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=Discussion page for [[ECE440F13LoveLab1|Lab 1 ECE440 Fall 2013]]= | =Discussion page for [[ECE440F13LoveLab1|Lab 1 ECE440 Fall 2013]]= | ||
| − | + | This discussion board is used to clarify issues on the lab and pre-lab. | |
| − | + | ||
| + | ----- | ||
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| + | Q: How do I get the RMS voltage of spectral components on the 5th question? | ||
| + | |||
| + | A: One can show that the RMS voltage of each spectral component is equal to the corresponding coefficient of the complex Fourier series. To show this, plug in the spectral component | ||
| + | |||
| + | a_k exp(j k w_0 t) | ||
| + | |||
| + | from the complex Fourier series into the formula for RMS | ||
| + | |||
| + | x_RMS = sqrt(1/T int_T( | x (t)|2 dt ) ), | ||
| + | |||
| + | where int_T denotes the integral over one period. | ||
| + | |||
| + | ----- | ||
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| + | Q: Do the RMS voltage of the spectral components need to sum up to the total RMS voltage? | ||
| + | |||
| + | A: To combine the RMS voltages to get the net RMS of the first nine spectral components, use the following: | ||
| + | |||
| + | Vrms,net = sqrt( v_0^2 + v_1^2 + ... + v_9^2), | ||
| + | |||
| + | where v_i is the RMS of the i-th spectral component. By Parseval's theorem, Vrms,net should converge to the RMS voltage of the overall signal as the number of spectral components included in the sum approaches infinity. | ||
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[[ECE440F13LoveLab1|Back to Lab 1 ECE440 Fall 2013]] | [[ECE440F13LoveLab1|Back to Lab 1 ECE440 Fall 2013]] | ||
Revision as of 14:59, 28 August 2013
Discussion page for Lab 1 ECE440 Fall 2013
This discussion board is used to clarify issues on the lab and pre-lab.
Q: How do I get the RMS voltage of spectral components on the 5th question?
A: One can show that the RMS voltage of each spectral component is equal to the corresponding coefficient of the complex Fourier series. To show this, plug in the spectral component
a_k exp(j k w_0 t)
from the complex Fourier series into the formula for RMS
x_RMS = sqrt(1/T int_T( | x (t)|2 dt ) ),
where int_T denotes the integral over one period.
Q: Do the RMS voltage of the spectral components need to sum up to the total RMS voltage?
A: To combine the RMS voltages to get the net RMS of the first nine spectral components, use the following:
Vrms,net = sqrt( v_0^2 + v_1^2 + ... + v_9^2),
where v_i is the RMS of the i-th spectral component. By Parseval's theorem, Vrms,net should converge to the RMS voltage of the overall signal as the number of spectral components included in the sum approaches infinity.
