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It is required to match a 200Ω load to a 300Ω transmission line to reduce the SWR along the line to 1. What must be the characteristic impedance of the quarter-wave transformer used for this purpose, if it is connected directly to the load?

It is required to match a 200Ω load to a 300Ω transmission line to reduce the SWR along the line to 1. What must be the characteristic impedance of the quarter-wave transformer used for this purpose, if it is connected directly to the load? Correct Answer 245Ω 

Concept:

In a quarter-wave impedance transformer, a quarter wavelength transmission line is used to change the impedance of the load to another value so that impedance is matched.

Quarter-wave impedance transformers are designed for a particular frequency and the length of the transformer is equal to λ/4 only at this designed frequency. ​

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Charecteristics impedance: Z1 = √(Z0 ZL) 

Calculation:

GIven;

ZL = 200 Ω 

Z0 = 300 Ω 

Charecteristics impedance:

Z1 = √(Z0 ZL)

= √(2000 × 300)

= 244.94 Ω ≈ 245 Ω

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