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< title > Measurements on the instrumentation< / title >
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< h1 class = "title" > Measurements on the instrumentation< / h1 >
< div id = "table-of-contents" >
< h2 > Table of Contents< / h2 >
< div id = "text-table-of-contents" >
< ul >
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< li > < a href = "#org0b9c6e7" > 1. Measure of the noise of the Voltage Amplifier< / a >
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< ul >
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< li > < a href = "#orgce5ef47" > 1.1. Measurement Description< / a > < / li >
< li > < a href = "#org4658c5c" > 1.2. Load data< / a > < / li >
< li > < a href = "#org5de2d60" > 1.3. Time Domain< / a > < / li >
< li > < a href = "#org5fc539a" > 1.4. Frequency Domain< / a > < / li >
< li > < a href = "#orgbc39043" > 1.5. Conclusion< / a > < / li >
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< / ul >
< / li >
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< li > < a href = "#org182f3d2" > 2. Measure of the influence of the AC/DC option on the voltage amplifiers< / a >
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< ul >
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< li > < a href = "#orgc5cfc61" > 2.1. Measurement Description< / a > < / li >
< li > < a href = "#org0c0a3f2" > 2.2. Load data< / a > < / li >
< li > < a href = "#orgb381461" > 2.3. Time Domain< / a > < / li >
< li > < a href = "#org831a8d7" > 2.4. Frequency Domain< / a > < / li >
< li > < a href = "#org0f7903d" > 2.5. Conclusion< / a > < / li >
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< / ul >
< / li >
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< li > < a href = "#orge486804" > 3. Transfer function of the Low Pass Filter< / a >
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< ul >
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< li > < a href = "#org400e34d" > 3.1. First LPF with a Cut-off frequency of 160Hz< / a >
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< ul >
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< li > < a href = "#org8e6b3f9" > 3.1.1. Measurement Description< / a > < / li >
< li > < a href = "#org3c2d014" > 3.1.2. Load data< / a > < / li >
< li > < a href = "#orgddafe0a" > 3.1.3. Transfer function of the LPF< / a > < / li >
< li > < a href = "#org7a0daf9" > 3.1.4. Conclusion< / a > < / li >
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< / ul >
< / li >
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< li > < a href = "#org5504322" > 3.2. Second LPF with a Cut-off frequency of 1000Hz< / a >
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< ul >
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< li > < a href = "#orge51e102" > 3.2.1. Measurement description< / a > < / li >
< li > < a href = "#org609fd78" > 3.2.2. Load data< / a > < / li >
< li > < a href = "#orgad7e872" > 3.2.3. Transfer function of the LPF< / a > < / li >
< li > < a href = "#org73a58fb" > 3.2.4. Conclusion< / a > < / li >
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< div id = "outline-container-org0b9c6e7" class = "outline-2" >
< h2 id = "org0b9c6e7" > < span class = "section-number-2" > 1< / span > Measure of the noise of the Voltage Amplifier< / h2 >
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< div class = "outline-text-2" id = "text-1" >
< p >
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< a id = "org6a52764" > < / a >
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< / p >
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< div class = "note" id = "orge2ed99a" >
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< p >
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All the files (data and Matlab scripts) are accessible < a href = "data/meas_volt_amp.zip" > here< / a > .
