RLC Transfer Function Magnitude and Phase Response

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1582251394 2018-9-23

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评论： 1582251394 2018-9-23

Hi,

I am trying to plot the magnitude and phase response for a parallel RLC circuit. The curves look close to what it should be but for the magnitude response, it peaks at 1MHz and I was expecting 3.55MHz (angular frequency). Also, my phase response looks ok but I am unable to get the curve to rotate 180 degrees on its axis.

clc;
syms L C R w
pretty(abs(w.*j*L*R./(w.*L*j+1+j^2*w.^2*C*L*R)));
L = 2e-9;
C = 1e-6;
R = 500;
w = linspace(0.99e6,1.01e6,10000);
j=sqrt(-1);
subplot(2,1,1);
Z1 = abs(w.*j*L*R./(w.*L*j+1+j^2*w.^2*C*L*R));
plot(w,Z1);
subplot(2,1,2);
w = linspace(2*pi,-2*pi,10000);
Z2 = angle(w.*j*L*R./(w.*L*j+1+j^2*w.^2*C*L*R));
plot(w,Z2);

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Answer 1

David Goodmanson 2018-9-23

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Hi 2e9,

I don't know why you feel that the resonant circular frequency (w) should be 3.55e6 since 1/sqrt(L*C) = 2.24e7. The main problem is the expression for Z, which should be

(w.*j*L*R./(w.*L*j + R + j^2*w.^2*C*L*R))
                     ^

There had to be something wrong since the original expression is not correct on units and dimensions. If you change the plot range to

w = linspace(22.3e6,22.4e6,10000);

the resonance is where it should be.

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1582251394 2018-9-23

Thank you for noticing the mistake in the function. I originally had it in a different form and when I switched to this one, I forgot to add the R in the denominator. And for some reason, I was converting to frequency.

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