# MSc Map Antennas and Propagation module exam 2000 (DJJ questions)

Antennas notes.

### Question 1.

(a)
Define the terms effective aperture, gain, efficiency, E-plane radiation pattern, boresight direction, null, half-power 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 E-plane radiation pattern is the far field contour of equal power density, such that the distance from the origin of co-ordinates 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 half-power 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 E-field 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 low-earth-orbit 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 signal-to-noise 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 = 4.076E-23 w/m^2
Power received = 3079*4.076E-23 watts = 1.25E-19 watts
Boltzmann's constant k = 1.38E-23 Joules/K, assume noise temperature 70K, bandwidth 10Hz
so kTB = 9.66E-21 watts
so S/N ratio = 1.25E-19/9.66E-21 = 12.9 = 11.1 dB

[20%]

(iii)
Estimate the half-power beamwidth of this 70 m Cassegrain antenna at 8.45 GHz.

• If the diameter of the beam at distance R metres is dR between half-power 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 self-consistent 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 half-wave dipoles.

(i)
Sketch the azimuth and elevation pattern for a half-wave dipole. Explain which pattern is an E-plane section and which is an H-plane 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 H-plane section.
• The elevation pattern has nulls along the rods. It is an E-plane 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 four-isotrope "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%]