# Microwave Engineering Questions and Answers – Surface Waves on Grounded Di-electric Sheet

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This set of Microwave Engineering Questions and Answers for Freshers focuses on “Surface Waves on Grounded Di-electric Sheet”.

1. Surface waves are typical by a field that decays ______away from the dielectric surface, with most of the field contained in or near the dielectric.
a) Linearly
b) Exponentially
c) Cubical
d) Field remains a constant

Explanation: Surface waves are typified by a field that decays exponentially away from the dielectric surface, with most of the field contained in or near the dielectric. At higher frequencies, the field generally becomes more tightly bound to the dielectric, making such waveguides practical.

2. Because of the presence of the dielectric, the phase velocity of a surface wave is:
a) Greater than that in vacuum
b) Lesser than that in vacuum
c) Independent of the presence of dielectric
d) Insufficient data

Explanation: The fields are stronger and concentrated near the dielectric, and hence because of the presence of the dielectric, the phase velocity of a surface wave is lesser than that in vacuum.

3. For wave propagation on grounded dielectric sheet, the equation to be satisfied by Ez , in the region of presence of dielectric 0≤x≤d for the propagation to be in Z direction
a) (∂2/∂x2 + ∈rk02– β2) eZ(x,y)=0
b) (∂2/∂x2 + k02– β2) eZ(x,y)=0
c) (∂2/∂x2 – k022) eZ(x,y)=0
d) (∂2/∂x2 + ∈rk02) eZ(x,y)=0

Explanation: The equation describes the variation of the electric field along the direction of propagation that is the Z direction. In the equation, it is clear that the relative permittivity of the dielectric is also a part of the second term of the equation.
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4. The cut off wavenumber for the region of dielectric in a grounded dielectric sheet is:
a) kC2= ∈rk022
b) kC2= ∈rk022
c) h2= -k022
d) kC2= k2 + β2

Explanation: Cutoff wave number signifies the minimum threshold wave number required for propagation. Here the expression kC2= ∈rk022 gives the cutoff wave number for the propagation of waves on a grounded dielectric sheet.

5. For surface waves on a dielectric sheet the cutoff frequency of the TM mode can be given as:
a) fC = nC/2d√(ϵr-1)
b) fC = C/2nd√(ϵr-1)
c) fC = C/2nd√ϵr
d) fC = 2C/nd√ϵr

Explanation: Grounded dielectric sheets allow TM mode of propagation on them. The cut off frequency for the propagation of TM mode is given by the expression fC = nC/2d√(ϵr-1).

6. The cutoff frequency in TM1 mode for the propagation of EM waves on dielectric slab of relative permittivity 2.6 and thickness 20 mm is:
a) 6.5 GHz
b) 5.92 GHz
c) 4 GHz
d) 2 GHz

Explanation: The expression for cutoff frequency for wave propagation in TMn mode is fC = nC/2d√(ϵr-1).here n represents the mode. Substituting the given values, cutoff frequency is 5.92 GHz.

7. In TE of propagation, HZ must obey the below equation for wave propagation in the region of presence of dielectric:
a) (∂2/∂x2 + kc2) hZ(x,y)=0
b) (∂2/∂x2– h2)hZ(x,y)=0
c) (∂2/∂x2 – Kc2)hZ(x,y)=0
d) (∂2/∂x2 +h2)hZ(x,y)=0

Explanation: In TE mode of propagation,, electric field does not exist in the direction of wave propagation. Hence only magnetic field exists in the direction of wave propagation. This magnetic field must obey the equation (∂2/∂x2 + kc2) hZ(x,y)=0

8. Cutoff frequency fC for TEM mode of propagation is:
a) Fc= (2n-1)c/4d√εr -1
b) Fc= (2n-c)/2d(√εr-1)
c) Fc= (2n-1)/4d(√εr)
d) Fc= (2n-1)/8d√εr – 1

Explanation: Grounded dielectric sheets allow TE mode of propagation on them. The cut off frequency for the propagation of TM mode is given by the expression (2n-1)c/4d√εr -1 .

9. What is the cutoff frequency of TE₁ mode of propagation if the relative permittivity of the slab is 3.2 and the thickness of the slab is 45 mm?
a) 2.24 GHz
b) 4 GHz
c) 1.12 GHz
d) 8 GHz

Explanation: The expression for cutoff frequency for wave propagation in TEN mode is (2n-1)c/4d√(εr -1). substituting the given values in the above expression, the cutoff frequency for TE₁ mode of propagation is 1.12 GHz.

10. The first propagating mode on a grounded dielectric is:
a) TMO mode
b) TM1 mode
c) TM2 mode
d) TM3 mode