Collected Antennas Problems


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Transmission line notes.

Antennas


Question A1

Define the term "isotropic radiator". A certain transmit antenna has boresight gain which is a factor 2.6 over isotropic. Express this gain as dBi.

This transmit antenna is fed with a signal of a certain power level, 800 Watts of which is accepted. Assuming that there are no scattering obstacles in the beam or the near field, and that there is no attenuation along the path, calculate the power density in watts/square metre, and the rms electric field, at a point at a range of 25km from the antenna along its boresight.


Question A2.


A receiver is fed by an array antenna. The array consists of a broadside arrangement of 8 identical elements connected with equal weights and the same phases to the receiver. Each element has boresight gain of 6 dBi perpendicular to the plane of the broadside array. The frequency of the link is 200MHz. Calculate the array pattern gain, the total gain, and the effective area of the receive antenna array.

If the transmitting system of Question A1 is pointing at this array from a distance of 100km, calculate the total received signal power.

If the receiver noise power is due to thermal noise in 10MHz bandwidth at a source temperature of 300K, calculate the possible range of the link for the receiver signal to noise ratio to be greater than 10dB. Comment on your result.


Question A3

Define the term "uniform array" as applied to a linear array antenna. Explain the term "null placement" and also indicate with an example how the nulls may be placed in specified directions for the radiation into the "array factor" from a uniform linear array antenna.

A linear antenna consists of 8 elements spaced a distance d metres apart along the x axis. Describe the excitation amplitudes and phases if the boresight direction of this antenna is to lie along the y axis. How would the phasing change if it was desired to steer the beam 30 degrees from the y axis in the direction of the positive x axis?

If this array has spacing d equal to half a wavelength, and the adjacent elements are fed in antiphase, determine the boresight direction and the angular position of the first null.

If the array spacing is now reduced to 1/4 wavelength between adjacent elements, describe how the currents on the elements may be phased to give an array gain of 8 in the positive x direction, and a null in the negative x direction. Here we neglect inter-element coupling effects.


Question A4.

With the aid of a sketch, explain the terms "boresight direction", "main beam", "azimuth angle", "elevation angle", "sidelobes", "nulls", "E-plane radiation pattern", and "vertical polarisation".

Explain why a vertical whip antenna may be expected to have a roughly omnidirectional radiation pattern in the horizontal (azimuth) plane, and describe its polarisation properties. How would you generate the orthogonal polarisation for a similar omnidirectional radiation pattern? Suggest a method of making an omnidirectional antenna having right or left hand circular polarisation along every direction in the azimuth plane.

Explain why you would expect an omnidirectional antenna to have boresight directivity greater than unity.

Calculate the beam solid angle for an antenna of gain 36 dBi. For a circular antenna beam from an antenna of gain 36 dBi pointing at a plane surface 20,000 km distant, orientated at right angles to boresight, estimate the circular footprint radius at the -1dB contour, assuming illumination of 0dB on boresight at this distance.

Estimate the maximum range (in number of wavelengths) for free space propagation between two antennas of gain 36 dBi pointing at each other, for a transmitter amplifier power of 1 microwatt and a system noise temperature of 300K in a bandwidth of 200kHz. You can assume the range is set at a receiver S/N ratio of 15dB.

Estimate, giving your reasons, the maximum line-of-sight range of a terrestrial microwave link using two 30cm square cross section pyramidal horns at 12GHz, for the transmission of PAL TV signals using some appropriate analogue modulation of a 15mW Gunn source.


Question MJU

Here is a question and answer given to me by Professor Underhill, transcribed exactly as I have it in front of me.

For a three element Yagi-Uda antenna explain why the element lengths are not the same. (hint: phasing of element currents?)

Given that an exact half wave dipole has an input impedance of 73+j42.5 ohms and for a particular thickness the dipole behaves as a transmission line of 500 ohms, calculate in units of wavelengths the lengths of:

(i) a director with a reactance of j10 ohms

(ii) a reflector giving a current phase lag of approximately 30 degrees.

I'm sorry I can't comment on this any further.
If you have any questions please email Professor Underhill at
m.underhill@ee.surrey.ac.uk



MSc Map Antennas and Propagation module exam 1998 (DJJ questions)


Question 1.