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< / p >
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< div id = "outline-container-orgce5ef47" class = "outline-3" >
< h3 id = "orgce5ef47" > < span class = "section-number-3" > 1.1< / span > Measurement Description< / h3 >
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< div class = "outline-text-3" id = "text-1-1" >
< p >
< b > Goal< / b > :
< / p >
< ul class = "org-ul" >
< li > Determine the Voltage Amplifier noise< / li >
< / ul >
< p >
< b > Setup< / b > :
< / p >
< ul class = "org-ul" >
< li > The two inputs (differential) of the voltage amplifier are shunted with 50Ohms< / li >
< li > The AC/DC option of the Voltage amplifier is on AC< / li >
< li > The low pass filter is set to 1hHz< / li >
< li > We measure the output of the voltage amplifier with a 16bits ADC of the Speedgoat< / li >
< / ul >
< p >
< b > Measurements< / b > :
< / p >
< ul class = "org-ul" >
< li > < code > data_003< / code > : Ampli OFF< / li >
< li > < code > data_004< / code > : Ampli ON set to 20dB< / li >
< li > < code > data_005< / code > : Ampli ON set to 40dB< / li >
< li > < code > data_006< / code > : Ampli ON set to 60dB< / li >
< / ul >
< / div >
< / div >
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< div id = "outline-container-org4658c5c" class = "outline-3" >
< h3 id = "org4658c5c" > < span class = "section-number-3" > 1.2< / span > Load data< / h3 >
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< div class = "outline-text-3" id = "text-1-2" >
< div class = "org-src-container" >
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< pre class = "src src-matlab" > amp_off = load(< span class = "org-string" > 'mat/data_003.mat'< / span > , < span class = "org-string" > 'data'< / span > ); amp_off = amp_off.data(< span class = "org-type" > :< / span > , [1,3]);
amp_20d = load(< span class = "org-string" > 'mat/data_004.mat'< / span > , < span class = "org-string" > 'data'< / span > ); amp_20d = amp_20d.data(< span class = "org-type" > :< / span > , [1,3]);
amp_40d = load(< span class = "org-string" > 'mat/data_005.mat'< / span > , < span class = "org-string" > 'data'< / span > ); amp_40d = amp_40d.data(< span class = "org-type" > :< / span > , [1,3]);
amp_60d = load(< span class = "org-string" > 'mat/data_006.mat'< / span > , < span class = "org-string" > 'data'< / span > ); amp_60d = amp_60d.data(< span class = "org-type" > :< / span > , [1,3]);
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< div id = "outline-container-org5de2d60" class = "outline-3" >
< h3 id = "org5de2d60" > < span class = "section-number-3" > 1.3< / span > Time Domain< / h3 >
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< div class = "outline-text-3" id = "text-1-3" >
< p >
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The time domain signals are shown on figure < a href = "#org2fccd36" > 1< / a > .
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< / p >
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< div id = "org2fccd36" class = "figure" >
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< p > < img src = "figs/ampli_noise_time.png" alt = "ampli_noise_time.png" / >
< / p >
< p > < span class = "figure-number" > Figure 1: < / span > Output of the amplifier< / p >
< / div >
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< div id = "outline-container-org5fc539a" class = "outline-3" >
< h3 id = "org5fc539a" > < span class = "section-number-3" > 1.4< / span > Frequency Domain< / h3 >
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< div class = "outline-text-3" id = "text-1-4" >
< p >
We first compute some parameters that will be used for the PSD computation.
< / p >
< div class = "org-src-container" >
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< pre class = "src src-matlab" > dt = amp_off(2, 2)< span class = "org-type" > -< / span > amp_off(1, 2);
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Fs = 1< span class = "org-type" > /< / span > dt; < span class = "org-comment" > % [Hz]< / span >
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win = hanning(ceil(10< span class = "org-type" > *< / span > Fs));
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< / pre >
< / div >
< p >
Then we compute the Power Spectral Density using < code > pwelch< / code > function.
< / p >
< div class = "org-src-container" >
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< pre class = "src src-matlab" > [pxoff, f] = pwelch(amp_off(< span class = "org-type" > :< / span > ,1), win, [], [], Fs);
[px20d, < span class = "org-type" > ~< / span > ] = pwelch(amp_20d(< span class = "org-type" > :< / span > ,1), win, [], [], Fs);
[px40d, < span class = "org-type" > ~< / span > ] = pwelch(amp_40d(< span class = "org-type" > :< / span > ,1), win, [], [], Fs);
[px60d, < span class = "org-type" > ~< / span > ] = pwelch(amp_60d(< span class = "org-type" > :< / span > ,1), win, [], [], Fs);
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< / pre >
< / div >
< p >
We compute the theoretical ADC noise.
