Antennas · Electromagnetics · GATE ECE
Marks 1
1
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 antennas, and $\lambda$ is the wavelength in free space.
Given: $G_T=G_R=1.0, \lambda=0.30 \mathrm{~m}$ and $P_T=+10 \mathrm{dBm}$.
Choose the distance (D), in km , from the following options at which the received power, $P_R=-90 \mathrm{dBm}$ ?
GATE ECE 2026
2
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 direction of 6 dB gain(rounded off to three decimal places is$\_\_\_\_$ $\mathrm{V} / \mathrm{m}$.
GATE ECE 2021
3
The directivity of an antenna array can be increased by adding more antenna elements, as a larger number of elements
GATE ECE 2015 Set 3
4
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$$\pi \Omega $$, the magnitude of average power density due to this antenna at a ditance of 2 km from the antenna (in n W/$${m^2}$$) is
GATE ECE 2014 Set 4
5
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
GATE ECE 2014 Set 4
6
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 directivity of the antenna is
GATE ECE 2012
7
For a Hertz dipole antenna, the half power beam width (HPBW) in the E-plane is
GATE ECE 2008
8
A transmission line is feeding 1 Watt of power to a horn antenna having gain of 10 dB. The antenna is matched to the transmission line. The total power radiated by the horn antenna into the free-space is
GATE ECE 2006
9
Refractive index of glass is 1.5. Find the wavelength of a beam of light with a frequency of $${10^{14}}$$ Hz in glass. Assume velocity of light is $$3\,\, \times \,{10^8}$$ m/s in vacuum.
GATE ECE 2005
10
Consider a lossless antenna with a directive gain of + 6 dB. If 1 m W of power is fed to it the total power radiated by the antenna will be
GATE ECE 2004
11
The line-of-sight communication requires the transmit and receive antennas to face each other. If the transmit antenna is vertically polarized for best reception the receiver antenna should be
GATE ECE 2002
12
If the diameter of a $$\lambda /2$$ dipole antenna is increased from $$\lambda /100$$ to $$\lambda /50$$ then is
GATE ECE 2000
13
The radiation resistance of a circular loop of one turn is 0.01 $$\Omega $$. The radiation resistance of five turns of such a loop will be
GATE ECE 1998
14
The far field of an antenna varies with distance r as
GATE ECE 1998
15
The vector $$\mathop H\limits^ \to $$ in the far field of an antenna satisfiels
GATE ECE 1998
16
An antenna in free space receives 2$$\mu $$ W of power when the incident electric field is 20 m V/m rms. The effective aperture of the antenna is
GATE ECE 1998
17
An antenna when radiating, has a highly directional radiation pattern. When the antenna is receiving its radiation pattern
GATE ECE 1995
18
For a dipole antenna
GATE ECE 1994
Marks 2
1
For an infinitesimally small dipole in free space, the electric field $E_\theta$ in the far field is proportional to $\frac{e^{-j k r}}{r} \sin \theta$, where $k=\frac{2 \pi}{\lambda}$. A vertical infinitesimally small electric dipole ( $\delta l \ll \lambda$ ) is placed at a distance $h(h>0)$ above an infinite ideal conducting plane, as shown in the figure. The minimum value of $h$, for which one of the maxima in the far field radiation pattern occurs at $\theta=60^{\circ}$, is
GATE ECE 2020
2
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 $$0 \le \phi \le \pi $$. Here the angle $$\theta \left( {0 \le \theta \le \pi } \right)$$ is measured from the z-axis, and the angle $$\phi \left( {0 \le \phi \le 2\pi } \right)$$ is measured from the x-axis in the x-y plane.
GATE ECE 2017 Set 1
3
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 are $$0.15$$ and $$0.18$$, respectively. The maximum directivities of the transmitting and receiving antennas (over the isotropic antenna) are $$18$$ $$dB$$ and $$22$$ $$dB$$, respectively. Assuming that the input power in the lossless transmission line connected to the antenna is $$2$$ $$W$$, and that the antennas are perfectly aligned and polarization matched, the power ( in mW) delivered to the load at the receiver is ________ .
