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in Physics by (45.7k points)

A transmission line with a characteristic impedance of 100 Ω is used to match a 50 Ω section to a 200 Ω 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

1 Answer

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Best answer

Correct option (c) 1.58 m  

Explanation:

This is quarter wave matching. The length would be odd multiples of λ/4.

l = (2m + 1) λ/4

f1 = 429MHz

 λ1/4 = (3 x 108)/(429 x 106 x 4)

l1 = 0.174m

f2 = 1GHz

λ2/4 = (3 x 108)/(109 x 4) = 0.075m

l2 = 0.075m

(2m + 1) = 1.58/l1 = 1.58/0.174 = 9

(2m + 1) = 1.58/l2 = 1.58/0.075 = 21

Only option (c) is odd multiples of both l1 and l2 .

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