Novel CMOS Circuit for Fuzzification: Implementing a Sigmoid Activation Function in Neural Networks

Abstract

This paper introduces a novel circuit design based on current-mode principles, tailored for the hardware implementation of a programmable analog Membership Function Circuit (MFC) Sigmoid function. It is simple CMOS compatible, operates on voltage signals, and delivers an output current corresponding to the desired activation function. By adjusting the reference voltage, the inflection point in the sigmoid function can be conveniently modified. This structure is also general purpose in tuning the slope of Membership Functions (MFs) using scaled transistors with different <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\frac{W}{L}$</tex> ratios. Simulation of the proposed circuit in the LTspice software using <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$45nm$</tex> CMOS technology, with level 54 parameters, indicates low power dissipation, measuring at <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$12\mu W$</tex> with a supply voltage of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\pm 1.1V$</tex>. This proposal represents a significant advancement for potential applications in neural networks.