GATE ECE 2016 Set 1
4
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 figure of 2 dB and an available gain of 40 dB over an effective bandwidth of $$12$$ $$MHz$$. The effective input noise temperature $${T_e}$$ for the amplifier and the noise power $${P_{ao}}$$ at the output of the preamplifier, respectively, are
GATE ECE 2016 Set 1
5
The far-zone power density radiated by a helical antenna is approximated as:
$$$\overrightarrow W {\,_{rad}} = \overrightarrow W \,average\, \approx \,\widehat a{}_rC{}_0\,{1 \over {{r^2}}}{\cos ^4}\theta $$$
The radiated power density is symmetrical with respect to $$\phi $$ and exists only in the upper hemisphere: $$0 \le \theta \le {\pi \over 2};\,\,\,\,0 \le \theta \le 2\pi ;$$
$${C_0}$$ is a constant. The power radiated by the antenna (in watts) and the maximum directivity of the antenna, respectively, are
GATE ECE 2016 Set 1
6
Two half-wave dipole antennas placed as shown in the figure are excited with sinusoidally varying currents of frequency 3 MHz and phase shift of $$\pi /2$$ between them (the element at the origin leads in phase). If the maximum radiated E-field at the point P in the x-y plane occurs at an azimuthal angle $${60^ \circ }$$, the distance d (in meters) between the antennas is ___________ .
GATE ECE 2015 Set 2
7
At 20 GHz, the gain of a parabolic dish antenna of 1 meter diameter and 70% efficiency is
GATE ECE 2008
8
A $$\lambda /2$$ dipole is kept horizontally at a height of $${\lambda _0}/2$$ above a perfectly conducting infinite ground plane. The radiation pattern in the plane of the dipole ($$\overrightarrow E $$ plane) looks approximately as
GATE ECE 2007
9
A mast antenna consisting of a 50 meter long vertical conductor operates over a perfectly conducting ground plane. It is base-fed at frequency of 600 kHz. The radiation resistance of the antenna in ohms is
GATE ECE 2006
10
Two identical and parallel dipole antennas are kept apart by a distance $$\lambda /4$$ of in the H-plane. They are fed with equal currents but the right most antenna has a phase shift of +90°. The radiation pattern is given as
GATE ECE 2005
11
Two identical antennas are placed in the $$\theta = \pi /2$$
plane as shown in figure. The
elements have equal amplitude excitation with 180° polarity difference, operating
at wavelength λ. The correct value of the magnitude of the far zone resultant
electric field strength normalized with that of a single element, both computed for $$\phi = 0$$ is
GATE ECE 2003
12
A person with a receiver is 5 Km away from the transmitter. What is the distance that this person must move further to detect a 3-dB decrease in signal strength?
GATE ECE 2002
13
In a uniform linear array, four isotropic radiating elements are spaced $$\lambda /4$$ apart. The progressive phase shift between the elements required for forming the main beam at 60° off the end-fire is
GATE ECE 2001
14
A medium wave radio transmitter operating at a wavelength of 492 m has a tower antenna of height 124m. What is the radiation resistance of the antenna?
GATE ECE 2001
15
The half-power beam widths (HPBW) of an antenna in the two orthogonal planes are $${100^ \circ }$$ and $${60^ \circ }$$ respectively. The directivity of the antenna is approximately equal to
GATE ECE 2000
16
For an 8 feet (2.4 m) parabolic disk antenna operating at 4 GHz, the minimum distance required for far field measurement is closest to
GATE ECE 2000
17
A transmitting antenna radiates 251 W isotropically. A receiving antenna, located 100m away from the transmitting antenna, has an effective aperture of 500 cm2. The total power received by the antenna is
GATE ECE 1999
18
A parabolic dish antenna has a conical beam 20 wide. The directivity of the antenna is approximately
GATE ECE 1997
19
A 1 km long microwave link uses two antennas each having 30dB gain. If the power transmitted by one antenna is 1 W at 3 GHz, the power received by the other antenna is approximately
GATE ECE 1996
20
A transverse electromagnetic wave with circular polarization is received by a dipole antenna. Due to polarization mismatch, the power transfer efficiency from the wave to the antenna is reduced to about
GATE ECE 1996
21
Two dissimilar antennas having their maximum directivities equal
GATE ECE 1992
22
The beam width-between-first-null of a uniform linear array of N equally-spaced (element spacing = d) equally-excited antennas is determined by
GATE ECE 1992
23
In a board side array of 20 isotropic radiators, equally spaced at a distance of $$\lambda /2$$, the veam width between first nulls is
GATE ECE 1991
24
Two isotropic antennas are separated by a distance of two wavelengths. If both the antennas are fed with currents of equal phase and magnitude, the number of lobes in the radiation pattern in the horizontal plane are
GATE ECE 1990
25
In the case of ground wave propagation, at far-off distances from the transmitting tower antenna, the Poynting vector is
GATE ECE 1989
26
The electric field E and the magnetic field H of a short dipole antenna satisfy the condition
GATE ECE 1988
Marks 4
Marks 5
1
Consider a linear array of two half - wave dipoles A and B as shown in Fig. The dipoles are $${\lambda \over 4}$$ apart and are excited in such a way that the current on element B lags that on element A by $${90^0}$$ in phase
(a) Obtain the expression for the radiation pattern for E in the XY plane, i.e.,$$\left( {\theta = {{90}^0}} \right)$$.
