Design Method of Analog Sigmoid Function and its Approximate Derivative

Lylia Thiziri Chabane (1, 2, 3, 4) , Dang-Kièn Germain Pham (1, 2, 3, 4) , Paul Chollet (1, 2, 3, 4) , Patricia Desgreys (1, 2, 3, 4)

1 IP Paris - Institut Polytechnique de Paris
2 Télécom Paris
3 COMELEC - Département Communications & Electronique
4 C2S - Circuits et Systèmes de Communication

In this paper, we propose to implement the sigmoid function, which will serve as an activation function of the neurons of a Multi Layer Perceptron (MLP) network, as well as its approximate derivative using an analog circuit. Several implementations have already been proposed in the literature, in particular, by Lu et al. (2000), which offers both a configurable and simple circuit realized in 1.2 µm technology. In this paper we demonstrate the circuit design of a sigmoid function based on Lu et al. using 65 nm technology in order to reduce energy consumption and circuit area. The design is based on an indepth theoretical analysis of the circuit and validated by circuit level simulations. The main contributions of the paper are a modification of topology of the circuit in order to meet the required nonlinear response of the circuit and the extraction of the DC power consumption of the resulting circuit.

Keywords: Activation function; analog CMOS circuit; approximate derivative; backpropagation; multi-layer perceptron; sigmoid function

Domains: Micro and nanotechnologies/Microelectronics

Lylia Thiziri Chabane, Dang-Kièn Germain Pham, Paul Chollet, Patricia Desgreys. Design Method of Analog Sigmoid Function and its Approximate Derivative. XXXVI Conference on Design of Circuits and Integrated Systems, Nov 2021, Vila do Conde (virtual), Portugal. ⟨10.1109/DCIS53048.2021.9666181⟩. ⟨hal-03331347⟩