A 50 ohmlossless air transmission line is terminated in a load impedance Z L = 1

Question

A 50 ohmlossless air transmission line is terminated in a load impedance ZL = 12.5 + j20 ohm. Find the following using a Smith Chart:

i)              the load admittance YL.

ii)            the closest distance to the load plane where the normalized admittance on the line is 1 + jbN.

iii)           the length of a short-circuited stub of characteristic impedance Zos=100 ohm which, upon placement in shunt with the line at the 1 + jbN admittance point, produces impedance matching on the line so that there exists no reflected wave to the left of the short-circuit placement plane.

A 50 ohmlossless air transmission line is terminated in a load impedance ZL = 12.5 + j20 ohm. Find the following using a Smith Chart: the load admittance YL. the closest distance to the load plane where the normalized admittance on the line is 1 + jbN. the length of a short-circuited stub of characteristic impedance Zos=100 ohm which, upon placement in shunt with the line at the 1 + jbN admittance point, produces impedance matching on the line so that there exists no reflected wave to the left of the short-circuit placement plane.

Explanation / Answer

the impedance of the circuit is

Z = (12.5^2 + 20^2)^1/2 ohm

the admittance is

Y = (1/Z)

the closest distance is

S = (1^2 + bN^2)^1/2

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