< / p >
< div class = "org-src-container" >
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< pre class = "src src-matlab" > q = 20< span class = "org-type" > /< / span > 2< span class = "org-type" > ^< / span > 16; < span class = "org-comment" > % quantization< / span >
Sq = q< span class = "org-type" > ^< / span > 2< span class = "org-type" > /< / span > 12< span class = "org-type" > /< / span > 1000; < span class = "org-comment" > % PSD of the ADC noise< / span >
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< / pre >
< / div >
< p >
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Finally, the ASD is shown on figure < a href = "#org46e6591" > 2< / a > .
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< / p >
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< div id = "org46e6591" class = "figure" >
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< p > < img src = "figs/ampli_noise_psd.png" alt = "ampli_noise_psd.png" / >
< / p >
< p > < span class = "figure-number" > Figure 2: < / span > Amplitude Spectral Density of the measured voltage at the output of the voltage amplifier< / p >
< / div >
< / div >
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< div id = "outline-container-orgbc39043" class = "outline-3" >
< h3 id = "orgbc39043" > < span class = "section-number-3" > 1.5< / span > Conclusion< / h3 >
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< div class = "outline-text-3" id = "text-1-5" >
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< div class = "important" id = "orgb8e9939" >
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< p >
< b > Questions< / b > :
< / p >
< ul class = "org-ul" >
< li > Where does those sharp peaks comes from? Can this be due to aliasing?< / li >
< / ul >
< p >
Noise induced by the voltage amplifiers seems not to be a limiting factor as we have the same noise when they are OFF and ON.
< / p >
< / div >
< / div >
< / div >
< / div >
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< div id = "outline-container-org182f3d2" class = "outline-2" >
< h2 id = "org182f3d2" > < span class = "section-number-2" > 2< / span > Measure of the influence of the AC/DC option on the voltage amplifiers< / h2 >
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< div class = "outline-text-2" id = "text-2" >
< p >
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< a id = "org4bf4c36" > < / a >
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< / p >
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< div class = "note" id = "org66d7fee" >
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< p >
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All the files (data and Matlab scripts) are accessible < a href = "data/meas_noise_ac_dc.zip" > here< / a > .
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< / p >
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< div id = "outline-container-orgc5cfc61" class = "outline-3" >
< h3 id = "orgc5cfc61" > < span class = "section-number-3" > 2.1< / span > Measurement Description< / h3 >
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< div class = "outline-text-3" id = "text-2-1" >
< p >
< b > Goal< / b > :
< / p >
< ul class = "org-ul" >
< li > Measure the influence of the high-pass filter option of the voltage amplifiers< / li >
< / ul >
< p >
< b > Setup< / b > :
< / p >
< ul class = "org-ul" >
< li > One geophone is located on the marble.< / li >
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< li > It’ s signal goes to two voltage amplifiers with a gain of 60dB.< / li >
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< li > One voltage amplifier is on the AC option, the other is on the DC option.< / li >
< / ul >
< p >
< b > Measurements< / b > :
First measurement (< code > mat/data_014.mat< / code > file):
< / p >
< table border = "2" cellspacing = "0" cellpadding = "6" rules = "groups" frame = "hsides" >
< colgroup >
< col class = "org-right" / >
< col class = "org-left" / >
< / colgroup >
< thead >
< tr >
< th scope = "col" class = "org-right" > Column< / th >
< th scope = "col" class = "org-left" > Signal< / th >
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< / thead >
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< tr >
< td class = "org-right" > 1< / td >
< td class = "org-left" > Amplifier 1 with AC option< / td >
< / tr >
< tr >
< td class = "org-right" > 2< / td >
< td class = "org-left" > Amplifier 2 with DC option< / td >
< / tr >
< tr >
< td class = "org-right" > 3< / td >
< td class = "org-left" > Time< / td >
< / tr >
< / tbody >
< / table >
< p >
Second measurement (< code > mat/data_015.mat< / code > file):
< / p >
< table border = "2" cellspacing = "0" cellpadding = "6" rules = "groups" frame = "hsides" >
< colgroup >
< col class = "org-right" / >
< col class = "org-left" / >
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< tr >
< th scope = "col" class = "org-right" > Column< / th >
< th scope = "col" class = "org-left" > Signal< / th >
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< / thead >
< tbody >
< tr >
< td class = "org-right" > 1< / td >
< td class = "org-left" > Amplifier 1 with DC option< / td >
< / tr >
< tr >
< td class = "org-right" > 2< / td >
< td class = "org-left" > Amplifier 2 with AC option< / td >
< / tr >
< tr >
< td class = "org-right" > 3< / td >
< td class = "org-left" > Time< / td >
< / tr >
< / tbody >
< / table >
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< div id = "org52bc26f" class = "figure" >
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< p > < img src = "./img/IMG_20190503_170936.jpg" alt = "IMG_20190503_170936.jpg" width = "500px" / >
< / p >
< p > < span class = "figure-number" > Figure 3: < / span > Picture of the two voltages amplifiers< / p >
< / div >
< / div >
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< div id = "outline-container-org0c0a3f2" class = "outline-3" >
< h3 id = "org0c0a3f2" > < span class = "section-number-3" > 2.2< / span > Load data< / h3 >
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< div class = "outline-text-3" id = "text-2-2" >
< p >
We load the data of the z axis of two geophones.
