# Plotting Impedance of Parallel RLC Circuit

• Engineering
In summary, the conversation discusses a circuit with elements in parallel, with R=100, C=600 pf, and L=10E-6 H. The resonant frequency is identified as f0=1/(2(pi)sqrt(LC)). The attempt at a solution involves converting between impedance and admittance, but contains algebraic mistakes. The plot in Matlab shows a vertical line due to dividing by zero and not taking the magnitude of the impedance expression. To fix this, the imaginary component must be removed and the magnitude must be plotted instead.

## Homework Statement

Plot |z| vs. f(Hz) of the circuit. R=100, C=600 pf = 6E-12 F, L=10E-6 H . All elements of the circuit are in parallel. Also identify the resonant frequency.

## Homework Equations

ZR=R
ZL=jwL
ZC=1/(jwC)=-j/(wC)
w=2(pi)f
w0=1/sqrt(LC)
f0=1/(2(pi)sqrt(LC))
G=1/R

## The Attempt at a Solution

Z1=ZR
Z2=ZL
Z3=ZC
Zeq= 1/((1/R)+1/(jwL)+jwc)

Switching to admittance and skipping a few steps, it can be found that
Y=G + j * 2 * pi * f * C * (1 - (f0 / f) ^ 2)
Z=R + 1 / (j * 2 * pi * f * C * (1-(f0 / f) ^ 2))
Z=100 + 1/(j * 2 * pi * f * 600E-12 *(1 - (2054681.48 / f) ^ 2)

To plot, i used a few lines in matlab:

f=linspace(0,4000000,100000);
x=1i.*2.*pi.*(600.^(-12));
z=100+(1./(x.*f.*(1-((2054681.48./f).^2))));
plot=semilogx(z);

The plot shows me a vertical line at f=100

My professor told us that the graph should be bell shaped, and i have no idea where I've gone wrong. Anyone see a mistake?

For one thing, 1/(a+b) isn't equal to 1/a + 1/b, which is what you did when you went from the admittance back to the impedance.

Ok, change it to this then:

Z=1/(100 + j * 2 * pi * f * 600E-12 *(1 - (2054681.48 / f) ^ 2))

The plot is still a vertical line.

Well, that's not quite right either. I'll leave it to you, however, to fix your algebra mistakes.

I don't know Matlab, but I'm guessing you're letting f start from 0. Two problems with that. At f=0, you're dividing by zero in your expression. Also, when f=0, Z=0 since the inductor is a short, so the log of Z is undefined.

In this expression:

x=1i.*2.*pi.*(600.^(-12));
...^

is that lower case i that I've pointed to supposed to represent SQRT(-1)?

If it is, that's a problem. You can't plot expressions that have an imaginary component. You have to plot the magnitude, or modulus, of the impedance expression.

Some mathematical packages have a command such as Abs[] that can do it. Or you can do it yourself by plotting SQRT(Z * Conjugate(Z)).