MSc Map Antennas and Propagation module exam 2002 (DJJ question)
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Antennas notes.
Question 1.
(a)
Define the terms numerical gain, boresight, polarisation, null,
and isotropic radiator.
Illustrate your answers with diagrams and write notes where needed.

The numerical gain of an antenna is the radiation intensity
(power density in watts per steradian) produced by an antenna
in a direction (theta, phi) divided by the radiation
intensity of an isotropic 100% efficient antenna which has the
same accepted input power.

Boresight:
There may be more than
one unique boresight direction. It is the direction (theta, phi)
for which the numerical gain is a maximum.

Polarisation:
The trajectory of the projection of the E field vector on a plane
normal to the propagation direction

Null: A direction in threedimensional space where there is
no farfield radiation.

Isotropic radiator: A radiator that emits equally in all directions
around a sphere centred on the source. Impossible to realise
in practice. The numerical gain is independent of (theta, phi).
[20%]
(b)
A certain antenna, ANT, consists of a number of parallel
straight rods. It has numerical gain 8.4 with respect to
a practical halfwave dipole. The practical halfwave
dipole is specified to have gain in decibels, after
accounting for losses, of 2.06 dBi. What is the numerical
gain of ANT with respect to an isotrope? Express this gain
also in dBi and indicate two directions in space where
nulls must lie. You may ignore any residual radiation from
the feed.

A halfwave dipole of gain 2.06 dBi has numerical gain
10^(0.206) = 1.607 with respect to an isotrope.
So the gain of ANT = 8.4*1.607 = 13.498 numerical.
This is 11.303 dBi.

The nulls lie along the rod directions.
[15%]
(c)
Distinguish between the terms omnidirectional and
isotropic. Explain how a loop antenna in combination with
a dipole, may be used to generate omnidirectional circular
polarisation in a horizontal plane. Sketch the radiation pattern
in an elevation plane.

Omnidirectional: for some coordinate system (theta(elevation), phi(azimuth))
the directivity is independent of phi but not
independent of theta.

Isotropic: for all coordinate systems (theta, phi),
the directivity is independent of both theta and phi.

A combination of a loop antenna and a dipole placed along
its axis of rotation, with the elements fed in phase
quadrature to give equal radiation intensities
in the plane of the loop in the far field, will generate
omnidirectional circular polarisation in the azimuth plane.
[15%]
(d)
(e)
Calculate the maximum range at which two copolarised lambda/2 dipoles
can communicate in free space. Assume a system noise temperature of 100K.
Express your answer in terms of the transmitter power P watts, the
system bandwidth B Hz, and the wavelength lambda metres.

The numerical gain of a half wave dipole is 1.66 so the effective
aperture, which is gain(lambda^2)/(4 pi) is 1.66 (lambda^2)/(4 pi)
Also, for transmitter power P watts and transmit antenna gain 1.66,
the generated power density at distance R metres is 1.66P/(4 pi R^2) watts per square metre.
The received power at distance R metres is (1.66)^2 P (lambda^2)/(4 pi R)^2 watts
which has to be equal or larger than the noise power at temperature T Kelvin
and bandwidth B Hz, which is kTB watts.
Equating these terms and rearranging, one obtains
R = sqrt[P/kTB]*1.66 lambda/(4 pi) which on putting in the
numbers is sqrt[P/B]*3.566E9 metres.
[30%]
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10th April 2003.