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< / head >
< body >
< div id = "content" >
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< h1 class = "title" > Measurements On the Slip-Ring< / 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 = "#org2781a7a" > 1. Effect of the Slip-Ring on the signal< / a >
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< ul >
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< li > < a href = "#org3dea630" > 1.1. Experimental Setup< / a > < / li >
< li > < a href = "#orgf0d1f5d" > 1.2. Load data< / a > < / li >
< li > < a href = "#org2b5c36e" > 1.3. Analysis - Time Domain< / a > < / li >
< li > < a href = "#org22f0fdc" > 1.4. Analysis - Frequency Domain< / a > < / li >
< li > < a href = "#org9abd380" > 1.5. Conclusion< / a > < / li >
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< / ul >
< / li >
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< li > < a href = "#org6002a8c" > 2. Effect of the rotation of the Slip-Ring< / a >
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< ul >
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< li > < a href = "#orgedc9c11" > 2.1. Measurement Description< / a > < / li >
< li > < a href = "#org5e95fbe" > 2.2. Load data< / a > < / li >
< li > < a href = "#org7a8e8fc" > 2.3. Analysis< / a > < / li >
< li > < a href = "#org24db8f6" > 2.4. Conclusion< / a > < / li >
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< / ul >
< / li >
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< li > < a href = "#org21fc4d2" > 3. Measure of the noise induced by the Slip-Ring< / a >
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< ul >
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< li > < a href = "#org901cf1f" > 3.1. Measurement Description< / a > < / li >
< li > < a href = "#org3aa7c6d" > 3.2. Load data< / a > < / li >
< li > < a href = "#org22f6115" > 3.3. Time Domain< / a > < / li >
< li > < a href = "#orgd6cbe96" > 3.4. Frequency Domain< / a > < / li >
< li > < a href = "#orgbb89292" > 3.5. Conclusion< / a > < / li >
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< / ul >
< / li >
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< li > < a href = "#orgf77f778" > 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 = "#org57fc212" > 4.1. First Measurement without LPF< / a >
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< ul >
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< li > < a href = "#org4e633db" > 4.1.1. Measurement Description< / a > < / li >
< li > < a href = "#orge652945" > 4.1.2. Load data< / a > < / li >
< li > < a href = "#orgfdc44bc" > 4.1.3. Time Domain< / a > < / li >
< li > < a href = "#org1747240" > 4.1.4. Frequency Domain< / a > < / li >
< li > < a href = "#org2082a3e" > 4.1.5. Conclusion< / a > < / li >
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< / ul >
< / li >
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< li > < a href = "#org0d10493" > 4.2. Measurement using an oscilloscope< / a >
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< ul >
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< li > < a href = "#org84a4af9" > 4.2.1. Measurement Setup< / a > < / li >
< li > < a href = "#orgba2e6ff" > 4.2.2. Observations< / a > < / li >
< li > < a href = "#org729aaf2" > 4.2.3. Conclusion< / a > < / li >
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< / ul >
< / li >
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< li > < a href = "#orge6ed6b4" > 4.3. New measurements with a LPF before the Voltage Amplifiers< / a >
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< ul >
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< li > < a href = "#org4501bcc" > 4.3.1. Setup description< / a > < / li >
< li > < a href = "#org7f64f45" > 4.3.2. Load data< / a > < / li >
< li > < a href = "#org168648f" > 4.3.3. Time Domain< / a > < / li >
< li > < a href = "#org18b3f68" > 4.3.4. Frequency Domain< / a > < / li >
< li > < a href = "#org5c54c76" > 4.3.5. Comparison of with and without LPF< / a > < / li >
< li > < a href = "#org44b238b" > 4.3.6. Conclusion< / a > < / li >
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< / ul >
< / li >
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< / ul >
< / li >
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< / ul >
< / div >
< / div >
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< div id = "outline-container-org2781a7a" class = "outline-2" >
< h2 id = "org2781a7a" > < span class = "section-number-2" > 1< / span > Effect of the Slip-Ring on the signal< / h2 >
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< div class = "outline-text-2" id = "text-1" >
< p >
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< a id = "org8c43795" > < / a >
< / p >
< p >
The data and matlab files are accessible < a href = "data/meas_slip_ring_geophone.zip" > here< / a > .
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< / p >
< / div >
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< div id = "outline-container-org3dea630" class = "outline-3" >
< h3 id = "org3dea630" > < span class = "section-number-3" > 1.1< / span > Experimental Setup< / h3 >
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< div class = "outline-text-3" id = "text-1-1" >
< p >
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Two measurements are made with the control systems of all the stages turned OFF.
