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< / head >
< body >
< div id = "content" >
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< h1 class = "title" > Measurements< / h1 >
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< div id = "table-of-contents" >
< h2 > Table of Contents< / h2 >
< div id = "text-table-of-contents" >
< ul >
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< li > < a href = "#org72a8967" > 1. Effect of the rotation of the Slip-Ring< / a >
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< ul >
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< li > < a href = "#org4b8f76d" > 1.1. Measurement Description< / a > < / li >
< li > < a href = "#org6e93e2e" > 1.2. Load data< / a > < / li >
< li > < a href = "#org47bc1f0" > 1.3. Analysis< / a > < / li >
< li > < a href = "#orgd87dca5" > 1.4. Conclusion< / a > < / li >
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< / ul >
< / li >
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< li > < a href = "#org7a2f4ff" > 2. Measure of the noise of the Voltage Amplifier< / a >
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< ul >
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< li > < a href = "#org5a4d29e" > 2.1. Measurement Description< / a > < / li >
< li > < a href = "#orgffece30" > 2.2. Load data< / a > < / li >
< li > < a href = "#orgec501b3" > 2.3. Time Domain< / a > < / li >
< li > < a href = "#org7d68dd0" > 2.4. Frequency Domain< / a > < / li >
< li > < a href = "#orgaba63f9" > 2.5. Conclusion< / a > < / li >
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< / ul >
< / li >
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< li > < a href = "#orgded919b" > 3. Measure of the noise induced by the Slip-Ring< / a >
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< ul >
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< li > < a href = "#orgde32f93" > 3.1. Measurement Description< / a > < / li >
< li > < a href = "#org661917b" > 3.2. Load data< / a > < / li >
< li > < a href = "#orgcd9a917" > 3.3. Time Domain< / a > < / li >
< li > < a href = "#org708090d" > 3.4. Frequency Domain< / a > < / li >
< li > < a href = "#org83ed722" > 3.5. Conclusion< / a > < / li >
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< / ul >
< / li >
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< li > < a href = "#orgfbf06e6" > 4. Measure of the noise induced by the slip ring when using a geophone< / a >
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< ul >
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< li > < a href = "#orgffb1bdb" > 4.1. First Measurement without LPF< / a >
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< ul >
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< li > < a href = "#org8e8831c" > 4.1.1. Measurement Description< / a > < / li >
< li > < a href = "#org167eeae" > 4.1.2. Load data< / a > < / li >
< li > < a href = "#org583abb2" > 4.1.3. Time Domain< / a > < / li >
< li > < a href = "#org35e29fe" > 4.1.4. Frequency Domain< / a > < / li >
< li > < a href = "#org3e43efe" > 4.1.5. Conclusion< / a > < / li >
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< / ul >
< / li >
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< li > < a href = "#orgf298379" > 4.2. Measurement using an oscilloscope< / a >
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< ul >
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< li > < a href = "#org68d1d31" > 4.2.1. Measurement Setup< / a > < / li >
< li > < a href = "#org5276b1f" > 4.2.2. Observations< / a > < / li >
< li > < a href = "#org54a8d62" > 4.2.3. Conclusion< / a > < / li >
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< / ul >
< / li >
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< li > < a href = "#orgcebb9a0" > 4.3. New measurements with a LPF before the Voltage Amplifiers< / a >
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< ul >
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< li > < a href = "#org4bdf600" > 4.3.1. Setup description< / a > < / li >
< li > < a href = "#org5c96c5f" > 4.3.2. Load data< / a > < / li >
< li > < a href = "#orgbcba5cf" > 4.3.3. Time Domain< / a > < / li >
< li > < a href = "#org0d5a581" > 4.3.4. Frequency Domain< / a > < / li >
< li > < a href = "#orgad63dd1" > 4.3.5. Comparison of with and without LPF< / a > < / li >
< li > < a href = "#orgdece1f2" > 4.3.6. Conclusion< / a > < / li >
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< / ul >
< / li >
< / ul >
< / li >
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< li > < a href = "#org23a8137" > 5. Measure of the influence of the AC/DC option on the voltage amplifiers< / a >
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< ul >
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< li > < a href = "#org58bc336" > 5.1. Measurement Description< / a > < / li >
< li > < a href = "#org137ca7d" > 5.2. Load data< / a > < / li >
< li > < a href = "#orgce0337d" > 5.3. Time Domain< / a > < / li >
< li > < a href = "#org1ca91db" > 5.4. Frequency Domain< / a > < / li >
< li > < a href = "#orge0411ce" > 5.5. Conclusion< / a > < / li >
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< / ul >
< / li >
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< li > < a href = "#org6d3a86e" > 6. Transfer function of the Low Pass Filter< / a >
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< ul >
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< li > < a href = "#org50dfe76" > 6.1. First LPF with a Cut-off frequency of 160Hz< / a >
< ul >
< li > < a href = "#orge61a68e" > 6.1.1. Measurement Description< / a > < / li >
< li > < a href = "#org229c82b" > 6.1.2. Load data< / a > < / li >
< li > < a href = "#org78a38da" > 6.1.3. Transfer function of the LPF< / a > < / li >
< li > < a href = "#org59dee72" > 6.1.4. Conclusion< / a > < / li >
< / ul >
< / li >
< li > < a href = "#org8b09702" > 6.2. Second LPF with a Cut-off frequency of 1000Hz< / a >
< ul >
< li > < a href = "#orged36cb1" > 6.2.1. Measurement description< / a > < / li >
< li > < a href = "#org7e593d2" > 6.2.2. Load data< / a > < / li >
< li > < a href = "#org2e7d91e" > 6.2.3. Transfer function of the LPF< / a > < / li >
< li > < a href = "#org04a0d6e" > 6.2.4. Conclusion< / a > < / li >
< / ul >
< / li >
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< / ul >
< / li >
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< / ul >
< / div >
< / div >
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< div id = "outline-container-org72a8967" class = "outline-2" >
< h2 id = "org72a8967" > < span class = "section-number-2" > 1< / span > Effect of the rotation of the Slip-Ring< / h2 >
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< div class = "outline-text-2" id = "text-1" >
< p >
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The data and matlab files are accessible < a href = "data/meas_effect_sr.zip" > here< / a > .
< / p >
< / div >
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< div id = "outline-container-org4b8f76d" class = "outline-3" >
< h3 id = "org4b8f76d" > < span class = "section-number-3" > 1.1< / span > Measurement Description< / h3 >
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< div class = "outline-text-3" id = "text-1-1" >
< p >
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Random Signal is generated by one DAC of the SpeedGoat.
< / p >
< p >
The signal going out of the DAC is split into two:
< / p >
< ul class = "org-ul" >
< li > one BNC cable is directly connected to one ADC of the SpeedGoat< / li >
< li > 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< / li >
< / ul >
< p >
Two measurements are done.
< / p >
< table border = "2" cellspacing = "0" cellpadding = "6" rules = "groups" frame = "hsides" >
< colgroup >
< col class = "org-left" / >
< col class = "org-left" / >
< / colgroup >
< thead >
< tr >
< th scope = "col" class = "org-left" > Data File< / th >
< th scope = "col" class = "org-left" > Description< / th >
< / tr >
< / thead >
< tbody >
< tr >
< td class = "org-left" > < code > mat/data_001.mat< / code > < / td >
< td class = "org-left" > Slip-ring not turning< / td >
< / tr >
< tr >
< td class = "org-left" > < code > mat/data_002.mat< / code > < / td >
< td class = "org-left" > Slip-ring turning< / td >
< / tr >
< / tbody >
< / table >
< p >
For each measurement, the measured signals are:
< / p >
< table border = "2" cellspacing = "0" cellpadding = "6" rules = "groups" frame = "hsides" >
< colgroup >
< col class = "org-left" / >
< col class = "org-left" / >
< / colgroup >
< thead >
< tr >
< th scope = "col" class = "org-left" > Data File< / th >
< th scope = "col" class = "org-left" > Description< / th >
< / tr >
< / thead >
< tbody >
< tr >
< td class = "org-left" > < code > t< / code > < / td >
< td class = "org-left" > Time vector< / td >
< / tr >
< tr >
< td class = "org-left" > < code > x1< / code > < / td >
< td class = "org-left" > Direct signal< / td >
< / tr >
< tr >
< td class = "org-left" > < code > x2< / code > < / td >
< td class = "org-left" > Signal going through the Slip-Ring< / td >
< / tr >
< / tbody >
< / table >
< p >
The goal is to determine is the signal is altered when the spindle is rotating.
< / p >
< p >
Here, the rotation speed of the Slip-Ring is set to 1rpm.
< / p >
< / div >
< / div >
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< div id = "outline-container-org6e93e2e" class = "outline-3" >
< h3 id = "org6e93e2e" > < span class = "section-number-3" > 1.2< / span > Load data< / h3 >
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< div class = "outline-text-3" id = "text-1-2" >
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< p >
We load the data of the z axis of two geophones.
< / p >
< div class = "org-src-container" >
< pre class = "src src-matlab" > sr_off = load< span class = "org-rainbow-delimiters-depth-1" > (< / span > < span class = "org-string" > 'mat/data_001.mat', 't', 'x1', 'x2'< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
sr_on = load< span class = "org-rainbow-delimiters-depth-1" > (< / span > < span class = "org-string" > 'mat/data_002.mat', 't', 'x1', 'x2'< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
< / pre >
< / div >
< / div >
< / div >
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< div id = "outline-container-org47bc1f0" class = "outline-3" >
< h3 id = "org47bc1f0" > < span class = "section-number-3" > 1.3< / span > Analysis< / h3 >
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< div class = "outline-text-3" id = "text-1-3" >
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< p >
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Let's first look at the signal produced by the DAC (figure < a href = "#orge7c2b99" > 1< / a > ).
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< / p >
< div class = "org-src-container" >
< pre class = "src src-matlab" > < span class = "org-type" > figure< / span > ;
hold on;
plot< span class = "org-rainbow-delimiters-depth-1" > (< / span > sr_on.t, sr_on.x1< span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
hold off;
xlabel< span class = "org-rainbow-delimiters-depth-1" > (< / span > < span class = "org-string" > 'Time < / span > < span class = "org-string" > < span class = "org-rainbow-delimiters-depth-2" > [< / span > < / span > < span class = "org-string" > s< / span > < span class = "org-string" > < span class = "org-rainbow-delimiters-depth-2" > ]< / span > < / span > < span class = "org-string" > '< / span > < span class = "org-string" > < span class = "org-rainbow-delimiters-depth-1" > )< / span > < / span > < span class = "org-string" > ; ylabel< / span > < span class = "org-string" > < span class = "org-rainbow-delimiters-depth-1" > (< / span > < / span > < span class = "org-string" > 'Voltage < / span > < span class = "org-string" > < span class = "org-rainbow-delimiters-depth-2" > [< / span > < / span > < span class = "org-string" > V< / span > < span class = "org-string" > < span class = "org-rainbow-delimiters-depth-2" > ]< / span > < / span > < span class = "org-string" > '< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
xlim< span class = "org-rainbow-delimiters-depth-1" > (< / span > < span class = "org-rainbow-delimiters-depth-2" > [< / span > < span class = "org-highlight-numbers-number" > 0< / span > < span class = "org-highlight-numbers-number" > 10< / span > < span class = "org-rainbow-delimiters-depth-2" > ]< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
< / pre >
< / div >
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< div id = "orge7c2b99" class = "figure" >
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< p > < img src = "figs/random_signal.png" alt = "random_signal.png" / >
< / p >
< p > < span class = "figure-number" > Figure 1: < / span > Random signal produced by the DAC< / p >
< / div >
< p >
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We now look at the difference between the signal directly measured by the ADC and the signal that goes through the slip-ring (figure < a href = "#org356df0f" > 2< / a > ).
