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Amplifying grid arrays, consisting of periodic unit cells loaded with active devices such as HEMTs, are currently being developed for high frequency quasi-optical use. Motivation for their development includes the inherent advantages of an approach that employs spatial power combining and spatial amplification. Thus, losses between multistage amplifiers are virtually eliminated. Also due to the spatial combining, the phase of the array is determined by the phase of the incident wave which is then amplified by the planar circuit. This eliminates the need for complex phase shifters and the associated lines for independent element control. Other advantages include the existence of graceful degradation when failures occur. Typically, a unit cell of these planar arrays has been analyzed using quasi-static transmission line approaches. This approach is used due to its simplicity and the easy addition of the port locations required by the active devices. The benefit of a grid amplifier design at high frequency is limited by this approach which may ignore strong mutual coupling or surface waves present at higher frequencies. Based on more conventional periodic array analysis, the method described extended the generalized scattering matrix approach to include the port locations of the device. This allows accurate inclusion of the effects of the mutual coupling between elements, the presence of bias lines, ground planes, and superstrates/substrates. In addition this numerically generated scattering matrix can be combined with the conventional scattering matrix of the device to form a composite matrix of a grid amplifier.