Antenna Arrays Questions and Answers

Answer: C

Beamwidth depends on the aperture measured in wavelengths, so adding elements lengthens the array and narrows the beam in inverse proportion. Side lobe level for a uniform distribution stays near minus thirteen decibels however many elements are used, which is one of the more surprising results of array theory. The number of side lobes rises with element count but their relative height does not, and lowering it requires amplitude tapering. The quantity that varies and the quantity that does not are worth naming before any substitution is attempted.

Answer: D

The pattern of a uniform aperture is a sinc like function whose first side lobe is 13.2 decibels below the main lobe regardless of how long the aperture is, because the ratio is set by the sharp edge rather than by the size. Only by tapering the illumination can it be reduced. Coupling, matching and spacing all affect an array but none of them explains this particular and very robust figure.

Answer: A

Weighting the elements by the binomial coefficients removes the side lobes entirely at half wavelength spacing, which is unmatched by any other distribution. The price is a much wider main beam and a very low aperture efficiency, since the outer elements contribute almost nothing. Equal side lobes belong to the Chebyshev distribution and maximum directivity to the uniform one, so the three classical distributions occupy the three corners of the same trade.

Answer: B

Because the outermost elements are fed very weakly, the effective aperture is far smaller than the physical length, so the beam is wide and the directivity low. The amplitude ratio also becomes impractical for more than a few elements: a nine element binomial array needs a seventy to one range. Side lobes are absent rather than rising, the frequency behaviour is unremarkable, and matching is no harder than for any other array.

Answer: C

The Chebyshev distribution gives all side lobes at the same chosen height and, for that height, the narrowest possible main beam, which makes it optimal in a precise sense. Choosing a very low side lobe level approaches the binomial case and a very high one approaches uniform. Equal amplitudes describe the uniform distribution, and bandwidth is governed by the elements and the feed rather than by the taper.

Answer: D

A uniform distribution uses the whole aperture equally and so gives the maximum directivity, at the price of thirteen decibel side lobes. Every taper trades some directivity for lower side lobes, the binomial being the extreme case. This is the central trade of array design and it cannot be evaded: side lobe suppression is always bought with beamwidth and aperture efficiency, and the designer chooses where on that curve to sit.

Answer: A

Both are true and the second is the reason. Weighting the edge elements down shrinks the effective aperture, and beamwidth is inversely proportional to aperture, so the beam necessarily broadens. The relationship is quantitative and unavoidable, and the Chebyshev distribution is simply the best available compromise for a stated side lobe level. The same trade appears in signal processing as the choice of window function.

Answer: B

Both problems are the same mathematics: the pattern is the Fourier transform of the aperture distribution, so an amplitude taper plays exactly the role of a window in suppressing spectral leakage. Hamming, Taylor and Chebyshev appear in both fields for that reason. Phase shift corresponds to a frequency shift, spacing to the sampling interval and element count to the record length, so the whole analogy carries across term by term.

Answer: C

When the spacing is large enough, a second direction exists in which the path differences are whole wavelengths, so the contributions add fully and a lobe as strong as the main one appears. Keeping the spacing at or below half a wavelength prevents them at any scan angle. Taper controls side lobes rather than grating lobes, cable errors raise the side lobe floor, and coupling alters impedance and the element pattern. The distinction between a side lobe and a grating lobe is one of kind rather than degree.

Answer: D

A grating lobe exists mathematically but only becomes visible when its direction falls within real space, and steering the beam pushes it towards the horizon. An array that never scans far can therefore use spacing up to nearly a full wavelength and use fewer elements for a given aperture. Coupling does not depend on the beam direction in that way, spacing certainly enters the array factor, and the element pattern attenuates rather than suppresses. Checking the units of each quantity catches a wrong formula before the arithmetic begins.