Synthesis of Symmetric, Two-Element Biomimetic Antenna Arrays Using Singular Value Decomposition

We present a method for determining the four-port S-matrix of the external coupling network (ECN) for symmetric, two-element biomimetic antenna arrays (BMAAs) by employing singular value decomposition (SVD). The presented approach greatly facilitates the synthesis procedure of symmetric, two-element BMAAs and allows all possible scattering matrices of a four-port network realizing the ECN to be easily determined. Unlike a previously-reported method that relies on solving a set of nonlinear equations to determine the S-parameters of the ECN, the present method uses only linear-algebraic equations that can be easily solved. We show that an infinite number of S-matrices exist for the ECN of a two-element BMAA given a fixed symmetric two-element antenna array. We also demonstrate that these S-matrices are different from each other only by two arbitrary phase shift matrices that represent free design parameters. In any given BMAA synthesis problem, these free parameters can be used to optimize other attributes of the response of the BMAA. We illustrated this by showing how the overall impedance-matching bandwidth of the BMAA varies as a function of a free design parameter. Two BMAAs corresponding to two different bandwidth values were fabricated and characterized to experimentally validate the proposed synthesis method.