Waveguides Practice Questions

The refractive indices of the core and cladding of an optical fiber are 1.50 and 1.48, respectively. The critical propagation angle, which is defined as the maximum angle that the light beam makes with the axis of the optical fiber to achieve the total internal reflection, (rounded off to two decimal places) is _____ degree.

Consider a rectangular coordinate system (x,y,z) with unit vectors $a_{x}\:a_{y}$ and $a_{z}$ . A plane wave traveling in the region $z\geq 0$ with electric field vector $E=10\cos\left ( 2\times 10^{8}t\:+\:\beta z\right )a_{y}$ is incident normally on the plane at $z=0$ , where $\beta$ is the phase constant. The region $z\geq 0$ is in free space and the region $z \lt 0$ is filled with a lossless medium (permittivity $\varepsilon \:=\:\varepsilon _{0}$ , permeability $\mu \:=\:4\mu _{0}$ , where $\varepsilon _{0}\:=\:8.85\times 10^{-12}\:\text{F/m}$ and $\mu _{0}\:=\:4\pi \times 10^{-7}\:\text{H/m})$ . The value of the reflection coefficient is

A standard air-filled rectangular waveguide with dimensions $\text{a=8 cm, b=4 cm}$ , operates at $\text{3.4 GHz}$ . For the dominant mode of wave propagation, the phase velocity of the signal in $v_{p}$ . The value (rounded off to two decimal places) of $v_{p}/c$ , where c denotes the velocity of light, is _____

A rectangular waveguide of width w and height h has cut-off frequencies for $TE_{10} \; and \;TE_{11}$ modes in the ratio 1:2. The aspect ratio w/h, rounded off to two decimal places, is ___________

The dispersion equation of a waveguide,which relates the wavenumber kto the frequency $\omega$ , is $k(\omega) =(1/c)\sqrt{\omega ^2 -{\omega _0}^2}$ where the speed of light $c=3 \times 10^8$ m/s, and $\omega_0$ is a constant. If the group velocity is $2 \times 10^8$ m/s, then the phase velocity is

The cutoff frequency of $TE_{01}$ mode of an air filled rectangular waveguide having inner dimensions $a cm \times b cm ( a \gt b)$ is twice that of the dominant $TE_{10}$ mode. When the waveguide is operated at a frequency which is 25% higher than the cutoff frequency of the dominant mode, the guide wavelength is found to be 4 cm. The value of b (in cm, correct to two decimal places) is _______.

Standard air-filled rectangular waveguides of dimensions a = 2.29 cm and b= 1.02 cm are designed for radar applications. It is desired that these waveguides operate only in the dominatnt $TE_{10}$ mode but not higher than 95% of the next higher cutoff frequency. The range of the allowable operating frequency f 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 $H_{z}(x,y,z,t)=0.1 cos(25\pi x) cos(30.3 \pi y)$ $cos(12 \pi *10^{9}t-\beta z) (A/m)$ 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 dimensions $a \; cm \times b \; cm \; (a \gt b)$ has a cutoff frequency of 6 GHz for the dominant $TE_{10}$ mode. For the same waveguide, if the cutoff frequencyof the $TM_{11}$ mode is 15 GHz, the cutoff frequency of the $TE_{01}$ mode in GHz is __________.

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

For a rectangular waveguide of internal dimensions $a \times b(a \gt b)$ , the cur-off frequency for the $TE_{11}$ mode is the arithmetic mean of the cut-off frequencies for $TE_{10}$ mode and $TE_{20}$ mode. If a = $\sqrt{5}$ cm, the value of b (in cm) is______.

The magnetic field along the propagation direction inside a rectangular waveguide with the crosssection shown in the figure is $H_{z}=3 cos(2.094 \times 10^{2}x)cos(2.618 \times 10^{2}y)$ $cos(6.283 \times 10^{10}t-\beta z)$ The phase velocity $v_{p}$ of the wave inside the waveguide satisfies

The modes in a rectangular waveguide are denoted by $\frac{TE_{mn}}{TM_{mn}}$ 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=4cm and b=3cm) is to be operated in $TE_{11}$ mode. The minimum operating frequency is

The $\vec{E}$ field in a rectangular waveguide of inner dimension $a \times b$ is given by $\vec{E}=\frac{\omega \mu }{h^{2}}(\frac{\pi}{a})H_{0}sin(\frac{2\pi x}{a})^{2}sin(\omega t-\beta z)\hat{y}$ where $H_{0}$ is a constant, and a and b are the dimensions along the x-axis and the y-axis respectively. The mode of propagation in the waveguide is

An air-filled rectangular waveguide has inner dimensions of 3cm x 2cm. The wave impedance of the TE20 mode of propagation in the waveguide at a frequency of 30 GHz is (free space impedance $\eta_{0}$ = 377 $\Omega$ )

A rectangular wave guide having $TE_{10}$ mode as dominant mode is having a cut off frequency 18-GHz for the mode $TE_{30}$ . The inner broad-wall dimension of the rectangular wave guide is