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Impedance Basics

May 12th, 2006

So I was sitting around today wondering what I know about impedance. I come across the term impedance a lot in analog circuit design. If you understand ohm’s law and the concept of resistance in DC circuit, then impedance is the generalization of the concent from DC to AC. In short, impedance is basically a measure of the total opposition to the current flow in an AC circuit. It is made up of two components, the resistance and the reactance. Impedance (Z) is expressed in complex number. Z=R+jX. Where R is the resistance and X is the reactance.

In AC we not only have the amplitude, we also have the frequency and phase, therefore impedance not only allow the current to flow but also changes the phase, as frequency changes, it also changes the ampltitudes and phases. In ideal resistor, which means ignoring all the parasitics, we should expect to see the same impedance for all frequencies. In ideal cap, we will have the impedance that goes down with increasing frequency. In an inductor, we will have the impedance that goes up with increasing frequency.

There is a linear relation between impedances for capacitor and inductor with respect to frequency. The phase for inductor’s voltage is always 90 degrees ahead of its current. The capacitor’s current leads the voltage.

Simple MATLAB Script to calculate impedance is shown below.
Download impedance.m

% Matlab script to calculate impedance for series and parallel circuits
% Author: Ridwan Chendarma Chin
mode=input(’Select 1 for series and 2 for parallel: ‘);

C=input(’C= ‘);
R=input(’R= ‘);
L=input(’L= ‘);
f=input(’f= ‘);

X_C=1/(2*pi*f*C);
X_L=2*pi*f*L;

Z_C=(0-j*X_C);
Z_L=(0+j*X_L);
Z_R=(R+j*0);

if (mode == 2)
Z_T=1/((1/Z_C)+(1/Z_L)+(1/Z_R));
else
Z_T=Z_C+Z_L+Z_R;
end

Z_mag=abs(Z_T) % magnitude
Z_angle=angle(Z_T)*(180/pi) % angle in degrees

Filed under: Analog Design