Theory of magnetostatic forward volume wave convolvers

The present paper reports a theory for MSFVW convolvers which incorporates the underlying nonlinear multiplication and spatial integration processes as well as the inherent dispersiveness of the MSFVW´s. The double-frequency convolution signal is assumed to be picked up by a full-turn microstrip loop lying on the YIG-film surface and to be generated by contra-propagating signals that are either cw or time-limited cw pulses. Computations of the convolver bilinearity factor FTindicate an efficient convolution process over a wide bandwidth, with values of FTthat are of the same order as, or better than, the reported experimental results for MSW convolution in a YIG cylindrical or plate geometry. The distortion in the convolution signal caused by the pronounced dispersive behaviour of MSFVW´s is significantly weaker than what one might have expected. This result is a consequence of the rather small bandwidth on either side of the carrier frequency of the cw pulses which contributes to the integral function representing the induced convolution pick-up signal.