Antenna Arrays Questions and Answers

Answer: A

Full hemispherical scanning requires the spacing to be half a wavelength or less, which is why large scanning arrays need so many elements. Limiting the scan range relaxes the requirement towards one wavelength. A quarter wavelength would be unnecessarily close and would worsen mutual coupling, and no amount of element directivity licenses two wavelength spacing for a wide scan. The element count of a phased array is set almost entirely by this criterion.

Answer: B

An N element uniform array has an array factor with up to N minus one nulls, and the same count of degrees of freedom is what allows an adaptive array of N elements to place N minus one independent nulls on interferers. Spacing decides where they fall rather than how many there are. The link between element count and available degrees of freedom is the foundation of adaptive beamforming.

Answer: C

The degrees of freedom of an N element array are N minus one, so eight elements can steer seven independent nulls while maintaining the main beam. That is why the element count of an adaptive system is chosen from the expected number of interferers rather than from the gain required. Using all the degrees of freedom for nulling leaves nothing for beam shaping, which is a real constraint in a crowded environment.

Answer: D

A phased array steers its beam electronically by adjusting the relative phase of the element feeds, with no moving parts, which allows beam positions to be changed in microseconds. That speed is what makes multifunction radar possible. In phase feeding gives a fixed broadside beam, and a mechanically steered antenna is precisely what a phased array replaces. The cost is one phase shifter and often one amplifier per element.

Answer: A

A fixed phase shift corresponds to a different time delay at each frequency, so the beam points in a slightly different direction across the signal band. For narrowband signals it is negligible, but a wideband array must use true time delay steering instead. Mechanical misalignment is boresight error, beam splitting is a grating lobe phenomenon, and beam broadening with scan is a separate and unavoidable effect of aperture foreshortening. Most errors here come from carrying a result across from a neighbouring case where it does not hold.

Answer: B

Seen from an angle, the projected aperture is the physical one multiplied by the cosine of the scan angle, so it appears smaller and the beam is correspondingly wider. Gain falls by the same factor. At sixty degrees the aperture is halved and three decibels of gain is lost, which is why planar arrays are rarely scanned much beyond that. Element pattern and coupling do vary with angle but the cosine law is the dominant and predictable effect. Naming the cost of a choice alongside its benefit is what turns a fact into a design decision.

Answer: C

The projected aperture falls by the cosine of the scan angle:

\[ 10\log_{10}(\cos 60^{\circ}) = 10\log_{10} 0.5 \approx -3 \]

so about 3 dB is lost, before any element pattern roll off is counted. This cosine law sets the practical scan limit of a planar array and is the reason radars needing full hemispherical coverage use three or four faces rather than one.

Answer: D

Because scan loss and grating lobes limit a face to about sixty degrees either side of its normal, three or four faces are used to cover the full circle. A single face cannot reach ninety degrees usefully since the projected aperture goes to zero, and two faces would leave large gaps at the seams. Six would be wasteful. The economics of face count against scan capability is a central decision in radar system design.

Answer: A

Replacing each phase shifter with an actual delay line makes the steering frequency independent, so a wideband signal is not squinted. It is more expensive and bulkier, which is why phase steering is used wherever the bandwidth allows. Mechanical rotation and beam switching are alternative approaches to pointing, and amplitude alone can shift a beam only in the crude sense of a monopulse comparison rather than steering it continuously. A single measurement chosen to respond to the one asymmetry beats several that respond to shared behaviour.

Answer: B

A corporate feed divides the power in a binary tree so that every element is reached by the same electrical length, which makes the array inherently broadband and free of squint from the feed itself. It costs more line and more space than a series feed, which taps power along a single run and does squint with frequency. The choice between them is one of the first made in array design.