Gain of phased array antennas under small random errors in element placement

Patrick Marron

doi:10.17918/etd-4480

A phased array is an arrangement of antennas whose emergent radiation pattern is controlled by the relative phases of the signals that are feeding its elements. Within implementation limits, the effective radiation pattern of the array is reinforced in a certain desired direction and repressed in other undesired directions. The pattern can thus be steered by introducing a relative phase shift between its elements so that its radiation adds constructively in a certain direction. This mechanism also means that error in the relative spacing between the elements of an array is likely to result in an error in the phase and a decrease in the gain of the array in the desired direction. The effects of element spacing error in phased array systems have been studied extensively. The approach in most studies was to show first that errors in the relative spacing of the elements results in error in the relative phase between the elements, then to characterize the distribution of the resulting gain. Often it was assumed that there are many elements in the array, and mathematical limits were used to calculate the radiation pattern under a large array assumption. Like most studies of the subject, we first quantize how errors in the relative spacing of the elements affect the error in the relative phase between the elements. We use a small-error assumption that is realistic in planned deterministic phased arrays. However, we do not make the assumption of a large number of elements in the array and our results are applicable to small arrays as well. We show that the gain loss can be approximated by the sum of the squares of the relative phase of each element with a scaling factor. Thus whenever the relative phase of each element is normally distributed with zero mean, the gain loss is distributed as a gamma distribution. Our key result is an expression for the allowed variance in the element position as a function of gain loss, the number of elements of the array, and the probability that this gain loss is realized. Using the expression a designer can specify placement tolerance as a function of the quality (in terms of gain in the desired direction) of the array. We use the expression for the element position variance to study the design of uniform linear arrays, uniform rectangular arrays, and uniform circular arrays. Simulations demonstrate that our derived distribution for the gain loss is very close to the expected distribution.

Gain of phased array antennas under small random errors in element placement

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Gain of phased array antennas under small random errors in element placement

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