< / p >
< div class = "org-src-container" >
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< pre class = "src src-matlab" > meas14 = load(< span class = "org-string" > 'mat/data_014.mat'< / span > , < span class = "org-string" > 'data'< / span > ); meas14 = meas14.data;
meas15 = load(< span class = "org-string" > 'mat/data_015.mat'< / span > , < span class = "org-string" > 'data'< / span > ); meas15 = meas15.data;
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< / pre >
< / div >
< / div >
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< div id = "outline-container-orgb381461" class = "outline-3" >
< h3 id = "orgb381461" > < span class = "section-number-3" > 2.3< / span > Time Domain< / h3 >
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< div class = "outline-text-3" id = "text-2-3" >
< p >
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The signals are shown on figure < a href = "#org26ff108" > 4< / a > .
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< / p >
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< div id = "org26ff108" class = "figure" >
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< p > < img src = "figs/ac_dc_option_time.png" alt = "ac_dc_option_time.png" / >
< / p >
< p > < span class = "figure-number" > Figure 4: < / span > Comparison of the signals going through the Voltage amplifiers< / p >
< / div >
< / div >
< / div >
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< div id = "outline-container-org831a8d7" class = "outline-3" >
< h3 id = "org831a8d7" > < span class = "section-number-3" > 2.4< / span > Frequency Domain< / h3 >
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< div class = "outline-text-3" id = "text-2-4" >
< p >
We first compute some parameters that will be used for the PSD computation.
< / p >
< div class = "org-src-container" >
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< pre class = "src src-matlab" > dt = meas14(2, 3)< span class = "org-type" > -< / span > meas14(1, 3);
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Fs = 1< span class = "org-type" > /< / span > dt; < span class = "org-comment" > % [Hz]< / span >
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win = hanning(ceil(10< span class = "org-type" > *< / span > Fs));
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< / pre >
< / div >
< p >
Then we compute the Power Spectral Density using < code > pwelch< / code > function.
< / p >
< div class = "org-src-container" >
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< pre class = "src src-matlab" > [pxamp1ac, f] = pwelch(meas14(< span class = "org-type" > :< / span > , 1), win, [], [], Fs);
[pxamp2dc, < span class = "org-type" > ~< / span > ] = pwelch(meas14(< span class = "org-type" > :< / span > , 2), win, [], [], Fs);
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[pxamp1dc, < span class = "org-type" > ~< / span > ] = pwelch(meas15(< span class = "org-type" > :< / span > , 1), win, [], [], Fs);
[pxamp2ac, < span class = "org-type" > ~< / span > ] = pwelch(meas15(< span class = "org-type" > :< / span > , 2), win, [], [], Fs);
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< / pre >
< / div >
< p >
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The ASD of the signals are compare on figure < a href = "#org252ca9f" > 5< / a > .
