Radiation from a Dipole Questions and Answers

Answer: C

The half wave dipole's directivity is 1.64, which is 2.15 decibels above isotropic. The figure 1.5 belongs to the ideal short dipole and 2.15 is the decibel value being offered as a ratio, which is the standard trap in this question. Doubling to 3.28 would correspond to a monopole over a perfect ground plane, which radiates the same pattern into half the space. Knowing these few numbers exactly saves a good deal of arithmetic elsewhere.

Answer: D

An exactly half wavelength thin dipole presents about 73 ohms of resistance with some 42.5 ohms of inductive reactance, and shortening it by a few per cent removes the reactance to leave a resonant 70 ohms or so. That trimming is why practical dipoles are cut a little short of a half wavelength. The 36.5 ohm figure belongs to the quarter wave monopole and 300 ohms to the folded dipole, both derived from this same base value.

Answer: A

At exactly half a wavelength the impedance is inductive, so shortening by around five per cent, more for a thick element, cancels the reactance and leaves a purely resistive feed. The resistance falls only slightly and certainly not to fifty ohms, the pattern is essentially unchanged over such a small adjustment, and conductor loss is negligible in either case. The shortening factor depends on the length to diameter ratio, which is why thick elements need more of it.

Answer: B

The monopole radiates the dipole's pattern into a hemisphere with the same terminal current, so it radiates half the power and its radiation resistance is half that of the dipole, about 36.5 ohms. Its directivity is correspondingly doubled to 3.28. Fifty ohms is a cable convention and the quarter value corresponds to nothing. The image principle gives both results at once and is much quicker than any direct integration.

Answer: C

A vertical element's image is the same length below the surface with its current in the same direction, so the two together form a full dipole. A horizontal element's image carries opposite current, which is why a low horizontal antenna nearly cancels itself at low angles. The image is a mathematical device that satisfies the boundary condition of zero tangential electric field at a perfect conductor, and it applies to any source above such a plane.

Answer: D

The out of phase image means the direct and reflected fields nearly cancel along the surface, leaving radiation directed steeply upward. Raising the antenna towards a half wavelength brings the reflection back into phase at useful angles. Ground absorbs partially rather than completely, radiation resistance changes but does not vanish, and lobe splitting occurs at greater heights rather than at low ones. It is the phase of the image, not any absorption, that governs the effect.

Answer: A

With the reflection reinforcing the direct wave, power that would have gone downward is redirected upward and the directivity can approach double the free space figure, giving up to six decibels of field enhancement in the favoured direction. The height above the plane determines the angles at which reinforcement occurs, so the result is certainly not height independent. This is the operating principle of the corner reflector and of every ground plane antenna.

Answer: B

The folded dipole is a loop of two closely spaced parallel wires, one broken at its centre for the feed, and it behaves as a dipole with four times the input impedance. The extra conductor also widens the bandwidth appreciably. Bending an element changes the pattern, turning the ends back is a shortening technique, and stacking is an array arrangement. The folded form is the standard driven element in Yagi arrays for exactly the impedance reason.

Answer: C

The current divides between the two conductors, so for the same radiated power the current at the terminals is halved and, since power goes as current squared times resistance, the impedance rises by four. The radiation is that of a single dipole carrying the total current. The wires carry current in the same sense rather than in antiphase, which is why the arrangement radiates at all, and its resonant frequency is essentially that of the equivalent dipole.

Answer: D

The larger effective conductor diameter lowers the quality factor, so the impedance varies more slowly with frequency and the useful band widens. Its pattern and directivity are essentially those of an ordinary dipole, since the radiating current distribution is the same. It is still a balanced structure and still needs a balun when fed with coaxial cable, usually a four to one type which also completes the transformation to fifty ohms.