GATE EC 2012 Electromagnetics Solution Q 6

GATE EC 2012 Electromagnetics Solution Q 6

A transmission line with a characteristic impedance of 100Ω  is used to match a 50Ω section to a 200Ω section. If the matching is to be done both at 429 MHz and 1 GHz, the length of the transmission line can be approximately _.

(a) 82.5 cm

(b) 1.05 m

(c) 1.58 m

(d) 1.75 m

Ans :- (c)

Explanation

Our problem could be solved by the length of line equal to odd multiple of λ/4; where λ is the LCM of given wavelengths.

\lambda_1=\frac{3\times10^8}{429\times10^6}=0.699\approx70\;cm \lambda_2=\frac{3\times10^8}{10^9}=0.3=30\;cm

LCM of \left(\lambda_1,\lambda_2\right),\;\lambda=210\;cm

Now, \frac\lambda4=\frac{210}4=52.5\;cm

Odd multiple of \lambda/4\;is\;3\times\frac\lambda4=157.5\approx1.58\;m

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