1

GATE ECE 2001

Subjective

+5

-0

A medium has breakdown strength of $$16$$ KV/m r.m.s. Its relative permeability is $$1.0$$ and relative permittivity is $$4.0$$. A plane electromagnetic wave is transmitted through the medium. Calculate the maximum possible power flow density and the associated magnetic filed.

2

GATE ECE 1999

Subjective

+5

-0

A plane wave in free space with

$$\overrightarrow E = \left( {\sqrt \pi } \right)\left( {10.0\,\widehat x + 11.8\,\widehat y} \right)\exp \left[ {j\left( {4\pi \times {{10}^8}\,t - k\,z} \right)} \right]$$

where $$\widehat x$$ and $$\widehat y$$ are unit vectors in the $$x$$- and $$y$$-directions respectively is incident normally on a semi-infinite block of ice as shown in Fig. For ice, $$\mu = {\mu _0},\,\,\,\sigma = 0$$ and $$\varepsilon = 9{\varepsilon _0}\left( {1 - j0.001} \right)$$.

$$\overrightarrow E = \left( {\sqrt \pi } \right)\left( {10.0\,\widehat x + 11.8\,\widehat y} \right)\exp \left[ {j\left( {4\pi \times {{10}^8}\,t - k\,z} \right)} \right]$$

where $$\widehat x$$ and $$\widehat y$$ are unit vectors in the $$x$$- and $$y$$-directions respectively is incident normally on a semi-infinite block of ice as shown in Fig. For ice, $$\mu = {\mu _0},\,\,\,\sigma = 0$$ and $$\varepsilon = 9{\varepsilon _0}\left( {1 - j0.001} \right)$$.

(a) Calculate the average power density associated with the incident wave.

(b) Calculate the skin depth in ice.

(c) Estimate the average power density at a distance of 5 times the skins depth in the ice block, measured from the interface.

3

GATE ECE 1998

Subjective

+5

-0

A plane wave with $$\overrightarrow E = 10\,{e^{j\left( {\omega t - \beta z} \right)\,}}\,\,{\overrightarrow a _{_y}}$$ is incident normally on a thick plane conductor lying in the $$X - Y$$ plane. Its conductivity is $$6 \times {10^6}\,\,\,S/m\,\,\,$$ and surface impedance is $$5 \times {0^{ - 4}}\,\angle {45^0}\Omega $$. Determine the propagation constant and the skin depth in the conductor.

4

GATE ECE 1998

Subjective

+5

-0

The electric field vector of a wave is given as
$$$\vec E = {E_0}{\mkern 1mu} {e^{j\left( {\omega t + 3x - 4y} \right)}}{\mkern 1mu} {{8{{\vec a}_x} + 6{{\vec a}_y} + 5{{\vec a}_z}} \over {\sqrt {125} }}\,\,V/m$$$

Its frequency is 10 GHz.

(i) Investigate if this wave is a plane wave.

(ii) Determine its propagation constant, and

(iii) Calculate the phase velocity in $$y$$-direction.

Questions Asked from Uniform Plane Waves (Marks 5)

Number in Brackets after Paper Indicates No. of Questions

GATE ECE Subjects

Network Theory

Control Systems

Electronic Devices and VLSI

Analog Circuits

Digital Circuits

Microprocessors

Signals and Systems

Representation of Continuous Time Signal Fourier Series Discrete Time Signal Fourier Series Fourier Transform Discrete Time Signal Z Transform Continuous Time Linear Invariant System Transmission of Signal Through Continuous Time LTI Systems Discrete Time Linear Time Invariant Systems Sampling Continuous Time Signal Laplace Transform Discrete Fourier Transform and Fast Fourier Transform Transmission of Signal Through Discrete Time Lti Systems Miscellaneous Fourier Transform

Communications

Electromagnetics

General Aptitude