(b) Sketch the radiation pattern obtained in (a).
GATE ECE 2002
2
The average power of an omni-directional antenna varies as the magnitude of cos($$\theta $$) where $$\theta $$ is the azimuthal angle. Calculate the maximum Directive Gain of the antenna and the angles at which it occurs.
GATE ECE 1999
3
A dipole antenna has a sin$$\theta $$ radiation pattern where the angle $$\theta $$ is measured from the axis of the dipole. The dipole is vertically located above an ideal ground plane (Fig.). What should be the height of the dipole H in terms of wave length so as to get a null in the radiation pattern at an angle of 450 from the ground plane? Find the direction of maximum radiation also.
GATE ECE 1997
4
Two isotropic antennas A and B from an array as shown in Fig. The currents fed to the two antennas are $${{\rm I}_0}\,\angle 0$$ and $${{\rm I}_0}\,\angle \alpha $$ respectively. What should be the value of $$\alpha $$ so that the radiation pattern has a null at $$\theta = {30^ \circ }$$. Find the direction of the maximum radiation for that value of $$\alpha $$ and draw the radiation pattern. ($$\lambda \,\,$$ is the wavelength of operation)
GATE ECE 1996
5
Two dipoles are so fed and oriented in free space that they produce the following electromagnetic waves:
$$${E_x} = 10\,{e^{j\left( {\omega t - z\pi /3} \right)}}\,\,volts/metre$$$
$$${E_y} = j\,\,10\,{e^{j\left( {\omega t - z\pi /3} \right)}}\,\,volts/metre$$$
(a) Write down the expression for the corresponding magnetic field strength vector.
(b) Calculate the frequency of the wave.
(C) Give the complete description of the polarization of the wave.
GATE ECE 1995
6
Two spacecrafts are separated by 3000 km. Each has a paraboloidal reflector antenna of 0.85 m diameter operating at a frequency of 2 GHz with an aperture efficiency of 64%. If the space crafts A's receiver requires 1pW for a 20 dB signal-to-noise ratio, what transmitter power is required on the spacecraft B to achieve this signal-to-noise ratio?
GATE ECE 1994
7
Consider an array of two non-directional radiators with spacing $$d\,\, = \,\,0.5\,\,\lambda $$. Determine the directions of maximum radiation when the radiators are excited as shown in Fig.. Calculate the phase shift required for turning the direction of the maximum radiation by $${90^ \circ }$$ keeping the separation d unchanged.
GATE ECE 1993
Marks 8
Marks 10
1
In the radiation pattern of a 3-element array of isotropic radiators equally spaced at distances of $${\lambda /4}$$ it is required to place a null at an angle of 33.56 degrees off the end-fire direction. Calculate the progressive phase shifts to be applied to the elements. Also calculate the angle at which the main beam is placed for this phase distribution.
GATE ECE 1991
2
Two vertically oriented half wave dipoles are spaced 1.5 wavelengths apart to from an array. Calculate the half power beam widths of the major lobes of the array, in the horizontal plane for the following two cases when the dipoles are fed with
(a) equal and in - phase currents (Broadside array)
(b) equal currents but with a phase difference of 5400 between the two currents (End fire array)
GATE ECE 1989