Microwave Engineering Multiple Choice Questions on “Lossless Lines”.
1. The value of ‘α’ for a lossless line is:
A. 0
B. 1
C. Infinity
D. Data insufficient
Answer: A
Clarification: α-for a transmission line signifies the attenuation constant. For a lossless transmission line attenuation constant is zero and the propagation occurs without losses.
2. If propagation constant is 12:60°, then the value of phase constant and attenuation constant is:
A. α=6, β=10.39
B. α=61, β=78
C. α=12, β=20.6
D. none of the mentioned
Answer: A
Clarification: The given propagation constant is in polar form .converting from polar form to rectangular form and equating the real and imaginary parts, we get α=6 and β=10.39.
3. If a transmission line with inductive reactance of 41.97 Ω and capacitive reactance of 1132.5Ω is operated at 1 GHz , then its phase constant is:
A. 0.0305
B. 0.3
C. 30.3
D. 0.6
Answer: A
Clarification: From the given inductive reactance and capacitive reactance, L and C are calculated using XL =2πfL and Xc = 1/2πfC. β=ω√LC, substituting the calculated L and C, we get β=0.0305.
4. The expression for a phase velocity of a transmission line is:
A. √LC
B. 1/√LC
C. XL+Xc
D. XL/Xc
Answer: B
Clarification: The expression for phase velocity is derived from known basic transmission line equations and the derived equation comes out to be 1/√LC .
5. If the admittance and the impedance of a transmission line are 100 Ω and 50 Ω of a respectively, then value of phase constant β is:
A. 0
B. 20
C. 132
D. 50
Answer: A
Clarification: β=ω√LC. Since both the line impedance and line admittance are both real, there is no phase difference caused and hence substituting in the above equation, we get β=0.
6. For a lossless line, which of the following is true?
A. γ=jβ
B. γ=α
C. γ=α+jβ
D. γ=α*jβ
Answer: A
Clarification: For a lossless line, attenuation constant α is 0. Hence substituting α=0 in γ=α+jβ, we get γ= jβ.
7. Expression for phase constant β is:
A. √LC
B. ω √LC
C.1/ (ω √LC.
D. None of the mentioned
Answer: B
Clarification: From the equation of γ in terms of Z and Y(impedance and admittance of the transmission line respectively), expanding the equation and making certain approximations, β= ω √LC.
8. A microwave generator at 1.2 GHz supplies power to a microwave transmission line having the parameters R=0.8Ω/m, G=O.8millisiemen/m, L=0.01µH/m and C=0.4PF/m. Propagation constant of the transmission line is:
A. 0.0654 +j0.48
B. 0.064+j4.8
C. 6.4+j4.8
D. none of the mentioned
Answer: A
Clarification: Z=R+jωL and Y=G+jωC, hence finding out Z and Y from these equations, substituting in γ=√ZY, value of γ is found out to be 0.0654+j0.48.
9. In a certain microwave transmission line, the characteristic impedance was found to be 210 10°Ω and propagation constant 0.2 78°.What is the impedance Z of the line, if the frequency of operation is 1 GHz?
A. 0.035+j41.97
B. 0.35+j4.97
C. 35.6+j4.28
D. 9.254+j4.6
Answer: A
Clarification: Impedance Z of a transmission line is given by the product of propagation constant γ and characteristic Zₒ, Z= γZₒ , we get Z=0.035+j41.97.
10. For a transmission line, L=1.8mh/m C=0.01pF/m, then the phase constant of the line when operated at a frequency of 1 GHz is:
A. 4.2426
B. 2.2
C. 0.3
D. 1
Answer: A
Clarification: Formula to calculate the phase constant β is β=ω√LC.substituting the given values of L,C and f, the value of β is 4.2426.
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