Define the terms "directivity", "gain", "efficiency", "polarisation", and "effective aperture" in the context of antenna design. [20%]

Using a diagram, illustrate the terms "boresight direction", "azimuth angle", "elevation angle", "main beam", and "sidelobes". Explain why an isotropic source cannot be constructed in practice, and distinguish carefully between the terms "isotropic" and "omnidirectional". Explain why an omnidirectional antenna necessarily has a maximum directivity greater than unity. [20%]

A hypothetical isotropic radiator has unity gain and effective aperture (lambda^2)/(4 pi) for radiation of wavelength lambda. Calculate the gain of a satellite dish antenna of effective aperture 3.75 square metres at a frequency of 14 GHz, and estimate the diameter of the parabolic reflector needed to implement such a dish, given an aperture efficiency factor of 0.65. [30%]

Estimate the pointing accuracy needed for an antenna dish of boresight gain 45dBi and explain with examples what technological steps can be taken to alleviate the effects of wind loading. [30%]

Outline solution 1.


Question 2.

Describe what is meant by the term "array antenna". Define the terms "array factor", "element pattern", and "pattern multiplication". Explain what constraints are imposed on the individual elements in order for the properties of the array antenna to be calculated by pattern multiplication. [25%]

An array consists of four half-wave dipoles, spaced in a straight line by a distance of one half wavelength along a line at right angles to their rods. Sketch the element pattern in the H plane and in the E plane. Sketch the array pattern and identify the direction(s) of the main beam(s). Calculate the boresight gain in the case that all elements are fed with equal amplitudes which are in phase. [35%]

It is desired to steer the beam by 30 degrees from boresight in the H-plane. Calculate the required phase shift between currents on adjacent elements. [15%]

Explain the term "Very Long Baseline Interferometry" (VLBI) and estimate the resolution of a VLBI system consisting of two dishes at a frequency of 8GHz, each of diameter 20m, spaced by a distance of 1000km. [25%]

Outline solution 2.




Microwave Option paper 97-98 (DJJ antenna question)


Question 4.

Define the terms "isotropic radiator", "boresight direction", "directivity", "gain", and "E- plane radiation pattern" in the context of antenna design. Explain why it is impossible to construct an isotropic radiator in practice. [30%]

A certain transmitter has a final amplifier that delivers 10 kW to an antenna with 85% efficiency. The antenna has boresight directivity of 14dBi above an isotropic source. Calculate the r.m.s. electric field strength at a distance of 50 km from an ISOTROPIC source radiating 10 kW with 100% efficiency, and compare it with the field strength at this distance from the hypothetical transmitter-antenna combination described above. [40%]

Give a formula relating the effective area of an antenna to its boresight gain and to the wavelength of the radiated signal. Estimate the area of a horn aperture antenna required to give a gain of 14dBi at 13 GHz. If such a dish were used to transmit the 10kW signal described above, estimate the power flow in watts per square metre at a distance of 10m from this horn along boresight, and comment on the safety implications. [30%]


Microwave Option paper 96-97 (DJJ's antenna-related questions)


Question 1

For waves travelling on a real coaxial cable connected to a linear antenna, define the following terms: (i) characteristic impedance (ii) complex reflection coefficient (iii) return loss (iv) complex voltage amplitude (v) propagation constant. [25%]

Assuming that the line is nearly lossless, express the forward and backward wave power flows, in watts, in terms of the quantities defined above. [10%]

Derive an expression for the stored energy per unit length, on the cable, for waves travelling in a single direction only. [15%]

A 75 ohm cable, assumed lossless, feeds an antenna having radiation resistance (30+j120) ohms at the signal frequency. If the forward wave power is 10 watts, calculate the return loss and the radiated power. [25%]

A generator feeds the 75 ohm cable and antenna of the last part. The generator has negligible internal impedance and is connected at a voltage standing-wave maximum. For a forward wave power of 10 watts, calculate the rms voltage at the generator terminals. Give a qualitative description of a method by which the antenna may be matched to the cable. [25%]


DJJ's antenna-related question, from 95-96



Question 5


Define the terms "directivity", "gain", "efficiency", and "effective area" for an antenna array. Explain how the boresight gain of an antenna is related to its effective area and efficiency. [25%]

A square array of 4 by 4 elements consisting of lambda/2 dipoles each having a maximum gain 3dB is fed by 16 signals of adjustable relative phase and equal amplitudes. Assuming 90% efficiency, calculate the boresight gain when the signals are all in phase. [50%]

Explain with a diagram how the direction of the beam from this array may be altered without moving the positions of the elements. [25%]


MSc Map Antennas and Propagation module exam 1999 (DJJ questions)


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Antennas notes.

