This paper presents a novel low-power low-voltage analog implementation of the softmax function, with electrically adjustable amplitude and slope parameters. We propose a modular design, which can be scaled by the number of inputs (and of corresponding outputs). It is composed of input current–voltage linear converter stages (1st stages), MOSFETs operating in a subthreshold regime implementing the exponential functions (2nd stages), and analog divider stages (3rd stages). Each stage is only composed of p-type MOSFET transistors. Designed in a 0.18 µm CMOS technology (TSMC), the proposed softmax circuit can be operated at a supply voltage of 500 mV. A ten-input/ten-output realization occupies a chip area of 2570 µm2 and consumes only 3 µW of power, representing a very compact and energy-efficient option compared to the corresponding digital implementations.

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An Artificial Neural Network (ANN) involves a complex network of interconnected nodes called artificial neurons (AN); the AN sums N weighted inputs and passes the result through a non-linear activation function (AF). In this work, a modified version of the sigmoid activation function is proposed . In order to obtain a voltage-to-voltage (V-V) transfer function required by our specific ANN, the proposed solution uses a pseudo-differential pair configuration at the input as voltage to current converter. The proposed circuit is designed in a 180nm CMOS technology of TSMC and is simulated in Cadence-Virtuoso for the proper transistor sizing in order to obtain the desired steepness of the sigmoid function. The simulations results show an overall a minimum error of 1.09 % compared to the mathematical function and power consumption of 6.77µW. Comparison with previous works and the actual mathematical function prove very favorable.