An Alternative Approach The Equivalent Circuit

This result is surprising to many readers. However, it has actually been known by implication for at least half a century. As any classical textbook about antennas will tell you [51], the receiving area of a large array with uniform aperture distribution and no groundplane is half its physical size. Thus, when conjugate-matched, such an array will receive half the power incident upon it. The other half (i.e., down 3dB) will be radiated equally in the forward and backward directions—that is, down another 3 dB. Thus we have simply verified the 6-dB Rule introduced earlier. 

Furthermore, it is also well known that if a large array is provided with a groundplane, the receiving area is simply eqnal to the physical area [52]. In other words, an array with a groundplane and conjugate match will receive all the energy incident upon it and will consequently not scatter any energy in the backward direction (Remember Only for uniform aperture distribution. The tapered aperture distribution is discussed in Section 2.11.2). 

As an antenna engineer these facts were well known to the author early on in his work with the RCS of antennas. In fact, they quickly became the guiding light in the pursuit of the invisible antenna concept. In all research it is a tremendous help if you know the final result ahead of time  

The equivalent circuit was developed earlier [53] and is actually used extensively in Chapter 6 of this book for understanding large arrays designed for a 

Note that the spacing d between array and groundplane can be anything but nk/2. See also discussion about this subject in Section 6.12.2. 

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