# Aperiodic and Conformal Arrays

Aperiodic Arrays. A periodic array that fully occupies an entire aperture has several advantages. The directivity of such a uniform array at broadside is that of the filled aper­ture, namely 4nA/X2 for an array with aperture area A. In addition the pattern (neglecting errors) can have very low sidelobes as long as spacings are chosen small enough
to eliminate grating lobes. However, there are times when (usually for economy) one chooses to populate an aperture with fewer elements. This procedure, called thinning, re­sults in an array with nearly the full aperture beam width but using only a fraction of the elements in the filled ar­ray. If this thinning were done by simply increasing the element spacing of a periodic array, then the resulting pat­tern would have many undesired grating lobes. In the limit it would take on an interferometerlike pattern.

Instead, in many thinned arrays, elements are placed at randomized locations, whether on a rectangular grid or not, and often excited with uniform illumination. With thinned arrays the structured sidelobes can be lowered by taper­ing the density of excited antenna elements, instead of the aperture power, as done for a filled aperture. This is done (13) by selecting element locations statistically and choos­ing element weights as unity or zero with probabilities ei­ther equal to or proportional to the filled-array taper. The proportionality constant K is unity if the one/zero proba­bility is chosen equal to the array taper ratio. At K = 1 the array is fully populated near the center, where the array taper is nearly unity. If K is chosen less than unity, then the array is not fully populated at the center, but the thin­ning is still proportional to taper. Since the algorithm is a statistical process, the resulting aperture illumination and pattern are not unique, but one can describe the av­erage of the ensemble of arrays constructed from the algo­rithm. For this ensemble one can show that the resulting average pattern is the sum of two patterns, one of which is the ideal pattern of the filled, tapered array, multiplied by the number K. The second pattern is the average side — lobe level, a constant value with no angle dependence. For a large, highly thinned array the average sidelobe level is ap­proximately 1/Nr, normalized relative to the pattern peak, where Nr is the number of remaining elements. The aver­age directivity is approximately Nr times the directivity of an element pattern. The reason for this result is that all signals add linearly at the beam peak, but elsewhere in the pattern they combine like the average of a random process. For this reason the normalized average sidelobe level is at the level of isotropic radiation, or the factor Nr below the peak directivity. Figure 11 shows a thinned array resulting from using the above algorithm directly. The dashes shown in the figure indicate elements left out of the square, half wavelength, lattice ofa 25 wavelength radius aperture. The selected ideal pattern for the filled array is a 50 dB Tay­lor pattern [Fig. 11(b)] and it is approximated with 7845 elements excited. Given this number of elements, the aver­age sidelobe level is about 39 dB, and this is about what is indicated in the Fig. 11(c). Nearly one hundred thousand elements would be needed to produce the 50 dB pattern desired, so clearly thinned arrays do not satisfy most low sidelobe array requirements. They do, however, present the least expensive way to provide very narrow beam width wide-angle-scanned patterns with moderate sidelobes.

Conformal Arrays. Conformal arrays are a special class of antennas that are built to conform to the surface of some vehicle, like an aircraft, spacecraft, missile, ship, or even an automobile. Depending on the array size and the local ra­dius of curvature, this can pose a significant problem to the

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 Figure 11. Circular array with elements removed). (a) Geome­try (dashes show elements removed. (b) Desired Taylor pattern of filled array. (c) Pattern of thinned array.

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 x Figure 12. Generalized array conformed to a body of revolution.

practical realization of any desired pattern. The primary technical challenge is that the elements point in different directions, so the control network needs to provide variable amplitude and phase weighting to scan the array. An ex­treme but very important example is the use of an array on a cylindrical surface like that of the vehicle shown in Fig. 12 for scanning over a hemisphere. When a beam radiates in one direction, it is necessary to commute the amplitude distribution around the cylinder in order to avoid radiating energy into undesired regions. Many elaborate networks have been designed for performing this commutation, but it remains an expensive process requiring sophisticated de­sign and packaging concepts.

Not all conformal arrays are mounted in such severely curved shapes as to require signal commutation. Most con — formal applications are for flush mounted or very low pro­file arrays on gently curved surfaces where the challenges are far less severe. Future applications include airborne arrays for satcom and aircraft to earth coverage, missile antennas, and a whole variety of commercial vehicle ap­plications. Conformal arrays will continue to be a major growth area for array antennas.

Updated: 23.02.2014 — 14:24