90, 0, 90, 180]);
xlabel('Frequency [Hz]'); ylabel('Phase');

linkaxes([ax1,ax2],'x');
xlim([1, 500]);

Glpf_bode.png

Figure 8: Bode Diagram of the measured Low Pass filter and the theoritical one

3.1.4 Conclusion

As we want to measure things up to \(500Hz\), we chose to change the value of the capacitor to obtain a cut-off frequency of \(1kHz\).

3.2 Second LPF with a Cut-off frequency of 1000Hz

3.2.1 Measurement description

This time, the value are

\begin{aligned} R &= 1k\Omega \\ C &= 150nF \end{aligned}

Which makes a low pass filter with a cut-off frequency of \(f_c = 1060Hz\).

3.2.2 Load data

We load the data of the z axis of two geophones. 

data = load('mat/data_019.mat', 'data'); data = data.data;

3.2.3 Transfer function of the LPF

We compute the transfer function from the signal without the LPF to the signal measured with the LPF. 

dt = data(2, 3)-data(1, 3);

Fs = 1/dt; % [Hz]

win = hanning(ceil(10*Fs));

[Glpf, f] = tfestimate(data(:, 2), data(:, 1), win, [], [], Fs);

We compare this transfer function with a transfer function corresponding to an ideal first order LPF with a cut-off frequency of \(1060Hz\). We obtain the result on figure 9. 

Gth = 1/(1+s/1060/2/pi);

figure;
ax1 = subplot(2, 1, 1);
hold on;
plot(f, abs(Glpf));
plot(f, abs(squeeze(freqresp(Gth, f, 'Hz'))));
hold off;
set(gca, 'xscale', 'log'); set(gca, 'yscale', 'log');
set(gca, 'XTickLabel',[]);
ylabel('Magnitude');

ax2 = subplot(2, 1, 2);
hold on;
plot(f, mod(180+180/pi*phase(Glpf), 360)-180);
plot(f, 180/pi*unwrap(angle(squeeze(freqresp(Gth, f, 'Hz')))));
hold off;
set(gca, 'xscale', 'log');
ylim([-180, 180]);
yticks([-180, -90, 0, 90, 180]);
xlabel('Frequency [Hz]'); ylabel('Phase');

linkaxes([ax1,ax2],'x');
xlim([1, 500]);

Glpf_bode_bis.png

Figure 9: Bode Diagram of the measured Low Pass filter and the theoritical one

3.2.4 Conclusion

The added LPF has the expected behavior.

Author: Thomas Dehaeze

Created: 2019-05-10 ven. 10:07

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