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 F(T) indicate an efficient convolution process over a wide bandwidth, with values of F(T) that 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 behavior of MSFVW's is significantly weaker than what might have been 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.