GATE Electronics & Communication

A $50 \Omega$ lossless transmission line is terminated with a load $Z_L$ of $(50-j 75) \Omega$. If the average incident power on the line is 10 mW , then the average power delivere...

An electric field of $0.01 \mathrm{~V} / \mathrm{m}$ is applied along the length of a copper wire of circular crosssection with diameter 1 mm . Copper has a conductivity of $5.8 \t...

Let $\hat{i}$ and $\hat{j}$ be the unit vectors along $x$ and $y$ axes, respectively and let $A$ be a positive constant. Which one of the following statements is true for the vecto...

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, $\dot{o}_r=1$...

A lossless transmission line with characteristic impedance $Z_0 = 50 \Omega$ is terminated with an unknown load. The magnitude of the reflection coefficient is $|\Gamma| = 0.6$. As...

Consider a narrow band signal, propagating in a lossless dielectric medium $$(\varepsilon_r=4,\mu_r=1)$$, with phase velocity $$v_p$$ and group velocity $$v_g$$. Which of the follo...

The electric field of a plane electromagnetic wave is $$E = {a_x}{C_{1x}}\cos (\omega t - \beta z) + {a_y}{C_{1y}}\cos (\omega t - \beta z + \theta )$$ V/m. Which of the following...

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

A transparent dielectric coating is applied to glass ($$\varepsilon _r=4,\mu_r=1$$) to eliminate the reflection of red light ($$\lambda_0=0.75~\mu\mathrm{m}$$). The minimum thickne...

In a circuit, there is a series connection of an ideal resistor and an ideal capacitor. The conduction current (in Amperes) through the resistor is 2sin(t + $$\pi$$/2). The displac...

Consider the following wave equation, $${{{\partial ^2}f(x,t)} \over {\partial {t^2}}} = 10000{{{\partial ^2}f(x,t)} \over {\partial {x^2}}}$$ Which of the given options is/are sol...

A waveguide consists of two infinite parallel plates (perfect conductors) at a separation of 10 $$-$$4 cm, with air as the dielectric. Assume the speed of light in air to be 3 $$\t...

In an electrostatic field, the electric displacement density vector, $$\overrightarrow D $$, is given by $$\overrightarrow D (x,y,z) = ({x^3}\overrightarrow i + {y^3}\overrightarro...

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 \...

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 l...

An antenna with a directive gain of 6 dB is radiating a total power of 16 kw . The amplitude of the electric field in free space at a distance of 8 km from the antenna in the direc...

A standard air-filled rectangular waveguide with dimensions $a=8 \mathrm{~cm}, b=4 \mathrm{~cm}$, operates at 3.4 GHz . For the dominant mode of wave propagation, the phase velocit...

For a vector field $\overrightarrow{\mathbf{D}}=\rho \cos ^2 \phi \hat{\mathbf{a}}_{\boldsymbol{\rho}}+z^2 \sin ^2 \phi \hat{\mathbf{a}}_\phi$ in a cylindrical coordinate system $(...

Consider the vector field $\overline{\mathbf{F}}=\hat{\mathbf{a}}_{\mathbf{x}}\left(4 y-c_1 z\right)+\hat{\mathbf{a}}_{\mathbf{y}}(4 x+2 z)+\hat{\mathbf{a}}_{\mathbf{z}}(2 y+z)$ in...

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

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

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 deci...

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 $$l$$ i...

An electron (q 1 ) is moving in free space with velocity 10 5 m/s towards a stationary electron (q 2 ) far away. The closest distance that this moving electron gets to the stationa...

Consider a wireless communication link between a transmitter and a receiver located in free space, with finite and strictly positive capacity. If the effective areas of the transmi...

The expression for an electric field in free space is $$E = {E_0}\left( {\widehat x + \widehat y + j2\widehat z} \right){e^{ - j\left( {\omega t - kx + ky} \right)}},$$ where $$x,{...

An optical fiber is kept along the$$\widehat Z$$ direction. The refractive indices for the electric fields along $$\widehat X$$ and $$\widehat Y$$ directions in the fiber are $${n_...

A two wire transmission line terminates in a television set. The VSWR measured on the line is 5.8. The percentage of power that is reflected from the television set is

Standard air filled rectangular waveguides of dimensions a = 2.29cm and b = 1.02cm are designed for radar applications. It is desired that these waveguides operate only in the domi...

A half wavelength dipole is kept in the x-y plane and oriented along $${45^ \circ }$$ from the x-axis. Determine the direction of null in the radiation pattern for $$0 \le \phi \le...

