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Antenna Arrays: A Computational Approach by Randy L. Haupt

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2Array Factor Analysis

This chapter presents the fundamental approaches to the analysis of linear and planar arrays of point sources. Element patterns, polarization, and mutual coupling are delayed until future chapters. Keeping the elements along a straight line or in a plane are the most common array configurations. Other types of nonplanar arrays will be discussed in future chapters.

2.1. THE ARRAY FACTOR

A single isotropic point source transmits a field as derived in Chapter 1. If that point source transmits to an array of point sources, then the output of the array is proportional to the weighted sum of the received signal from each element in the array.

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where Rn = distance from element n to the point at (xf, yf zf). As shown in Chapter 1, the phase of the received signal at the element is positive, because the signal is traveling toward the element. A transmit array has a minus sign in the phase, because the radiation is going away from the antenna. Figure 2.1 is a diagram of a point source transmitting to an array of point sources. When the array is very far from the point source, then all the Rn in the denominator of (2.1) are approximately the same. Consequently, the field is proportional to the sum of the weighted phase factors.

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Most arrays are either linear or planar. ...

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