The determination of active array impedance with multielement waveguide simulators

Abstract

The basic principles behind a multielement waveguide simulator are presented for the case of general symmetric elements in a rectangular or triangular spaced infinite array. The techniques are applicable to any polarization and are valid for array spacings which allow grating lobes in real space. It is shown that a single simulator containing <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N \times M</tex> elements can be used to measure the reflection coefficient for the infinite array at <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N \times M</tex> scan angles. The measurement involves the determination of the <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N \times M</tex> transmission coefficients between one element and each of the other elements in the simulator when the simulator waveguide is terminated in a matched load. It is shown that the <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N \times M</tex> reflection coefficients so obtained are actually the eigenvalues of the scattering matrix of the network formed by the <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N \times M</tex> input ports to the simulator. An interpolation scheme is presented which allows the infinite array impedance to be approximated over a large range of scan angles by means of an expansion in terms of the eigenvalues of the simulator. The physical significance of the interpolation is discussed, and experimental results for a 25-element simulator utilizing stripline slots are presented.