GATE EC Electromagnetics questions

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 ________________________

An antenna with a directive gain of $6\text{ dB}$ is radiating a total power of $\text{16 kW}$. The amplitude of the electric field in free space at a distance of $\text{8 km}$ from the antenna in the direction of $\text{6 dB}$ gain (rounded off to three decimal places) is ____________________ $\text{V/m}$.

The impedances $Z=jX,$ for all $X$ in the range $\left ( -\infty ,\infty \right )$, map to the Smith chart as

A transmission line of length $3\lambda /4$ and having a characteristic impedance of $50$ $\Omega$ is terminated with a load of $400 \Omega$. The impedance (rounded off to two decimal places) seen at the input end of the transmission line is __________ $\Omega$.

For an infinitesimally small dipole in free space, the electric field $E_{\theta }$ in the far field is proportional to $e^{-jkr/r}\sin\theta$, where $k=2\pi /\lambda$. A vertical infinitesimally small electric dipole $\left (\delta l \ll \lambda \right )$ is placed at a distance $h\left ( h> 0 \right )$ above an infinite ideal conducting plane, …

The magnetic field of a uniform plane wave in vacuum is given by $$\overrightarrow{H}\left ( x,y,z,t \right )=(\hat{a_{x}}+2\hat{a_{y}}+b\hat{a_{z}})\cos\left ( \omega t+3x-y-z\right ).$$ The value of $b$ is ___________.

For a $2$-port network consisting of an ideal lossless transformer, the parameter $S_{21}$ (rounded off to two decimal places) for a reference impedance of $10 \Omega$, is __________.

In the table shown, List I and List II, respectively, contain terms appearing on the left-hand side and the right-hand side of Maxwell’s equations (in their standard form). Match the left-hand side with the corresponding right-hand side. …

Radiation resistance of a small dipole current element of length $l$ at a frequency of $3$ GHz is $3$ ohms. If the length is changed by $1\%$, then the percentage change in the radiation resistance, rounded off to two decimal places, is ________ $\%.$

In the circuit shown, $V_{s}$ is square wave of period $T$ with maximum and minimum values of $8\: V$ and $-10\: V$, respectively. Assume that the diode is ideal and $R_{1}=R_{2}=50\: \Omega.$ The average value of $V_{L}$ is _______ volts (rounded off to $1$ decimal place).

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

A Germanium sample of dimensions $1\: cm \times 1\: cm$ is illuminated with a $20\:mW,$ $600\: nm$ laser light source as shown in the figure. The illuminated sample surface has a $100\: nm$ of loss-less Silicon dioxide layer that reflects one-fourth of the incident light. From the remaining light, one-third of the power is reflected from the Silicon …

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

A good transimpedance amplifier has

The points $\text{P, Q, and R}$ shown on the Smith chart (normalized impedance chart) in the following figure represent:

A lossy transmission line has resistance per unit length $R=0.05\:\Omega/m.$ The line is distortionless and has characteristic impedance of $50\:\Omega.$ The attenuation constant (in $\text{Np/m}$, correct to three decimal places) of the line is ________.

The cutoff frequency of $TE_{01}$ mode of an air filled rectangular waveguide having inner dimensions $a\:\text{cm} \: \times \: b\: \text{cm}\:\left ( a> b \right )$ 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 …

A uniform plane wave traveling in free space and having the electric field $$\overrightarrow{E} =\left ( \sqrt{2}\:\hat{a}_{x} -\hat{a}_{z}\right )cos\left [ 6\sqrt{3}\: \pi \times 10^{8}t-2\:\pi \left ( x+\sqrt{2} \:z\right )\right ]V/m$$ is incident on a dielectric medium (relative permittivity $>1$, relative permeability $=1$) as shown in the …

A bar of Gallium Arsenide (GaAs) is doped with silicon such that the silicon atoms occupy Gallium and Arsenic sites in the GaAs crystal. Which one of the following statements is true?

The voltage of an electromagnetic wave propagating in a coaxial cable with uniform characteristic impedance is $V(l)= e^{-\gamma l +j\omega t }$ Volts, where $l$ is the distance along the length of the cable in meters, $\gamma=(0.1+j40)m^{-1}$ is the complex propagation constant, and $\omega=2 \pi \times 10^{9}$ rad/s is the angular frequency. The …