MSc Map Antennas and Propagation module exam 2000 (DJJ questions)
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Antennas notes.
Question 1.
(a)
Define the terms effective aperture, gain, efficiency,
Eplane radiation pattern, boresight direction, null, halfpower
beamwidth and polarisation for a large Cassegrain
reflector antenna. Use diagrams to illustrate your answers,
where appropriate.

Effective aperture of a receive antenna is the {power delivered to receiver in Watts}/{average radiant
power flux density across the antenna in Watts/square metre.}
 Gain of a receive antenna is the {power delivered (Watts) by the antenna to the receiver}/
{Power which would be delivered to the receiver by a hypothetical perfect isotropic receive antenna}
The gain in general depends on the directional orientation of the receive antenna with respect
to the source.
 Efficiency is {Power delivered to receiver}/{Total power incident on antenna}.
 The Eplane radiation pattern is the far field contour of equal power density, such
that the distance from the origin of coordinates to the pattern surface is
proportional to the power radiated in that direction, taken in a plane containing
the direction of propagation and the electric field direction. It is only really
defined for linearly polarised antennas.
 The boresight is the direction, or the directions if there are more than one,
of maximum radiated intensity.
 A null in the radiation pattern lies along a direction of
minimum radiation intensity, ideally zero.
 The halfpower beamwidth is the angle between directions, on a plane
radiation polar plot section, where the radiated power has fallen to
one half its value on boresight.
 Polarisation is the projection of the Efield vector, in the far
field region, onto a plane normal to the propagation direction. Polarisation
may be undefined, linear, circular (LH or RH), or elliptical.
[30%]
(b)
Explain why all practical antennas necessarily have
maximum directivity greater than unity.

The polarisation direction is, in general, transverse to the propagation
direction. Consider the complete sphere surrounding the origin:
at some direction of propagation, the polarisation vector
cannot be uniquely defined, so there can be no radiation
in such a direction. Alternatively, there is no radiation
along a direction where the average current in the antenna
structure is directed. Therefore there must be at least one null.
If the radiation falls to zero in a certain direction, it must
exceed unity in some other direction, for the average directivity
value is unity (all the power is radiated uniformly from an
isotrope with unity in every direction).
[10%]
(c)
Give three methods which might be used to generate
circular polarisation for a lowearthorbit satellite
antenna communication system.
 Helical antenna structure
 Crossed dipoles or yagis fed in phase quadrature
 Quarter wave plate for microwave aperture antennas
[15%]
(d)
A deep space communication system uses a Cassegrain
antenna of diameter 70m at a frequency of 8.45 GHz.
(i)
Determine the gain of this dish (in dBi) assuming an
aperture efficiency of 80%

Numerical gain = {efficiency factor}*4 pi A/lambda^2
with {efficiency factor} = 0.8
A = {pi 70^2}/4 (area of a circle of diameter 70 metres)
lambda = 3E8/8.45E9 = 3.55cm = 0.0355m
Numerical gain = 30.7E6
dBi gain = 10log[10]{30.7E6} = 74.9 dBi
[10%]
(ii)
Determine the power received by this dish from a transmission
from a satellite having antenna gain 2.2 dBi and transmitter power
of 10 W at a distance of 180 million kilometres. Assume a receiver
noise temperature of 70 K and a receiver bandwidth of 10 Hz.
Estimate the maximum receiver signaltonoise ratio.

The effective area of the dish = 0.8*{pi 70^2}/4 = 3079 square metres
2.2 dBi is equivalent to a numerical factor 10^0.22 = 1.66
10 watts times 1.66 = 16.6 watts e.i.r.p.
180E6 km = 1.8E11 metres
Power density at antenna = 16.6/{4 pi 1.8^2 10^22} watts per square metre = 4.076E23 w/m^2
Power received = 3079*4.076E23 watts = 1.25E19 watts
Boltzmann's constant k = 1.38E23 Joules/K, assume noise temperature 70K, bandwidth 10Hz
so kTB = 9.66E21 watts
so S/N ratio = 1.25E19/9.66E21 = 12.9 = 11.1 dB
[20%]
(iii)
Estimate the halfpower beamwidth of this 70 m Cassegrain
antenna at 8.45 GHz.

If the diameter of the beam at distance R metres is dR between halfpower
points then the beam solid angle is {pi d^2}/4 steradians and the
beamwidth is d radians.

The gain is {4 pi}/{beam solid angle} = 30.7E6 numerical,
so d = 4/(sqrt{30.7}) milliradians = 0.72 milliradians = 0.04 degrees about.
[15%]
Question 2.
(a)
Define the terms element, element factor, array factor,
pattern multiplication, and total radiation
pattern for an array antenna. State what constraints
have to be applied to the individual elements for pattern
multiplication to be possible.

Element: one of a number n of identical radiating structures
orientated in the same direction in space contributing to the
total radiation from the antenna. They do not have to be fed
with identical amplitudes and phases, but the signal to each
element has to be the same.

Element factor: The radiation pattern (gain or directivity as
a function of direction) of a single isolated element of the array.

Array factor: The radiation pattern of a collection of isotropes
placed on the element centres and fed with the same amplitudes
and phases as are applied to the actual elements of the array.

Pattern multiplication: Pointwise multiplication of the
element pattern by the array factor to obtain the
total radiation pattern for the array.
[25%]
(b)
Distinguish between active arrays and passive
arrays and discuss to what extent the method of
moments calculation process for antenna structures
may be applied to array antennas.

An active array consists of elements each of which is
driven by a physical feed. Passive arrays have one element
actively driven, and the others couple to it electromagnetically
through the near field.

The method of moments derives the radiated field pattern
and also the antenna currents from a selfconsistent matrix
calculation using the Green's function of a little
element of antenna current, and pointwise matching
the solutions to the given antenna feed currents or
voltages. In the case of multiply fed antennas,
power may be transferred between the feeds.
In the case of passive array antennas, any power
delivered to the driven element must eventually
be radiated or absorbed in resistive loss.
[35%]
(c)
An active array antenna is to be constructed from four
halfwave dipoles.
(i)
Sketch the azimuth and elevation pattern for a halfwave
dipole. Explain which pattern is an Eplane section and which
is an Hplane section.

Looking along the rod direction of the dipole, there
is no structure to determine a preferred direction in
azimuth, so the radiation pattern is a circle
centred on the rod. Since the H field is at right
angles to the E field, and the E field lies
along the rod, the azimuth pattern is an Hplane section.

The elevation pattern has nulls along the rods. It is an
Eplane section and has very approximately a cos^2{theta}
distribution where theta is the elevation angle,
being zero at right angles to the rod.
[10%]
(ii)
Sketch the array factor for two isotropes spaced
(a) lambda/4, (b) lambda/2, and (c) lambda apart.
(iii)
Choose an element spacing and suitable drive amplitudes
for the elements so that the fourisotrope "array factor"
has only two main lobes, but no side lobes.

Space the four elements by lambda/2 and feed them with
the excitation pattern 1:3:3:1
which is a combination of 1:2:1 spaced lambda/2
and the 1:2:1 is a combination of 1:1 spaced lambda/2.
[10%]
(iv)
Choose an orientation and spacing for the dipole elements
so that the entire array antenna has maximum directivity
of about 8 dBi.

For a single dipole the element gain is about 2dBi
so we need another 6dBi from the array factor. This is
a numerical factor of 4, and because there are 4 elements
in the array, the boresight gain will be close to
4 for the array factor if we feed them in phase and with
equal amplitudes. The spacing does not affect the
boresight gain.
[10%]
Copyright © D.Jefferies 2000, 2003.
D.Jefferies email
25th March 2003.