GATE EC Electromagnetics questions

Consider the Friis' transmission equation $P_{R}=\left(P_{T} G_{T} G_{R} \lambda^{2}\right) /(4 \pi D)^{2}$, where $P_{R}$ and $P_{T}$ are the received and the transmitted powers, respectively. $G_{T}$ and $G_{R}$ are the gain of transmitting and receiving antennas, respectively, $D$ is the distance between the transmitting and receiving …

The electric field of a monochromatic plane wave travelling in a lossless isotropic and homogenous medium is given by $$\vec{E}(z, t)=E_{0}[\hat{x} \cos (\omega t-k z)+\hat{y} \sin (\omega t-k z)]$$ in a right-handed orthogonal co-ordinate system. Which of the following is the correct polarization of the electromagnetic wave?

The cutoff frequency ( $\text{in GHz}$ ) for the dominant $\mathrm{TE}_{10}$ mode of an air-filled rectangular waveguide of inner dimension $0.28$ inch $\times 0.14$ inch is $\_\_\_\_$ . (rounded off to two decimal places).

A complex load (in $\Omega$ ) is represented as $\Gamma_{L}=0.5 \angle 30^{\circ}$ on the Smith chart. A co-axial cable with a characteristic impedance of $50 ~\Omega$ is connected to the load. The new input impedance of the load now moves to a diametrically opposite point on the same $\Gamma$ circle on the Smith chart. Which option is the nearest …

A square metal sheet of $4 \mathrm{~m} \times 4 \mathrm{~m}$ is placed on the $x-y$ plane as shown in the figure below. If the surface charge density (in $\mu \mathrm{C} / \mathrm{m}^{2}$ ) on the sheet is $\rho_{s}(x, y)=4\mid y \mid$, then the total charge (in $\mu \mathrm{C}$, rounded off to the nearest integer) on the sheet is $\_\_\_\_\_\_$

An electric field of $0.01 \mathrm{~V} / \mathrm{m}$ is applied along the length of a copper wire of circular cross-section with diameter $1 \: \mathrm{mm}$. Copper has a conductivity of $5.8 \times 10^{7} \mathrm{~S} / \mathrm{m}$. The current (in Amperes, rounded off to two decimal places) flowing through the wire is $\_\_\_\_\_\_$.

A $50 \Omega$ lossless transmission line is terminated with a load $\mathrm{Z}_{\mathrm{L}}$ of $(50-\mathrm{j} 75) \Omega$. If the average incident power on the line is $10 \: \mathrm{mW}$, then the average power delivered to the load (in $\mathrm{mW}$, rounded off to one decimal place) is $\_\_\_\_\_\_\_$.

​​​​Consider a lossless transmission line terminated with a short circuit as shown in the figure below. As one moves towards the generator from the load, the normalized impedances $z_{\text{inA }}, z_{i n B}, z_{i n C}$, and $z_{i n D}$ (indicated in the figure) are $\_\_\_\_\_\_.$

A uniform plane wave with electric field $\vec{E}(x)=A_{y} \hat{a}_{y} e^{-j \frac{2 \pi x}{3}} \mathrm{~V} / \mathrm{m}$ is travelling in the air (relative permittivity, $\epsilon_{r}=1$ and relative permeability, $\mu_{r}=1$ ) in the $+x$ direction ( $A_{y}$ is a positive constant, $\hat{a}_{y}$ is the unit vector along the $y$ axis). It is …

A lossless transmission line with characteristic impedance $\mathrm{Z}_{0}=50 \Omega$ is terminated with an unknown load. The magnitude of the reflection co-efficient is $|\Gamma|=0.6$. As one moves towards the generator from the load, the maximum value of the input impedance magnitude looking towards the load (in $\Omega$ ) is $\_\_\_\_\_\_.$

Consider a narrow band signal, propagating in a lossless dielectric medium $\left(\varepsilon_{r}=4, \mu_{r}=1\right)$, with phase velocity $v_{p}$ and group velocity $v_{g}$. Which of the following statement is true? ($c$ is the velocity of light in vacuum.)

The $S$-parameters of a two-port network is given as $$[S]=\left[\begin{array}{ll} S_{11} & S_{12} \\ S_{21} & S_{22} \end{array}\right]$$ with reference to $Z_0$. Two lossless transmission line sections of electrical lengths $\theta_1=\beta l_1$ and $\theta_2=\beta l_2$ are added to the input and output ports for measurement purposes, …

The standing wave ratio on a $50 \; \Omega$ lossless transmission line terminated in an unknown load impedance is found to be $2.0$. The distance between successive voltage minima is $30 \mathrm{~cm}$ and the first minimum is located at $10 \mathrm{~cm}$ from the load. $Z_L$ can be replaced by an equivalent length $l_m$ and terminating resistance …

The electric field of a plane electromagnetic wave is $\boldsymbol{E}=\boldsymbol{a}_{x} C_{1 x} \cos (\omega t-\beta z)+\boldsymbol{a}_{y} C_{1 y} \cos (\omega t-\beta z+\theta) \quad \mathrm{V} / \mathrm{m}$. Which of the following combination(s) will give rise to a left handed elliptically polarized $\text{(LHEP)}$ wave?

The following circuit(s) representing a lumped element equivalent of an infinitesimal section of a transmission line is/are

A transparent dielectric coating is applied to glass $\left(\varepsilon_r=4, \mu_r=1\right)$ to eliminate the reflection of red light $\left(\lambda_0=0.75 \; \mu \mathrm{m}\right)$. The minimum thickness of the dielectric coating, in $\mu \mathrm{m}$, that can be used is_____________(rounded off to two decimal places).

A waveguide consists of two infinite parallel plates (perfect conductors) at a separation of $10^{-4} \; \text{cm},$ with air as the dielectric. Assume the speed of light in air to be $3 \times 10^{8} \; \text{m/s}.$ The frequency/frequencies of $\text{TM}$ waves which can propagate in this waveguide is/are _________.

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 …

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.

The impedance matching network shown n the figure is to match a lossless line having characteristic impedance $Z_{0}= 50 \:\Omega$ with a load impedance $Z_{L}$. A quarter-wave line having a characteristic impedance $Z_1=75\:\Omega$ is connected to $Z_{L}$. Two stubs having characteristic impedance of $75\:\Omega$ each are connected to this …