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< / p >
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< div id = "org252ca9f" class = "figure" >
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< p > < img src = "figs/ac_dc_option_asd.png" alt = "ac_dc_option_asd.png" / >
< / p >
< p > < span class = "figure-number" > Figure 5: < / span > Amplitude Spectral Density of the measured signals< / p >
< / div >
< / div >
< / div >
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< div id = "outline-container-org0f7903d" class = "outline-3" >
< h3 id = "org0f7903d" > < span class = "section-number-3" > 2.5< / span > Conclusion< / h3 >
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< div class = "outline-text-3" id = "text-2-5" >
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< div class = "important" id = "orga7652b6" >
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< ul class = "org-ul" >
< li > The voltage amplifiers include some very sharp high pass filters at 1.5Hz (maybe 4th order)< / li >
< li > There is a DC offset on the time domain signal because the DC-offset knob was not set to zero< / li >
< / ul >
< / div >
< / div >
< / div >
< / div >
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< div id = "outline-container-orge486804" class = "outline-2" >
< h2 id = "orge486804" > < span class = "section-number-2" > 3< / span > Transfer function of the Low Pass Filter< / h2 >
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< div class = "outline-text-2" id = "text-3" >
< p >
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< a id = "orgae11ccf" > < / a >
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< / p >
< p >
The computation files for this section are accessible < a href = "data/low_pass_filter_measurements.zip" > here< / a > .
< / p >
< / div >
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< div id = "outline-container-org400e34d" class = "outline-3" >
< h3 id = "org400e34d" > < span class = "section-number-3" > 3.1< / span > First LPF with a Cut-off frequency of 160Hz< / h3 >
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< div class = "outline-text-3" id = "text-3-1" >
< / div >
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< div id = "outline-container-org8e6b3f9" class = "outline-4" >
< h4 id = "org8e6b3f9" > < span class = "section-number-4" > 3.1.1< / span > Measurement Description< / h4 >
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< div class = "outline-text-4" id = "text-3-1-1" >
< p >
< b > Goal< / b > :
< / p >
< ul class = "org-ul" >
< li > Measure the Low Pass Filter Transfer Function< / li >
< / ul >
< p >
The values of the components are:
< / p >
\begin{aligned}
R & = 1k\Omega \\
C & = 1\mu F
\end{aligned}
< p >
Which makes a cut-off frequency of \(f_c = \frac{1}{RC} = 1000 rad/s = 160Hz\).
< / p >
< div class = "org-src-container" >
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< pre class = "src src-latex" id = "orgebabef7" > < span class = "org-font-latex-sedate" > < span class = "org-keyword" > \begin< / span > < / span > {< span class = "org-function-name" > tikzpicture< / span > }
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< span class = "org-font-latex-sedate" > \draw< / span > (0,2)
to [R=< span class = "org-font-latex-sedate" > < span class = "org-font-latex-math" > \(R\)< / span > < / span > ] ++(2,0) node[circ]
to ++(2,0)
++(-2,0)
to [C=< span class = "org-font-latex-sedate" > < span class = "org-font-latex-math" > \(C\)< / span > < / span > ] ++(0,-2) node[circ]
++(-2,0)
to ++(2,0)
to ++(2,0)
< span class = "org-font-latex-sedate" > < span class = "org-keyword" > \end< / span > < / span > {< span class = "org-function-name" > tikzpicture< / span > }
< / pre >
< / div >
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< div id = "org19a615d" class = "figure" >
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< p > < img src = "figs/lpf.png" alt = "lpf.png" / >
< / p >
< p > < span class = "figure-number" > Figure 6: < / span > Schematic of the Low Pass Filter used< / p >
< / div >
< p >
< b > Setup< / b > :
< / p >
< ul class = "org-ul" >
< li > We are measuring the signal from from Geophone with a BNC T< / li >
< li > On part goes to column 1 through the LPF< / li >
< li > The other part goes to column 2 without the LPF< / li >
< / ul >
< p >
< b > Measurements< / b > :
< code > mat/data_018.mat< / code > :
< / p >
< table border = "2" cellspacing = "0" cellpadding = "6" rules = "groups" frame = "hsides" >
< colgroup >
< col class = "org-right" / >
< col class = "org-left" / >
< / colgroup >
< thead >
< tr >
< th scope = "col" class = "org-right" > Column< / th >
< th scope = "col" class = "org-left" > Signal< / th >
< / tr >
< / thead >
< tbody >
< tr >
< td class = "org-right" > 1< / td >
< td class = "org-left" > Amplifier 1 with LPF< / td >
< / tr >
< tr >
< td class = "org-right" > 2< / td >
< td class = "org-left" > Amplifier 2< / td >
< / tr >
< tr >
< td class = "org-right" > 3< / td >
< td class = "org-left" > Time< / td >
< / tr >
< / tbody >
< / table >
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< div id = "org91c0742" class = "figure" >
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< p > < img src = "./img/IMG_20190507_102756.jpg" alt = "IMG_20190507_102756.jpg" width = "500px" / >
< / p >
< p > < span class = "figure-number" > Figure 7: < / span > Picture of the low pass filter used< / p >
< / div >
< / div >
< / div >
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< div id = "outline-container-org3c2d014" class = "outline-4" >
< h4 id = "org3c2d014" > < span class = "section-number-4" > 3.1.2< / span > Load data< / h4 >
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< div class = "outline-text-4" id = "text-3-1-2" >
< p >
We load the data of the z axis of two geophones.
