Question

The characteristic impedance of a quarter wave transformer with load and input impedances given by 30 and 75 respectively is

(a) 47.43

(b) 37.34

(c) 73.23

(d) 67.45

I have been asked this question by my school teacher while I was bunking the class.

My question is based upon Input and Characteristic Impedances topic in chapter Transmission Lines of Electromagnetic Theory

Answer 1

Correct option is (a) 47.43

To elaborate: In quarter wave transformer, the characteristic impedance will be the geometric mean of the input impedance and the load impedance. Thus Zo^2 = ZIN ZL. On substituting for ZIN = 75 and ZL = 30, we get the characteristic impedance as 47.43 units.