Analog non-linear function synthesis with resistive networks

Networks of resistors have been identified as interesting devices for analog computation. Since the analytical model of a network of constant resistors is a set of linear equations, such a circuit can be used to solve a large number of linear equations concurrently. Whenever such a resistive embodiment of a computational problem can be found, the resulting circuit is usually very simple, fast and dense compared to CPU-based hardware. Particular problems solved by such networks include simulation of electromagnetic fields [1], linear image filtering [2], regularization for image processing [3], and D/A conversion [4]. Networks of resistors are especially attractive for CMOS integrated circuits, since it has been shown that a circuit obtained by replacing every resistor by a single MOS transistor has exactly the same branch currents as its resistive counterpart [5]. In the following, a resistive network combining constant and controlled resistors is described, as well as its implementation with MOS transistors. The purpose of this circuit is to synthesize non-linear functions of possibly several variables. The circuit can be considered as an implementation of fuzzy rules, since its constituents can be identified as membership functions, fuzzy logic gates and center-of-gravity "defuzzification" circuits. Alternatively, the circuit can also be considered as a look-up table with interpolation, since fuzzy rules and look-up table entries are actually about the same thing. With a single generic circuit structure, a number of different nonlinear functions can be synthesized by customizing geometrical parameters or connection patterns.