Radiation from a Dipole Questions and Answers

Answer: A

At a full wavelength the current at the feed point is a minimum of the standing wave, so the impedance rises to several thousand ohms, which is very hard to match. This is why full wave dipoles are fed off centre or at a current maximum instead. The impedance passes through resonances every half wavelength, alternating between low values at current maxima and very high ones at current minima, and knowing where the feed point falls on the standing wave predicts the whole behaviour.

Answer: B

Lengthening to a full wavelength narrows the broadside lobe and raises the directivity to about 2.4, though the impedance becomes awkward. Beyond about 1.25 wavelengths the main lobe begins to split and the broadside directivity falls again. Cancellation is complete only in particular directions rather than everywhere. The general lesson is that longer is better only up to the point where the current distribution develops regions of opposing phase.

Answer: C

The standing wave reverses direction every half wavelength along the wire, so once the antenna is long enough, oppositely directed currents cancel in the broadside direction and the energy appears in lobes to either side. Radiation resistance never goes negative for an isolated element, feed position affects impedance rather than pattern, and a travelling wave requires a terminated rather than an open wire. The same reasoning predicts the many lobed patterns of long wire antennas.

Answer: D

A resistively terminated wire carries current in one direction only, with no reflection and so no standing wave, which gives a broadband unidirectional pattern at the cost of the power absorbed in the termination. Rhombic and Beverage antennas work this way. Length and feed position are secondary, and no antenna radiates from direct current. The trade of efficiency for bandwidth and pattern is the defining characteristic of the whole travelling wave family.

Answer: A

An infinite biconical structure is defined entirely by angles, so it presents the same impedance at every frequency, and a truncated practical version is broadband over many octaves. Its pattern resembles a fat dipole, broadside with axial nulls, rather than a narrow beam. It radiates linear polarisation and needs a feed like anything else. The idea that a structure specified only by angles is frequency independent also underlies the log periodic and spiral antennas.

Answer: B

A loop much smaller than a wavelength carries essentially uniform current and radiates like a magnetic dipole, with its electric and magnetic fields interchanged relative to the short electric dipole. Its pattern is the same doughnut shape but with the null perpendicular to the plane of the loop rather than along a wire. This duality between the electric and magnetic cases is one of the tidiest results in antenna theory and makes the loop's fields obtainable without fresh integration.

Answer: C

Substituting the area ratio directly:

\[ R_{r} = 31171 \times (0.01)^{2} \approx 3.1 \]

giving about 3.1 ohms. The fourth power dependence on linear size is even more severe than the dipole's square law, which is why small loops are notoriously inefficient transmitting antennas and are used chiefly for receiving, where efficiency matters less than pattern and noise pickup.

Answer: D

The loop's deep nulls perpendicular to its plane make it excellent for direction finding and for nulling a local interferer, and at low frequencies external noise dominates so inefficiency costs nothing in signal to noise ratio. Its gain is not higher, it is strongly inductive rather than resistive, and it responds primarily to the magnetic field, which is why it is less affected by local electric field noise. The last point is itself a practical advantage.

Answer: A

The loop radiates maximum in its own plane and has nulls along the axis perpendicular to it, which is the exact complement of the short dipole's behaviour. Rotating the loop until the signal disappears therefore gives a bearing to the source, with a hundred and eighty degree ambiguity that is resolved by adding a sense antenna. The null is sharper than the maximum, which is why direction finding always works on nulls rather than on peaks.

Answer: B

Both are true and the second explains the first. A cosine shaped pattern changes very slowly near its peak and very rapidly through its null, so the bearing can be read far more precisely from the null. The price is a front to back ambiguity, which a sense antenna combined in quadrature resolves by producing a cardioid pattern with a single null. The same preference for nulls over peaks recurs wherever an angle must be measured accurately.