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< / p >
< div class = "org-src-container" >
< pre class = "src src-matlab" > < span class = "org-type" > figure< / span > ;
hold on;
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plot< span class = "org-rainbow-delimiters-depth-1" > (< / span > sr_on.t, sr_on.x1 < span class = "org-type" > -< / span > sr_on.x2, < span class = "org-string" > 'DisplayName', '< / span > Slip< span class = "org-type" > -< / span > Ring < span class = "org-type" > -< / span > $< span class = "org-type" > \< / span > omega = < span class = "org-highlight-numbers-number" > 1rpm$< / span > '< span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
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plot< span class = "org-rainbow-delimiters-depth-1" > (< / span > sr_off.t, sr_off.x1 < span class = "org-type" > -< / span > sr_off.x2,< span class = "org-string" > 'DisplayName', 'Slip-Ring off'< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
hold off;
xlabel< span class = "org-rainbow-delimiters-depth-1" > (< / span > < span class = "org-string" > 'Time < / span > < span class = "org-string" > < span class = "org-rainbow-delimiters-depth-2" > [< / span > < / span > < span class = "org-string" > s< / span > < span class = "org-string" > < span class = "org-rainbow-delimiters-depth-2" > ]< / span > < / span > < span class = "org-string" > '< / span > < span class = "org-string" > < span class = "org-rainbow-delimiters-depth-1" > )< / span > < / span > < span class = "org-string" > ; ylabel< / span > < span class = "org-string" > < span class = "org-rainbow-delimiters-depth-1" > (< / span > < / span > < span class = "org-string" > 'Voltage < / span > < span class = "org-string" > < span class = "org-rainbow-delimiters-depth-2" > [< / span > < / span > < span class = "org-string" > V< / span > < span class = "org-string" > < span class = "org-rainbow-delimiters-depth-2" > ]< / span > < / span > < span class = "org-string" > '< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
xlim< span class = "org-rainbow-delimiters-depth-1" > (< / span > < span class = "org-rainbow-delimiters-depth-2" > [< / span > < span class = "org-highlight-numbers-number" > 0< / span > < span class = "org-highlight-numbers-number" > 10< / span > < span class = "org-rainbow-delimiters-depth-2" > ]< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
legend< span class = "org-rainbow-delimiters-depth-1" > (< / span > < span class = "org-string" > 'Location', 'northeast'< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
< / pre >
< / div >
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< div id = "org356df0f" class = "figure" >
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< p > < img src = "figs/slipring_comp_signals.png" alt = "slipring_comp_signals.png" / >
< / p >
< p > < span class = "figure-number" > Figure 2: < / span > Alteration of the signal when the slip-ring is turning< / p >
< / div >
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< div class = "org-src-container" >
< pre class = "src src-matlab" > dt = sr_on.t< span class = "org-rainbow-delimiters-depth-1" > (< / span > < span class = "org-highlight-numbers-number" > 2< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > < span class = "org-type" > -< / span > sr_on.t< span class = "org-rainbow-delimiters-depth-1" > (< / span > < span class = "org-highlight-numbers-number" > 1< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
Fs = < span class = "org-highlight-numbers-number" > 1< / span > < span class = "org-type" > /< / span > dt; < span class = "org-comment" > % [Hz]< / span >
win = hanning< span class = "org-rainbow-delimiters-depth-1" > (< / span > ceil< span class = "org-rainbow-delimiters-depth-2" > (< / span > < span class = "org-highlight-numbers-number" > 1< / span > < span class = "org-type" > *< / span > Fs< span class = "org-rainbow-delimiters-depth-2" > )< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
< / pre >
< / div >
< div class = "org-src-container" >
< pre class = "src src-matlab" > < span class = "org-rainbow-delimiters-depth-1" > [< / span > pxx_on, f< span class = "org-rainbow-delimiters-depth-1" > ]< / span > = pwelch< span class = "org-rainbow-delimiters-depth-1" > (< / span > sr_on.x1 < span class = "org-type" > -< / span > sr_on.x2, win, < span class = "org-rainbow-delimiters-depth-2" > []< / span > , < span class = "org-rainbow-delimiters-depth-2" > []< / span > , Fs< span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
< span class = "org-rainbow-delimiters-depth-1" > [< / span > pxx_off, < span class = "org-type" > ~< / span > < span class = "org-rainbow-delimiters-depth-1" > ]< / span > = pwelch< span class = "org-rainbow-delimiters-depth-1" > (< / span > sr_off.x1 < span class = "org-type" > -< / span > sr_off.x2, win, < span class = "org-rainbow-delimiters-depth-2" > []< / span > , < span class = "org-rainbow-delimiters-depth-2" > []< / span > , Fs< span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
< / pre >
< / div >
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< div id = "org808978d" class = "figure" >
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< p > < img src = "figs/psd_noise.png" alt = "psd_noise.png" / >
< / p >
< p > < span class = "figure-number" > Figure 3: < / span > ASD of the measured noise< / p >
< / div >
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< / div >
< / div >
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< div id = "outline-container-orgd87dca5" class = "outline-3" >
< h3 id = "orgd87dca5" > < span class = "section-number-3" > 1.4< / span > Conclusion< / h3 >
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< div class = "outline-text-3" id = "text-1-4" >
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< div class = "note" >
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< p >
< b > Remaining questions< / b > :
< / p >
< ul class = "org-ul" >
< li > Should the measurement be redone using voltage amplifiers?< / li >
< li > Use higher rotation speed and measure for longer periods (to have multiple revolutions) ?< / li >
< / ul >
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< / div >
< / div >
< / div >
< / div >
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< div id = "outline-container-org7a2f4ff" class = "outline-2" >
< h2 id = "org7a2f4ff" > < span class = "section-number-2" > 2< / span > Measure of the noise of the Voltage Amplifier< / h2 >
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< div class = "outline-text-2" id = "text-2" >
< p >
The data and matlab files are accessible < a href = "data/meas_volt_amp.zip" > here< / a > .
< / p >
< / div >
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< div id = "outline-container-org5a4d29e" class = "outline-3" >
< h3 id = "org5a4d29e" > < span class = "section-number-3" > 2.1< / span > Measurement Description< / h3 >
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< div class = "outline-text-3" id = "text-2-1" >
< p >
< b > Goal< / b > :
< / p >
< ul class = "org-ul" >
< li > Determine the Voltage Amplifier noise< / li >
< / ul >
< p >
< b > Setup< / b > :
< / p >
< ul class = "org-ul" >
< li > The two inputs (differential) of the voltage amplifier are shunted with 50Ohms< / li >
< li > The AC/DC option of the Voltage amplifier is on AC< / li >
< li > The low pass filter is set to 1hHz< / li >
< li > We measure the output of the voltage amplifier with a 16bits ADC of the Speedgoat< / li >
< / ul >
< p >
< b > Measurements< / b > :
< / p >
< ul class = "org-ul" >
< li > < code > data_003< / code > : Ampli OFF< / li >
< li > < code > data_004< / code > : Ampli ON set to 20dB< / li >
< li > < code > data_005< / code > : Ampli ON set to 40dB< / li >
< li > < code > data_006< / code > : Ampli ON set to 60dB< / li >
< / ul >
< / div >
< / div >
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< div id = "outline-container-orgffece30" class = "outline-3" >
< h3 id = "orgffece30" > < span class = "section-number-3" > 2.2< / span > Load data< / h3 >
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< div class = "outline-text-3" id = "text-2-2" >
< div class = "org-src-container" >
< pre class = "src src-matlab" > amp_off = load< span class = "org-rainbow-delimiters-depth-1" > (< / span > < span class = "org-string" > 'mat/data_003.mat', 'data'< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ; amp_off = amp_off.data< span class = "org-rainbow-delimiters-depth-1" > (< / span > < span class = "org-type" > :< / span > , < span class = "org-rainbow-delimiters-depth-2" > [< / span > < span class = "org-highlight-numbers-number" > 1< / span > ,< span class = "org-highlight-numbers-number" > 3< / span > < span class = "org-rainbow-delimiters-depth-2" > ]< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
amp_20d = load< span class = "org-rainbow-delimiters-depth-1" > (< / span > < span class = "org-string" > 'mat/data_004.mat', 'data'< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ; amp_20d = amp_20d.data< span class = "org-rainbow-delimiters-depth-1" > (< / span > < span class = "org-type" > :< / span > , < span class = "org-rainbow-delimiters-depth-2" > [< / span > < span class = "org-highlight-numbers-number" > 1< / span > ,< span class = "org-highlight-numbers-number" > 3< / span > < span class = "org-rainbow-delimiters-depth-2" > ]< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
amp_40d = load< span class = "org-rainbow-delimiters-depth-1" > (< / span > < span class = "org-string" > 'mat/data_005.mat', 'data'< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ; amp_40d = amp_40d.data< span class = "org-rainbow-delimiters-depth-1" > (< / span > < span class = "org-type" > :< / span > , < span class = "org-rainbow-delimiters-depth-2" > [< / span > < span class = "org-highlight-numbers-number" > 1< / span > ,< span class = "org-highlight-numbers-number" > 3< / span > < span class = "org-rainbow-delimiters-depth-2" > ]< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
amp_60d = load< span class = "org-rainbow-delimiters-depth-1" > (< / span > < span class = "org-string" > 'mat/data_006.mat', 'data'< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ; amp_60d = amp_60d.data< span class = "org-rainbow-delimiters-depth-1" > (< / span > < span class = "org-type" > :< / span > , < span class = "org-rainbow-delimiters-depth-2" > [< / span > < span class = "org-highlight-numbers-number" > 1< / span > ,< span class = "org-highlight-numbers-number" > 3< / span > < span class = "org-rainbow-delimiters-depth-2" > ]< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
< / pre >
< / div >
< / div >
< / div >
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< div id = "outline-container-orgec501b3" class = "outline-3" >
< h3 id = "orgec501b3" > < span class = "section-number-3" > 2.3< / span > Time Domain< / h3 >
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< div class = "outline-text-3" id = "text-2-3" >
< p >
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The time domain signals are shown on figure < a href = "#org88028bf" > 4< / a > .
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< / p >
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< div id = "org88028bf" class = "figure" >
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< p > < img src = "figs/ampli_noise_time.png" alt = "ampli_noise_time.png" / >
< / p >
< p > < span class = "figure-number" > Figure 4: < / span > Output of the amplifier< / p >
< / div >
< / div >
< / div >
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< div id = "outline-container-org7d68dd0" class = "outline-3" >
< h3 id = "org7d68dd0" > < span class = "section-number-3" > 2.4< / span > Frequency Domain< / h3 >
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< div class = "outline-text-3" id = "text-2-4" >
< p >
We first compute some parameters that will be used for the PSD computation.
< / p >
< div class = "org-src-container" >
< pre class = "src src-matlab" > dt = amp_off< span class = "org-rainbow-delimiters-depth-1" > (< / span > < span class = "org-highlight-numbers-number" > 2< / span > , < span class = "org-highlight-numbers-number" > 2< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > < span class = "org-type" > -< / span > amp_off< span class = "org-rainbow-delimiters-depth-1" > (< / span > < span class = "org-highlight-numbers-number" > 1< / span > , < span class = "org-highlight-numbers-number" > 2< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
Fs = < span class = "org-highlight-numbers-number" > 1< / span > < span class = "org-type" > /< / span > dt; < span class = "org-comment" > % [Hz]< / span >
win = hanning< span class = "org-rainbow-delimiters-depth-1" > (< / span > ceil< span class = "org-rainbow-delimiters-depth-2" > (< / span > < span class = "org-highlight-numbers-number" > 10< / span > < span class = "org-type" > *< / span > Fs< span class = "org-rainbow-delimiters-depth-2" > )< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
< / pre >
< / div >
< p >
Then we compute the Power Spectral Density using < code > pwelch< / code > function.
< / p >
< div class = "org-src-container" >
< pre class = "src src-matlab" > < span class = "org-rainbow-delimiters-depth-1" > [< / span > pxoff, f< span class = "org-rainbow-delimiters-depth-1" > ]< / span > = pwelch< span class = "org-rainbow-delimiters-depth-1" > (< / span > amp_off< span class = "org-rainbow-delimiters-depth-2" > (< / span > < span class = "org-type" > :< / span > ,< span class = "org-highlight-numbers-number" > 1< / span > < span class = "org-rainbow-delimiters-depth-2" > )< / span > , win, < span class = "org-rainbow-delimiters-depth-2" > []< / span > , < span class = "org-rainbow-delimiters-depth-2" > []< / span > , Fs< span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
< span class = "org-rainbow-delimiters-depth-1" > [< / span > px20d, < span class = "org-type" > ~< / span > < span class = "org-rainbow-delimiters-depth-1" > ]< / span > = pwelch< span class = "org-rainbow-delimiters-depth-1" > (< / span > amp_20d< span class = "org-rainbow-delimiters-depth-2" > (< / span > < span class = "org-type" > :< / span > ,< span class = "org-highlight-numbers-number" > 1< / span > < span class = "org-rainbow-delimiters-depth-2" > )< / span > , win, < span class = "org-rainbow-delimiters-depth-2" > []< / span > , < span class = "org-rainbow-delimiters-depth-2" > []< / span > , Fs< span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
< span class = "org-rainbow-delimiters-depth-1" > [< / span > px40d, < span class = "org-type" > ~< / span > < span class = "org-rainbow-delimiters-depth-1" > ]< / span > = pwelch< span class = "org-rainbow-delimiters-depth-1" > (< / span > amp_40d< span class = "org-rainbow-delimiters-depth-2" > (< / span > < span class = "org-type" > :< / span > ,< span class = "org-highlight-numbers-number" > 1< / span > < span class = "org-rainbow-delimiters-depth-2" > )< / span > , win, < span class = "org-rainbow-delimiters-depth-2" > []< / span > , < span class = "org-rainbow-delimiters-depth-2" > []< / span > , Fs< span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
< span class = "org-rainbow-delimiters-depth-1" > [< / span > px60d, < span class = "org-type" > ~< / span > < span class = "org-rainbow-delimiters-depth-1" > ]< / span > = pwelch< span class = "org-rainbow-delimiters-depth-1" > (< / span > amp_60d< span class = "org-rainbow-delimiters-depth-2" > (< / span > < span class = "org-type" > :< / span > ,< span class = "org-highlight-numbers-number" > 1< / span > < span class = "org-rainbow-delimiters-depth-2" > )< / span > , win, < span class = "org-rainbow-delimiters-depth-2" > []< / span > , < span class = "org-rainbow-delimiters-depth-2" > []< / span > , Fs< span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
< / pre >
< / div >
< p >
We compute the theoretical ADC noise.
< / p >
< div class = "org-src-container" >
< pre class = "src src-matlab" > q = < span class = "org-highlight-numbers-number" > 20< / span > < span class = "org-type" > /< / span > < span class = "org-highlight-numbers-number" > 2< / span > < span class = "org-type" > ^< / span > < span class = "org-highlight-numbers-number" > 16< / span > ; < span class = "org-comment" > % quantization< / span >
Sq = q< span class = "org-type" > ^< / span > < span class = "org-highlight-numbers-number" > 2< / span > < span class = "org-type" > /< / span > < span class = "org-highlight-numbers-number" > 12< / span > < span class = "org-type" > /< / span > < span class = "org-highlight-numbers-number" > 1000< / span > ; < span class = "org-comment" > % PSD of the ADC noise< / span >
< / pre >
< / div >
< p >
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Finally, the ASD is shown on figure < a href = "#org4935d97" > 5< / a > .
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< / p >
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< div id = "org4935d97" class = "figure" >
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< p > < img src = "figs/ampli_noise_psd.png" alt = "ampli_noise_psd.png" / >
< / p >
< p > < span class = "figure-number" > Figure 5: < / span > Amplitude Spectral Density of the measured voltage at the output of the voltage amplifier< / p >
< / div >
< / div >
< / div >
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< div id = "outline-container-orgaba63f9" class = "outline-3" >
< h3 id = "orgaba63f9" > < span class = "section-number-3" > 2.5< / span > Conclusion< / h3 >
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< div class = "outline-text-3" id = "text-2-5" >
< div class = "important" >
< p >
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< b > Questions< / b > :
< / p >
< ul class = "org-ul" >
< li > Where does those sharp peaks comes from? Can this be due to aliasing?< / li >
< / ul >
< p >
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.
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< / p >
< / div >
< / div >
< / div >
< / div >
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< div id = "outline-container-orgded919b" class = "outline-2" >
< h2 id = "orgded919b" > < span class = "section-number-2" > 3< / span > Measure of the noise induced by the Slip-Ring< / h2 >
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< div class = "outline-text-2" id = "text-3" >
< p >
The data and matlab files are accessible < a href = "data/meas_slip_ring.zip" > here< / a > .