Question 1.

Write definitions and notes on the terms boresight, polarisation, null, isotropic radiator, efficiency, far-field radiation pattern, and directivity in the context of antenna descriptions.
[35%]

Describe, giving quantitative detail, the construction of a typical fifteen element linearly polarised Yagi-Uda 800MHz television receiving antenna. State the number of elements which are directly driven from the feeder, and explain why only a single reflector element is needed. Estimate, giving reasons, an upper limit to the maximum boresight gain (dBi) of this antenna.
[25%]

A receive Yagi-Uda antenna has boresight gain 5.6 dBi. Calculate the effective receive cross-sectional area of this antenna at 1.8 GHz. Estimate the maximum power which can be received by this antenna from a transmitting source directly overhead (along boresight) at a distance of 100 km, assuming the transmitter power is 1 watt and the transmit antenna gain is 2.6 dBi.
[25%]

If the receive channel noise temperature is 450 K, estimate the receiver signal-to-noise ratio (dB0 for this link, for 10 MHz bandwidth.
[15%]

Outline solution 1.


Question 2.

Explain, illustrating with examples and sketches, the terms array antenna, element, array pattern, element pattern, and pattern multiplication . Distinguish between the element placings in a one-dimensional and a two-dimensional array.
[30%]

An array antenna is formed from two elements consisting of 50 dBi gain aperture antennas, which are separated in space by 100,000 wavelengths. Calculate the boresight gain of the array. Estimate how many interference fringes of the array pattern lie within the -3dB contours of the element pattern.
[40%]

Explain the term very long baseline interferometry (VLBI) and state its use. Estimate the resolution obtained with Earth-based VLBI at 1 GHz using the maximum possible practical separation of the elements.
[30%]

Outline solution 2.


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


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.

(b)
Explain why all practical antennas necessarily have maximum directivity greater than unity.

(c)
Give three methods which might be used to generate circular polarisation for a low-earth-orbit satellite antenna communication system.

(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%

(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.

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


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.

(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.

(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.

(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.

(iv)
Choose an orientation and spacing for the dipole elements so that the entire array antenna has maximum directivity of about 8 dBi.


MSc Map Antennas and Propagation module exam 2001 (DJJ questions)


Question 1.

(a)
Define the terms radiation impedance, feeder, antenna efficiency, null, boresight, and VSWR2 bandwidth for a terrestrial fixed-link antenna installation.


[25%]

(b)
Calculate the percentage of power reflected from an antenna if the VSWR on the feed is 2:1.


[10%]

(c)
Explain why the radiation resistance of a short rod antenna is approximately proportional to the square of its length.


[15%]

(d)
Sketch the position of the nulls, in 3-d space, for a short dipole antenna.


[10%]

(e)
Explain how the radiation impedance and bandwidth of a short dipole antenna depend on the diameter/length ratio of its rods.


[15%]

(f)
A free-space link is set up between two co-polarised half-wave dipole antennas at a frequency of 800MHz and a bandwidth of 10MHz.


Question 2.

(a)
Describe the principal components, construction, and properties of an offset-fed reflector antenna.


[15%]

(b)
A pyramidal square horn antenna is excited by the TE10 mode in rectangular waveguide at 12GHz. It has boresight gain 22.0 dBi. Calculate the dimensions of the horn mouth, assuming constant phase across the horn aperture.


[15%]

(c)
The horn of part (b) illuminates a circular parabolic reflector of area 80 square metres in a front-fed arrangement.

(d)
Write notes on the causes of sidelobe production in reflector antennas. Explain what steps may be taken to minimise the sidelobes.


MSc Map Antennas and Propagation module exam 2002 (DJJ question)


Question 1.

(a)
Define the terms numerical gain, boresight, polarisation, null, and isotropic radiator. Illustrate your answers with diagrams and write notes where needed.


[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 half-wave dipole. The practical half-wave 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.


[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.


[15%]

(d)

(e)
Calculate thje maximum range at which two co-polarised 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.

[30%]



Copyright(c) D.Jefferies 1996, 1997, 1998, 1999, 2000, 2001, 2002, 2003.
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7th April 2003.