Radiation from a Dipole Questions and Answers

Answer: A

Because the power density falls as the inverse square of range while the sphere's area rises as its square, the total power crossing any far field sphere is the same. Power density and field strength both fall with distance, and radiation resistance is a terminal circuit quantity rather than something defined on a sphere. This conservation is precisely what distinguishes the radiation term from the reactive ones, whose net flux integrates to zero.

Answer: B

Radiation resistance depends on the length measured in wavelengths, so raising the frequency of a fixed antenna makes it electrically longer and the resistance rises, at least until resonance is passed. A whip that is nearly useless at one frequency can be efficient an octave higher for exactly this reason. It is not a material property, and although the resistance varies strongly and passes through maxima and minima with length, it does not vanish.

Answer: C

A one metre whip is a hundredth of a wavelength at 30 MHz and a half wavelength at 150, so its radiation resistance rises from a fraction of an ohm to tens of ohms and its efficiency with it. The ground plane and noise arguments have some force but are secondary, and the transmitter is unchanged. This single relation explains most of why antenna practice differs so sharply between the high frequency and very high frequency bands.

Answer: D

With 73 ohms of radiation resistance against a fraction of an ohm of copper loss, a half wave dipole is essentially a hundred per cent efficient, which is why it is such a good reference antenna. The picture is entirely different for a short dipole or a small loop, where the two resistances become comparable. Beamwidth and resonance are unaffected by a small series resistance. Where the loss sits relative to the radiation resistance is the question to ask of any antenna.

Answer: A

The small loop's radiation resistance in that case is around three hundredths of an ohm, so a one ohm loss would leave an efficiency of a few per cent. The dipole at 73 ohms, the folded dipole at 292 and the monopole at 36.5 would all be barely affected. Comparing the loss with the radiation resistance is the whole calculation, and it explains at once why loops and short verticals demand such care in construction while dipoles do not.

Answer: B

A magnetic loop's radiation resistance is a fraction of an ohm, so every milliohm of conductor loss matters and thick tubing with a large surface area is essential to reach even moderate efficiency. Circulating currents of tens of amperes are normal. Mechanical strength is a bonus, the resonant frequency is set by the tuning capacitor, and no direct current flows. It is the clearest case in antenna practice of a design driven entirely by loss resistance.

Answer: C

The loop is an inductor, and a high quality vacuum or butterfly capacitor across its gap resonates it, tuning being achieved by varying that capacitance. The circumference sets the inductance and therefore the range covered, but not the operating frequency directly. Height affects the pattern and ground loss, and feed line length should be irrelevant if the antenna is properly matched. The extremely high circulating voltage across that capacitor is the loop's main practical hazard.

Answer: D

A high ratio of stored to dissipated energy is precisely a high quality factor, and a small efficient loop stores a great deal of energy and loses very little, so its bandwidth may be only a few kilohertz. Retuning is needed for every small frequency change, which is why remote capacitor drives are standard. Its radiation resistance is very small rather than large relative to the reactance, capacitor loss reduces the quality factor rather than raising it, and radiation occurs off resonance too, though feebly.

Answer: A

Both are true and the second is the reason. The same property that makes an efficient small loop possible, a very low loss resonant circuit, necessarily gives it a narrow bandwidth, since bandwidth is the resonant frequency divided by the quality factor. It is the Chu limit appearing in a practical form: a small antenna may be efficient or broadband but not both. Remote tuning is the engineering answer rather than any escape at all from the underlying physics.

Answer: B

The standard relation is bandwidth equals resonant frequency over quality factor, so a quality factor of a hundred at ten megahertz gives a hundred kilohertz of bandwidth. It applies to any resonator, antenna or otherwise. Since the Chu limit sets a minimum quality factor for an antenna of a given electrical size, this relation converts that limit directly into a maximum achievable bandwidth, which is how the size, bandwidth and efficiency trade is made quantitative.