Antenna Arrays Questions and Answers

Answer: A

An array is a group of elements whose radiated fields add vectorially to produce a pattern none of them could give alone, and the amplitudes and phases of the feeds are the design variables. A multiband antenna, a reflector and a collection of independent antennas on a common support are all different things. The point of an array is that the aperture, and therefore the directivity, can be made as large as the structure allows without any single element being large.

Answer: B

The array factor is the pattern that would result if every element were replaced by an isotropic radiator, so it captures the geometry and the excitation alone. Multiplying it by the element pattern gives the total. Element count does not simply multiply gain, mutual impedance is a separate calculation, and feed efficiency affects amplitude rather than shape. Separating geometry from element in this way is what makes array design tractable at all. The shared properties explain why these belong to one family, and the differences explain why more than one exists.

Answer: C

Pattern multiplication holds when every element has the same pattern and the same orientation, so that a single element factor can be taken outside the sum. Spacing, amplitude and phase are free variables that appear in the array factor. Resonance is a matching matter rather than a condition of the theorem. Where elements differ, as when edge elements see a different environment from central ones, the principle becomes approximate and the active element pattern is used instead.

Answer: D

A uniform linear array has elements equally spaced along a line, fed with equal amplitudes and with a constant phase increment from one to the next. That combination gives the highest directivity for a given aperture but also the worst side lobe level, about minus thirteen decibels. Equal cable lengths are one way of achieving equal phase but are not the definition, and the other options describe properties that no array possesses. A limit that survives making every external component ideal is an intrinsic one, and worth knowing for that reason.

Answer: A

Feeding every element in phase makes the contributions add in the direction perpendicular to the array line, where all path lengths are equal, giving the broadside beam. A progressive phase matching the inter-element delay gives end fire instead. Antiphase excitation produces a null broadside, and amplitude tapering is a side lobe control applied on top of whichever phase distribution is chosen. Phase decides where the beam points; amplitude decides what the side lobes look like.

Answer: B

Making each element lag its neighbour by exactly the propagation delay between them means the contributions arrive together along the array axis, so the beam points end fire. For half wavelength spacing that is a hundred and eighty degree step. In phase feeding gives broadside, and the amplitude options describe tapering rather than steering. The whole of beam steering is contained in this idea of compensating the path difference with a feed phase. Most errors here come from carrying a result across from a neighbouring case where it does not hold.

Answer: C

Broadside means theta equal to ninety degrees, whose cosine is zero, so:

\[ \beta = -kd\cos 90^{\circ} = 0 \]

and the required phase step is zero, that is all elements in phase. Setting theta to zero instead gives beta equal to minus kd, which is the end fire condition. The single formula covers every steering angle between, which is exactly what a phased array exploits.

Answer: D

Adding a small extra phase beyond the ordinary end fire value narrows the main beam and raises the directivity of a long end fire array by about four decibels, at the cost of higher side lobes. It is a deliberate departure from the intuitive in-phase-at-the-axis condition. Grating lobe spacing, Chebyshev tapering and bandwidth optimisation are all separate results. The increased directivity comes from a broader effective aperture in the phase domain rather than from any extra length.

Answer: A

For a linear broadside array the directivity is about twice the length in wavelengths, so doubling the aperture doubles the directivity and gives three decibels. A planar array, being two dimensional, gains as the area and therefore as the square of a linear dimension. The distinction between linear and planar scaling is worth keeping clear, since it decides whether extending an array in one direction is worth the cost.

Answer: B

The standard approximation for a linear broadside array gives:

\[ D \approx \tfrac{2L}{\lambda} = 2 \times 10 = 20 \]

so about 20, which is 13 decibels. The element pattern adds a little more in practice. Estimating directivity from aperture length before any detailed design is the quickest way to see whether an array of a given size can meet a requirement, and it is accurate enough for that purpose.