1
GATE ECE 2023
MCQ (More than One Correct Answer)
+2
-0.67

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 combination(s) will give rise to a left handed elliptically polarized (LHEP) wave?

A
$${C_{1x}} = 1,{C_{1y}} = 1,\theta = \pi /4$$
B
$${C_{1x}} = 2,{C_{1y}} = 1,\theta = \pi /2$$
C
$${C_{1x}} = 1,{C_{1y}} = 2,\theta = 3\pi /2$$
D
$${C_{1x}} = 2,{C_{1y}} = 1,\theta = 3\pi /4$$
2
GATE ECE 2023
Numerical
+2
-0.67

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 thickness of the dielectric coating, in $$\mu\mathrm{m}$$, that can be used is __________ (rounded off to two decimal places).

Your input ____
3
GATE ECE 2017 Set 1
MCQ (Single Correct Answer)
+2
-0.6
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 $$x,{\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} y,{\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} z\,\,\,\,\,\,\,$$ represent the spatial coordinates, $$t$$ represents time, and $$\omega ,\,\,k$$ are contants. This electric field
A
does not represent a plane wave.
B
represents a circular polarized plane wave propagating normal to the z-axis.
C
represents an elliptically polarized plane wave propagating along x-y plane.
D
represents a linearly polarized plane wave
4
GATE ECE 2016 Set 1
MCQ (Single Correct Answer)
+2
-0.6
The electric field of a uniform plane wave travelling along the negative $$z$$ direction is given by the following equation: $$$\overrightarrow E {}_w^i = \left( {{{\widehat a}_{_x}} + j{{\widehat a}_{_y}}} \right){E_0}{e^{jkz}}$$$

This wave is incident upon a receiving antenna placed at the origin and whose radiated electric field towards the incident wave is given by the following equation:

$$${\overrightarrow E _{_a}} = \left( {{{\widehat a}_{_x}} + 2{{\widehat a}_{_y}}} \right){E_1}{1 \over r}{e^{ - jkr}}$$$

The polarization of the incident wave, the polarization of the antenna and losses due to the polarization mismatch are, respectively,

A
Linear, Circular (clockwise), $$−5dB$$
B
Circular (clockwise), Linear, $$−5dB$$
C
Circular (clockwise), Linear, $$−3dB$$
D
Circular (anti clockwise), Linear, $$−3dB$$
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