1
GATE ECE 2014 Set 1
MCQ (Single Correct Answer)
+1
-0.3
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 two - port is short circuited, the $${{s_{11}}}$$ parameter for the resultant one - port network is
A
$${{{s_{11}} - {s_{11}}{s_{22}} + {s_{12}}{s_{21}}} \over {1 + {s_{22}}}}$$
B
$${{{s_{11}} + {s_{11}}{s_{22}} - {s_{12}}{s_{21}}} \over {1 + {s_{22}}}}$$
C
$${{{s_{11}} + {s_{11}}{s_{22}} + {s_{12}}{s_{21}}} \over {1 - {s_{22}}}}$$
D
$${{{s_{11}} - {s_{11}}{s_{22}} + {s_{12}}{s_{21}}} \over {1 - {s_{22}}}}$$
2
GATE ECE 2012
MCQ (Single Correct Answer)
+1
-0.3
The electric field of a uniform plane electromagnetic wave in free spce, along the positive x direction, is given by $$\vec E = 10\left( {{{\widehat a}_y} + j{{\widehat a}_z}} \right){e^{ - j25x}}.$$ The frequency and polarization of the wave respectively are
A
$$1.2 GHz$$ and left circular
B
$$4 Hz$$ and left circular
C
$$1.2 GHz$$ and right circular
D
$$4 Hz$$ and right circular
3
GATE ECE 2012
MCQ (Single Correct Answer)
+1
-0.3
A plane wave propagating in air with $$\vec E = \left( {8{{\widehat a}_x} + 6{{\widehat a}_y} + 5{{\widehat a}_z}} \right){\mkern 1mu} {\mkern 1mu} {e^{j\left( {\omega t + 3x - 4y} \right)}}{\mkern 1mu} {\mkern 1mu} V/m$$ is incident on a perfectly conducting slab positioned at $$x \le 0$$. The $$\overrightarrow E $$ field of the reflected wave is
A
$$\left( { - 8{{\widehat a}_x} - 6{{\widehat a}_y} - 5{{\widehat a}_z}} \right){\mkern 1mu} {e^{j\left( {\omega t + 3x + 4y} \right)}}{\mkern 1mu} {\mkern 1mu} V/m$$
B
$$\left( { - 8{{\widehat a}_x} + 6{{\widehat a}_y} - 5{{\widehat a}_z}} \right){\mkern 1mu} {e^{j\left( {\omega t + 3x + 4y} \right)}}{\mkern 1mu} {\mkern 1mu} V/m$$
C
$$\left( { - 8{{\widehat a}_x} - 6{{\widehat a}_y} - 5{{\widehat a}_z}} \right){\mkern 1mu} {e^{j\left( {\omega t - 3x - 4y} \right)}}{\mkern 1mu} {\mkern 1mu} V/m$$
D
$$\left( { - 8{{\widehat a}_x} + 6{{\widehat a}_y} - 5{{\widehat a}_z}} \right){\mkern 1mu} {e^{j\left( {\omega t - 3x - 4y} \right)}}{\mkern 1mu} {\mkern 1mu} V/m$$
4
GATE ECE 2007
MCQ (Single Correct Answer)
+1
-0.3
A plane wave of wavelength $$\lambda $$ is traveling in a direction making an angle $${{{30}^ \circ }}$$ with positive $$x$$-axis and $${{{90}^ \circ }}$$ with positiv $$y$$-axis. The $$\overrightarrow E $$ field of the plane wave can be represented as ($${E_0}$$ is a constant)
A
$$\vec E = \widehat y\,\,{E_0}{\mkern 1mu} {e^{j\left( {\omega t - {{\sqrt 3 {\kern 1pt} \pi } \over \lambda }x - {\pi \over \lambda }z} \right)}}$$
B
$$\vec E = \widehat y\,\,{E_0}{\mkern 1mu} {e^{j\left( {\omega t - {\pi \over \lambda }x - {{\sqrt 3 {\kern 1pt} \pi } \over \lambda }z} \right)}}$$
C
$$\vec E = \widehat y\,\,{E_0}{\mkern 1mu} {e^{j\left( {\omega t + {{\sqrt 3 {\kern 1pt} \pi } \over \lambda }x + {\pi \over \lambda }z} \right)}}$$
D
$$\vec E = \widehat y\,\,{\mkern 1mu} {E_0}{\mkern 1mu} {e^{j\left( {\omega t - {\pi \over \lambda }x + {{\sqrt 3 {\kern 1pt} \pi } \over \lambda }z} \right)}}$$
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