# Microwave Engineering Questions and Answers – Transmission Line Resonators

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

1. Lumped elements can be used to make resonators that rare to be operated at microwave frequencies.
a) True
b) False

Explanation: Lumped elements cannot be used at microwave frequencies since their behavior is not deterministic at these frequencies and the required response cannot be achieved.

2. Short circuited λ/2 transmission line has a quality factor of:
a) β/2α
b) 2β/α
c) β/α
d) Z0/ZL

Explanation: Quality factor of a short circuited transmission line is a function of attenuation constant and phase constant of the transmission line. Higher is the attenuation in the transmission line, lower is the quality factor of the transmission line.

3. Quality factor of a coaxial cable transmission line is independent of the medium between the wires of the transmission line.
a) True
b) False

Explanation: Quality factor is dependent on the permeability of the medium between the inner and outer conductor of the co-axial cable. For example, air has twice the quality factor as that of Teflon filled co-axial fiber.
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4. A coaxial cable is air filled with air as dielectric with inner and outer radius equal to 1 mm and 4 mm. If the surface resistivity is 1.84*10-2Ω,then the attenuation due to conductor loss is:
a) 0.011
b) 0.022
c) 0.11
d) 0.22

Explanation: Conductor loss in a coaxial cable is given by Rs(a-1+b-1)/2ln (b/a). Here ‘a’ and ‘b’ are the inner and outer radii of the coaxial cable. is the intrinsic impedance of the medium, for air is 377Ω. Substituting the given values in the equation, conductor loss is 0.022 Np/m.

5. An air coaxial cable has attenuation of 0.022 and phase constant of 104.7, then the quality factor of a λ/2 short circuited resonator made out of this material is:
a) 2380
b) 1218
c) 1416
d) Insufficient data

Explanation: Quality factor of a λ/2 short circuited transmission line is β/2α. β is the phase constant and α is the attenuation constant of the line, substituting the given values, the quality factor of the transmission line is 2380.

6. The equivalent resistance of a short circuited λ/4 transmission line is independent of the characteristic impedance of the transmission line.
a) True
b) False

Explanation: The equivalent resistance of a short circuited λ/4 transmission line is dependent of the characteristic impedance of the transmission line. The expression for equivalent resistance is Z0/αl. Resistance of a short circuited line is directly proportional to the characteristic impedance of the transmission line.

7. A microstrip patch antenna has a width of 5.08mm and surface resistivity of 1.84*10-2. Then the attenuation due to conductor loss is:
a) 0.0724
b) 0.034
c) 0.054
d) None of the mentioned

Explanation: Attenuation due to conductor loss of a microstrip line is given by Rs/Z0W. Substituting the given values, attenuation due to conductor loss is 0.0724 Np/m.

8. If the attenuation due to dielectric loss and attenuation due to conductor loss in a microstrip transmission line is 0.024Np/m and 0.0724 Np/m, then the unloaded quality factor if the propagation constant is 151 is:
a) 150
b) 783
c) 587
d) 234

Explanation: Unloaded Q for a microstrip line is given by β/2α. Α is the sum of attenuation due to conductor loss and dielectric loss. Substituting the given values the equation, unloaded Q is 783.

9. The equivalent capacitance of a short circuited λ/4 transmission line is dependent on the characteristic impedance of the transmission line.
a) True
b) False

Explanation: Equivalent capacitance of a short circuited λ/4 transmission line is dependent on the characteristic impedance of the transmission line. It is inversely proportional to the characteristic impedance of the transmission line. Equivalent capacitance is π/4ω0Z0.

10. Inductance of an open circuited λ/2 transmission line is dependent on the characteristic impedance of the transmission line.
a) True
b) False

Explanation: Inductance of an open circuited λ/2 transmission line is dependent on the characteristic impedance of the transmission line. Expression for inductance is 1/ω02c, C is the equivalent capacitance of the open circuited line. C has the expression π/4ω0Z0.

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