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< / p >
< p >
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One geophone is located on the marble while the other is located at the sample location (figure < a href = "#orgc4f61a9" > 1< / a > ).
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< / p >
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< div id = "orgc4f61a9" class = "figure" >
< p > < img src = "./img/IMG_20190430_112615.jpg" alt = "IMG_20190430_112615.jpg" width = "500px" / >
< / p >
< p > < span class = "figure-number" > Figure 1: < / span > Experimental Setup< / p >
< / div >
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< p >
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The two measurements are:
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< / p >
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< col class = "org-left" / >
< / colgroup >
< thead >
< tr >
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< th scope = "col" class = "org-left" > Measurement File< / th >
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< th scope = "col" class = "org-left" > Description< / th >
< / tr >
< / thead >
< tbody >
< tr >
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< td class = "org-left" > < code > meas_018.mat< / code > < / td >
< td class = "org-left" > Signal from the top geophone does not goes through the Slip-ring< / td >
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< / tr >
< tr >
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< td class = "org-left" > < code > meas_019.mat< / code > < / td >
< td class = "org-left" > Signal goes through the Slip-ring (as shown on the figure above)< / td >
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< / tr >
< / tbody >
< / table >
< p >
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Each of the measurement < code > mat< / code > file contains one < code > data< / code > array with 3 columns:
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< th scope = "col" class = "org-right" > Column number< / th >
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< th scope = "col" class = "org-left" > Description< / th >
< / tr >
< / thead >
< tbody >
< tr >
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< td class = "org-right" > 1< / td >
< td class = "org-left" > Geophone - Marble< / td >
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< / tr >
< tr >
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< td class = "org-right" > 2< / td >
< td class = "org-left" > Geophone - Sample< / td >
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< / tr >
< tr >
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< td class = "org-right" > 3< / td >
< td class = "org-left" > Time< / td >
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< div id = "outline-container-orgf0d1f5d" class = "outline-3" >
< h3 id = "orgf0d1f5d" > < 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 >
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< div class = "org-src-container" >
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< pre class = "src src-matlab" > d8 = 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 > ; d8 = d8.data;
d9 = 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 > ; d9 = d9.data;
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< / pre >
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< / div >
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< div id = "outline-container-org2b5c36e" class = "outline-3" >
< h3 id = "org2b5c36e" > < span class = "section-number-3" > 1.3< / span > Analysis - Time Domain< / h3 >
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< div class = "outline-text-3" id = "text-1-3" >
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< p >
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First, we compare the time domain signals for the two experiments (figure < a href = "#org49ef389" > 2< / a > ).
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< / p >
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< 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 > d9< span class = "org-rainbow-delimiters-depth-2" > (< / span > < span class = "org-type" > :< / span > , < span class = "org-highlight-numbers-number" > 3< / span > < span class = "org-rainbow-delimiters-depth-2" > )< / span > , d9< 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 > , < span class = "org-string" > 'DisplayName', 'Slip-Ring'< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
plot< span class = "org-rainbow-delimiters-depth-1" > (< / span > d8< span class = "org-rainbow-delimiters-depth-2" > (< / span > < span class = "org-type" > :< / span > , < span class = "org-highlight-numbers-number" > 3< / span > < span class = "org-rainbow-delimiters-depth-2" > )< / span > , d8< 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 > , < span class = "org-string" > 'DisplayName', 'Wire'< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
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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 > ;
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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" > 50< / 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 > ;
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< / pre >
< / div >
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< div id = "org49ef389" class = "figure" >
< p > < img src = "figs/slipring_time.png" alt = "slipring_time.png" / >
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< / p >
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< p > < span class = "figure-number" > Figure 2: < / span > Effect of the Slip-Ring on the measured signal - Time domain< / p >
< / div >
< / div >
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< / div >
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< div id = "outline-container-org22f0fdc" class = "outline-3" >
< h3 id = "org22f0fdc" > < span class = "section-number-3" > 1.4< / span > Analysis - Frequency Domain< / h3 >
< div class = "outline-text-3" id = "text-1-4" >
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< p >
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We then compute the Power Spectral Density of the two signals and we compare them (figure < a href = "#orgcc2d186" > 3< / a > ).
