# GATE Questions & Answers of Waveguides: modes, boundary conditions, cut-off frequencies, dispersion relations

## What is the Weightage of Waveguides: modes, boundary conditions, cut-off frequencies, dispersion relations in GATE Exam?

Total 18 Questions have been asked from Waveguides: modes, boundary conditions, cut-off frequencies, dispersion relations topic of Electromagnetics subject in previous GATE papers. Average marks 1.67.

An optical fiber is kept along the $\stackrel{^}{z}$ direction. The refractive indicates for the electric fields along $\stackrel{^}{x}$ and $\stackrel{^}{y}$ directions in the fiber are nx=1.5000 and ny=1.5001, respectively ($n_x\neq n_y$ due to the imperfection in the fiber cross-section). The free space wavelength of a light wave propagating in the fiber is 1.5 µm. If the lightwave is circularly polarized at the input of the fiber, the minimum propagation distance after which it becomes linearly polarized, in centimeters, is____________.

Standard air-filled rectangular waveguides of dimension = 2.29 cm and = 1.02 cm are designed for radar application. It is desired that these waveguides operate only in the dominant TE10 mode but not higher than 95% of the next cutoff frequency. The range of the allowable operating frequency f is

The permittivity of water at optical frequencies is 1.75 $\varepsilon_0$. It is found that an isotropic light source at a distance d under water forms an illuminated circular area of radius 5 m, as shown in the figure. The critical angle is $\theta_c$ .

The value of d (in meter) is___________

Light from free space is incident at an angle ${\theta }_{i}$ to the normal of the facet of a step-index large core optical fibre. The core and cladding refractive indices are n1=1.5 and n2=1.4, respectively.
The maximum value of ${\theta }_{i}$ (in degrees) for which the incident light will be guided in the core of the fibre is ________

Consider an air-filled rectangular waveguide with dimensions a = 2.286 cm and b = 1.016 cm. At 10 GHz operating frequency, the value of the propagation constant (per meter) of the corresponding propagating mode is __________

Consider an air-filled rectangular waveguide with dimensions a = 2.286 cm and b = 1.016 cm. The increasing order of the cut-off frequencies for different modes is

The longitudinal component of the magnetic field inside an air-filled rectangular waveguide made of a perfect electric conductor is given by the following expression

The cross-sectional dimensions of the waveguide are given as a = 0.08 m and b = 0.033 m. The mode of propagation inside the waveguide is

An air-filled rectangular waveguide of internal dimension a cm X b cm (a > b) has a cutoff frequency of 6 GHz for the dominant TE10 mode. For the same waveguide, if the cutoff frequency of the TM11 mode is 15 GHz, the cutoff frequency of the TE01 mode in GHz is __________.

A two-port network has scattering parameters given by $\left[S\right]=\left[\begin{array}{cc}{s}_{11}& {s}_{12}\\ {s}_{21}& {s}_{22}\end{array}\right]$. If the port-2 of the two- port is short circuited , the ${s}_{11}$ parameter for the resultant one-port network is

Which one of the following field patterns represents a TEM wave travelling in the positive x direction?

For a rectangular waveguide of internal dimensions a × b (a>b), the cut-off frequency for the TE11 mode is the arithmetic mean of the cut-off frequencies for TE10 mode and TE20 mode. If $a=\sqrt{5}$cm, the value of b (in cm) is _____.

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 TE21 mode is _________.

The magnetic field along the propagation direction inside a rectangular waveguide with the crosssection shown in the figure is

${\mathrm{H}}_{\mathrm{z}}=3\mathrm{cos}\left(2.094×{10}^{2}\mathrm{x}\right)\mathrm{cos}\left(2.618×{10}^{2}\mathrm{y}\right)\mathrm{cos}\left(6.283×{10}^{10}\mathrm{t}-\mathrm{\beta z}\right)$

The phase velocity vp of the wave inside the waveguide satisfies

The modes in a rectangular waveguide are denoted by TEmn/TMmn where m and n are the eigen numbers along the larger and smaller dimensions of the waveguide respectively. Which one of the following statements is TRUE?

Which of the following statements is true regarding the fundamental mode of the metallic waveguides shown?

A rectangular waveguide of internal dimensions (a = 4 cm and b = 3 cm) is to be operated in TE11 mode. The minimum operating frequency is

An air-filled rectangular waveguide has inner dimensions of 3 cm × 2 cm. The wave impedance of the TE20 mode of propagation in the waveguide at a frequency of 30 GHz is (free space impedance ${\mathrm{\eta }}_{0}=377\mathrm{\Omega }$)
The $\stackrel{\to }{E}$ field in rectangular waveguide of inner dimensions $a×b$ is given by $\stackrel{\to }{E}=\frac{\omega \mu }{{h}^{2}}\left(\frac{\pi }{a}\right){H}_{0}\mathrm{sin}\left(\frac{2\pi x}{a}\right)\mathrm{sin}\left(\omega t-\beta z\right)\stackrel{^}{y}$