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# GATE : Transmission lines questions

1) Two very long loss-less cables of characteristic impedances of 50 $\Omega$ and 100 $\Omega$ respectively are to be joined for reflection less transmission. If the quarter wave transformer is used for matching, what should be the value of its impedance(in ohms)?

a) 70.7
b) 35.7
c) 50
d) 2

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

a) 82.5cm
b) 1.05m
c) 1.58m
d) 1.75m

3) Impedance of a transmission line repeats itself every

a) $\lambda$/4
b) $\lambda$/2
c) $\lambda$
d) 2$\lambda$

4) If $Z_{open}$ is the impedance of a open circuited transmission line and $Z_{short}$ is the impedance of a short circuited transmission line whose characteristic impedance is $Z_o$. Then which of the following relationship is true?

a) $Z_o$ =$\frac{Z_{open}}{Z_{short}}$
b) $Z_o$ =$Z_{open}$ * $Z_{short}$
c) $Z_o$ =$\sqrt{\frac{Z_{open}}{Z_{short}}}$
d) $Z_o$ =$\sqrt {Z_{open}*Z_{short}}$

5) A transmission line of characteristic impedance 50 $\Omega$ is terminated by a 50 $\Omega$ load. When excited by a sinusoidal voltage source at 10 GHz, the phase difference between two points spaced 2 mm
apart on the line is found to be π/4 radians. The phase velocity of the wave along the line is

a) 0.8* $10^8$ m/s
b) 1.2*$10^8$ m/s
c) 1.6*$10^8$ m/s
d) 3*$10^8$ m/s

A transmission line of characteristic impedance 50 $\Omega$ is terminated in a load impedance . The
VSWR of the line is measured as 5 and the first of the voltage maxima in the line is observed at a
distance of $\lambda$/4 from the load. The value of $Z_L$ is
(A) 10 $\Omega$
(B) 250 $\Omega$
(C) (19.23 + j46.15) $\Omega$
(D) (19.23 – j46.15) $\Omega$

….

1-a, 2-c , 3-b, 4-d