GATE 2014 EC (EC1) – Question 65
A lossless line has characteristic impedance 50 Ω. The input impedance of a $\lambda/8$ section is real when terminated by $Z_L=R+jX$ Ω. For X = 30 Ω, find R (Ω).
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Correct answer: 39 to 41
Explanation
For lengthλ/8, tan(βl)=1. Thus Zin=50[R+j(X+50)]/[(50−X)+jR]. Multiplying by the conjugate denominator, its imaginary numerator is(50+X)(50−X)−R²=2500−X²−R². Setting it to zero with X=30Ω gives R²=1600, hence the passive load has **R=40Ω**.