< / p >
< / div >
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< div id = "outline-container-orgde32f93" class = "outline-3" >
< h3 id = "orgde32f93" > < span class = "section-number-3" > 3.1< / span > Measurement Description< / h3 >
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< div class = "outline-text-3" id = "text-3-1" >
< p >
< b > Goal< / b > :
< / p >
< ul class = "org-ul" >
< li > Determine the noise induced by the slip-ring< / li >
< / ul >
< p >
< b > Setup< / b > :
< / p >
< ul class = "org-ul" >
< li > 0V is generated by the DAC of the Speedgoat< / li >
< li > Using a T, one part goes directly to the ADC< / li >
< li > The other part goes to the slip-ring 2 times and then to the ADC< / li >
< li > The parameters of the Voltage Amplifier are: 80dB, AC, 1kHz< / li >
< li > Every stage of the station is OFF< / li >
< / ul >
< p >
First column: Direct measure
Second column: Slip-ring measure
< / p >
< p >
< b > Measurements< / b > :
< / p >
< ul class = "org-ul" >
< li > < code > data_008< / code > : Slip-Ring OFF< / li >
< li > < code > data_009< / code > : Slip-Ring ON< / li >
< li > < code > data_010< / code > : Slip-Ring ON and omega=6rpm< / li >
< li > < code > data_011< / code > : Slip-Ring ON and omega=60rpm< / li >
< / ul >
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< div id = "orgd7dd6a9" class = "figure" >
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< p > < img src = "./img/VID_20190503_160831.gif" alt = "VID_20190503_160831.gif" / >
< / p >
< p > < span class = "figure-number" > Figure 6: < / span > Slip-Ring rotating at 6rpm< / p >
< / div >
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< div id = "org4a57a9c" class = "figure" >
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< p > < img src = "./img/VID_20190503_161401.gif" alt = "VID_20190503_161401.gif" / >
< / p >
< p > < span class = "figure-number" > Figure 7: < / span > Slip-Ring rotating at 60rpm< / p >
< / div >
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< / div >
< / div >
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< div id = "outline-container-org661917b" class = "outline-3" >
< h3 id = "org661917b" > < span class = "section-number-3" > 3.2< / span > Load data< / h3 >
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< div class = "outline-text-3" id = "text-3-2" >
< p >
We load the data of the z axis of two geophones.
< / p >
< div class = "org-src-container" >
< pre class = "src src-matlab" > sr_off = load< span class = "org-rainbow-delimiters-depth-1" > (< / span > < span class = "org-string" > 'mat/data_008.mat', 'data'< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ; sr_off = sr_off.data;
sr_on = load< span class = "org-rainbow-delimiters-depth-1" > (< / span > 'mat< span class = "org-type" > /< / span > data_009.mat', < span class = "org-string" > 'data'< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ; sr_on = sr_on.data;
sr_6r = load< span class = "org-rainbow-delimiters-depth-1" > (< / span > < span class = "org-string" > 'mat/data_010.mat', 'data'< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ; sr_6r = sr_6r.data;
sr_60r = load< span class = "org-rainbow-delimiters-depth-1" > (< / span > < span class = "org-string" > 'mat/data_011.mat', 'data'< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ; sr_60r = sr_60r.data;
< / pre >
< / div >
< / div >
< / div >
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< div id = "outline-container-orgcd9a917" class = "outline-3" >
< h3 id = "orgcd9a917" > < span class = "section-number-3" > 3.3< / span > Time Domain< / h3 >
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< div class = "outline-text-3" id = "text-3-3" >
< p >
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We plot the time domain data for the direct measurement (figure < a href = "#orgd6b2170" > 8< / a > ) and for the signal going through the slip-ring (figure < a href = "#orga83c518" > 9< / a > );
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< / p >
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< div id = "orgd6b2170" class = "figure" >
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< p > < img src = "figs/sr_direct_time.png" alt = "sr_direct_time.png" / >
< / p >
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< p > < span class = "figure-number" > Figure 8: < / span > Direct measurement< / p >
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< / div >
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< div id = "orga83c518" class = "figure" >
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< p > < img src = "figs/sr_slipring_time.png" alt = "sr_slipring_time.png" / >
< / p >
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< p > < span class = "figure-number" > Figure 9: < / span > Measurement of the signal going through the Slip-Ring< / p >
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< / div >
< / div >
< / div >
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< div id = "outline-container-org708090d" class = "outline-3" >
< h3 id = "org708090d" > < span class = "section-number-3" > 3.4< / span > Frequency Domain< / h3 >
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< div class = "outline-text-3" id = "text-3-4" >
< p >
We first compute some parameters that will be used for the PSD computation.
< / p >
< div class = "org-src-container" >
< pre class = "src src-matlab" > dt = sr_off< span class = "org-rainbow-delimiters-depth-1" > (< / span > < span class = "org-highlight-numbers-number" > 2< / span > , < span class = "org-highlight-numbers-number" > 3< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > < span class = "org-type" > -< / span > sr_off< span class = "org-rainbow-delimiters-depth-1" > (< / span > < span class = "org-highlight-numbers-number" > 1< / span > , < span class = "org-highlight-numbers-number" > 3< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
Fs = < span class = "org-highlight-numbers-number" > 1< / span > < span class = "org-type" > /< / span > dt; < span class = "org-comment" > % [Hz]< / span >
win = hanning< span class = "org-rainbow-delimiters-depth-1" > (< / span > ceil< span class = "org-rainbow-delimiters-depth-2" > (< / span > < span class = "org-highlight-numbers-number" > 10< / span > < span class = "org-type" > *< / span > Fs< span class = "org-rainbow-delimiters-depth-2" > )< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
< / pre >
< / div >
< p >
Then we compute the Power Spectral Density using < code > pwelch< / code > function.
< / p >
< div class = "org-src-container" >
< pre class = "src src-matlab" > < span class = "org-rainbow-delimiters-depth-1" > [< / span > pxdir, f< span class = "org-rainbow-delimiters-depth-1" > ]< / span > = pwelch< span class = "org-rainbow-delimiters-depth-1" > (< / span > sr_off< span class = "org-rainbow-delimiters-depth-2" > (< / span > < span class = "org-type" > :< / span > , < span class = "org-highlight-numbers-number" > 1< / span > < span class = "org-rainbow-delimiters-depth-2" > )< / span > , win, < span class = "org-rainbow-delimiters-depth-2" > []< / span > , < span class = "org-rainbow-delimiters-depth-2" > []< / span > , Fs< span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
< span class = "org-rainbow-delimiters-depth-1" > [< / span > pxoff, < span class = "org-type" > ~< / span > < span class = "org-rainbow-delimiters-depth-1" > ]< / span > = pwelch< span class = "org-rainbow-delimiters-depth-1" > (< / span > sr_off< span class = "org-rainbow-delimiters-depth-2" > (< / span > < span class = "org-type" > :< / span > , < span class = "org-highlight-numbers-number" > 2< / span > < span class = "org-rainbow-delimiters-depth-2" > )< / span > , win, < span class = "org-rainbow-delimiters-depth-2" > []< / span > , < span class = "org-rainbow-delimiters-depth-2" > []< / span > , Fs< span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
< span class = "org-rainbow-delimiters-depth-1" > [< / span > pxon, < span class = "org-type" > ~< / span > < span class = "org-rainbow-delimiters-depth-1" > ]< / span > = pwelch< span class = "org-rainbow-delimiters-depth-1" > (< / span > sr_on< span class = "org-rainbow-delimiters-depth-2" > (< / span > < span class = "org-type" > :< / span > , < span class = "org-highlight-numbers-number" > 2< / span > < span class = "org-rainbow-delimiters-depth-2" > )< / span > , win, < span class = "org-rainbow-delimiters-depth-2" > []< / span > , < span class = "org-rainbow-delimiters-depth-2" > []< / span > , Fs< span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
< span class = "org-rainbow-delimiters-depth-1" > [< / span > px6r, < span class = "org-type" > ~< / span > < span class = "org-rainbow-delimiters-depth-1" > ]< / span > = pwelch< span class = "org-rainbow-delimiters-depth-1" > (< / span > sr_6r< span class = "org-rainbow-delimiters-depth-2" > (< / span > < span class = "org-type" > :< / span > , < span class = "org-highlight-numbers-number" > 2< / span > < span class = "org-rainbow-delimiters-depth-2" > )< / span > , win, < span class = "org-rainbow-delimiters-depth-2" > []< / span > , < span class = "org-rainbow-delimiters-depth-2" > []< / span > , Fs< span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
< span class = "org-rainbow-delimiters-depth-1" > [< / span > px60r, < span class = "org-type" > ~< / span > < span class = "org-rainbow-delimiters-depth-1" > ]< / span > = pwelch< span class = "org-rainbow-delimiters-depth-1" > (< / span > sr_60r< span class = "org-rainbow-delimiters-depth-2" > (< / span > < span class = "org-type" > :< / span > , < span class = "org-highlight-numbers-number" > 2< / span > < span class = "org-rainbow-delimiters-depth-2" > )< / span > , win, < span class = "org-rainbow-delimiters-depth-2" > []< / span > , < span class = "org-rainbow-delimiters-depth-2" > []< / span > , Fs< span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
< / pre >
< / div >
< p >
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And we plot the ASD of the measured signals (figure < a href = "#org7125217" > 10< / a > );
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< / p >
< div class = "org-src-container" >
< pre class = "src src-matlab" > < span class = "org-type" > figure< / span > ;
hold on;
plot< span class = "org-rainbow-delimiters-depth-1" > (< / span > f, sqrt< span class = "org-rainbow-delimiters-depth-2" > (< / span > pxoff< span class = "org-rainbow-delimiters-depth-2" > )< / span > , < span class = "org-string" > 'DisplayName', 'OFF'< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
plot< span class = "org-rainbow-delimiters-depth-1" > (< / span > f, sqrt< span class = "org-rainbow-delimiters-depth-2" > (< / span > pxon< span class = "org-rainbow-delimiters-depth-2" > )< / span > , < span class = "org-string" > 'DisplayName', 'ON'< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
plot< span class = "org-rainbow-delimiters-depth-1" > (< / span > f, sqrt< span class = "org-rainbow-delimiters-depth-2" > (< / span > px6r< span class = "org-rainbow-delimiters-depth-2" > )< / span > , 'DisplayName', '< span class = "org-highlight-numbers-number" > 6rpm< / span > '< span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
plot< span class = "org-rainbow-delimiters-depth-1" > (< / span > f, sqrt< span class = "org-rainbow-delimiters-depth-2" > (< / span > px60r< span class = "org-rainbow-delimiters-depth-2" > )< / span > , 'DisplayName', '< span class = "org-highlight-numbers-number" > 60rpm< / span > '< span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
plot< span class = "org-rainbow-delimiters-depth-1" > (< / span > f, sqrt< span class = "org-rainbow-delimiters-depth-2" > (< / span > pxdir< span class = "org-rainbow-delimiters-depth-2" > )< / span > , < span class = "org-string" > 'k-', 'DisplayName', 'Direct'< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
hold off;
< span class = "org-type" > set< / span > < span class = "org-rainbow-delimiters-depth-1" > (< / span > < span class = "org-variable-name" > gca< / span > , < span class = "org-string" > 'xscale', 'log'< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
< span class = "org-type" > set< / span > < span class = "org-rainbow-delimiters-depth-1" > (< / span > < span class = "org-variable-name" > gca< / span > , < span class = "org-string" > 'yscale', 'log'< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
xlabel< span class = "org-rainbow-delimiters-depth-1" > (< / span > < span class = "org-string" > 'Frequency < / span > < span class = "org-string" > < span class = "org-rainbow-delimiters-depth-2" > [< / span > < / span > < span class = "org-string" > Hz< / span > < span class = "org-string" > < span class = "org-rainbow-delimiters-depth-2" > ]< / span > < / span > < span class = "org-string" > '< / span > < span class = "org-string" > < span class = "org-rainbow-delimiters-depth-1" > )< / span > < / span > < span class = "org-string" > ; ylabel< / span > < span class = "org-string" > < span class = "org-rainbow-delimiters-depth-1" > (< / span > < / span > < span class = "org-string" > '< / span > ASD of the measured Voltage $< span class = "org-type" > \< / span > left< span class = "org-rainbow-delimiters-depth-2" > [< / span > < span class = "org-type" > \< / span > frac< span class = "org-rainbow-delimiters-depth-3" > {< / span > V< span class = "org-rainbow-delimiters-depth-3" > }{< / span > < span class = "org-type" > \< / span > sqrt< span class = "org-rainbow-delimiters-depth-4" > {< / span > Hz< span class = "org-rainbow-delimiters-depth-4" > }< / span > < span class = "org-rainbow-delimiters-depth-3" > }< / span > < span class = "org-type" > \< / span > right< span class = "org-rainbow-delimiters-depth-2" > ]< / span > $'< span class = "org-rainbow-delimiters-depth-1" > )< / span >
legend< span class = "org-rainbow-delimiters-depth-1" > (< / span > < span class = "org-string" > 'Location', 'northeast'< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
xlim< span class = "org-rainbow-delimiters-depth-1" > (< / span > < span class = "org-rainbow-delimiters-depth-2" > [< / span > < span class = "org-highlight-numbers-number" > 0< / span > .< span class = "org-highlight-numbers-number" > 1< / span > , < span class = "org-highlight-numbers-number" > 500< / span > < span class = "org-rainbow-delimiters-depth-2" > ]< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
< / pre >
< / div >
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< div id = "org7125217" class = "figure" >
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< p > < img src = "figs/sr_psd_compare.png" alt = "sr_psd_compare.png" / >
< / p >
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< p > < span class = "figure-number" > Figure 10: < / span > Comparison of the ASD of the measured signals when the slip-ring is ON, OFF and turning< / p >
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< / div >
< / div >
< / div >
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< div id = "outline-container-org83ed722" class = "outline-3" >
< h3 id = "org83ed722" > < span class = "section-number-3" > 3.5< / span > Conclusion< / h3 >
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< div class = "outline-text-3" id = "text-3-5" >
< div class = "important" >
< p >
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< b > Questions:< / b >
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< / p >
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< ul class = "org-ul" >
< li > Why is there some sharp peaks? Can this be due to aliasing?< / li >
< li > It is possible that the amplifiers were saturating during the measurements => should redo the measurements with a low pass filter before the voltage amplifier< / li >
< / ul >
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< / div >
< / div >
< / div >
< / div >
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< div id = "outline-container-orgfbf06e6" class = "outline-2" >
< h2 id = "orgfbf06e6" > < span class = "section-number-2" > 4< / span > Measure of the noise induced by the slip ring when using a geophone< / h2 >
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< div class = "outline-text-2" id = "text-4" >
< p >
The data and matlab files are accessible < a href = "data/meas_sr_geophone.zip" > here< / a > .
