A 300Ohm lossless transmission line is connected on one side

A 300Ohm, lossless transmission line is connected on one side to a generator and the other to a load. The generator is matched to the line. The load is an antenna with impedance 73+j42Ohm. The antenna is matched to the line with a short circuited stub, made of a lossless transmission line with characteristic impedance of 200Ohm connected in parallel to the line. Find the location of the stub and its length to accomplish the required task.

Solution

For a lossless transmission line the propagation constant is purely imaginary, =j, so the reflection coefficient can be written as

Where

in calculating B the wavelength is generally different inside the transmission line to what it would be free space and the velocity constant of the material the transmission line is made of needs to be taken care of , when doing calculation.