Fourier Transform on the ODE of the RLC circuit

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#1 21673251 20 Jan 2015 06:36

hassan salem hassan salem

Anonymous

Post #1
21673251 20 Jan 2015 06:36

i have an series RLC circuit and i asked to write its ordinary differential equation and then to apply fourier transform to get the output of the circuit, the output across the capacitor.

please help and thank you all
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#2 21673252 20 Jan 2015 10:56

Enrico Koeck Enrico Koeck

Anonymous

Post #2
21673252 20 Jan 2015 10:56

Usually you derive the transfer function from the differential equation (with capacitor voltage as output) and afterwards split it into magnitude and phase to draw a bode plot. But you can Fourier transform the transfer function as well an get the complex Fourier spectrum of the output.
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#3 21673253 20 Jan 2015 11:08

hassan salem hassan salem

Anonymous

Post #3
21673253 20 Jan 2015 11:08

can you please write the solution for me, i mean just write the differential equation and the fourier transform steps to get the output of the capacitor.
here is the circuit
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#4 21673254 20 Jan 2015 15:29

Enrico Koeck Enrico Koeck

Anonymous

Post #4
21673254 20 Jan 2015 15:29

As to be found in every book covering the topic.. now apply the kind of Fourier transformation you need as learned (had to look it up myself as well).
#5 21673255 20 Jan 2015 15:48

hassan salem hassan salem

Anonymous

Post #5
21673255 20 Jan 2015 15:48

actually i tried and i get the transfer function as :

y(w) / x(w) = 1 / (-LCw^2 + RCwj + 1 )

but i dont know how to continue to find y(t)

given values R=4 ,, L=3 ,, C=1 and x(w)= 1
#6 21673256 21 Jan 2015 05:23

Enrico Koeck Enrico Koeck

Anonymous

Post #6
21673256 21 Jan 2015 05:23

If x(t) = 1 then you have a DC excitation and it makes no sense to apply a Fourier transform. This only makes sense if you either have a sinusoid input or want to analyze the frequency response. Otherwise transform x(t) as well and solve for y(w) and transform back to time domain.
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#7 21673257 21 Jan 2015 05:31

hassan salem hassan salem

Anonymous

Post #7
21673257 21 Jan 2015 05:31

x(w) =1 not x(t)
#8 21673258 21 Jan 2015 09:42

Enrico Koeck Enrico Koeck

Anonymous

Post #8
21673258 21 Jan 2015 09:42

Maybe take a look at this page: http://www.thefouriertransform.com/applications/differentialequations.php I've never been working with Fourier transformation to solve differential equations, mostly only Laplace.
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Fourier Transform on the ODE of the RLC circuit

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