The determination of active array impedance with multielement waveguide simulators

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 elements can be used to measure the reflection coefficient for the infinite array at scan angles. The measurement involves the determination of the 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 reflection coefficients so obtained are actually the eigenvalues of the scattering matrix of the network formed by the 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.