Measurements

Random Signal is generated by one DAC of the SpeedGoat.

The signal going out of the DAC is split into two:

• one BNC cable is directly connected to one ADC of the SpeedGoat
• one BNC cable goes two times in the Slip-Ring (from bottom to top and then from top to bottom) and then is connected to one ADC of the SpeedGoat

Two measurements are done.

For each measurement, the measured signals are:

The goal is to determine is the signal is altered when the spindle is rotating.

Here, the rotation speed of the Slip-Ring is set to 1rpm.

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

sr_off = load('mat/data_001.mat', 't', 'x1', 'x2');
sr_on  = load('mat/data_002.mat', 't', 'x1', 'x2');

Let's first look at the signal produced by the DAC (figure 1).

figure;
hold on;
plot(sr_on.t,  sr_on.x1);
hold off;
xlabel('Time [s]'); ylabel('Voltage [V]');
xlim([0 10]);

We now look at the difference between the signal directly measured by the ADC and the signal that goes through the slip-ring (figure 2).

figure;
hold on;
plot(sr_on.t,  sr_on.x1  -  sr_on.x2,  'DisplayName', 'Slip-Ring - $\omega = 1rpm$');
plot(sr_off.t, sr_off.x1 - sr_off.x2,'DisplayName', 'Slip-Ring off');
hold off;
xlabel('Time [s]'); ylabel('Voltage [V]');
xlim([0 10]);
legend('Location', 'northeast');

dt = sr_on.t(2) - sr_on.t(1);
Fs = 1/dt; % [Hz]

win = hanning(ceil(1*Fs));

[pxx_on,  f] = pwelch(sr_on.x1  - sr_on.x2,  win, [], [], Fs);
[pxx_off, ~] = pwelch(sr_off.x1 - sr_off.x2, win, [], [], Fs);

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

The time domain signals are shown on figure 4.

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 5.

Goal:

• Determine the noise induced by the slip-ring

Setup:

• 0V is generated by the DAC of the Speedgoat
• Using a T, one part goes directly to the ADC
• The other part goes to the slip-ring 2 times and then to the ADC
• The parameters of the Voltage Amplifier are: 80dB, AC, 1kHz
• Every stage of the station is OFF

First column: Direct measure Second column: Slip-ring measure

Measurements:

• data_008: Slip-Ring OFF
• data_009: Slip-Ring ON
• data_010: Slip-Ring ON and omega=6rpm
• data_011: Slip-Ring ON and omega=60rpm

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

sr_off = load('mat/data_008.mat', 'data'); sr_off = sr_off.data;
sr_on  = load('mat/data_009.mat', 'data'); sr_on  = sr_on.data;
sr_6r  = load('mat/data_010.mat', 'data'); sr_6r  = sr_6r.data;
sr_60r = load('mat/data_011.mat', 'data'); sr_60r = sr_60r.data;

We plot the time domain data for the direct measurement (figure 8) and for the signal going through the slip-ring (figure 9);

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

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

Fs = 1/dt; % [Hz]

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

Then we compute the Power Spectral Density using pwelch function.

[pxdir, f] = pwelch(sr_off(:, 1), win, [], [], Fs);
[pxoff, ~] = pwelch(sr_off(:, 2), win, [], [], Fs);
[pxon,  ~] = pwelch(sr_on(:, 2),  win, [], [], Fs);
[px6r,  ~] = pwelch(sr_6r(:, 2),  win, [], [], Fs);
[px60r, ~] = pwelch(sr_60r(:, 2), win, [], [], Fs);

And we plot the ASD of the measured signals (figure 10);

figure;
hold on;
plot(f, sqrt(pxoff), 'DisplayName', 'OFF');
plot(f, sqrt(pxon),  'DisplayName', 'ON');
plot(f, sqrt(px6r),  'DisplayName', '6rpm');
plot(f, sqrt(px60r), 'DisplayName', '60rpm');
plot(f, sqrt(pxdir), 'k-', 'DisplayName', 'Direct');
hold off;
set(gca, 'xscale', 'log');
set(gca, 'yscale', 'log');
xlabel('Frequency [Hz]'); ylabel('ASD of the measured Voltage $\left[\frac{V}{\sqrt{Hz}}\right]$')
legend('Location', 'northeast');
xlim([0.1, 500]);

Goal:

• Determine if the noise induced by the slip-ring is a limiting factor when measuring the signal coming from a geophone

Setup:

• The geophone is located at the sample location
• The two Voltage amplifiers have the following settings:
  • AC
  • 60dB
  • 1kHz
• The signal from the geophone is split into two using a T-BNC:
  • One part goes directly to the voltage amplifier and then to the ADC.
  • The other part goes to the slip-ring=>voltage amplifier=>ADC.

First column: Direct measure Second column: Slip-ring measure

Measurements:

• data_012: Slip-Ring OFF
• data_013: Slip-Ring ON

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

sr_off = load('mat/data_012.mat', 'data'); sr_off = sr_off.data;
sr_on  = load('mat/data_013.mat', 'data'); sr_on  = sr_on.data;

We compare the signal when the Slip-Ring is OFF (figure 11) and when it is ON (figure 12).

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

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

Fs = 1/dt; % [Hz]

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

Then we compute the Power Spectral Density using pwelch function.

% Direct measure
[pxdoff, ~] = pwelch(sr_off(:, 1), win, [], [], Fs);
[pxdon,  ~] = pwelch(sr_on(:, 1),  win, [], [], Fs);

% Slip-Ring measure
[pxsroff, f] = pwelch(sr_off(:, 2), win, [], [], Fs);
[pxsron,  ~] = pwelch(sr_on(:, 2),  win, [], [], Fs);

Finally, we compare the Amplitude Spectral Density of the signals (figure [[]]);

figure;
hold on;
plot(f, sqrt(pxdoff), 'DisplayName', 'Direct - OFF');
plot(f, sqrt(pxsroff), 'DisplayName', 'Slip-Ring - OFF');
plot(f, sqrt(pxdon),  'DisplayName', 'Direct - ON');
plot(f, sqrt(pxsron),  'DisplayName', 'Slip-Ring - ON');
hold off;
set(gca, 'xscale', 'log');
set(gca, 'yscale', 'log');
xlabel('Frequency [Hz]'); ylabel('ASD of the measured Voltage $\left[\frac{V}{\sqrt{Hz}}\right]$')
legend('Location', 'northeast');
xlim([0.1, 500]);

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):

Second measurement (mat/data_015.mat file):

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;

The signals are shown on figure 16.

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 17.