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Find the characteristic impedance of a quarter wave with input and load impedances given by 50 and 25 respectively.

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in Electromagnetic Theory by (188k points)
Find the characteristic impedance of a quarter wave with input and load impedances given by 50 and 25 respectively.

(a) 50

(b) 25

(c) 75

(d) 35.35

I have been asked this question in my homework.

Asked question is from Transmission Line Equations topic in section Transmission Lines of Electromagnetic Theory

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Right answer is (d) 35.35

To explain I would say: For a quarter line wave, the characteristic impedance is the geometric mean of input and load impedances. Thus Zo^2 = Zin ZL. On substituting for Zin = 50 and ZL = 25, we get Zo^2 = 50 x 25. The characteristic impedance will be 35.35 ohm.

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