The propagation constant of a lossy transmission line is (2 + j5) $${m^{ - 1}}$$ and its characteristic impedance is (50 + j0) $$\Omega $$ at $$\omega = \,{10^6}\,rad\,{S^{ - 1}}$$...

Let the electric field vector of a plane electromagnetic wave propagating in a homogenous medium be expressed as $$E = \widehat x{E_x}\,{e^{ - j\left( {wt - \beta z} \right)}},$$ ,...

Concentric spherical shells of radii 2 m, 4 m, and 8 m carry uniform surface charge densities of 20 nC/m 2 , −4 nC/m 2 and ρ s ,respectively. The value of ρ s (nC/m 2 ) required to...

A uniform and constant magnetic field $$B=\widehat zB$$ exists in the $$\widehat z$$ direction in vacuum. A particle of mass m with a small charge q is introduced into this region...

Faraday's law of electromagnetic induction is mathematically described by which one of the following equations?

Consider the time-varying vector $$I = \,\hat x\,\,15\,\cos \,(\omega \,t) + \,\hat y\,5\,sin(\omega \,t)$$ in Cartesian coordinates, where $$\omega $$ > 0 is a constant. When the...

Two lossless X-band horn antennas are separated by a distance of $$200\lambda $$. The amplitude reflection coefficients at the terminals of the transmitting and receiving antennas...

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

An antenna pointing in a certain direction has a noise temperature of $$50K$$. The ambient temperature is $$290K$$. The antenna is connected to a pre-amplifier that has a noise fig...

The electric field of a uniform plane wave travelling along the negative $$z$$ direction is given by the following equation: $$$\overrightarrow E {}_w^i = \left( {{{\widehat a}_{_x...

The far-zone power density radiated by a helical antenna is approximated as: $$$\overrightarrow W {\,_{rad}} = \overrightarrow W \,average\, \approx \,\widehat a{}_rC{}_0\,{1 \over...

If a right-handed circularly polarized wave is incident normally on a plane perfect conductor, then the reflected wave will be

A radar operating at 5 GHz uses a common antenna for transmission and reception. The antenna has a gain of 150 and is aligned for maximum directional radiation and reception to a t...

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

In a source free region in vacuum, if the electrostatic potential $$\varphi\;=\;2x^2\;+y^2+cz^2$$ , the value of constant c must be ________________.

A coaxial capacitor of inner radius 1 mm and outer radius 5 mm has a capacitance per unit length of 172 pF/m. If the ratio of outer radius to inner is doubled, the capacitance per...

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,...

The electric field intensity of a plane wave traveling in free space is given by the following expression $$E\left( {x,t} \right) = {\widehat a_{_y}}24\pi \,\,\cos \left( {\omega t...

The electric field intensity of a plane wave propagating in a lossless non-magnetic medium is given by the following expression $$\overrightarrow E \left( {z,t} \right) = {\widehat...

An air-filled rectangular waveguide of internal dimension $$a\,\,cm\,\, \times \,\,b\,\,cm$$ (a > b) has a cutoff frequency of 6 GHz for the dominant $$T{E_{10}}$$ mode. For the sa...

The directivity of an antenna array can be increased by adding more antenna elements, as a larger number of elements

The electric field component of a plane wave traveling in a lossless dielectric medium is given by $$$\overrightarrow E \left( {z,t} \right) = {\widehat a_y}2\cos \left( {{{10}^8}t...

The electric field of a uniform plane electromagnetic wave is $$$\vec E = \left( {{{\overrightarrow a }_x} + j4{{\overrightarrow a }_y}} \right)\exp \left[ {j\left( {2\pi \times {{...

A coaxial cable is made of two brass conductors. The spacing between the conductors is filled with Teflon $$\left( {{\varepsilon _r} = 2.1,\,\,\tan \,\,\delta = \,0} \right)$$. Whi...

For a parallel plate transmission line, let v be the speed of propagation and Z be the characteristic impedance. Neglecting fringe effects, a redution of the spacing between the pl...

Given the vector $$$\mathrm A=\left(\cos\;\mathrm x\right)\left(\sin\;\mathrm y\right)\;{\widehat{\mathrm a}}_\mathrm x\;+\;\left(\sin\;\mathrm x\right)\left(\cos\;\mathrm y\right)...

If $$\overrightarrow{\mathrm E}=-\left(2\mathrm y^2\;-3\mathrm{yz}^2\right)\widehat{\mathrm x}\;-\left(6\mathrm{xy}^2-3\mathrm{xz}^2\right)\widehat{\mathrm y}+\left(6\mathrm{xyz}\r...

