Antenna and 300 ohm feeder

concentric300ohm

So what happens if you use a, say, 300 ohm feeder cable for your antenna.

First, We need to assume the feed point impedance, ZL, of the antenna. Let’s say the VSWR of the antenna when used with a coaxial cable is around 2, which means the absolute value of the reflection coefficient, abs(gamma), is 1/3 (red circle).

VSWR=(1+abs(gamma))/(1-abs(gamma))
abs(gamma)=(VSWR-1)/(VSWR+1)

Since the VSWR value tells you nothing about the phase of gamma, we assume 8 points (yellow dots) equispaced on the red circle.

By varying the cable length, the input impedance (red dots), Zin, observed at the near end of the cable, changes as is shown in the figure.

Appendix: How to get equispaced ZLs on a constant VSWR circle. Here VSWR is assumed to be 2, and therefore abs(gamma) to be 1/3. The code is in pseud-maxima.

z(g):=(1+g)/(1-g);
g(t):=(1/3)*(cos(t)+%i*sin(t));
t(n):=n*2.0*%pi/8.0;
n:1
50.0*float(realpart(z(g(t(n)))));
50.0*float(imagpart(z(g(t(n)))));