< / p >
< / div >
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< div id = "outline-container-orgffb1bdb" class = "outline-3" >
< h3 id = "orgffb1bdb" > < span class = "section-number-3" > 4.1< / span > First Measurement without LPF< / h3 >
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< div class = "outline-text-3" id = "text-4-1" >
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< / div >
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< div id = "outline-container-org8e8831c" class = "outline-4" >
< h4 id = "org8e8831c" > < span class = "section-number-4" > 4.1.1< / span > Measurement Description< / h4 >
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< div class = "outline-text-4" id = "text-4-1-1" >
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< p >
< b > Goal< / b > :
< / p >
< ul class = "org-ul" >
< li > Determine if the noise induced by the slip-ring is a limiting factor when measuring the signal coming from a geophone< / li >
< / ul >
< p >
< b > Setup< / b > :
< / p >
< ul class = "org-ul" >
< li > The geophone is located at the sample location< / li >
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< li > The two Voltage amplifiers have the same following settings:
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< ul class = "org-ul" >
< li > AC< / li >
< li > 60dB< / li >
< li > 1kHz< / li >
< / ul > < / li >
< li > The signal from the geophone is split into two using a T-BNC:
< ul class = "org-ul" >
< li > One part goes directly to the voltage amplifier and then to the ADC.< / li >
< li > The other part goes to the slip-ring=> voltage amplifier=> ADC.< / li >
< / ul > < / li >
< / ul >
< p >
First column: Direct measure
Second column: Slip-ring measure
< / p >
< p >
< b > Measurements< / b > :
< / p >
< ul class = "org-ul" >
< li > < code > data_012< / code > : Slip-Ring OFF< / li >
< li > < code > data_013< / code > : Slip-Ring ON< / li >
< / ul >
< / div >
< / div >
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< div id = "outline-container-org167eeae" class = "outline-4" >
< h4 id = "org167eeae" > < span class = "section-number-4" > 4.1.2< / span > Load data< / h4 >
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< div class = "outline-text-4" id = "text-4-1-2" >
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< p >
We load the data of the z axis of two geophones.
< / p >
< div class = "org-src-container" >
< pre class = "src src-matlab" > sr_off = load< span class = "org-rainbow-delimiters-depth-1" > (< / span > < span class = "org-string" > 'mat/data_012.mat', 'data'< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ; sr_off = sr_off.data;
sr_on = load< span class = "org-rainbow-delimiters-depth-1" > (< / span > < span class = "org-string" > 'mat/data_013.mat', 'data'< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ; sr_on = sr_on.data;
< / pre >
< / div >
< / div >
< / div >
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< div id = "outline-container-org583abb2" class = "outline-4" >
< h4 id = "org583abb2" > < span class = "section-number-4" > 4.1.3< / span > Time Domain< / h4 >
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< div class = "outline-text-4" id = "text-4-1-3" >
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< p >
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We compare the signal when the Slip-Ring is OFF (figure < a href = "#org86338a6" > 11< / a > ) and when it is ON (figure < a href = "#org9c8364f" > 12< / a > ).
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< / p >
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< div id = "org86338a6" class = "figure" >
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< p > < img src = "figs/sr_geophone_time_off.png" alt = "sr_geophone_time_off.png" / >
< / p >
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< p > < span class = "figure-number" > Figure 11: < / span > Comparison of the time domain signals when the slip-ring is OFF< / p >
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< / div >
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< div id = "org9c8364f" class = "figure" >
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< p > < img src = "figs/sr_geophone_time_on.png" alt = "sr_geophone_time_on.png" / >
< / p >
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< p > < span class = "figure-number" > Figure 12: < / span > Comparison of the time domain signals when the slip-ring is ON< / p >
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< / div >
< / div >
< / div >
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< div id = "outline-container-org35e29fe" class = "outline-4" >
< h4 id = "org35e29fe" > < span class = "section-number-4" > 4.1.4< / span > Frequency Domain< / h4 >
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< div class = "outline-text-4" id = "text-4-1-4" >
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< p >
We first compute some parameters that will be used for the PSD computation.
< / p >
< div class = "org-src-container" >
< pre class = "src src-matlab" > dt = sr_off< span class = "org-rainbow-delimiters-depth-1" > (< / span > < span class = "org-highlight-numbers-number" > 2< / span > , < span class = "org-highlight-numbers-number" > 3< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > < span class = "org-type" > -< / span > sr_off< span class = "org-rainbow-delimiters-depth-1" > (< / span > < span class = "org-highlight-numbers-number" > 1< / span > , < span class = "org-highlight-numbers-number" > 3< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
Fs = < span class = "org-highlight-numbers-number" > 1< / span > < span class = "org-type" > /< / span > dt; < span class = "org-comment" > % [Hz]< / span >
win = hanning< span class = "org-rainbow-delimiters-depth-1" > (< / span > ceil< span class = "org-rainbow-delimiters-depth-2" > (< / span > < span class = "org-highlight-numbers-number" > 10< / span > < span class = "org-type" > *< / span > Fs< span class = "org-rainbow-delimiters-depth-2" > )< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
< / pre >
< / div >
< p >
Then we compute the Power Spectral Density using < code > pwelch< / code > function.
< / p >
< div class = "org-src-container" >
< pre class = "src src-matlab" > < span class = "org-comment" > % Direct measure< / span >
< span class = "org-rainbow-delimiters-depth-1" > [< / span > pxdoff, < span class = "org-type" > ~< / span > < span class = "org-rainbow-delimiters-depth-1" > ]< / span > = pwelch< span class = "org-rainbow-delimiters-depth-1" > (< / span > sr_off< span class = "org-rainbow-delimiters-depth-2" > (< / span > < span class = "org-type" > :< / span > , < span class = "org-highlight-numbers-number" > 1< / span > < span class = "org-rainbow-delimiters-depth-2" > )< / span > , win, < span class = "org-rainbow-delimiters-depth-2" > []< / span > , < span class = "org-rainbow-delimiters-depth-2" > []< / span > , Fs< span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
< span class = "org-rainbow-delimiters-depth-1" > [< / span > pxdon, < span class = "org-type" > ~< / span > < span class = "org-rainbow-delimiters-depth-1" > ]< / span > = pwelch< span class = "org-rainbow-delimiters-depth-1" > (< / span > sr_on< span class = "org-rainbow-delimiters-depth-2" > (< / span > < span class = "org-type" > :< / span > , < span class = "org-highlight-numbers-number" > 1< / span > < span class = "org-rainbow-delimiters-depth-2" > )< / span > , win, < span class = "org-rainbow-delimiters-depth-2" > []< / span > , < span class = "org-rainbow-delimiters-depth-2" > []< / span > , Fs< span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
< span class = "org-comment" > % Slip-Ring measure< / span >
< span class = "org-rainbow-delimiters-depth-1" > [< / span > pxsroff, f< span class = "org-rainbow-delimiters-depth-1" > ]< / span > = pwelch< span class = "org-rainbow-delimiters-depth-1" > (< / span > sr_off< span class = "org-rainbow-delimiters-depth-2" > (< / span > < span class = "org-type" > :< / span > , < span class = "org-highlight-numbers-number" > 2< / span > < span class = "org-rainbow-delimiters-depth-2" > )< / span > , win, < span class = "org-rainbow-delimiters-depth-2" > []< / span > , < span class = "org-rainbow-delimiters-depth-2" > []< / span > , Fs< span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
< span class = "org-rainbow-delimiters-depth-1" > [< / span > pxsron, < span class = "org-type" > ~< / span > < span class = "org-rainbow-delimiters-depth-1" > ]< / span > = pwelch< span class = "org-rainbow-delimiters-depth-1" > (< / span > sr_on< span class = "org-rainbow-delimiters-depth-2" > (< / span > < span class = "org-type" > :< / span > , < span class = "org-highlight-numbers-number" > 2< / span > < span class = "org-rainbow-delimiters-depth-2" > )< / span > , win, < span class = "org-rainbow-delimiters-depth-2" > []< / span > , < span class = "org-rainbow-delimiters-depth-2" > []< / span > , Fs< span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
< / pre >
< / div >
< p >
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Finally, we compare the Amplitude Spectral Density of the signals (figure < a href = "#org4e3b998" > 13< / a > );
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< / p >
< div class = "org-src-container" >
< pre class = "src src-matlab" > < span class = "org-type" > figure< / span > ;
hold on;
plot< span class = "org-rainbow-delimiters-depth-1" > (< / span > f, sqrt< span class = "org-rainbow-delimiters-depth-2" > (< / span > pxdoff< span class = "org-rainbow-delimiters-depth-2" > )< / span > , < span class = "org-string" > 'DisplayName', 'Direct - OFF'< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
plot< span class = "org-rainbow-delimiters-depth-1" > (< / span > f, sqrt< span class = "org-rainbow-delimiters-depth-2" > (< / span > pxsroff< span class = "org-rainbow-delimiters-depth-2" > )< / span > , < span class = "org-string" > 'DisplayName', 'Slip-Ring - OFF'< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
plot< span class = "org-rainbow-delimiters-depth-1" > (< / span > f, sqrt< span class = "org-rainbow-delimiters-depth-2" > (< / span > pxdon< span class = "org-rainbow-delimiters-depth-2" > )< / span > , < span class = "org-string" > 'DisplayName', 'Direct - ON'< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
plot< span class = "org-rainbow-delimiters-depth-1" > (< / span > f, sqrt< span class = "org-rainbow-delimiters-depth-2" > (< / span > pxsron< span class = "org-rainbow-delimiters-depth-2" > )< / span > , < span class = "org-string" > 'DisplayName', 'Slip-Ring - ON'< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
hold off;
< span class = "org-type" > set< / span > < span class = "org-rainbow-delimiters-depth-1" > (< / span > < span class = "org-variable-name" > gca< / span > , < span class = "org-string" > 'xscale', 'log'< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
< span class = "org-type" > set< / span > < span class = "org-rainbow-delimiters-depth-1" > (< / span > < span class = "org-variable-name" > gca< / span > , < span class = "org-string" > 'yscale', 'log'< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
xlabel< span class = "org-rainbow-delimiters-depth-1" > (< / span > < span class = "org-string" > 'Frequency < / span > < span class = "org-string" > < span class = "org-rainbow-delimiters-depth-2" > [< / span > < / span > < span class = "org-string" > Hz< / span > < span class = "org-string" > < span class = "org-rainbow-delimiters-depth-2" > ]< / span > < / span > < span class = "org-string" > '< / span > < span class = "org-string" > < span class = "org-rainbow-delimiters-depth-1" > )< / span > < / span > < span class = "org-string" > ; ylabel< / span > < span class = "org-string" > < span class = "org-rainbow-delimiters-depth-1" > (< / span > < / span > < span class = "org-string" > '< / span > ASD of the measured Voltage $< span class = "org-type" > \< / span > left< span class = "org-rainbow-delimiters-depth-2" > [< / span > < span class = "org-type" > \< / span > frac< span class = "org-rainbow-delimiters-depth-3" > {< / span > V< span class = "org-rainbow-delimiters-depth-3" > }{< / span > < span class = "org-type" > \< / span > sqrt< span class = "org-rainbow-delimiters-depth-4" > {< / span > Hz< span class = "org-rainbow-delimiters-depth-4" > }< / span > < span class = "org-rainbow-delimiters-depth-3" > }< / span > < span class = "org-type" > \< / span > right< span class = "org-rainbow-delimiters-depth-2" > ]< / span > $'< span class = "org-rainbow-delimiters-depth-1" > )< / span >
legend< span class = "org-rainbow-delimiters-depth-1" > (< / span > < span class = "org-string" > 'Location', 'northeast'< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
xlim< span class = "org-rainbow-delimiters-depth-1" > (< / span > < span class = "org-rainbow-delimiters-depth-2" > [< / span > < span class = "org-highlight-numbers-number" > 0< / span > .< span class = "org-highlight-numbers-number" > 1< / span > , < span class = "org-highlight-numbers-number" > 500< / span > < span class = "org-rainbow-delimiters-depth-2" > ]< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
< / pre >
< / div >
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< div id = "org4e3b998" class = "figure" >
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< p > < img src = "figs/sr_geophone_asd.png" alt = "sr_geophone_asd.png" / >
< / p >
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< p > < span class = "figure-number" > Figure 13: < / span > Comparison of the Amplitude Spectral Sensity< / p >
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< / div >
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< div id = "org6078350" class = "figure" >
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< p > < img src = "figs/sr_geophone_asd_zoom.png" alt = "sr_geophone_asd_zoom.png" / >
< / p >
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< p > < span class = "figure-number" > Figure 14: < / span > Comparison of the Amplitude Spectral Sensity - Zoom< / p >
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< / div >
< / div >
< / div >
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< div id = "outline-container-org3e43efe" class = "outline-4" >
< h4 id = "org3e43efe" > < span class = "section-number-4" > 4.1.5< / span > Conclusion< / h4 >
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< div class = "outline-text-4" id = "text-4-1-5" >
< div class = "important" >
< ul class = "org-ul" >
< li > The fact that the Slip-Ring is turned ON adds some noise to the signal.< / li >
< li > The signal going through the Slip-Ring is less noisy than the one going directly to the ADC.< / li >
< li > This could be due to less good electromagnetic isolation.< / li >
< / ul >
< p >
< b > Questions< / b > :
< / p >
< ul class = "org-ul" >
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< li > Can the sharp peak on figure < a href = "#org6078350" > 14< / a > be due to the Aliasing?< / li >
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< / ul >
< / div >
< / div >
< / div >
< / div >
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< div id = "outline-container-orgf298379" class = "outline-3" >
< h3 id = "orgf298379" > < span class = "section-number-3" > 4.2< / span > Measurement using an oscilloscope< / h3 >
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< div class = "outline-text-3" id = "text-4-2" >
< / div >
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< div id = "outline-container-org68d1d31" class = "outline-4" >
< h4 id = "org68d1d31" > < span class = "section-number-4" > 4.2.1< / span > Measurement Setup< / h4 >
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< div class = "outline-text-4" id = "text-4-2-1" >
< p >
Know we are measuring the same signals but using an oscilloscope instead of the Speedgoat ADC.
