Aperture Antennas Questions and Answers

Answer: A

An aperture antenna is analysed by taking the electric and magnetic fields across a surface and computing the far field from them, rather than by integrating a wire current. Horns, reflectors, slots and lenses all belong to the class. The feed may be waveguide or coaxial, and the opening may be any size from a fraction of a wavelength to hundreds, so neither of the last two options is part of the definition. The distinction is one of method as much as of physical form, and it is chosen because the aperture field is easier to know than the current that produces it.

Answer: B

Huygens' principle says that a wavefront may be replaced by a distribution of secondary sources whose envelope forms the next wavefront, and it is the physical idea behind the whole aperture method: knowing the field across a surface is enough to determine the field everywhere beyond it. Radiation from currents is the wire antenna picture, diffraction is a consequence rather than the statement, and field decomposition is a matter of vector algebra. The principle converts a difficult source problem into a manageable boundary one.

Answer: C

The equivalence principle states that the field outside a closed surface is unchanged if the sources within are removed and replaced by suitable electric and magnetic surface currents. That is what makes it legitimate to compute a horn's pattern from the field in its mouth, ignoring everything inside. It is a rigorous theorem rather than an approximation. The other options describe engineering substitutions of quite different kinds, none of which follows from any equivalence theorem, and confusing them with it leads to errors of principle.

Answer: D

The far field is the Fourier transform of the aperture distribution, because the path difference to a distant point varies linearly with position across the aperture and so contributes a linear phase. Every property of the pattern follows from this: a wider aperture gives a narrower beam, a sharp edge gives high side lobes, and a smooth taper suppresses them. It is not a scaling, a convolution or a derivative, and recognising the transform is what allows the whole vocabulary of signal processing windows to be carried across into antenna design unchanged.

Answer: A

The transform of a rectangle is a sinc, so each principal plane shows the familiar narrow main lobe with side lobes 13.2 decibels below it. A circular aperture gives the Bessel form instead, which is the Airy pattern of optics with side lobes at minus 17.6 decibels. A Gaussian aperture would give a Gaussian pattern but cannot exist in finite size, and the cosine squared form belongs to a particular taper rather than to uniform illumination. Knowing the two canonical transform pairs covers most aperture problems at the estimating stage.

Answer: B

The circular case gives minus 17.6 decibels, appreciably better than the rectangular aperture's 13.2, because the circular geometry effectively tapers the illumination towards the edges in one dimension. Reaching minus thirty decibels requires deliberate amplitude tapering and costs beamwidth and efficiency. The figure of minus six corresponds to nothing standard. These two numbers, 13.2 and 17.6, are the reference points against which any measured side lobe level should first be compared.

Answer: C

At 10 GHz the wavelength is 0.03 m, so:

\[ \theta \approx \tfrac{58 \times 0.03}{2} = 0.87 \]

degrees, that is about 0.87 degrees. A tapered illumination would widen this to around one and a quarter degrees while lowering the side lobes. The coefficient is 51 for a uniform line source, 58 for a uniform circular aperture and around 70 for a heavily tapered one, and quoting which convention is in use matters as much as the arithmetic itself.

Answer: D

The physical area is pi times one squared, about 3.14 square metres, so:

\[ \begin{aligned} G &= \tfrac{4\pi \times 3.14 \times 0.6}{0.03^{2}} \\ &\approx 26300 \end{aligned} \]

which is about 44 dBi. The relation shows that gain rises as the square of both diameter and frequency, which is why a modest dish gives enormous gain at microwave frequencies and almost none at high frequency. It is the single most used formula in aperture antenna work and is worth being able to evaluate quickly in the head to within a decibel.

Answer: A

Aperture efficiency is effective area divided by physical area, and it collects together taper, spillover, blockage, phase error and surface tolerance into one number. A prime focus reflector reaches fifty to sixty per cent and a well designed Cassegrain rather more. Radiated over accepted power is radiation efficiency, main lobe power fraction is beam efficiency, and gain bandwidth is a separate specification. Three efficiencies with similar names is a genuine trap, and each is defined by a different ratio that must be quoted explicitly.

Answer: B

A non-uniform illumination uses the outer parts of the aperture less than the centre, so the effective area falls below the physical one, and that ratio is the taper efficiency. It is exactly the price paid for lower side lobes. A uniform distribution has a taper efficiency of one and the worst side lobes. Horn geometry, bandwidth and spillover are separate matters, though spillover trades directly against taper: illuminating the edge strongly reduces taper loss but spills more power past the reflector.