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< / p >
< div class = "org-src-container" >
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< pre class = "src src-matlab" > dt = d8< 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 > d8< 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;
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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 >
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< / div >
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< div class = "org-src-container" >
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< pre class = "src src-matlab" > < span class = "org-rainbow-delimiters-depth-1" > [< / span > pxx8, f< span class = "org-rainbow-delimiters-depth-1" > ]< / span > = pwelch< span class = "org-rainbow-delimiters-depth-1" > (< / span > d8< 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 > pxx9, < span class = "org-type" > ~< / span > < span class = "org-rainbow-delimiters-depth-1" > ]< / span > = pwelch< span class = "org-rainbow-delimiters-depth-1" > (< / span > d9< 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 > ;
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< / pre >
< / div >
< div class = "org-src-container" >
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< 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 > pxx9< span class = "org-rainbow-delimiters-depth-2" > )< / span > , < span class = "org-string" > 'DisplayName', 'Slip-Ring'< / 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 > pxx8< span class = "org-rainbow-delimiters-depth-2" > )< / span > , < span class = "org-string" > 'DisplayName', 'Wire'< / 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 > Amplitude Spectral Density $< 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 >
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 > ;
legend< span class = "org-rainbow-delimiters-depth-1" > (< / span > < span class = "org-string" > 'Location', 'southwest'< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
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< / pre >
< / div >
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< div id = "orgcc2d186" class = "figure" >
< p > < img src = "figs/slipring_asd.png" alt = "slipring_asd.png" / >
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< / p >
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< p > < span class = "figure-number" > Figure 3: < / span > Effect of the Slip-Ring on the measured signal - Frequency domain< / p >
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< / div >
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< / div >
< / div >
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< div id = "outline-container-org9abd380" class = "outline-3" >
< h3 id = "org9abd380" > < span class = "section-number-3" > 1.5< / span > Conclusion< / h3 >
< div class = "outline-text-3" id = "text-1-5" >
< div class = "important" >
< ul class = "org-ul" >
< li > Connecting the geophone through the Slip-Ring seems to induce a lot of noise.< / li >
< / ul >
< / div >
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< div class = "note" >
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< p >
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< b > Remaining questions to answer< / b > :
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< / p >
< ul class = "org-ul" >
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< li > Why is there a sharp peak at 300Hz?< / li >
< li > Why the use of the Slip-Ring does induce a noise?< / li >
< li > Can the capacitive/inductive properties of the wires in the Slip-ring does not play well with the geophone? (resonant RLC circuit)< / li >
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< / ul >
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< / div >
< / div >
< / div >
< / div >
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< div id = "outline-container-org6002a8c" class = "outline-2" >
< h2 id = "org6002a8c" > < span class = "section-number-2" > 2< / span > Effect of the rotation of the Slip-Ring< / h2 >
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< div class = "outline-text-2" id = "text-2" >
< p >
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< a id = "org953d721" > < / a >
< / p >
< p >
The data and matlab files are accessible < a href = "data/meas_effect_sr.zip" > here< / a > .
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< / p >
< / div >
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< div id = "outline-container-orgedc9c11" class = "outline-3" >
< h3 id = "orgedc9c11" > < 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 >
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Random Signal is generated by one DAC of the SpeedGoat.
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< / p >
< p >
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The signal going out of the DAC is split into two:
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< / p >
< ul class = "org-ul" >
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< 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 >
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< / ul >
< p >
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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.
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< / p >
< / div >
< / div >
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< div id = "outline-container-org5e95fbe" class = "outline-3" >
< h3 id = "org5e95fbe" > < span class = "section-number-3" > 2.2< / span > Load data< / h3 >
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< div class = "outline-text-3" id = "text-2-2" >
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< p >
We load the data of the z axis of two geophones.
< / p >
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< div class = "org-src-container" >
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< 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 > ;
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< / pre >
< / div >
< / div >
< / div >
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< div id = "outline-container-org7a8e8fc" class = "outline-3" >
< h3 id = "org7a8e8fc" > < span class = "section-number-3" > 2.3< / span > Analysis< / h3 >
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< div class = "outline-text-3" id = "text-2-3" >
< p >
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Let's first look at the signal produced by the DAC (figure < a href = "#org340bcf5" > 4< / a > ).
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< / p >
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< 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 = "org340bcf5" class = "figure" >
< p > < img src = "figs/random_signal.png" alt = "random_signal.png" / >
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< / p >
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< p > < span class = "figure-number" > Figure 4: < / span > Random signal produced by the DAC< / p >
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< / 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 = "#org7a50ceb" > 5< / a > ).
