The interpolation of general active array impedance from multielement simulators

The multielement waveguide simulator gives the active reflection coefficient of an infinite array at a discrete number of scan angles. A general method to estimate the active reflection coefficient at in between angles is presented. The method expands any array excitation into a series using the orthogonal set of waveguide modes of the simulator. The portion of the simulator reflections which is proportional to the applied excitation is extracted. An estimate of the accuracy of the interpolation is also derived in terms of the form of the power reflected from the simulator. The technique is demonstrated on a 30- element simulator and comparisons are made with calculations for an infinite array composed of open-ended circular waveguides.