< / p >
< / div >
< / div >
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< div id = "outline-container-org5276b1f" class = "outline-4" >
< h4 id = "org5276b1f" > < span class = "section-number-4" > 4.2.2< / span > Observations< / h4 >
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< div class = "outline-text-4" id = "text-4-2-2" >
< p >
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Then the Slip-Ring is ON (figure < a href = "#org6ea2865" > 15< / a > ), we observe a signal at 40kHz with a peak-to-peak amplitude of 200mV for the direct measure and 100mV for the signal going through the Slip-Ring.
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< / p >
< p >
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Then the Slip-Ring is OFF, we don't observe this 40kHz anymore (figure < a href = "#org2bd880f" > 16< / a > ).
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< / p >
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< div id = "org6ea2865" class = "figure" >
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< p > < img src = "./img/IMG_20190506_160420.jpg" alt = "IMG_20190506_160420.jpg" width = "500px" / >
< / p >
< p > < span class = "figure-number" > Figure 15: < / span > Signals measured by the oscilloscope - Slip-Ring ON - Yellow: Direct measure - Blue: Through Slip-Ring< / p >
< / div >
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< div id = "org2bd880f" class = "figure" >
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< p > < img src = "./img/IMG_20190506_160438.jpg" alt = "IMG_20190506_160438.jpg" width = "500px" / >
< / p >
< p > < span class = "figure-number" > Figure 16: < / span > Signals measured by the oscilloscope - Slip-Ring OFF - Yellow: Direct measure - Blue: Through Slip-Ring< / p >
< / div >
< / div >
< / div >
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< div id = "outline-container-org54a8d62" class = "outline-4" >
< h4 id = "org54a8d62" > < span class = "section-number-4" > 4.2.3< / span > Conclusion< / h4 >
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< div class = "outline-text-4" id = "text-4-2-3" >
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< div class = "important" >
< ul class = "org-ul" >
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< li > By looking at the signals using an oscilloscope, there is a lot of high frequency noise when turning on the Slip-Ring< / li >
< li > This can eventually saturate the voltage amplifiers (seen by a led indicating saturation)< / li >
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< li > The choice is to < b > add a Low pass filter before the voltage amplifiers< / b > to not saturate them and filter the noise.< / li >
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< / ul >
< / div >
< / div >
< / div >
< / div >
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< div id = "outline-container-orgcebb9a0" class = "outline-3" >
< h3 id = "orgcebb9a0" > < span class = "section-number-3" > 4.3< / span > New measurements with a LPF before the Voltage Amplifiers< / h3 >
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< div class = "outline-text-3" id = "text-4-3" >
< / div >
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< div id = "outline-container-org4bdf600" class = "outline-4" >
< h4 id = "org4bdf600" > < span class = "section-number-4" > 4.3.1< / span > Setup description< / h4 >
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< div class = "outline-text-4" id = "text-4-3-1" >
< p >
A first order low pass filter is added before the Voltage Amplifiers with the following values:
< / p >
\begin{aligned}
R & = 1k\Omega \\
C & = 1\mu F
\end{aligned}
< p >
And we have a cut-off frequency of \(f_c = \frac{1}{RC} = 160Hz\).
< / p >
< p >
We are measuring the signal from a geophone put on the marble with and without the added LPF:
< / p >
< ul class = "org-ul" >
< li > with the slip ring OFF: < code > mat/data_016.mat< / code > < / li >
< li > with the slip ring ON: < code > mat/data_017.mat< / code > < / li >
< / ul >
< / div >
< / div >
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< div id = "outline-container-org5c96c5f" class = "outline-4" >
< h4 id = "org5c96c5f" > < span class = "section-number-4" > 4.3.2< / span > Load data< / h4 >
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< div class = "outline-text-4" id = "text-4-3-2" >
< p >
We load the data of the z axis of two geophones.
< / p >
< div class = "org-src-container" >
< pre class = "src src-matlab" > sr_lpf_off = load< span class = "org-rainbow-delimiters-depth-1" > (< / span > < span class = "org-string" > 'mat/data_016.mat', 'data'< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ; sr_lpf_off = sr_lpf_off.data;
sr_lpf_on = load< span class = "org-rainbow-delimiters-depth-1" > (< / span > < span class = "org-string" > 'mat/data_017.mat', 'data'< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ; sr_lpf_on = sr_lpf_on.data;
< / pre >
< / div >
< / div >
< / div >
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< div id = "outline-container-orgbcba5cf" class = "outline-4" >
< h4 id = "orgbcba5cf" > < span class = "section-number-4" > 4.3.3< / span > Time Domain< / h4 >
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< div class = "outline-text-4" id = "text-4-3-3" >
< p >
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We compare the signal when the Slip-Ring is OFF (figure < a href = "#org521d3fb" > 17< / a > ) and when it is ON (figure < a href = "#org49d5513" > 18< / a > ).
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< / p >
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< div id = "org521d3fb" class = "figure" >
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< p > < img src = "figs/sr_lpf_geophone_time_off.png" alt = "sr_lpf_geophone_time_off.png" / >
< / p >
< p > < span class = "figure-number" > Figure 17: < / span > Comparison of the time domain signals when the slip-ring is OFF< / p >
< / div >
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< div id = "org49d5513" class = "figure" >
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< p > < img src = "figs/sr_lpf_geophone_time_on.png" alt = "sr_lpf_geophone_time_on.png" / >
< / p >
< p > < span class = "figure-number" > Figure 18: < / span > Comparison of the time domain signals when the slip-ring is ON< / p >
< / div >
< / div >
< / div >
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< div id = "outline-container-org0d5a581" class = "outline-4" >
< h4 id = "org0d5a581" > < span class = "section-number-4" > 4.3.4< / span > Frequency Domain< / h4 >
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< div class = "outline-text-4" id = "text-4-3-4" >
< p >
We first compute some parameters that will be used for the PSD computation.
< / p >
< div class = "org-src-container" >
< pre class = "src src-matlab" > dt = sr_lpf_off< span class = "org-rainbow-delimiters-depth-1" > (< / span > < span class = "org-highlight-numbers-number" > 2< / span > , < span class = "org-highlight-numbers-number" > 3< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > < span class = "org-type" > -< / span > sr_lpf_off< span class = "org-rainbow-delimiters-depth-1" > (< / span > < span class = "org-highlight-numbers-number" > 1< / span > , < span class = "org-highlight-numbers-number" > 3< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
Fs = < span class = "org-highlight-numbers-number" > 1< / span > < span class = "org-type" > /< / span > dt; < span class = "org-comment" > % [Hz]< / span >
win = hanning< span class = "org-rainbow-delimiters-depth-1" > (< / span > ceil< span class = "org-rainbow-delimiters-depth-2" > (< / span > < span class = "org-highlight-numbers-number" > 10< / span > < span class = "org-type" > *< / span > Fs< span class = "org-rainbow-delimiters-depth-2" > )< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
< / pre >
< / div >
< p >
Then we compute the Power Spectral Density using < code > pwelch< / code > function.
< / p >
< div class = "org-src-container" >
< pre class = "src src-matlab" > < span class = "org-comment" > % Direct measure< / span >
< span class = "org-rainbow-delimiters-depth-1" > [< / span > pxd_lpf_off, < span class = "org-type" > ~< / span > < span class = "org-rainbow-delimiters-depth-1" > ]< / span > = pwelch< span class = "org-rainbow-delimiters-depth-1" > (< / span > sr_lpf_off< span class = "org-rainbow-delimiters-depth-2" > (< / span > < span class = "org-type" > :< / span > , < span class = "org-highlight-numbers-number" > 1< / span > < span class = "org-rainbow-delimiters-depth-2" > )< / span > , win, < span class = "org-rainbow-delimiters-depth-2" > []< / span > , < span class = "org-rainbow-delimiters-depth-2" > []< / span > , Fs< span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
< span class = "org-rainbow-delimiters-depth-1" > [< / span > pxd_lpf_on, < span class = "org-type" > ~< / span > < span class = "org-rainbow-delimiters-depth-1" > ]< / span > = pwelch< span class = "org-rainbow-delimiters-depth-1" > (< / span > sr_lpf_on< span class = "org-rainbow-delimiters-depth-2" > (< / span > < span class = "org-type" > :< / span > , < span class = "org-highlight-numbers-number" > 1< / span > < span class = "org-rainbow-delimiters-depth-2" > )< / span > , win, < span class = "org-rainbow-delimiters-depth-2" > []< / span > , < span class = "org-rainbow-delimiters-depth-2" > []< / span > , Fs< span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
< span class = "org-comment" > % Slip-Ring measure< / span >
< span class = "org-rainbow-delimiters-depth-1" > [< / span > pxsr_lpf_off, f< span class = "org-rainbow-delimiters-depth-1" > ]< / span > = pwelch< span class = "org-rainbow-delimiters-depth-1" > (< / span > sr_lpf_off< span class = "org-rainbow-delimiters-depth-2" > (< / span > < span class = "org-type" > :< / span > , < span class = "org-highlight-numbers-number" > 2< / span > < span class = "org-rainbow-delimiters-depth-2" > )< / span > , win, < span class = "org-rainbow-delimiters-depth-2" > []< / span > , < span class = "org-rainbow-delimiters-depth-2" > []< / span > , Fs< span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
< span class = "org-rainbow-delimiters-depth-1" > [< / span > pxsr_lpf_on, < span class = "org-type" > ~< / span > < span class = "org-rainbow-delimiters-depth-1" > ]< / span > = pwelch< span class = "org-rainbow-delimiters-depth-1" > (< / span > sr_lpf_on< span class = "org-rainbow-delimiters-depth-2" > (< / span > < span class = "org-type" > :< / span > , < span class = "org-highlight-numbers-number" > 2< / span > < span class = "org-rainbow-delimiters-depth-2" > )< / span > , win, < span class = "org-rainbow-delimiters-depth-2" > []< / span > , < span class = "org-rainbow-delimiters-depth-2" > []< / span > , Fs< span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
< / pre >
< / div >
< p >
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Finally, we compare the Amplitude Spectral Density of the signals (figure < a href = "#org09681f1" > 19< / a > );
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< / p >
< div class = "org-src-container" >
< pre class = "src src-matlab" > < span class = "org-type" > figure< / span > ;
hold on;
plot< span class = "org-rainbow-delimiters-depth-1" > (< / span > f, sqrt< span class = "org-rainbow-delimiters-depth-2" > (< / span > pxd_lpf_off< span class = "org-rainbow-delimiters-depth-2" > )< / span > , < span class = "org-string" > 'DisplayName', 'Direct - OFF'< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
plot< span class = "org-rainbow-delimiters-depth-1" > (< / span > f, sqrt< span class = "org-rainbow-delimiters-depth-2" > (< / span > pxsr_lpf_off< span class = "org-rainbow-delimiters-depth-2" > )< / span > , < span class = "org-string" > 'DisplayName', 'Slip-Ring - OFF'< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
plot< span class = "org-rainbow-delimiters-depth-1" > (< / span > f, sqrt< span class = "org-rainbow-delimiters-depth-2" > (< / span > pxd_lpf_on< span class = "org-rainbow-delimiters-depth-2" > )< / span > , < span class = "org-string" > 'DisplayName', 'Direct - ON'< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
plot< span class = "org-rainbow-delimiters-depth-1" > (< / span > f, sqrt< span class = "org-rainbow-delimiters-depth-2" > (< / span > pxsr_lpf_on< span class = "org-rainbow-delimiters-depth-2" > )< / span > , < span class = "org-string" > 'DisplayName', 'Slip-Ring - ON'< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
hold off;
< span class = "org-type" > set< / span > < span class = "org-rainbow-delimiters-depth-1" > (< / span > < span class = "org-variable-name" > gca< / span > , < span class = "org-string" > 'xscale', 'log'< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
< span class = "org-type" > set< / span > < span class = "org-rainbow-delimiters-depth-1" > (< / span > < span class = "org-variable-name" > gca< / span > , < span class = "org-string" > 'yscale', 'log'< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
xlabel< span class = "org-rainbow-delimiters-depth-1" > (< / span > < span class = "org-string" > 'Frequency < / span > < span class = "org-string" > < span class = "org-rainbow-delimiters-depth-2" > [< / span > < / span > < span class = "org-string" > Hz< / span > < span class = "org-string" > < span class = "org-rainbow-delimiters-depth-2" > ]< / span > < / span > < span class = "org-string" > '< / span > < span class = "org-string" > < span class = "org-rainbow-delimiters-depth-1" > )< / span > < / span > < span class = "org-string" > ; ylabel< / span > < span class = "org-string" > < span class = "org-rainbow-delimiters-depth-1" > (< / span > < / span > < span class = "org-string" > '< / span > ASD of the measured Voltage $< span class = "org-type" > \< / span > left< span class = "org-rainbow-delimiters-depth-2" > [< / span > < span class = "org-type" > \< / span > frac< span class = "org-rainbow-delimiters-depth-3" > {< / span > V< span class = "org-rainbow-delimiters-depth-3" > }{< / span > < span class = "org-type" > \< / span > sqrt< span class = "org-rainbow-delimiters-depth-4" > {< / span > Hz< span class = "org-rainbow-delimiters-depth-4" > }< / span > < span class = "org-rainbow-delimiters-depth-3" > }< / span > < span class = "org-type" > \< / span > right< span class = "org-rainbow-delimiters-depth-2" > ]< / span > $'< span class = "org-rainbow-delimiters-depth-1" > )< / span >
legend< span class = "org-rainbow-delimiters-depth-1" > (< / span > < span class = "org-string" > 'Location', 'northeast'< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
xlim< span class = "org-rainbow-delimiters-depth-1" > (< / span > < span class = "org-rainbow-delimiters-depth-2" > [< / span > < span class = "org-highlight-numbers-number" > 0< / span > .< span class = "org-highlight-numbers-number" > 1< / span > , < span class = "org-highlight-numbers-number" > 500< / span > < span class = "org-rainbow-delimiters-depth-2" > ]< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
< / pre >
< / div >
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< div id = "org09681f1" class = "figure" >
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< p > < img src = "figs/sr_lpf_geophone_asd.png" alt = "sr_lpf_geophone_asd.png" / >
< / p >
< p > < span class = "figure-number" > Figure 19: < / span > Comparison of the Amplitude Spectral Sensity< / p >
< / div >
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< div id = "orgc8c197a" class = "figure" >
