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x_RMS = sqrt(1/T int_T( | x (t)|2 dt ) ), | x_RMS = sqrt(1/T int_T( | x (t)|2 dt ) ), | ||
| − | where int_T denotes the integral over one period. | + | where int_T denotes the integral over one period, i.e. |
| + | |||
| + | <math> x_{RMS} = \sqrt{ \frac{1}{T} \int_T | x (t)|^2 dt } </math> | ||
| + | |||
| + | |||
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Vrms,net = sqrt( v_0^2 + v_1^2 + ... + v_9^2), | Vrms,net = sqrt( v_0^2 + v_1^2 + ... + v_9^2), | ||
| + | |||
| + | <math>V_{rms,net} = \sqrt{ v_0^2 + v_1^2 + ... + v_9^2}</math> | ||
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. | 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 03:04, 29 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, i.e.
$ x_{RMS} = \sqrt{ \frac{1}{T} \int_T | x (t)|^2 dt } $
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),
$ V_{rms,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.
