Difference between revisions of "Lab 3 RS"
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=Questions= | =Questions= | ||
− | + | ==1. Compare the theoretical and experimentally measured break frequencies. (5 pnts)== | |
− | ==method 1. Using fitting line== | + | ===method 1. Using fitting line=== |
:Theoretical break frequency: 12.1 kHz | :Theoretical break frequency: 12.1 kHz | ||
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<math>Error = \left| \frac{f_{exp} - f_{theor}}{f_{theor}} \right| = \left| \frac{9.59 - 12.1}{12.1} \right|= 20.7\ %</math> | <math>Error = \left| \frac{f_{exp} - f_{theor}}{f_{theor}} \right| = \left| \frac{9.59 - 12.1}{12.1} \right|= 20.7\ %</math> | ||
− | ==method 2. Using the -3 dB point== | + | ===method 2. Using the -3 dB point=== |
At the break point the voltage gain is down by 3 dB relative to the gain of unity at zero frequency. So the value of <math>\mbox{log}(V_{out}/V_{in}) = (3/20) = 0.15 </math>. Using this value I found from plot above <math>\mbox{log}(f_b) = 1.1\ \mbox{kHz}</math>. So <math>f_b = (10^{1.1}) = 12.6\ \mbox{kHz}</math>. The error in this case is 4.1 %. | At the break point the voltage gain is down by 3 dB relative to the gain of unity at zero frequency. So the value of <math>\mbox{log}(V_{out}/V_{in}) = (3/20) = 0.15 </math>. Using this value I found from plot above <math>\mbox{log}(f_b) = 1.1\ \mbox{kHz}</math>. So <math>f_b = (10^{1.1}) = 12.6\ \mbox{kHz}</math>. The error in this case is 4.1 %. | ||
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− | + | ==3. Sketch the phasor diagram for <math>V_{in}</math>,<math> V_{out}</math>, <math>V_{R}</math>, and <math>V_{C}</math>. Put the current <math>I</math> along the real voltage axis. (30 pnts)== | |
[[File:Phase diagram m.png | 600 px]] | [[File:Phase diagram m.png | 600 px]] | ||
− | + | ==4. Compare the theoretical and experimental value for the phase shift <math>\theta</math>. (5 pnts)== | |
− | |||
The experimental phase shift is <math>\ \Delta F_{exp} = \left(\omega_{exp} \Delta T_{exp}\right)= \left(2\pi f_{exp} \Delta T_{exp}\right)</math> | The experimental phase shift is <math>\ \Delta F_{exp} = \left(\omega_{exp} \Delta T_{exp}\right)= \left(2\pi f_{exp} \Delta T_{exp}\right)</math> | ||
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− | + | ==5. what is the phase shift <math>\theta</math> for a DC input and a very-high frequency input?(5 pnts)== | |
− | + | ==6. calculate and expression for the phase shift <math>\theta</math> as a function of <math>\nu</math>, <math>R</math>, <math>C</math> and graph <math>\theta</math> -vs <math>\nu</math>. (20 pnts)== | |
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Revision as of 01:52, 26 January 2011
- RC Low-pass filter
1-50 kHz filter (20 pnts)
1. Design a low-pass RC filter with a break point between 1-50 kHz. The break point is the frequency at which the filter starts to attenuate the AC signal. For a Low pass filter, AC signals with a frequency above 1-50 kHz will start to be attenuated (not passed).
- To design low-pass RC filter I had:
2. Now construct the circuit using a non-polar capacitor.
3. Use a sinusoidal variable frequency oscillator to provide an input voltage to your filter.
4. Measure the input
and output voltages for at least 8 different frequencies which span the frequency range from 1 Hz to 1 MHz.0.1 | 5.0 | 5.0 | 1.0 | ||
1.0 | 4.2 | 4.2 | 1.0 | 14.0 | 0.094 |
2.0 | 3.2 | 3.1 | 0.97 | 14.0 | 0.188 |
5.0 | 1.8 | 1.6 | 0.89 | 14.0 | 0.471 |
10.0 | 1.14 | 0.88 | 0.77 | 11.0 | 0.628 |
16.7 | 0.90 | 0.54 | 0.60 | 8.5 | 1.049 |
20.0 | 0.88 | 0.48 | 0.54 | 8.0 | 1.005 |
25.0 | 0.82 | 0.38 | 0.46 | 7.0 | 1.099 |
33.3 | 0.78 | 0.28 | 0.36 | 6.0 | 1.255 |
50.0 | 0.76 | 0.18 | 0.24 | 4.5 | 1.413 |
100.0 | 0.75 | 0.09 | 0.12 | 2.0 | 1.256 |
125.0 | 0.74 | 0.07 | 0.095 | 1.8 | 1.413 |
200.0 | 0.75 | 0.04 | 0.053 | 0.9 | 1.005 |
333.3 | 0.76 | 0.03 | 0.039 | 0.25 | 0.523 |
200.0 | 0.76 | 0.03 | 0.039 | -0.25 | -0.785 |
1000.0 | 0.78 | 0.06 | 0.077 | -0.25 | -1.570 |
5. Graph the
-vs-phase shift (10 pnts)
- measure the phase shift between and as a function of frequency . Hint: you could use as an external trigger and measure the time until reaches a max on the scope .
See table above, columns #5 and #6.
Questions
1. Compare the theoretical and experimentally measured break frequencies. (5 pnts)
method 1. Using fitting line
- Theoretical break frequency: 12.1 kHz
- Experimentally measured break frequency: 9.59 kHz
Q: The above was read off the graph? Why not use fit results? A: The fit was made by using GIMP Image Editor. I do not have so much experience with ROOT. But I will try to do it. Thank you for comment. A1: The fit was done by ROOT
- The fit line equation from the plot above is .
- From intersection point of line with x-axis we find:
- The error is:
method 2. Using the -3 dB point
At the break point the voltage gain is down by 3 dB relative to the gain of unity at zero frequency. So the value of
. Using this value I found from plot above . So . The error in this case is 4.1 %.
2. Calculate and expression for as a function of , , and . The Gain is defined as the ratio of to .(5 pnts)
We have:
Dividing second equation into first one we get the voltage gain:
And we are need the real part:
3. Sketch the phasor diagram for , , , and . Put the current along the real voltage axis. (30 pnts)
4. Compare the theoretical and experimental value for the phase shift . (5 pnts)
The experimental phase shift is
The theoretical phase shift is