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< p > < img src = "figs/sr_lpf_geophone_asd_zoom.png" alt = "sr_lpf_geophone_asd_zoom.png" / >
< / p >
< p > < span class = "figure-number" > Figure 20: < / span > Comparison of the Amplitude Spectral Sensity - Zoom< / p >
< / div >
< / div >
< / div >
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< div id = "outline-container-orgad63dd1" class = "outline-4" >
< h4 id = "orgad63dd1" > < span class = "section-number-4" > 4.3.5< / span > Comparison of with and without LPF< / h4 >
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< div class = "outline-text-4" id = "text-4-3-5" >
< div class = "org-src-container" >
< pre class = "src src-matlab" > < span class = "org-type" > figure< / span > ;
hold on;
plot< span class = "org-rainbow-delimiters-depth-1" > (< / span > f, sqrt< span class = "org-rainbow-delimiters-depth-2" > (< / span > pxdon< span class = "org-rainbow-delimiters-depth-2" > )< / span > , < span class = "org-string" > 'DisplayName', 'Direct - ON'< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
plot< span class = "org-rainbow-delimiters-depth-1" > (< / span > f, sqrt< span class = "org-rainbow-delimiters-depth-2" > (< / span > pxsron< span class = "org-rainbow-delimiters-depth-2" > )< / span > , < span class = "org-string" > 'DisplayName', 'Slip-Ring - ON'< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
plot< span class = "org-rainbow-delimiters-depth-1" > (< / span > f, sqrt< span class = "org-rainbow-delimiters-depth-2" > (< / span > pxd_lpf_on< span class = "org-rainbow-delimiters-depth-2" > )< / span > , < span class = "org-string" > 'DisplayName', 'Direct - ON - LPF'< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
plot< span class = "org-rainbow-delimiters-depth-1" > (< / span > f, sqrt< span class = "org-rainbow-delimiters-depth-2" > (< / span > pxsr_lpf_on< span class = "org-rainbow-delimiters-depth-2" > )< / span > , < span class = "org-string" > 'DisplayName', 'Slip-Ring - ON - LPF'< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
hold off;
< span class = "org-type" > set< / span > < span class = "org-rainbow-delimiters-depth-1" > (< / span > < span class = "org-variable-name" > gca< / span > , < span class = "org-string" > 'xscale', 'log'< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
< span class = "org-type" > set< / span > < span class = "org-rainbow-delimiters-depth-1" > (< / span > < span class = "org-variable-name" > gca< / span > , < span class = "org-string" > 'yscale', 'log'< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
xlabel< span class = "org-rainbow-delimiters-depth-1" > (< / span > < span class = "org-string" > 'Frequency < / span > < span class = "org-string" > < span class = "org-rainbow-delimiters-depth-2" > [< / span > < / span > < span class = "org-string" > Hz< / span > < span class = "org-string" > < span class = "org-rainbow-delimiters-depth-2" > ]< / span > < / span > < span class = "org-string" > '< / span > < span class = "org-string" > < span class = "org-rainbow-delimiters-depth-1" > )< / span > < / span > < span class = "org-string" > ; ylabel< / span > < span class = "org-string" > < span class = "org-rainbow-delimiters-depth-1" > (< / span > < / span > < span class = "org-string" > '< / span > ASD of the measured Voltage $< span class = "org-type" > \< / span > left< span class = "org-rainbow-delimiters-depth-2" > [< / span > < span class = "org-type" > \< / span > frac< span class = "org-rainbow-delimiters-depth-3" > {< / span > V< span class = "org-rainbow-delimiters-depth-3" > }{< / span > < span class = "org-type" > \< / span > sqrt< span class = "org-rainbow-delimiters-depth-4" > {< / span > Hz< span class = "org-rainbow-delimiters-depth-4" > }< / span > < span class = "org-rainbow-delimiters-depth-3" > }< / span > < span class = "org-type" > \< / span > right< span class = "org-rainbow-delimiters-depth-2" > ]< / span > $'< span class = "org-rainbow-delimiters-depth-1" > )< / span >
legend< span class = "org-rainbow-delimiters-depth-1" > (< / span > < span class = "org-string" > 'Location', 'northeast'< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
xlim< span class = "org-rainbow-delimiters-depth-1" > (< / span > < span class = "org-rainbow-delimiters-depth-2" > [< / span > < span class = "org-highlight-numbers-number" > 0< / span > .< span class = "org-highlight-numbers-number" > 1< / span > , < span class = "org-highlight-numbers-number" > 500< / span > < span class = "org-rainbow-delimiters-depth-2" > ]< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
< / pre >
< / div >
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< div id = "org85b75e8" class = "figure" >
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< p > < img src = "figs/comp_with_without_lpf.png" alt = "comp_with_without_lpf.png" / >
< / p >
< p > < span class = "figure-number" > Figure 21: < / span > Comparison of the measured signals with and without LPF< / p >
< / div >
< / div >
< / div >
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< div id = "outline-container-orgdece1f2" class = "outline-4" >
< h4 id = "orgdece1f2" > < span class = "section-number-4" > 4.3.6< / span > Conclusion< / h4 >
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< div class = "outline-text-4" id = "text-4-3-6" >
< div class = "important" >
< ul class = "org-ul" >
< li > Using the LPF, we don't have any perturbation coming from the slip-ring when it is on.< / li >
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< li > However, we should use a smaller value of the capacitor to have a cut-off frequency at \(1kHz\).< / li >
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< / ul >
< / div >
< / div >
< / div >
< / div >
< / div >
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< div id = "outline-container-org23a8137" class = "outline-2" >
< h2 id = "org23a8137" > < span class = "section-number-2" > 5< / span > Measure of the influence of the AC/DC option on the voltage amplifiers< / h2 >
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< div class = "outline-text-2" id = "text-5" >
< p >
The data and matlab files are accessible < a href = "data/meas_noise_ac_dc.zip" > here< / a > .
< / p >
< / div >
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< div id = "outline-container-org58bc336" class = "outline-3" >
< h3 id = "org58bc336" > < span class = "section-number-3" > 5.1< / span > Measurement Description< / h3 >
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< div class = "outline-text-3" id = "text-5-1" >
< p >
< b > Goal< / b > :
< / p >
< ul class = "org-ul" >
< li > Measure the influence of the high-pass filter option of the voltage amplifiers< / li >
< / ul >
< p >
< b > Setup< / b > :
< / p >
< ul class = "org-ul" >
< li > One geophone is located on the marble.< / li >
< li > It's signal goes to two voltage amplifiers with a gain of 60dB.< / li >
< li > One voltage amplifier is on the AC option, the other is on the DC option.< / li >
< / ul >
< p >
< b > Measurements< / b > :
First measurement (< code > mat/data_014.mat< / code > file):
< / p >
< table border = "2" cellspacing = "0" cellpadding = "6" rules = "groups" frame = "hsides" >
< colgroup >
< col class = "org-right" / >
< col class = "org-left" / >
< / colgroup >
< thead >
< tr >
< th scope = "col" class = "org-right" > Column< / th >
< th scope = "col" class = "org-left" > Signal< / th >
< / tr >
< / thead >
< tbody >
< tr >
< td class = "org-right" > 1< / td >
< td class = "org-left" > Amplifier 1 with AC option< / td >
< / tr >
< tr >
< td class = "org-right" > 2< / td >
< td class = "org-left" > Amplifier 2 with DC option< / td >
< / tr >
< tr >
< td class = "org-right" > 3< / td >
< td class = "org-left" > Time< / td >
< / tr >
< / tbody >
< / table >
< p >
Second measurement (< code > mat/data_015.mat< / code > file):
< / p >
< table border = "2" cellspacing = "0" cellpadding = "6" rules = "groups" frame = "hsides" >
< colgroup >
< col class = "org-right" / >
< col class = "org-left" / >
< / colgroup >
< thead >
< tr >
< th scope = "col" class = "org-right" > Column< / th >
< th scope = "col" class = "org-left" > Signal< / th >
< / tr >
< / thead >
< tbody >
< tr >
< td class = "org-right" > 1< / td >
< td class = "org-left" > Amplifier 1 with DC option< / td >
< / tr >
< tr >
< td class = "org-right" > 2< / td >
< td class = "org-left" > Amplifier 2 with AC option< / td >
< / tr >
< tr >
< td class = "org-right" > 3< / td >
< td class = "org-left" > Time< / td >
< / tr >
< / tbody >
< / table >
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< div id = "orgde4e8ac" class = "figure" >
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< p > < img src = "./img/IMG_20190503_170936.jpg" alt = "IMG_20190503_170936.jpg" width = "500px" / >
< / p >
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< p > < span class = "figure-number" > Figure 22: < / span > Picture of the two voltages amplifiers< / p >
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< / div >
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< / div >
< / div >
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< div id = "outline-container-org137ca7d" class = "outline-3" >
< h3 id = "org137ca7d" > < span class = "section-number-3" > 5.2< / span > Load data< / h3 >
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< div class = "outline-text-3" id = "text-5-2" >
< p >
We load the data of the z axis of two geophones.
< / p >
< div class = "org-src-container" >
< pre class = "src src-matlab" > meas14 = load< span class = "org-rainbow-delimiters-depth-1" > (< / span > < span class = "org-string" > 'mat/data_014.mat', 'data'< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ; meas14 = meas14.data;
meas15 = load< span class = "org-rainbow-delimiters-depth-1" > (< / span > < span class = "org-string" > 'mat/data_015.mat', 'data'< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ; meas15 = meas15.data;
< / pre >
< / div >
< / div >
< / div >
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< div id = "outline-container-orgce0337d" class = "outline-3" >
< h3 id = "orgce0337d" > < span class = "section-number-3" > 5.3< / span > Time Domain< / h3 >
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< div class = "outline-text-3" id = "text-5-3" >
< p >
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The signals are shown on figure < a href = "#org24fe5db" > 23< / a > .
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< / p >
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< div id = "org24fe5db" class = "figure" >
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< p > < img src = "figs/ac_dc_option_time.png" alt = "ac_dc_option_time.png" / >
< / p >
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< p > < span class = "figure-number" > Figure 23: < / span > Comparison of the signals going through the Voltage amplifiers< / p >
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< / div >
< / div >
< / div >
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< div id = "outline-container-org1ca91db" class = "outline-3" >
< h3 id = "org1ca91db" > < span class = "section-number-3" > 5.4< / span > Frequency Domain< / h3 >
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< div class = "outline-text-3" id = "text-5-4" >
< p >
We first compute some parameters that will be used for the PSD computation.
< / p >
< div class = "org-src-container" >
< pre class = "src src-matlab" > dt = meas14< span class = "org-rainbow-delimiters-depth-1" > (< / span > < span class = "org-highlight-numbers-number" > 2< / span > , < span class = "org-highlight-numbers-number" > 3< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > < span class = "org-type" > -< / span > meas14< span class = "org-rainbow-delimiters-depth-1" > (< / span > < span class = "org-highlight-numbers-number" > 1< / span > , < span class = "org-highlight-numbers-number" > 3< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
Fs = < span class = "org-highlight-numbers-number" > 1< / span > < span class = "org-type" > /< / span > dt; < span class = "org-comment" > % [Hz]< / span >
win = hanning< span class = "org-rainbow-delimiters-depth-1" > (< / span > ceil< span class = "org-rainbow-delimiters-depth-2" > (< / span > < span class = "org-highlight-numbers-number" > 10< / span > < span class = "org-type" > *< / span > Fs< span class = "org-rainbow-delimiters-depth-2" > )< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
< / pre >
< / div >
< p >
Then we compute the Power Spectral Density using < code > pwelch< / code > function.
< / p >
< div class = "org-src-container" >
< pre class = "src src-matlab" > < span class = "org-rainbow-delimiters-depth-1" > [< / span > pxamp1ac, f< span class = "org-rainbow-delimiters-depth-1" > ]< / span > = pwelch< span class = "org-rainbow-delimiters-depth-1" > (< / span > meas14< span class = "org-rainbow-delimiters-depth-2" > (< / span > < span class = "org-type" > :< / span > , < span class = "org-highlight-numbers-number" > 1< / span > < span class = "org-rainbow-delimiters-depth-2" > )< / span > , win, < span class = "org-rainbow-delimiters-depth-2" > []< / span > , < span class = "org-rainbow-delimiters-depth-2" > []< / span > , Fs< span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
< span class = "org-rainbow-delimiters-depth-1" > [< / span > pxamp2dc, < span class = "org-type" > ~< / span > < span class = "org-rainbow-delimiters-depth-1" > ]< / span > = pwelch< span class = "org-rainbow-delimiters-depth-1" > (< / span > meas14< span class = "org-rainbow-delimiters-depth-2" > (< / span > < span class = "org-type" > :< / span > , < span class = "org-highlight-numbers-number" > 2< / span > < span class = "org-rainbow-delimiters-depth-2" > )< / span > , win, < span class = "org-rainbow-delimiters-depth-2" > []< / span > , < span class = "org-rainbow-delimiters-depth-2" > []< / span > , Fs< span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
< span class = "org-rainbow-delimiters-depth-1" > [< / span > pxamp1dc, < span class = "org-type" > ~< / span > < span class = "org-rainbow-delimiters-depth-1" > ]< / span > = pwelch< span class = "org-rainbow-delimiters-depth-1" > (< / span > meas15< span class = "org-rainbow-delimiters-depth-2" > (< / span > < span class = "org-type" > :< / span > , < span class = "org-highlight-numbers-number" > 1< / span > < span class = "org-rainbow-delimiters-depth-2" > )< / span > , win, < span class = "org-rainbow-delimiters-depth-2" > []< / span > , < span class = "org-rainbow-delimiters-depth-2" > []< / span > , Fs< span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
< span class = "org-rainbow-delimiters-depth-1" > [< / span > pxamp2ac, < span class = "org-type" > ~< / span > < span class = "org-rainbow-delimiters-depth-1" > ]< / span > = pwelch< span class = "org-rainbow-delimiters-depth-1" > (< / span > meas15< span class = "org-rainbow-delimiters-depth-2" > (< / span > < span class = "org-type" > :< / span > , < span class = "org-highlight-numbers-number" > 2< / span > < span class = "org-rainbow-delimiters-depth-2" > )< / span > , win, < span class = "org-rainbow-delimiters-depth-2" > []< / span > , < span class = "org-rainbow-delimiters-depth-2" > []< / span > , Fs< span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
< / pre >
< / div >
< p >
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The ASD of the signals are compare on figure < a href = "#orgf2f8049" > 24< / a > .
