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RLC Circuit

Carel

Jun 21, 2009
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Jun 21, 2009
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Hi guys, I need to do a few calculations regarding the RLC circuit, but have no idea where to start or how to do it. I need to calculate at which frequency the input voltage will be in phase with the output voltage for the RLC circuit. Any hints, tips or guidance will be greatly appreciated as I have no idea where to start.
 

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Harald Kapp

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Nov 17, 2011
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Carel,
one good ay to start this work is by writing down the complex impedances of the components as a function of frequency. You should be able to do this, otherwise the assignmnet given to you would be useless. So:
X(L1) = f1(f)
X(R1)=f2(f)
X(C1)=f3(f)
where f1...f3 are the frequency dependend functions for the impedance of the components L1, R1 and C1 and f is the frequency.
Step 2 would be to write down the network equations.
2.1: Look at R1 and C1, this circuit can be replaced by a single complex impedance X(CR). To do this, forget L1 for a while, look only at R1 and C1 and the circuit they make.
2.2: Having replace R1 and C1 by a single impedance X(CR), now include L1 into the equation. What kind of circuit make X(CR) and X(L)? Calculate Vout as a function of Vin, X(L1) and X(CR).
Step 3: Now you should have something like Vout=Vin*foo(f) where foo(f) is the complex equation you have developed in the other steps. You next convert this to Vout/Vin=foo(f).
Step 4: From foo(f) you can find the amplitude and phase of the transfer function with respect to frequency. By putting the desired phase and/or amplitude into these equations and solving for the frequency f you'll arrive at the result.

This is the "hard" way, the way I was meant to learn it. Of course, you could built the circuit and find the result by testing and measuring it. Or you could use a simulator like SPICE. But both these ways will not help you gain insight about what's going on in the circuit.

Harald
 

Laplace

Apr 4, 2010
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A simple method for doing it the hard way is to write the node equations (in this case write one equation since there is only one node in the circuit) then have a symbolic algebra engine create the Bode plot. One can examine the transfer function of the circuit to determine a frequency where the reactive component goes to zero as the point where there is no phase shift from input to output. But no such point other than DC could be found for this circuit. See attachment. For some unknown (to me) reason the program would not use a log scale frequency axis.
 

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