# Microwave Engineering Questions and Answers – Lossy Transmission Lines

This set of Microwave Engineering Multiple Choice Questions & Answers (MCQs) focuses on “Lossy Transmission Lines”.

1. For a low loss line when both conductor and di-electric loss is small, the assumption that could be made is:
a) R < < ωL and G < < ωC
b) R > > ωL and G > >ωC
c) R < <ωC and G < < ωL
d) R > >ωC and G > >ωL

Explanation: For a low loss line, the real part of impedance and admittance, that is resistance and conductance must be very small compared to the complex part of admittance and impedance for maximum power transfer. Hence R < <ωL and G < < ωC.

2. Expression for α(attenuation constant) in terms of R , G, L and C of a transmission line is:
a) (R√(C/L)+G√(L/C))0.5
b) (R√(C/L)+G√(L/C))
c) (R√(L/C)+G√(C/L))
d) (R√(L/C)+G√(C/L))0.5

Explanation: For a low loss line, the real part of impedance and admittance, that is resistance and conductance must be very small compared to the complex part of admittance and impedance for maximum power transfer. Hence R < <ωL and G < < ωC, with this assumption, modifying the expression for propagation constant, the simplified expression for attenuation constant α is (R√(C/L)+G√(L/C))0.5.

3. Expression for characteristic impedance Zₒ of a transmission line in terms of L and C the transmission line is:
a) √(C/L)
b) √(CL)
c) √(L/C)
d) 1/√(LC)

Explanation: For a low loss line, the real part of impedance and admittance, that is resistance and conductance must be very small compared to the complex part of admittance and impedance for maximum power transfer. HenceR < <ωL and G < < ωC, with this assumption, modifying the expression for characteristic impedance√(((R+jωL))/√(G+jωC)), the ratio reduces to √ (L/c).

4. If the inductance and capacitance of a loss line transmission line are 45 mH/m and10 µF/m, the characteristic impedance of the transmission line is:
a) 50Ω
b) 67.08Ω
c) 100Ω
d) none of the mentioned

Explanation: The expression for characteristic impedance of a transmission line in terms of inductance and capacitance of a transmission line is√((L)/C). Substituting the given values in this equation, the characteristic impedance of the transmission line is 67.08Ω.

5. If the characteristic impedance of a transmission line is 50 Ω, and the inductance of the transmission line being 25 mH/m, the capacitance of the lossy transmission line is:
a) 1µF
b) 10 µF
c) 0.1 µF
d) 50 µF

Explanation: The expression for characteristic impedance of a transmission line in terms of inductance and capacitance of a transmission line is√((L)/C). Substituting the given values in this equation, and solving for C, value of C is 10µF.

6. If R = 1.5Ω/m, G = 0.2 mseimens/m, L = 2.5 nH/m, C = 0.1 pF/m for a low loss transmission line, then the attenuation constant of the transmission line is:
a) 0.0.158
b) 0.0523
c) 0.0216
d) 0.0745

Explanation: The expression for attenuation constant of a low loss transmission line is (R√(C/L)+G√(L/C))0.5. Substituting the given values in the above expression, the value of attenuation constant is 0.0158.

7. A lossy line that has a linear phase factor as a function of frequency is called:
a) distortion less line
b) terminated lossy line
c) loss less line
d) lossy line

Explanation: A distortion less transmission line is a type of a lossy transmission line that has a linear phase factor as a function of frequency. That is, as the frequency of operation changes, the phase variation is linearly dependent.

8. The condition for a distortion less line is:
a) R/L=G/C
b) R/C=G/L
c) R=G
d) C=L

Explanation: The special case of a lossy transmission line that has a linear phase factor as a function of frequency is called distortion less line. The relation between the transmission line constants for such a distortion less line R/L=G/C.

9. For a distortion less line, R= 0.8Ω/m, G= 0.8 msiemens/m, L= 0.01µH/m then C is:
a) 10 pF
b) 1pF
c) 1nF
d) 10nF

Explanation: The special case of a lossy transmission line that has a linear phase factor as a function of frequency is called distortion less line. The relation between the transmission line constants for such a distortion less line R/L=G/C. substituting the given values in the equation, we get 10pF.

10. For a lossy transmission line, γ=0.02+j0.15 and is 20m long. The line is terminated with an impedance of a 400Ω. Then the input impedance of the transmission line given that the characteristic impedance of the transmission line is 156.13+j11.38Ω is:
a) 100+j50 Ω
b) 228+j36.8 Ω
c) 50+36.8j Ω
d) none of the mentioned

Explanation: The relation between source impedance, propagation constant and characteristic impedance is given by ZS= Z0 (ZLcosh(γl) + Z0 sinh(γl))/( Z0cosh(γl) + ZL sinh(γl)). Substituting the given values in the above equation, input impedance of the transmission line is 228+j36.8 Ω.

Sanfoundry Global Education & Learning Series – Microwave Engineering.
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