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< / p >
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< div id = "orgf2f8049" class = "figure" >
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< p > < img src = "figs/ac_dc_option_asd.png" alt = "ac_dc_option_asd.png" / >
< / p >
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< p > < span class = "figure-number" > Figure 24: < / span > Amplitude Spectral Density of the measured signals< / p >
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< / div >
< / div >
< / div >
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< div id = "outline-container-orge0411ce" class = "outline-3" >
< h3 id = "orge0411ce" > < span class = "section-number-3" > 5.5< / span > Conclusion< / h3 >
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< div class = "outline-text-3" id = "text-5-5" >
< div class = "important" >
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< ul class = "org-ul" >
< li > The voltage amplifiers include some very sharp high pass filters at 1.5Hz (maybe 4th order)< / li >
< li > There is a DC offset on the time domain signal because the DC-offset knob was not set to zero< / li >
< / ul >
< / div >
< / div >
< / div >
< / div >
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< div id = "outline-container-org6d3a86e" class = "outline-2" >
< h2 id = "org6d3a86e" > < span class = "section-number-2" > 6< / span > Transfer function of the Low Pass Filter< / h2 >
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< div class = "outline-text-2" id = "text-6" >
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< p >
The computation files for this section are accessible < a href = "data/low_pass_filter_measurements.zip" > here< / a > .
< / p >
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< / div >
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< div id = "outline-container-org50dfe76" class = "outline-3" >
< h3 id = "org50dfe76" > < span class = "section-number-3" > 6.1< / span > First LPF with a Cut-off frequency of 160Hz< / h3 >
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< div class = "outline-text-3" id = "text-6-1" >
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< / div >
< div id = "outline-container-orge61a68e" class = "outline-4" >
< h4 id = "orge61a68e" > < span class = "section-number-4" > 6.1.1< / span > Measurement Description< / h4 >
< div class = "outline-text-4" id = "text-6-1-1" >
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< p >
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< b > Goal< / b > :
< / p >
< ul class = "org-ul" >
< li > Measure the Low Pass Filter Transfer Function< / li >
< / ul >
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< p >
The values of the components are:
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< / p >
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\begin{aligned}
R & = 1k\Omega \\
C & = 1\mu F
\end{aligned}
< p >
Which makes a cut-off frequency of \(f_c = \frac{1}{RC} = 1000 rad/s = 160Hz\).
< / p >
< div class = "org-src-container" >
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< pre class = "src src-latex" id = "org1bfb14a" > < span class = "org-font-latex-sedate" > < span class = "org-keyword" > \begin< / span > < / span > {< span class = "org-function-name" > tikzpicture< / span > }
< span class = "org-font-latex-sedate" > \draw< / span > (0,2)
to [R=< span class = "org-font-latex-sedate" > < span class = "org-font-latex-math" > \(R\)< / span > < / span > ] ++(2,0) node[circ]
to ++(2,0)
++(-2,0)
to [C=< span class = "org-font-latex-sedate" > < span class = "org-font-latex-math" > \(C\)< / span > < / span > ] ++(0,-2) node[circ]
++(-2,0)
to ++(2,0)
to ++(2,0)
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< span class = "org-font-latex-sedate" > < span class = "org-keyword" > \end< / span > < / span > {< span class = "org-function-name" > tikzpicture< / span > }
< / pre >
< / div >
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< div id = "orge941987" class = "figure" >
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< p > < img src = "figs/lpf.png" alt = "lpf.png" / >
< / p >
< p > < span class = "figure-number" > Figure 25: < / span > Schematic of the Low Pass Filter used< / p >
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< / div >
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< p >
< b > Setup< / b > :
< / p >
< ul class = "org-ul" >
< li > We are measuring the signal from from Geophone with a BNC T< / li >
< li > On part goes to column 1 through the LPF< / li >
< li > The other part goes to column 2 without the LPF< / li >
< / ul >
< p >
< b > Measurements< / b > :
< code > mat/data_018.mat< / code > :
< / p >
< table border = "2" cellspacing = "0" cellpadding = "6" rules = "groups" frame = "hsides" >
< colgroup >
< col class = "org-right" / >
< col class = "org-left" / >
< / colgroup >
< thead >
< tr >
< th scope = "col" class = "org-right" > Column< / th >
< th scope = "col" class = "org-left" > Signal< / th >
< / tr >
< / thead >
< tbody >
< tr >
< td class = "org-right" > 1< / td >
< td class = "org-left" > Amplifier 1 with LPF< / td >
< / tr >
< tr >
< td class = "org-right" > 2< / td >
< td class = "org-left" > Amplifier 2< / td >
< / tr >
< tr >
< td class = "org-right" > 3< / td >
< td class = "org-left" > Time< / td >
< / tr >
< / tbody >
< / table >
< / div >
< / div >
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< div id = "outline-container-org229c82b" class = "outline-4" >
< h4 id = "org229c82b" > < span class = "section-number-4" > 6.1.2< / span > Load data< / h4 >
< div class = "outline-text-4" id = "text-6-1-2" >
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< p >
We load the data of the z axis of two geophones.
< / p >
< div class = "org-src-container" >
< pre class = "src src-matlab" > data = load< span class = "org-rainbow-delimiters-depth-1" > (< / span > < span class = "org-string" > 'mat/data_018.mat', 'data'< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ; data = data.data;
< / pre >
< / div >
< / div >
< / div >
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< div id = "outline-container-org78a38da" class = "outline-4" >
< h4 id = "org78a38da" > < span class = "section-number-4" > 6.1.3< / span > Transfer function of the LPF< / h4 >
< div class = "outline-text-4" id = "text-6-1-3" >
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< p >
We compute the transfer function from the signal without the LPF to the signal measured with the LPF.
< / p >
< div class = "org-src-container" >
< pre class = "src src-matlab" > dt = data< span class = "org-rainbow-delimiters-depth-1" > (< / span > < span class = "org-highlight-numbers-number" > 2< / span > , < span class = "org-highlight-numbers-number" > 3< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > < span class = "org-type" > -< / span > data< span class = "org-rainbow-delimiters-depth-1" > (< / span > < span class = "org-highlight-numbers-number" > 1< / span > , < span class = "org-highlight-numbers-number" > 3< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
Fs = < span class = "org-highlight-numbers-number" > 1< / span > < span class = "org-type" > /< / span > dt; < span class = "org-comment" > % [Hz]< / span >
win = hanning< span class = "org-rainbow-delimiters-depth-1" > (< / span > ceil< span class = "org-rainbow-delimiters-depth-2" > (< / span > < span class = "org-highlight-numbers-number" > 10< / span > < span class = "org-type" > *< / span > Fs< span class = "org-rainbow-delimiters-depth-2" > )< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
< / pre >
< / div >
< div class = "org-src-container" >
< pre class = "src src-matlab" > < span class = "org-rainbow-delimiters-depth-1" > [< / span > Glpf, f< span class = "org-rainbow-delimiters-depth-1" > ]< / span > = tfestimate< span class = "org-rainbow-delimiters-depth-1" > (< / span > data< span class = "org-rainbow-delimiters-depth-2" > (< / span > < span class = "org-type" > :< / span > , < span class = "org-highlight-numbers-number" > 2< / span > < span class = "org-rainbow-delimiters-depth-2" > )< / span > , data< span class = "org-rainbow-delimiters-depth-2" > (< / span > < span class = "org-type" > :< / span > , < span class = "org-highlight-numbers-number" > 1< / span > < span class = "org-rainbow-delimiters-depth-2" > )< / span > , win, < span class = "org-rainbow-delimiters-depth-2" > []< / span > , < span class = "org-rainbow-delimiters-depth-2" > []< / span > , Fs< span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
< / pre >
< / div >
< p >
We compare this transfer function with a transfer function corresponding to an ideal first order LPF with a cut-off frequency of \(1000rad/s\).
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We obtain the result on figure < a href = "#org9c29fd5" > 26< / a > .
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< / p >
< div class = "org-src-container" >
< pre class = "src src-matlab" > Gth = < span class = "org-highlight-numbers-number" > 1< / span > < span class = "org-type" > /< / span > < span class = "org-rainbow-delimiters-depth-1" > (< / span > < span class = "org-highlight-numbers-number" > 1< / span > < span class = "org-type" > +< / span > s< span class = "org-type" > /< / span > < span class = "org-highlight-numbers-number" > 1000< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span >
< / pre >
< / div >
< div class = "org-src-container" >
< pre class = "src src-matlab" > < span class = "org-type" > figure< / span > ;
ax1 = subplot< span class = "org-rainbow-delimiters-depth-1" > (< / span > < span class = "org-highlight-numbers-number" > 2< / span > , < span class = "org-highlight-numbers-number" > 1< / span > , < span class = "org-highlight-numbers-number" > 1< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
hold on;
plot< span class = "org-rainbow-delimiters-depth-1" > (< / span > f, abs< span class = "org-rainbow-delimiters-depth-2" > (< / span > Glpf< span class = "org-rainbow-delimiters-depth-2" > )< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
plot< span class = "org-rainbow-delimiters-depth-1" > (< / span > f, abs< span class = "org-rainbow-delimiters-depth-2" > (< / span > squeeze< span class = "org-rainbow-delimiters-depth-3" > (< / span > freqresp< span class = "org-rainbow-delimiters-depth-4" > (< / span > Gth, f, < span class = "org-string" > 'Hz'< / span > < span class = "org-rainbow-delimiters-depth-4" > )< / span > < span class = "org-rainbow-delimiters-depth-3" > )< / span > < span class = "org-rainbow-delimiters-depth-2" > )< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
hold off;
< span class = "org-type" > set< / span > < span class = "org-rainbow-delimiters-depth-1" > (< / span > < span class = "org-variable-name" > gca< / span > , < span class = "org-string" > 'xscale', 'log'< / span > < span class = "org-string" > < span class = "org-rainbow-delimiters-depth-1" > )< / span > < / span > < span class = "org-string" > ; set< / span > < span class = "org-string" > < span class = "org-rainbow-delimiters-depth-1" > (< / span > < / span > < span class = "org-string" > gca, 'yscale', 'log'< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
< span class = "org-type" > set< / span > < span class = "org-rainbow-delimiters-depth-1" > (< / span > < span class = "org-variable-name" > gca< / span > , < span class = "org-string" > 'XTickLabel'< / span > ,< span class = "org-rainbow-delimiters-depth-2" > []< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
ylabel< span class = "org-rainbow-delimiters-depth-1" > (< / span > < span class = "org-string" > 'Magnitude'< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
ax2 = subplot< span class = "org-rainbow-delimiters-depth-1" > (< / span > < span class = "org-highlight-numbers-number" > 2< / span > , < span class = "org-highlight-numbers-number" > 1< / span > , < span class = "org-highlight-numbers-number" > 2< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
hold on;
plot< span class = "org-rainbow-delimiters-depth-1" > (< / span > f, mod< span class = "org-rainbow-delimiters-depth-2" > (< / span > < span class = "org-highlight-numbers-number" > 180< / span > < span class = "org-type" > +< / span > < span class = "org-highlight-numbers-number" > 180< / span > < span class = "org-type" > /< / span > < span class = "org-constant" > pi< / span > < span class = "org-type" > *< / span > phase< span class = "org-rainbow-delimiters-depth-3" > (< / span > Glpf< span class = "org-rainbow-delimiters-depth-3" > )< / span > , < span class = "org-highlight-numbers-number" > 360< / span > < span class = "org-rainbow-delimiters-depth-2" > )< / span > < span class = "org-type" > -< / span > < span class = "org-highlight-numbers-number" > 180< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
plot< span class = "org-rainbow-delimiters-depth-1" > (< / span > f, < span class = "org-highlight-numbers-number" > 180< / span > < span class = "org-type" > /< / span > < span class = "org-constant" > pi< / span > < span class = "org-type" > *< / span > unwrap< span class = "org-rainbow-delimiters-depth-2" > (< / span > angle< span class = "org-rainbow-delimiters-depth-3" > (< / span > squeeze< span class = "org-rainbow-delimiters-depth-4" > (< / span > freqresp< span class = "org-rainbow-delimiters-depth-5" > (< / span > Gth, f, < span class = "org-string" > 'Hz'< / span > < span class = "org-rainbow-delimiters-depth-5" > )< / span > < span class = "org-rainbow-delimiters-depth-4" > )< / span > < span class = "org-rainbow-delimiters-depth-3" > )< / span > < span class = "org-rainbow-delimiters-depth-2" > )< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
hold off;
< span class = "org-type" > set< / span > < span class = "org-rainbow-delimiters-depth-1" > (< / span > < span class = "org-variable-name" > gca< / span > , < span class = "org-string" > 'xscale', 'log'< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
ylim< span class = "org-rainbow-delimiters-depth-1" > (< / span > < span class = "org-rainbow-delimiters-depth-2" > [< / span > < span class = "org-type" > -< / span > < span class = "org-highlight-numbers-number" > 180< / span > , < span class = "org-highlight-numbers-number" > 180< / span > < span class = "org-rainbow-delimiters-depth-2" > ]< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
yticks< span class = "org-rainbow-delimiters-depth-1" > (< / span > < span class = "org-rainbow-delimiters-depth-2" > [< / span > < span class = "org-type" > -< / span > < span class = "org-highlight-numbers-number" > 180< / span > , < span class = "org-type" > -< / span > < span class = "org-highlight-numbers-number" > 90< / span > , < span class = "org-highlight-numbers-number" > 0< / span > , < span class = "org-highlight-numbers-number" > 90< / span > , < span class = "org-highlight-numbers-number" > 180< / span > < span class = "org-rainbow-delimiters-depth-2" > ]< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
xlabel< span class = "org-rainbow-delimiters-depth-1" > (< / span > < span class = "org-string" > 'Frequency < / span > < span class = "org-string" > < span class = "org-rainbow-delimiters-depth-2" > [< / span > < / span > < span class = "org-string" > Hz< / span > < span class = "org-string" > < span class = "org-rainbow-delimiters-depth-2" > ]< / span > < / span > < span class = "org-string" > '< / span > < span class = "org-string" > < span class = "org-rainbow-delimiters-depth-1" > )< / span > < / span > < span class = "org-string" > ; ylabel< / span > < span class = "org-string" > < span class = "org-rainbow-delimiters-depth-1" > (< / span > < / span > < span class = "org-string" > 'Phase'< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
linkaxes< span class = "org-rainbow-delimiters-depth-1" > (< / span > < span class = "org-rainbow-delimiters-depth-2" > [< / span > ax1,ax2< span class = "org-rainbow-delimiters-depth-2" > ]< / span > ,< span class = "org-string" > 'x'< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
xlim< span class = "org-rainbow-delimiters-depth-1" > (< / span > < span class = "org-rainbow-delimiters-depth-2" > [< / span > < span class = "org-highlight-numbers-number" > 1< / span > , < span class = "org-highlight-numbers-number" > 500< / span > < span class = "org-rainbow-delimiters-depth-2" > ]< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
< / pre >
< / div >
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< div id = "org9c29fd5" class = "figure" >
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< p > < img src = "figs/Glpf_bode.png" alt = "Glpf_bode.png" / >
< / p >
< p > < span class = "figure-number" > Figure 26: < / span > Bode Diagram of the measured Low Pass filter and the theoritical one< / p >
< / div >
< / div >
< / div >
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< div id = "outline-container-org59dee72" class = "outline-4" >
< h4 id = "org59dee72" > < span class = "section-number-4" > 6.1.4< / span > Conclusion< / h4 >
< div class = "outline-text-4" id = "text-6-1-4" >
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< div class = "important" >
< p >
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 \(1kHz\).
