Abstract: In this paper, a new theory is developed for the analysis of the real-time air-gap coupled SAW convolvers. There are two important features about the theory we propose here. First, we rigcirously consider the role of surface states of semiconductors in aco-ustoelectric nonlinear interactions. Second, by means of a new equivalent circuit for the convolver, we derive various new analytical expressions which describe the linear coupling coefficient for air-gap, nonlinear coupling coefficient for aeoustoelectric nonlinear interactions, and convolution output （or figure of merit） ; these expressions exhibit obvious dependence on bias.The frequency response of surface states is also analyzed.
The theory presented here is a general formalism applicable to deal with the situation when the semiconductor surface is accumulated, at flat-band, depleted, or inverted.
The presented theory can essentially explain experimental results of SAW acoustoelec-tric nonlinear interactions which were carried out by ourself and others.