# Microwave Engineering Questions and Answers – Rectangular Waveguide

This set of Microwave Engineering Multiple Choice Questions & Answers (MCQs) focuses on “Rectangular Waveguide”.

1. The modes of propagation supported by a rectangular wave guide is:
a) TM, TEM, TE modes
b) TM, TE
c) TM, TEM
d) TE, TEM

Explanation: A hollow rectangular waveguide can propagate TE and TM modes. Since only a single conductor is present, it does not support TEM mode of propagation.

2. A hollow rectangular waveguide cannot propagate TEM waves because:
a) Of the existence of only one conductor
b) Of the losses caused
c) It is dependent on the type of the material used
d) None of the mentioned

Explanation: A rectangular hollow waveguide can propagate both TE and TM modes of propagation. But due the presence of only one conductor, rectangular waveguide does not support the propagation of TEM mode.

3. For any mode of propagation in a rectangular waveguide, propagation occurs:
a) Above the cut off frequency
b) Below the cut off frequency
c) Only at the cut-off frequency
d) Depends on the dimension of the waveguide

Explanation: Both TE and TM modes of propagation in rectangular waveguide have certain separate and specific cut off frequencies below which propagation is not possible. Hence propagation of signal occurs above the cut off frequency.

4. In TE mode of wave propagation in a rectangular waveguide, what is the equation that has to be satisfied?
a) (∂2/ ∂x2 + ∂2/ ∂y2+ kC2).HZ(x, y) =0
b) (∂2/ ∂x2 + ∂2/ ∂y2– kC2).HZ(x, y) =0
c) (∂2/ ∂x2 – ∂2/ ∂y2+ kC2).HZ(x, y) =0
d) None of the mentioned

Explanation: For TE mode of propagation in a rectangular waveguide, electric field along the direction of propagation is 0. Hence for propagation, the above partial differential equation in terms of magnetic field along Z direction has to be satisfied.

5. Dominant mode is defined as:
a) Mode with the lowest cut off frequency
b) Mode with the highest cut off frequency
c) Any TEM mode is called a dominant mode
d) None of the mentioned

Explanation: Among the various modes of propagation in a rectangular waveguide, the mode of propagation having the lowest cutoff frequency or the highest wavelength of propagation among the other propagating modes is called dominant mode.
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6. For TE1ₒ mode, if the waveguide is filled with air and the broader dimension of the waveguide is 2 cm, then the cutoff frequency is:
a) 5 MHz
b) 7.5 MHz
c) 7.5 GHz
d) 5 GHz

Explanation: The cutoff frequency for TE 10 mode of propagation in a rectangular waveguide is 1/2a√(∈μ) where ‘a’ is the broader dimension of the waveguide. Substituting for the given value and 1/√(∈μ)=3*108. The cutoff frequency is 7.5 GHz.

7. TEₒₒ mode for a rectangular waveguide:
a) Exists
b) Exists but defined only under special cases
c) Does not exist
d) Cannot be determined

Explanation: The field expressions for TEₒₒ mode disappears or becomes zero theoretically. Hence, TEₒₒ mode does not exist.

8. For dominant mode propagation in TE mode, if the rectangular waveguide has a broader dimension of 31.14 mm , then the cutoff wave number:
a) 100
b) 500
c) 50
d) 1000

Explanation: The cutoff wave number for the dominant mode of a rectangular waveguide is given by π/a where ‘a’ is the broader dimension of the waveguide, substituting the given values, the wave number 100.

9. The lowest mode of TM wave propagation is:
a) TM10 mode
b) TM01 mode
c) TM11 mode
d) TM12 mode

Explanation: The field components for other lower modes of propagation in TM mode disappear for other lower modes of propagation. Hence, the lowest mode of propagation is TM11 mode.

10. The cutoff frequency for the dominant mode in TM mode propagation for a rectangular waveguide of dimension of 30mm*40mm is:
a) 2 GHz
b) 1 GHz
c) 2 MHz
d) 4 MHz

Explanation: The cutoff frequency of dominant mode in TM mode is √((π/a)2 + (π/b)2). Here, ‘a’ and ‘b’ are the dimensions of the waveguide. Substituting the corresponding values, the cutoff frequency is 2 GHz.

11. In TE10 mode of wave propagation in a rectangular waveguide, if the broader dimension of the waveguide is 40 cm, then the cutoff wavelength for that mode is:
a) 8 cm
b) 6 cm
c) 4 cm
d) 2 cm

Explanation: In TE10 mode of propagation in a rectangular waveguide, the cutoff wavelength of the waveguide is given by 2a where ‘a’ is the broader dimension of the waveguide. Substituting, the cutoff wavelength is 8 cm.

12. In TE01 mode of wave propagation in a rectangular waveguide, if the smaller dimension of the waveguide is 2 cm, then the cutoff wavelength for that mode is:
a) 4 cm
b) 8 cm
c) 1 cm
d) 2 cm

Explanation: For TE01 mode of wave propagation in a rectangular wave guide, if the smaller dimension of the wave guide is 2 cm, then the cut off wavelength is 2b where b is the smaller dimension of the waveguide. substituting, the cutoff wavelength is 4 cm.

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