# Microwave Engineering Questions and Answers – General Solutions-TE,TEM,TM Waves

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This set of Microwave Engineering Problems focuses on “General Solutions-TE,TEM,TM Waves”.

1. Maxwell’s equation for electromagnetic waves in a waveguide is:
a) ∇×E = -jωµ(vector H)
b) ∇×E =-jωμ(vector E)
c) ∇×H=-jωμ(vector H)
d) ∇×H=jωμ(vector H)

Explanation: Maxwell’s equation governs the propagation of waves in a waveguide. This equation describes the relation between electric field and magnetic field inside the waveguide.

2. If the wavelength of a signal is 10 mm, then the wavenumber of the material when a waveguide is filled with that material is:
a) 628
b) 345
c) 123
d) None of the mentioned

Explanation: The wave number is given by the expression 2π/λ. Substituting the given wavelength, wave number is 628.

3. If a waveguide is filled with a lossy material then the expression for ∈ for that material is:
a) ∈=∈∈r(1-jtan δ)
b) ∈= ∈ₒ∈r (1/ j tanδ)
c) ∈=∈ₒ∈r/(1+ j tan δ )
d) ∈=∈ₒ∈r/(1-j tan δ )

Explanation: When a waveguide is filled with a dielectric of or any lossy material, the relative permittivity is given by ∈=∈∈r(1-jtan δ).
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4. If a waveguide is filled with a lossless material of relative permeability 2, then the wave impedance in the TEM mode is:
a) 188.5 Ω
b) 170 Ω
c) 123 Ω
d) 345 Ω

Explanation: The wave impedance is given by the expression /√∈. is the intrinsic impedance of the medium substituting the given values in the above expression, wave impedance is 188.5 Ω.

5. If the wave impedance of a medium is 200 Ω, then what is the relative permittivity of that medium?
a) 1.885
b) 2
c) 2.2
d) 2.5

Explanation: The wave impedance is given by the expression /√∈. is the intrinsic impedance of the medium substituting the given values in the above expression, the relative permittivity is 1.885.

6. If p=0.3 and the wave number of air in TM mode is 16, then the intrinsic impedance of air in TM mode given wave number is 125 is:
a) 1 Ω
b) 0.9 Ω
c) 0.8 Ω
d) 2 Ω

Explanation: Intrinsic impedance for TM mode of propagation is given by β/k. substituting the given values in the above equation; the intrinsic impedance is 0.9 Ω.

7. If the intrinsic impedance of a medium is 0.8 Ω, with wave number 125 and β being 0.2, then the relative permeability of the medium is:
a) 1.326
b) 2.34
c) 4.5
d) 6.7

Explanation: Intrinsic impedance for TM mode of propagation is given by β/k. substituting the given values in the above equation; the permeability of the medium is 1.326.

8. The losses that occur in a transmission line is:
a) Conduction losses
b) Di-electric loss
c) Both of the mentioned
d) None of the mentioned

Explanation: Both conductor loss and dielectric loss occur in a transmission medium. Conductor loss is due to the property of the transmission line while dielectric loss is due to the medium inside the transmission line.

9. Which of the following is true regarding attenuation?
a) Conductor loss
b) Di-electric loss
c) Sum of both conductor loss and di electric loss
d) Attenuation is different from the losses

Explanation: Attenuation of a propagating wave is due to both the irregularities in the waveguide and as the property of the dielectric material. Hence attenuation of a propagating wave is due to both conductor loss and dielectric loss.

10. If the wave number of a medium is 20 and loss tangent is 0.4 , then the dielectric loss caused by the medium is:
a) 4
b) 2
c) 3
d) 6

Explanation: Dielectric loss in a medium is given by the expression k tan δ/2. Substituting the given value of loss tangent and wave number dielectric loss is 4 Np/m.

11. If the dielectric loss of a medium is 0.2 Np/m with a wave number of 12, then the value of loss tangent is:
a) 0.0334
b) 0.05
c) 0.08
d) 0.09

Explanation: Dielectric loss in a medium is given by the expression k tan δ/2. Substituting the given values, the loss tangent of the medium is 0.0334.

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