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< / p >
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< 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-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 > ;
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 > ;
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< / pre >
< / div >
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< div id = "org7a50ceb" class = "figure" >
< p > < img src = "figs/slipring_comp_signals.png" alt = "slipring_comp_signals.png" / >
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< / p >
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< p > < span class = "figure-number" > Figure 5: < / span > Alteration of the signal when the slip-ring is turning< / p >
< / div >
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< div class = "org-src-container" >
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< 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 > ;
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< / pre >
< / div >
< div class = "org-src-container" >
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< 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 > ;
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< / pre >
< / div >
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< div id = "org5986467" class = "figure" >
< p > < img src = "figs/psd_noise.png" alt = "psd_noise.png" / >
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< / p >
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< p > < span class = "figure-number" > Figure 6: < / span > ASD of the measured noise< / p >
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< / div >
< / div >
< / div >
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< div id = "outline-container-org24db8f6" class = "outline-3" >
< h3 id = "org24db8f6" > < span class = "section-number-3" > 2.4< / span > Conclusion< / h3 >
< div class = "outline-text-3" id = "text-2-4" >
< div class = "note" >
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< p >
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< b > Remaining questions< / b > :
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< / p >
< ul class = "org-ul" >
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< 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 >
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< / ul >
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< / div >
< / div >
< / div >
< / div >
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< div id = "outline-container-org21fc4d2" class = "outline-2" >
< h2 id = "org21fc4d2" > < 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" >
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< p >
< a id = "orgddb1e83" > < / a >
< / p >
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< 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-org901cf1f" class = "outline-3" >
< h3 id = "org901cf1f" > < 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 = "org1e3bbb6" class = "figure" >
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< p > < img src = "./img/VID_20190503_160831.gif" alt = "VID_20190503_160831.gif" / >
< / p >
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< p > < span class = "figure-number" > Figure 7: < / span > Slip-Ring rotating at 6rpm< / p >
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< / div >
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< div id = "orgc9e3e39" class = "figure" >
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< p > < img src = "./img/VID_20190503_161401.gif" alt = "VID_20190503_161401.gif" / >
< / p >
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< p > < span class = "figure-number" > Figure 8: < / span > Slip-Ring rotating at 60rpm< / p >
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< / div >
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< / div >
< / div >
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< div id = "outline-container-org3aa7c6d" class = "outline-3" >
< h3 id = "org3aa7c6d" > < 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-org22f6115" class = "outline-3" >
< h3 id = "org22f6115" > < 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 = "#org841f525" > 9< / a > ) and for the signal going through the slip-ring (figure < a href = "#orgdc9de69" > 10< / a > );
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< / p >
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< div id = "org841f525" 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 9: < / span > Direct measurement< / p >
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< / div >
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< div id = "orgdc9de69" 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 10: < / 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-orgd6cbe96" class = "outline-3" >
< h3 id = "orgd6cbe96" > < 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 = "#org70efd75" > 11< / 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 = "org70efd75" 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 11: < / 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-orgbb89292" class = "outline-3" >
< h3 id = "orgbb89292" > < 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-orgf77f778" class = "outline-2" >
< h2 id = "orgf77f778" > < 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" >
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< p >
< a id = "org34dee33" > < / a >
< / p >
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< 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-org57fc212" class = "outline-3" >
< h3 id = "org57fc212" > < 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-org4e633db" class = "outline-4" >
< h4 id = "org4e633db" > < 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-orge652945" class = "outline-4" >
< h4 id = "orge652945" > < 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-orgfdc44bc" class = "outline-4" >
< h4 id = "orgfdc44bc" > < 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 = "#org2b29bbb" > 12< / a > ) and when it is ON (figure < a href = "#org0c98be5" > 13< / a > ).
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< / p >
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< div id = "org2b29bbb" 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 12: < / 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 = "org0c98be5" 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 13: < / 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-org1747240" class = "outline-4" >
< h4 id = "org1747240" > < 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 = "#org6f7187f" > 14< / 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 = "org6f7187f" 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 14: < / span > Comparison of the Amplitude Spectral Sensity< / p >
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< / div >
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< div id = "orgacb2d5e" 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 15: < / span > Comparison of the Amplitude Spectral Sensity - Zoom< / p >
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< / div >
< / div >
< / div >
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< div id = "outline-container-org2082a3e" class = "outline-4" >
< h4 id = "org2082a3e" > < 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 = "#orgacb2d5e" > 15< / a > be due to the Aliasing?< / li >
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< / ul >
< / div >
< / div >
< / div >
< / div >
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< div id = "outline-container-org0d10493" class = "outline-3" >
< h3 id = "org0d10493" > < 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-org84a4af9" class = "outline-4" >
< h4 id = "org84a4af9" > < 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-orgba2e6ff" class = "outline-4" >
< h4 id = "orgba2e6ff" > < 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 = "#org8cbaa23" > 16< / 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 = "#orgeeac555" > 17< / a > ).