< / p >
< / div >
< / div >
< / div >
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< / div >
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< div id = "outline-container-org8b09702" class = "outline-3" >
< h3 id = "org8b09702" > < span class = "section-number-3" > 6.2< / span > Second LPF with a Cut-off frequency of 1000Hz< / h3 >
< div class = "outline-text-3" id = "text-6-2" >
< / div >
< div id = "outline-container-orged36cb1" class = "outline-4" >
< h4 id = "orged36cb1" > < span class = "section-number-4" > 6.2.1< / span > Measurement description< / h4 >
< div class = "outline-text-4" id = "text-6-2-1" >
2019-05-07 13:51:35 +02:00
< p >
This time, the value are
< / p >
\begin{aligned}
R & = 1k\Omega \\
C & = 150nF
\end{aligned}
< p >
Which makes a low pass filter with a cut-off frequency of \(f_c = 1060Hz\).
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2019-05-02 14:09:20 +02:00
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2019-05-02 14:06:23 +02:00
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2019-05-07 18:30:04 +02:00
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< h4 id = "org7e593d2" > < span class = "section-number-4" > 6.2.2< / span > Load data< / h4 >
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< p >
We load the data of the z axis of two geophones.
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< pre class = "src src-matlab" > data = load< span class = "org-rainbow-delimiters-depth-1" > (< / span > 'mat< span class = "org-type" > /< / span > data_019.mat', < span class = "org-string" > 'data'< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ; data = data.data;
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< h4 id = "org2e7d91e" > < span class = "section-number-4" > 6.2.3< / span > Transfer function of the LPF< / h4 >
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< p >
We compute the transfer function from the signal without the LPF to the signal measured with the LPF.
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< pre class = "src src-matlab" > dt = data< span class = "org-rainbow-delimiters-depth-1" > (< / span > < span class = "org-highlight-numbers-number" > 2< / span > , < span class = "org-highlight-numbers-number" > 3< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > < span class = "org-type" > -< / span > data< span class = "org-rainbow-delimiters-depth-1" > (< / span > < span class = "org-highlight-numbers-number" > 1< / span > , < span class = "org-highlight-numbers-number" > 3< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
Fs = < span class = "org-highlight-numbers-number" > 1< / span > < span class = "org-type" > /< / span > dt; < span class = "org-comment" > % [Hz]< / span >
win = hanning< span class = "org-rainbow-delimiters-depth-1" > (< / span > ceil< span class = "org-rainbow-delimiters-depth-2" > (< / span > < span class = "org-highlight-numbers-number" > 10< / span > < span class = "org-type" > *< / span > Fs< span class = "org-rainbow-delimiters-depth-2" > )< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
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< pre class = "src src-matlab" > < span class = "org-rainbow-delimiters-depth-1" > [< / span > Glpf, f< span class = "org-rainbow-delimiters-depth-1" > ]< / span > = tfestimate< span class = "org-rainbow-delimiters-depth-1" > (< / span > data< span class = "org-rainbow-delimiters-depth-2" > (< / span > < span class = "org-type" > :< / span > , < span class = "org-highlight-numbers-number" > 2< / span > < span class = "org-rainbow-delimiters-depth-2" > )< / span > , data< span class = "org-rainbow-delimiters-depth-2" > (< / span > < span class = "org-type" > :< / span > , < span class = "org-highlight-numbers-number" > 1< / span > < span class = "org-rainbow-delimiters-depth-2" > )< / span > , win, < span class = "org-rainbow-delimiters-depth-2" > []< / span > , < span class = "org-rainbow-delimiters-depth-2" > []< / span > , Fs< span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
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< p >
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 < a href = "#org60b202b" > 27< / a > .
< / p >
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< pre class = "src src-matlab" > Gth = < span class = "org-highlight-numbers-number" > 1< / span > < span class = "org-type" > /< / span > < span class = "org-rainbow-delimiters-depth-1" > (< / span > < span class = "org-highlight-numbers-number" > 1< / span > < span class = "org-type" > +< / span > s< span class = "org-type" > /< / span > < span class = "org-highlight-numbers-number" > 1060< / span > < span class = "org-type" > /< / span > < span class = "org-highlight-numbers-number" > 2< / span > < span class = "org-type" > /< / span > < span class = "org-constant" > pi< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
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< pre class = "src src-matlab" > < span class = "org-type" > figure< / span > ;
ax1 = subplot< span class = "org-rainbow-delimiters-depth-1" > (< / span > < span class = "org-highlight-numbers-number" > 2< / span > , < span class = "org-highlight-numbers-number" > 1< / span > , < span class = "org-highlight-numbers-number" > 1< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
hold on;
plot< span class = "org-rainbow-delimiters-depth-1" > (< / span > f, abs< span class = "org-rainbow-delimiters-depth-2" > (< / span > Glpf< span class = "org-rainbow-delimiters-depth-2" > )< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
plot< span class = "org-rainbow-delimiters-depth-1" > (< / span > f, abs< span class = "org-rainbow-delimiters-depth-2" > (< / span > squeeze< span class = "org-rainbow-delimiters-depth-3" > (< / span > freqresp< span class = "org-rainbow-delimiters-depth-4" > (< / span > Gth, f, < span class = "org-string" > 'Hz'< / span > < span class = "org-rainbow-delimiters-depth-4" > )< / span > < span class = "org-rainbow-delimiters-depth-3" > )< / span > < span class = "org-rainbow-delimiters-depth-2" > )< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
hold off;
< span class = "org-type" > set< / span > < span class = "org-rainbow-delimiters-depth-1" > (< / span > < span class = "org-variable-name" > gca< / span > , < span class = "org-string" > 'xscale', 'log'< / span > < span class = "org-string" > < span class = "org-rainbow-delimiters-depth-1" > )< / span > < / span > < span class = "org-string" > ; set< / span > < span class = "org-string" > < span class = "org-rainbow-delimiters-depth-1" > (< / span > < / span > < span class = "org-string" > gca, 'yscale', 'log'< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
< span class = "org-type" > set< / span > < span class = "org-rainbow-delimiters-depth-1" > (< / span > < span class = "org-variable-name" > gca< / span > , < span class = "org-string" > 'XTickLabel'< / span > ,< span class = "org-rainbow-delimiters-depth-2" > []< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
ylabel< span class = "org-rainbow-delimiters-depth-1" > (< / span > < span class = "org-string" > 'Magnitude'< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
ax2 = subplot< span class = "org-rainbow-delimiters-depth-1" > (< / span > < span class = "org-highlight-numbers-number" > 2< / span > , < span class = "org-highlight-numbers-number" > 1< / span > , < span class = "org-highlight-numbers-number" > 2< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
hold on;
plot< span class = "org-rainbow-delimiters-depth-1" > (< / span > f, mod< span class = "org-rainbow-delimiters-depth-2" > (< / span > < span class = "org-highlight-numbers-number" > 180< / span > < span class = "org-type" > +< / span > < span class = "org-highlight-numbers-number" > 180< / span > < span class = "org-type" > /< / span > < span class = "org-constant" > pi< / span > < span class = "org-type" > *< / span > phase< span class = "org-rainbow-delimiters-depth-3" > (< / span > Glpf< span class = "org-rainbow-delimiters-depth-3" > )< / span > , < span class = "org-highlight-numbers-number" > 360< / span > < span class = "org-rainbow-delimiters-depth-2" > )< / span > < span class = "org-type" > -< / span > < span class = "org-highlight-numbers-number" > 180< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
plot< span class = "org-rainbow-delimiters-depth-1" > (< / span > f, < span class = "org-highlight-numbers-number" > 180< / span > < span class = "org-type" > /< / span > < span class = "org-constant" > pi< / span > < span class = "org-type" > *< / span > unwrap< span class = "org-rainbow-delimiters-depth-2" > (< / span > angle< span class = "org-rainbow-delimiters-depth-3" > (< / span > squeeze< span class = "org-rainbow-delimiters-depth-4" > (< / span > freqresp< span class = "org-rainbow-delimiters-depth-5" > (< / span > Gth, f, < span class = "org-string" > 'Hz'< / span > < span class = "org-rainbow-delimiters-depth-5" > )< / span > < span class = "org-rainbow-delimiters-depth-4" > )< / span > < span class = "org-rainbow-delimiters-depth-3" > )< / span > < span class = "org-rainbow-delimiters-depth-2" > )< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
hold off;
< span class = "org-type" > set< / span > < span class = "org-rainbow-delimiters-depth-1" > (< / span > < span class = "org-variable-name" > gca< / span > , < span class = "org-string" > 'xscale', 'log'< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
ylim< span class = "org-rainbow-delimiters-depth-1" > (< / span > < span class = "org-rainbow-delimiters-depth-2" > [< / span > < span class = "org-type" > -< / span > < span class = "org-highlight-numbers-number" > 180< / span > , < span class = "org-highlight-numbers-number" > 180< / span > < span class = "org-rainbow-delimiters-depth-2" > ]< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
yticks< span class = "org-rainbow-delimiters-depth-1" > (< / span > < span class = "org-rainbow-delimiters-depth-2" > [< / span > < span class = "org-type" > -< / span > < span class = "org-highlight-numbers-number" > 180< / span > , < span class = "org-type" > -< / span > < span class = "org-highlight-numbers-number" > 90< / span > , < span class = "org-highlight-numbers-number" > 0< / span > , < span class = "org-highlight-numbers-number" > 90< / span > , < span class = "org-highlight-numbers-number" > 180< / span > < span class = "org-rainbow-delimiters-depth-2" > ]< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
xlabel< span class = "org-rainbow-delimiters-depth-1" > (< / span > < span class = "org-string" > 'Frequency < / span > < span class = "org-string" > < span class = "org-rainbow-delimiters-depth-2" > [< / span > < / span > < span class = "org-string" > Hz< / span > < span class = "org-string" > < span class = "org-rainbow-delimiters-depth-2" > ]< / span > < / span > < span class = "org-string" > '< / span > < span class = "org-string" > < span class = "org-rainbow-delimiters-depth-1" > )< / span > < / span > < span class = "org-string" > ; ylabel< / span > < span class = "org-string" > < span class = "org-rainbow-delimiters-depth-1" > (< / span > < / span > < span class = "org-string" > 'Phase'< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
linkaxes< span class = "org-rainbow-delimiters-depth-1" > (< / span > < span class = "org-rainbow-delimiters-depth-2" > [< / span > ax1,ax2< span class = "org-rainbow-delimiters-depth-2" > ]< / span > ,< span class = "org-string" > 'x'< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
xlim< span class = "org-rainbow-delimiters-depth-1" > (< / span > < span class = "org-rainbow-delimiters-depth-2" > [< / span > < span class = "org-highlight-numbers-number" > 1< / span > , < span class = "org-highlight-numbers-number" > 500< / span > < span class = "org-rainbow-delimiters-depth-2" > ]< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
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< div id = "org60b202b" class = "figure" >
< p > < img src = "figs/Glpf_bode_bis.png" alt = "Glpf_bode_bis.png" / >
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< p > < span class = "figure-number" > Figure 27: < / span > Bode Diagram of the measured Low Pass filter and the theoritical one< / p >
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< h4 id = "org04a0d6e" > < span class = "section-number-4" > 6.2.4< / span > Conclusion< / h4 >
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< p >
The added LPF has the expected behavior.
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2019-05-02 14:06:23 +02:00
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< div id = "postamble" class = "status" >
< p class = "author" > Author: Thomas Dehaeze< / p >
2019-05-07 18:30:04 +02:00
< p class = "date" > Created: 2019-05-07 mar. 16:56< / p >
2019-05-02 14:06:23 +02:00
< p class = "validation" > < a href = "http://validator.w3.org/check?uri=referer" > Validate< / a > < / p >
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