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

Assume that a plane wave in air with an electric field $$\overrightarrow E = 10\cos \left( {\omega t - 3x - \sqrt {3z} } \right){\widehat a_{_y}}\,\,\,V/m$$ is incident on a non-ma...

Match column A with column B. Column 1. Point electromagnetic source 2. Dish antenna 3. Yagi-Uda antenna Column P. Highly directional Q. End fire R. Isotropic

For an antenna radiating in free space, the electric field at a distance of 1 km is found to be 12 m V/m. Given that intrinsic impedance of the free space is 120$$\pi \Omega $$, th...

A two - port network has scattering parameters given by $$[S]$$ $$ = \left[ {\matrix{ {{s_{11}}} & {{s_{12}}} \cr {{s_{21}}} & {{s_{22}}} \cr } } \right].$$ If the port - 2 of the...

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

For a rectangular waveguide of internal dimensions $$a\,\, \times \,\,b$$ (a > b), the cut-off frequency for the $$T{E_{11}}$$ mode is the arithmetic mean of the cut-off frequencie...

If the electric field of a plane wave is $$$\overrightarrow E \left( {z,t} \right) = \widehat x3\cos \left( {\omega t - kz + {{30}^ \circ }} \right) - \widehat y4\sin \left( {\omeg...

In spherical coordinates, let $${{{\widehat a}_{_0}},\,{{\widehat a}_{_\phi }}}$$ denote unit vectors along the $$\theta ,\,\,\phi $$directions. $$$E = {{100} \over r}\sin \,\theta...

The return loss of a device is found to be 20 dB. The voltage standing wave ratio (VSWR) and magnitude of reflection coefficient are respectively.

The divergence of the vector field $$\overrightarrow A\;=\;x{\widehat a}_x\;+\;y{\widehat a}_y\;+\;z{\widehat a}_z$$ is

A plane wave propagating in air with $$\vec E = \left( {8{{\widehat a}_x} + 6{{\widehat a}_y} + 5{{\widehat a}_z}} \right){\mkern 1mu} {\mkern 1mu} {e^{j\left( {\omega t + 3x - 4y}...

An infinitely long uniform solid wire of radius a carries a uniform dc current of density $$\widehat{\mathrm j}$$ The magnetic field at a distance r from the center of the wire is...

A transmission line with a characteristic impedance of 100 $$\Omega $$ is used to match a 50 $$\Omega $$ section to a 200 $$\Omega $$ section. If the matching is to be done both at...

A coaxial cable with an inner diameter of 1 mm and outer diameter of 2.4 mm is filled with a dielectric of relative permittivity 10.89. Given $${\mu _0} = \,4\,\pi \, \times \,{10^...

The electric field of a uniform plane electromagnetic wave in free spce, along the positive x direction, is given by $$\vec E = 10\left( {{{\widehat a}_y} + j{{\widehat a}_z}} \rig...

The radiation pattern of an antenna in spherical co-ordinates is given by $$$F\,(\theta )\, = {\cos ^4}\,\theta \,\,\,;\,\,0\,\, \le \,\,\theta \,\, \le \,\,\pi /2$$$ The directivi...

The modes in a rectangular waveguide are denoted by $$T{E_{mn}}\,$$/$$T{M_{mn}}\,$$ where m and n are the eigen numbers along the larger and smaller dimensions of the waveguide res...

A transmission line of characteristic impedance 50 $$\Omega $$ is terminated by a 50 $$\Omega $$ load. When excited by a sinusoidal voltage source at 10 GHz, the phase difference b...

A transmission line of characteristic impedance 50 $$\Omega $$ is terminated in a load impedance $$Z_L$$. The VSWR of the line is measured as 5 and the first of the voltage naxima...

The electric and magnetic fields for a TEM wave of frequency $$14 GHz$$ in a homogeneous medium of relative permittivity $${\varepsilon _r}$$ and relative permeability $${\mu _r} =...

If the scattering matrix [S] of a two port network is $$$\left[ S \right] = \left[ {\matrix{ {0.2\,\angle \,\,{0^ \circ }} & {0.9\,\,\angle \,\,{{90}^ \circ }} \cr {0.9\,\angle \,\...

A plane wave having the electric field component $$${\overrightarrow E _i} = 24\,\,\cos \,\,\left( {3 \times {{10}^8}\,t - \beta \,y} \right){\widehat a_z}\,\,V/m$$$ and traveling...