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< / p >
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< div id = "org8cbaa23" class = "figure" >
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< p > < img src = "./img/IMG_20190506_160420.jpg" alt = "IMG_20190506_160420.jpg" width = "500px" / >
< / p >
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< p > < span class = "figure-number" > Figure 16: < / span > Signals measured by the oscilloscope - Slip-Ring ON - Yellow: Direct measure - Blue: Through Slip-Ring< / p >
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< / div >
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< div id = "orgeeac555" class = "figure" >
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< p > < img src = "./img/IMG_20190506_160438.jpg" alt = "IMG_20190506_160438.jpg" width = "500px" / >
< / p >
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< p > < span class = "figure-number" > Figure 17: < / span > Signals measured by the oscilloscope - Slip-Ring OFF - Yellow: Direct measure - Blue: Through Slip-Ring< / p >
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< / div >
< / div >
< / div >
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< div id = "outline-container-org729aaf2" class = "outline-4" >
< h4 id = "org729aaf2" > < 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-orge6ed6b4" class = "outline-3" >
< h3 id = "orge6ed6b4" > < 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-org4501bcc" class = "outline-4" >
< h4 id = "org4501bcc" > < 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-org7f64f45" class = "outline-4" >
< h4 id = "org7f64f45" > < 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-org168648f" class = "outline-4" >
< h4 id = "org168648f" > < 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 = "#org82abb68" > 18< / a > ) and when it is ON (figure < a href = "#org7701819" > 19< / a > ).
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< / p >
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< div id = "org82abb68" class = "figure" >
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< p > < img src = "figs/sr_lpf_geophone_time_off.png" alt = "sr_lpf_geophone_time_off.png" / >
< / p >
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< p > < span class = "figure-number" > Figure 18: < / 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 = "org7701819" class = "figure" >
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< p > < img src = "figs/sr_lpf_geophone_time_on.png" alt = "sr_lpf_geophone_time_on.png" / >
< / p >
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< p > < span class = "figure-number" > Figure 19: < / 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-org18b3f68" class = "outline-4" >
< h4 id = "org18b3f68" > < 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 = "#org58407c0" > 20< / 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 = "org58407c0" class = "figure" >
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< p > < img src = "figs/sr_lpf_geophone_asd.png" alt = "sr_lpf_geophone_asd.png" / >
< / p >
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< p > < span class = "figure-number" > Figure 20: < / span > Comparison of the Amplitude Spectral Sensity< / p >
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< / div >
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< div id = "orge9dc071" class = "figure" >
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< p > < img src = "figs/sr_lpf_geophone_asd_zoom.png" alt = "sr_lpf_geophone_asd_zoom.png" / >
< / p >
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< p > < span class = "figure-number" > Figure 21: < / span > Comparison of the Amplitude Spectral Sensity - Zoom< / p >
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< / div >
< / div >
< / div >
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< div id = "outline-container-org5c54c76" class = "outline-4" >
< h4 id = "org5c54c76" > < 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 = "org9493d78" class = "figure" >
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< p > < img src = "figs/comp_with_without_lpf.png" alt = "comp_with_without_lpf.png" / >
< / p >
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< p > < span class = "figure-number" > Figure 22: < / span > Comparison of the measured signals with and without LPF< / p >
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< / div >
< / div >
< / div >
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< div id = "outline-container-org44b238b" class = "outline-4" >
< h4 id = "org44b238b" > < 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 >
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< / div >
< / div >
< / div >
< / div >
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< / div >
< / div >
< div id = "postamble" class = "status" >
< p class = "author" > Author: Thomas Dehaeze< / p >
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< p class = "date" > Created: 2019-05-10 ven. 10:06< / p >
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< p class = "validation" > < a href = "http://validator.w3.org/check?uri=referer" > Validate< / a > < / p >
< / div >
< / body >
< / html >
