# Electromagnetic Theory Questions and Answers – Transmission Line Equations

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This set of Electromagnetic Theory Multiple Choice Questions & Answers (MCQs) focuses on “Transmission Line Equations”.

1. Which of the following parameters does not exist in the transmission line equation?
a) R
b) Zo
c) ZL
d) Propagation constant

Explanation: The transmission line equation consists of secondary parameters only, which are derived from the primary parameters. The propagation constant, load impedance and the characteristic impedance are related in the transmission line equation.

2. For an infinite transmission line, the characteristic impedance is given by 50 ohm. Find the input impedance.
a) 25
b) 100
c) 2500
d) 50

Explanation: From the transmission line equation, the infinite line will have an input impedance same as that of the characteristic impedance. Thus Zin = Zo for l->∞. This shows that the line will be matched. The input impedance for the given case is 50 ohm.

3. The best transmission length for effective transmission of power is
a) L = λ/4
b) L = λ/8
c) L = λ/2
d) L = ∞

Explanation: Maximum transmission of power will occur, when the transmission line is matched. This implies that the input and characteristic impedances are the same. This condition is possible for l = λ/8 and l = ∞. Since l = ∞ is not feasible, the best option is l = λ/8.
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4. When the length of the transmission line is same as that of the wavelength, then which condition holds good?
a) Zin = Zo
b) Z = Zo
c) ZL = Zo
d) Zin = ZL

Explanation: When the transmission line has a length same as that of the wavelength of the wave propagating through it, the input impedance will be same as the load impedance. This is the case where the wave is not amplified. The transmission line acts as a buffer.

5. The input impedance of a half wave transmission line with a load impedance of 12.5 ohm is
a) 25
b) 50
c) 6.25
d) 12.5

Explanation: For a half wave transmission line L = λ/2, the input and the load impedances will be the same. Thus for the given data, the input impedance will be 12.5 ohm.

6. The condition for a quarter wave transformer is
a) Zo2 = Zin ZL
b) Zo = Zin ZL
c) ZL2 = Zin Zo
d) Zo = Zin

Explanation: The quarter wave transformer represents L = λ/4. In this case, the characteristic impedance is the geometric mean of the input and load impedances. Thus Zo2 = Zin ZL is the required condition.

7. Find the characteristic impedance of a quarter wave with input and load impedances given by 50 and 25 respectively.
a) 50
b) 25
c) 75
d) 35.35

Explanation: For a quarter line wave, the characteristic impedance is the geometric mean of input and load impedances. Thus Zo2 = Zin ZL. On substituting for Zin = 50 and ZL = 25, we get Zo2 = 50 x 25. The characteristic impedance will be 35.35 ohm.

8. Find the load impedance in a quarter line transformer with characteristic impedance of 75 ohm and input impedance of 200 ohm.
a) 28.125
b) 12.285
c) 52.185
d) 85.128

Explanation: For a quarter line wave, the characteristic impedance is the geometric mean of input and load impedances. Thus Zo2 = Zin ZL. On substituting for Zo = 75 and Zin = 200, we get ZL = Zo2/Zin = 752/200 = 28.125 ohm.

9. The reflection coefficient of a perfectly matched transmission line is
a) 1
b) -1
c) 0
d) ∞

Explanation: In a perfectly matched line, maximum power transfer will occur. Losses will be minimal. This implies unity transmission coefficient and zero reflection coefficient.

10. The purpose of the transmission line equation is to
a) Find primary parameters
b) Find secondary parameters
c) Find the reflection cofficient
d) Impedance matching

Explanation: The transmission line equation is useful in finding the length of the line which gives maximum power transfer. Thus it is useful for impedance matching.

11. The quarter wave transformer can be considered as a
a) Impedance inverter
b) Impedance doubler
c) Impedance tripler

Explanation: A quarter wave transformer may be considered as an impedance inverter as it can transform a low impedance into a high impedance and vice-versa.

12. Which transmission line is called as one to one transformer?
a) L = λ
b) L = λ/2
c) L = λ/4
d) L = λ/8

Explanation: The half wave transformer line repeats its terminating impedance. In other words, when l = λ/2, Zin = ZL. Thus it is considered to be one to one transformer.

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