Radiation from a Dipole Questions and Answers

Answer: C

Applying the relation between directivity and aperture to a directivity of 1.64 gives about 0.13 square wavelengths, which at low frequencies is a surprisingly large collecting area for a thin wire. That an antenna's effective aperture bears no simple relation to its physical size is one of the more counter-intuitive results in the subject, and it applies just as much to a dipole as to a reflector, which is why the last option is wrong in principle rather than merely in arithmetic.

Answer: D

With a directivity of 1.64 and a wavelength of three metres:

\[ A_{e} = \tfrac{1.64 \times 9}{4\pi} \approx 1.17 \]

giving about 1.2 square metres for a wire a metre and a half long. The collecting area is far larger than anything the physical wire suggests, and it shrinks as the square of the frequency, which is why the same dipole gathers so much less power at microwave frequencies.

Answer: A

The relation contains the wavelength squared, so holding the gain constant while raising the frequency shrinks the collecting area in proportion to the square of the frequency. This is the real content of the frequency term in the Friis equation, which is often misread as a property of the intervening space. Absorption, radiation resistance and efficiency all vary with frequency but none of them is the reason for this particular relation.

Answer: B

Half of two metres is 1 m, before the few per cent of shortening that brings it to resonance. The wavelength in metres is three hundred divided by the frequency in megahertz, so a two metre wavelength corresponds to 150 MHz and the dipole is about 0.95 m of wire in practice. Being able to move quickly between frequency, wavelength and element length is the most basic arithmetic in antenna work.

Answer: C

Dividing the speed of light by the frequency gives 3 m, which is the standard shortcut of three hundred divided by the frequency in megahertz. A half wave dipole for the FM broadcast band is therefore about 1.5 m of wire, which matches the familiar size of a domestic aerial. Thirty metres would be 10 MHz and 0.3 m would be a gigahertz, so keeping the decimal point straight is the whole of the difficulty.

Answer: D

The maximum is broadside to the wire, so a vertical element radiates towards the horizon, uniformly in azimuth, and has a null straight up. That is exactly what is wanted for terrestrial communication and exactly wrong for a satellite directly overhead. Choosing the orientation of a simple antenna to suit the direction of interest is the first practical decision in any installation.

Answer: A

Polarisation follows the direction of the current, so a horizontal wire radiates a horizontally polarised wave. Matching this at both ends of a link matters, since the loss between crossed linear polarisations is very large. Circular and elliptical polarisation require two orthogonal currents in phase quadrature, which a single straight wire cannot produce however it is oriented.

Answer: B

The centre is a current maximum and a voltage minimum, giving a convenient impedance near 73 ohms. Feeding at the end would present several thousand ohms, which is why end fed antennas need a matching network. Off centre feeding gives an intermediate impedance and is used deliberately in some multiband designs. Where a feed point falls on the standing wave determines the impedance seen, and that is the single most useful idea in wire antenna practice.

Answer: C

Radiation resistance is a resistance and so is measured in ohms, being the resistance that would dissipate the radiated power if it carried the antenna's terminal current. Watts measure the power itself, volts per metre the field strength at a point, and steradians the solid angle used in defining radiation intensity. Checking the units of a quantity is a quick way to confirm that its definition has been remembered correctly.

Answer: D

The dBd scale refers gain to a half wave dipole, whose own gain is 2.15 dBi, so a dBd figure is always 2.15 less than the corresponding dBi one. The isotropic radiator is the reference for dBi and cannot be built, which is why a physical dipole is often preferred for a measurement comparison. Always checking which reference is meant prevents the commonest error in reading antenna specifications.