< / p >
< div class = "org-src-container" >
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< pre class = "src src-matlab" > data = load(< span class = "org-string" > 'mat/data_018.mat'< / span > , < span class = "org-string" > 'data'< / span > ); data = data.data;
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< / pre >
< / div >
< / div >
< / div >
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< div id = "outline-container-orgddafe0a" class = "outline-4" >
< h4 id = "orgddafe0a" > < span class = "section-number-4" > 3.1.3< / span > Transfer function of the LPF< / h4 >
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< div class = "outline-text-4" id = "text-3-1-3" >
< p >
We compute the transfer function from the signal without the LPF to the signal measured with the LPF.
< / p >
< div class = "org-src-container" >
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< pre class = "src src-matlab" > dt = data(2, 3)< span class = "org-type" > -< / span > data(1, 3);
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Fs = 1< span class = "org-type" > /< / span > dt; < span class = "org-comment" > % [Hz]< / span >
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win = hanning(ceil(10< span class = "org-type" > *< / span > Fs));
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< / pre >
< / div >
< div class = "org-src-container" >
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< pre class = "src src-matlab" > [Glpf, f] = tfestimate(data(< span class = "org-type" > :< / span > , 2), data(< span class = "org-type" > :< / span > , 1), win, [], [], Fs);
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< / pre >
< / div >
< p >
We compare this transfer function with a transfer function corresponding to an ideal first order LPF with a cut-off frequency of \(1000rad/s\).
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We obtain the result on figure < a href = "#orgb174301" > 8< / a > .
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< / p >
< div class = "org-src-container" >
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< pre class = "src src-matlab" > Gth = 1< span class = "org-type" > /< / span > (1< span class = "org-type" > +< / span > s< span class = "org-type" > /< / span > 1000)
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< / pre >
< / div >
< div class = "org-src-container" >
< pre class = "src src-matlab" > < span class = "org-type" > figure< / span > ;
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ax1 = subplot(2, 1, 1);
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hold on;
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plot(f, abs(Glpf));
plot(f, abs(squeeze(freqresp(Gth, f, < span class = "org-string" > 'Hz'< / span > ))));
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hold off;
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< span class = "org-type" > set< / span > (< span class = "org-variable-name" > gca< / span > , < span class = "org-string" > 'xscale'< / span > , < span class = "org-string" > 'log'< / span > ); < span class = "org-type" > set< / span > (< span class = "org-variable-name" > gca< / span > , < span class = "org-string" > 'yscale'< / span > , < span class = "org-string" > 'log'< / span > );
< span class = "org-type" > set< / span > (< span class = "org-variable-name" > gca< / span > , < span class = "org-string" > 'XTickLabel'< / span > ,[]);
ylabel(< span class = "org-string" > 'Magnitude'< / span > );
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ax2 = subplot(2, 1, 2);
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hold on;
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plot(f, mod(180< span class = "org-type" > +< / span > 180< span class = "org-type" > /< / span > < span class = "org-constant" > pi< / span > < span class = "org-type" > *< / span > phase(Glpf), 360)< span class = "org-type" > -< / span > 180);
plot(f, 180< span class = "org-type" > /< / span > < span class = "org-constant" > pi< / span > < span class = "org-type" > *< / span > unwrap(angle(squeeze(freqresp(Gth, f, < span class = "org-string" > 'Hz'< / span > )))));
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hold off;
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< span class = "org-type" > set< / span > (< span class = "org-variable-name" > gca< / span > , < span class = "org-string" > 'xscale'< / span > , < span class = "org-string" > 'log'< / span > );
ylim([< span class = "org-type" > -< / span > 180, 180]);
