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

navigation page

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.

• Definitions
  • Boresight: direction(s) of maximum gain, or directivity, or radiated field strength
  • Polarisation: direction of Electric field vector projected on a plane normal to the propagation direction. It can be linear, elliptical, or circular (RH or LH). It can be time-dependent.
  • Null: A direction at which there is zero radiation. It is a point or line from a continuous set; one cannot have zero radiation over a range of angles between two lobes.
  • Isotropic radiator: A hypotehtical source radiating equally in all directions in three dimensions. Sinve EM waves are transverse, isotropic radiators can only be approximated in practice, but cannot be accurately realised.
  • Efficiency: The amount of power accepted by the antenna from the feed that is actually radiated. Gain/directivity.
  • Far field radiation pattern: A plot of the gain or directivity as a function of azimuth and elevation directions, at a sufficient distance that the pattern shape does not depend on the distance from the source.
  • Directivity: Ratio of field strength in a certain direction to the field strength at that distance, from an isotropic radiator having the same total integrated radiated power as the antenna under investigation.
  
  [35%]

• At 800 MHz, a half-wavelength is 18.75 cms. The antenna has a single element driven from the feed (75 ohm coax usually) which consists of a folded dipole which is a little shorter than a half-wavelength. Behind this driven element is a single reflector, of length about a half wavelength and spacing about lambda/5 from the driven element In front of the driven element are 13 directors, each about 15% shorter than a half-wavelength, and spaced by about 1/3 lambda. The diameter of the rods is typically 5 mm. As the reflector returns most of the power to the forward direction, there are only small fields behind it so extra reflector elements have little effect. An estimate of the gain is (number of elements) times (gain of dipole) which is approximately (in dBi) 10 log[10](15) + 2dBi or 14 dBi. The antenna construction can be varied quite widely without greatly affecting the forward gain, and we have not considered broadbanding techniques.
  [25%]

• A gain of 5.6 dBi is a numerical factor of 10^(5.6/10) = 3.63. This factor is equated to (4 pi Ae)/(lambda^2) and lambda at 1.8 GHz is 30/1.8 cms or 0.1667 metres. So the value of the effective area Ae is 80.23 sq cms or 8.023E-3 sq metres The transmitter power e.i.r.p is 1 watt times 10^(2.6/10) or 1.82 watts. The received signal strength is 1.82/(4 pi R^2) watts/square metre at a distance R metres, so at 100 km = 1E5 metres, the received power is (Ae 1.45E-11) = 1.16E-13 watts.
  [25%]

• The receiver noise power is kTB = (1.38E-23)(450)(1E7) or 6.21 E -14 watts so the signal-to-noise ratio is 11.6/6.21 = 1.87 or 2.72dB.
  [15%]

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.

• An array antenna comprises a collection of spaced "similar" elements. "Similar" means that they all have the same radiation patterns, considered individually, and they are all orientated in the same direction in 3-d space, with identical polarisation properties. An "element" may consist of an array of "sub-elements", so the array antenna can be built up recursively. A "linear" array has elements spaced along a single direction or dimension in 3-d space. An "area" array has elements spaced on a single plane in 3-d space, in 2 dimensions. The elements do not have to be fed with the same amplitudes and phases of signal, but they do have to be fed with the same signals in terms of the frequency spectrum or Fourier decomposition.

  The "array pattern" consists of the far field interference pattern set up by a collection of hypothetical isotropic radiators, located at the positions of the actual elements, and fed with the same signals as the actual elements.

  The "element" pattern is the far field radiation pattern of a single element, on a single site, having the same orientation as the actual array of elements.

  "Pattern multiplication":- pointwise multiplication of the "element pattern" by the "array pattern" to obtain the total radiation pattern for the antenna array. Pointwise multiplication means that we choose a direction in 3-d space, determine the array pattern gain and the element pattern gain in this direction, multiply them to find the total gain, then repeat for all possible radiation directions.
  [30%]

• For two elements the gain is twice that of one element, so the array pattern gain is 10 log[10](2) = 3 dBi and the total gain is 50 + 3 = 53 dBi.

  A single element has numerical gain 10^(50/10) = 100,000 numerical gain. If all the radiation is contained within a cone of semiangle alpha radians, then we have that 100,000 = 4 pi steradians divided by the solid angle of the cone, so 100,000 = (4 pi)/(pi (alpha^2)/4) whence 1E5 = 16/(alpha^2) and alpha = 12.6 milliradians.

  For an array spacing of 1E5 wavelengths, the angular spacing of the lobes is very nearly 1E-5 radians. So there are about 1260 array lobes inside the main beam of a single element.
  [40%]

• At 1GHz, the wavelength lambda is 30 cms. The maximum separation of antennas on the Earth's surface, such that they can both see in the same direction in space, is about 11,000 km. This is 3.67E6 wavelengths, so the angular resolution between adjacent nulls is 1/[3.67E6] radians, or 2.7 E -7 radians, or 0.056 arc seconds.
  [30%]