Practical limitations to the implementation of resistive grid filtering in Cellular Neural Networks

This paper analyzes the effect of mismatch in the realization of resistive grid filtering by VLSI CNN hardware. The study of the dynamic routes of a simple network consisting in only two CNN cells is enough to point out the dramatic consequences of the unavoidable mismatches between the circuit building blocks of the cells. Previous works consider that small perturbations in the network parameters lead to small deviations from the ideal behaviour, rendering their studies valid. We find, however, that these models are overly optimistic. The nonlinear nature of the cell output and the singular location of the roots in the ideal system imply that small perturbations in the parameters may render a qualitatively different, non-convergent and undesired dynamics. These effects are greatly noticeable when the network is driven by its initial conditions, and not through the B-template. The numerical study of these effects in a 64 x 64 network confirms the extrapolation of the results found in the evolution of the 2-cell assembly. In order to point out the importance of using the same paths for the transmission of symmetric contributions, we have tested the influence of mismatch in a non-ideal resistive grid built from n-type MOS transistors in ohmic region. In spite of the nonlinearity in the behavior of these resistors, the resulting network seems to be much more robust to mismatch. This last result coinciding with previous studies.