yticks([< span class = "org-type" > -< / span > 180, < span class = "org-type" > -< / span > 90, 0, 90, 180]);
xlabel(< span class = "org-string" > 'Frequency [Hz]'< / span > ); ylabel(< span class = "org-string" > 'Phase'< / span > );
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linkaxes([ax1,ax2],< span class = "org-string" > 'x'< / span > );
xlim([1, 500]);
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< / pre >
< / div >
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< div id = "orgb174301" class = "figure" >
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< p > < img src = "figs/Glpf_bode.png" alt = "Glpf_bode.png" / >
< / p >
< p > < span class = "figure-number" > Figure 8: < / span > Bode Diagram of the measured Low Pass filter and the theoritical one< / p >
< / div >
< / div >
< / div >
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< div id = "outline-container-org7a0daf9" class = "outline-4" >
< h4 id = "org7a0daf9" > < span class = "section-number-4" > 3.1.4< / span > Conclusion< / h4 >
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< div class = "outline-text-4" id = "text-3-1-4" >
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< div class = "important" id = "org84503a8" >
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< p >
As we want to measure things up to \(500Hz\), we chose to change the value of the capacitor to obtain a cut-off frequency of \(1kHz\).
< / p >
< / div >
< / div >
< / div >
< / div >
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< div id = "outline-container-org5504322" class = "outline-3" >
< h3 id = "org5504322" > < span class = "section-number-3" > 3.2< / span > Second LPF with a Cut-off frequency of 1000Hz< / h3 >
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< div class = "outline-text-3" id = "text-3-2" >
< / div >
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< div id = "outline-container-orge51e102" class = "outline-4" >
< h4 id = "orge51e102" > < span class = "section-number-4" > 3.2.1< / span > Measurement description< / h4 >
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< div class = "outline-text-4" id = "text-3-2-1" >
< p >
This time, the value are
< / p >
\begin{aligned}
R & = 1k\Omega \\
C & = 150nF
\end{aligned}
< p >
Which makes a low pass filter with a cut-off frequency of \(f_c = 1060Hz\).
< / p >
< / div >
< / div >
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< div id = "outline-container-org609fd78" class = "outline-4" >
< h4 id = "org609fd78" > < span class = "section-number-4" > 3.2.2< / span > Load data< / h4 >
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< div class = "outline-text-4" id = "text-3-2-2" >
< p >
We load the data of the z axis of two geophones.
< / p >
< div class = "org-src-container" >
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< pre class = "src src-matlab" > data = load(< span class = "org-string" > 'mat/data_019.mat'< / span > , < span class = "org-string" > 'data'< / span > ); data = data.data;
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< / pre >
< / div >
< / div >
< / div >
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< div id = "outline-container-orgad7e872" class = "outline-4" >
< h4 id = "orgad7e872" > < span class = "section-number-4" > 3.2.3< / span > Transfer function of the LPF< / h4 >
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< div class = "outline-text-4" id = "text-3-2-3" >
< p >
We compute the transfer function from the signal without the LPF to the signal measured with the LPF.
< / p >
< div class = "org-src-container" >
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< pre class = "src src-matlab" > dt = data(2, 3)< span class = "org-type" > -< / span > data(1, 3);
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Fs = 1< span class = "org-type" > /< / span > dt; < span class = "org-comment" > % [Hz]< / span >
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win = hanning(ceil(10< span class = "org-type" > *< / span > Fs));
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< / pre >
< / div >
< div class = "org-src-container" >
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< pre class = "src src-matlab" > [Glpf, f] = tfestimate(data(< span class = "org-type" > :< / span > , 2), data(< span class = "org-type" > :< / span > , 1), win, [], [], Fs);
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< / pre >
< / div >
< p >
We compare this transfer function with a transfer function corresponding to an ideal first order LPF with a cut-off frequency of \(1060Hz\).
