# Matlab help - plotting in polar coordinates

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#### StoppTidigare

##### Full Member level 2
Matlab help

Hi all, could somebody explain to what this
z = (r/(r+1) + 1/(r+1)*exp(j*theta));
comes from in the matlab-function below?

I know that constant r-circles are given by the eqn:
(U-r/(r-1))^2 +V^2=(1/(r+1))^2
and the constant x-circles is givne by
(U-1)^2 +(V-1/x)^2=(1/x)^2
Do you remember it from basic Smithchart theory ?

function [h] = smircirc(r)
%SMIRCIRC Draw impedance circle in the Smith chart. This function
%written by Soeren Laursen (slau93@control.auc.dk).
% [H] = SMIRCIRC(R) draws a circle with r = R and returns
% a handle to the circle in H.

global SMITH_CHART_UNDO
theta=linspace(-pi, pi, 63);
z = (r/(r+1) + 1/(r+1)*exp(j*theta));
if nargout > 0
h = plot(z);
SMITH_CHART_UNDO = [SMITH_CHART_UNDO h];
else
SMITH_CHART_UNDO = [SMITH_CHART_UNDO plot(z)];
end

What does he mean with impedance circle ? There's no such!
/StoppTidigare

#### flatulent

improper term

It should say that it draws the circles of constant real part of impedances (resistance)

I downloaded the complete program and played with it. The argument of smircirc (x) is the intersection of the left end of the circle with the horizontan axis through the center of the chart.

##### Newbie level 6
The constant impedance(r) circle is represented by the equation:
(U-r/(r+1))^2+V^2=(1/(r+1))^2,
It is a circle centered at the coordinates (r/(r+1),0) and having a radius
1/(r+1). So in a polar plot, it can be represented by
r/(r+1)+1/(r+1)*exp(j*theta).

the equation you refered: (U-r/(r-1))^2+V^2=(1/(r+1))^2) is not for the constant impedence circle.

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