Ques.1. In a dispersive medium, the group velocity is:

Less than the phase velocity only

Equal to the phase velocity only

More than the phase velocity, depending on the nature of the dispersive medium

More than the phase velocity

Answer.1. Less than the phase velocity only

Explanation:

In a dispersive medium, the group velocity is less than the phase velocity only. The phase velocity is always greater than the speed of light and group velocity is always less than the speed of light. Hence, the group velocity is less than the phase velocity

Ques.2. The EM wave which does not propagate through a rectangular waveguide with a = 30 mm & b = 15 mm is:

EM wave of frequency 5.5 GHz

EM wave of frequency 50 GHz

EM wave of frequency 4.5 GHz

EM wave of frequency 300 GHz

Answer.3. EM wave of frequency 4.5 GHz

Explanation:

The dominant mode in a particular waveguide is the mode having the lowest cutoff frequency. For rectangular waveguides, this is the TE10 mode.

For TE_{10} mode:

f_{c} = c/2a

Given:

a = 30 mm

b = 15 mm

For TE_{10} mode,

f_{c} = (3 × 10^{8})/(2 × 10^{−3})

f_{c} = 5 GHz

So, the waves having the frequency above cutoff frequency (f_{c}) will only pass.

Hence from the options given 4.5 GHz will not pass.

Ques.3. The waveguide can be considered as

High pass filter

Low pass filter

Bandpass filter

None of these

Answer.1. High pass filter

Explanation:

Waveguides only allow frequencies above cut-off frequency and do not pass below the cut-off frequencies. Hence it acts as a high pass filter. Below the cut-off frequency, the propagation decays exponentially, yielding the evanescent wave, and above it the wave propagates without attenuation for a perfect waveguide. The waveguide is a very effective barrier to low-frequency waves and thus acts as a high pass filter.

Ques.4. Microwave energies propagate the length of the waveguide by ____ its sidewalls.

Moving off

Refraction

Reflection off

None of these

Answer.3. Reflection off

Explanation:

A rectangular waveguide is a hollow metal tube with a rectangular cross-section. The conducting walls of the waveguide confine the electromagnetic fields and thereby guide the electromagnetic wave. Microwave energies propagate the length of the waveguide by the reflection of its sidewalls.

Ques.5. What is the value of the major cross-sectional dimension(width) of a rectangular waveguide with dominant TE10 mode propagation, if it is cut-off frequency is 10 GHz?

45 mm

30 mm

7.5 mm

15 mm

Answer.4. 15 mm

Explanation:

The dominant mode in a particular waveguide is the mode having the lowest cut-off frequency.

TE_{10} mode means m = 1, n = 0

The cut-off frequency of the dominant mode TE10 of the rectangular waveguide is:

f_{c} = c/2a

Where a is the dimension of the inner broad wall

a = (3 × 10^{10})/(2 × 10 × 10^{9})

a = 1.5 cm

a = 15 mm

Ques.6. Consider an air-filled rectangular waveguide with a cross-section of 5 cm × 3 cm. For this waveguide, the cut-off frequency (in MHz) of TE_{21} mode is _________.

8000.24 MHz

7810.24 MHz

78000 MHz

6158.25 MHz

Answer.2. 7810.24 MHz

Explanation:

The cut-off frequency for a rectangular waveguide is given by:

Ques.7. An air-filled rectangular waveguide of dimension 7 × 3.5 cm^{2} operates in the dominant TE_{10} mode. The value of phase velocity of the wave in the guide at a frequency of 3.5 GHz is given by:

Ques.9. In a waveguide, attenuation near the cut-off frequency is

Low

High

Very high

Zero

Answer.4. zero

Explanation:

Waveguides only allow frequencies above the cut-off frequency to pass through. It blocks or attenuates the frequencies below the cut-off frequencies, i.e. there is no attenuation near the cut-off frequency. It is only for frequencies greater than or equal to the cut-off frequency, the attenuation is very high.

Every waveguide functions as a high-pass filter with a certain cut-off frequency f_{c}. Frequencies below the f_{c} cannot pass through it while all frequencies above fc pass through unattenuated, in the ideal case. The cut-off frequency of a waveguide depends on the size of its cross-section and its shape. Multiple modes can propagate along a line, and the one with the smallest cut-off frequency is called the dominant mode. Usually, only the dominant mode is used for signal transfer. We can choose the dimensions of a waveguide so as to allow only the dominant mode to exist. Waveguides can be identified as circular, square, rectangular, and elliptical waveguides. The cut-off frequency decreases as the size of the waveguide increases.

Ques.10. The dominant mode in the rectangular waveguides is

TE_{11}

TEM

TE_{01}

TE_{10}

Answer.4. TE_{10}

Explanation:

Every waveguide functions as a high-pass filter with a certain cut-off frequency f_{c}. Frequencies below the f_{c} cannot pass through it while all frequencies above fc pass through unattenuated, in the ideal case. The cut-off frequency of a waveguide depends on the size of its cross-section and its shape.

Multiple modes can propagate along a line, and the one with the smallest cut-off frequency is called the dominant mode. The dominant mode in a particular waveguide is the mode having the lowest cut-off frequency. Usually, only the dominant mode is used for signal transfer. The dominant mode in the rectangular waveguides is TE_{10} mode. We can choose the dimensions of a waveguide so as to allow only the dominant mode to exist. Waveguides can be identified as circular, square, rectangular, and elliptical waveguides. The cut-off frequency decreases as the size of the waveguide increases.

Choice of TE_{10} mode in a rectangular waveguide:

In a rectangular waveguide, the transmission of microwave energy occurs mainly through TE_{10 }mode owing to the following reasons:

(a) The excitation of TE_{10} mode is much easier as compared to all other modes

(b) For transmission of higher-order modes, large waveguide dimensions (a x b) are required. Hence to reduce the waveguide dimensions, it is preferable to go to a lower order mode. the best one is TE_{10}, which gives the smallest waveguide dimension.

(c) TE_{10 }mode has the lowest attenuation.

(d) The electric field is definitely polarized in one direction everywhere.