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We obtain the result on figure < a href = "#org9707219" > 9< / a > .
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< / p >
< div class = "org-src-container" >
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< pre class = "src src-matlab" > Gth = 1< span class = "org-type" > /< / span > (1< span class = "org-type" > +< / span > s< span class = "org-type" > /< / span > 1060< span class = "org-type" > /< / span > 2< span class = "org-type" > /< / span > < span class = "org-constant" > pi< / span > );
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< / pre >
< / div >
< div class = "org-src-container" >
< pre class = "src src-matlab" > < span class = "org-type" > figure< / span > ;
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ax1 = subplot(2, 1, 1);
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hold on;
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plot(f, abs(Glpf));
plot(f, abs(squeeze(freqresp(Gth, f, < span class = "org-string" > 'Hz'< / span > ))));
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hold off;
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< span class = "org-type" > set< / span > (< span class = "org-variable-name" > gca< / span > , < span class = "org-string" > 'xscale'< / span > , < span class = "org-string" > 'log'< / span > ); < span class = "org-type" > set< / span > (< span class = "org-variable-name" > gca< / span > , < span class = "org-string" > 'yscale'< / span > , < span class = "org-string" > 'log'< / span > );
< span class = "org-type" > set< / span > (< span class = "org-variable-name" > gca< / span > , < span class = "org-string" > 'XTickLabel'< / span > ,[]);
ylabel(< span class = "org-string" > 'Magnitude'< / span > );
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ax2 = subplot(2, 1, 2);
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hold on;
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plot(f, mod(180< span class = "org-type" > +< / span > 180< span class = "org-type" > /< / span > < span class = "org-constant" > pi< / span > < span class = "org-type" > *< / span > phase(Glpf), 360)< span class = "org-type" > -< / span > 180);
plot(f, 180< span class = "org-type" > /< / span > < span class = "org-constant" > pi< / span > < span class = "org-type" > *< / span > unwrap(angle(squeeze(freqresp(Gth, f, < span class = "org-string" > 'Hz'< / span > )))));
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hold off;
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< span class = "org-type" > set< / span > (< span class = "org-variable-name" > gca< / span > , < span class = "org-string" > 'xscale'< / span > , < span class = "org-string" > 'log'< / span > );
ylim([< span class = "org-type" > -< / span > 180, 180]);
yticks([< span class = "org-type" > -< / span > 180, < span class = "org-type" > -< / span > 90, 0, 90, 180]);
xlabel(< span class = "org-string" > 'Frequency [Hz]'< / span > ); ylabel(< span class = "org-string" > 'Phase'< / span > );
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linkaxes([ax1,ax2],< span class = "org-string" > 'x'< / span > );
xlim([1, 500]);
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< / pre >
< / div >
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< div id = "org9707219" class = "figure" >
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< p > < img src = "figs/Glpf_bode_bis.png" alt = "Glpf_bode_bis.png" / >
< / p >
< p > < span class = "figure-number" > Figure 9: < / span > Bode Diagram of the measured Low Pass filter and the theoritical one< / p >
< / div >
< / div >
< / div >
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< div id = "outline-container-org73a58fb" class = "outline-4" >
< h4 id = "org73a58fb" > < span class = "section-number-4" > 3.2.4< / span > Conclusion< / h4 >
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< div class = "outline-text-4" id = "text-3-2-4" >
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< div class = "important" id = "org1fede99" >
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< p >
The added LPF has the expected behavior.
< / p >
< / div >
< / div >
< / div >
< / div >
< / div >
< / div >
< div id = "postamble" class = "status" >
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< p class = "author" > Author: Dehaeze Thomas< / p >
< p class = "date" > Created: 2020-11-12 jeu. 10:28< / p >
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< / div >
< / body >
< / html >
