Enhanced Voltage Reference Circuit Design Using Quadratic Function Modeling of MOSFET Characteristics in the Saturation Region

This paper investigates a voltage reference circuit that incorporates an equivalent MOSFET, which adjusts the threshold voltage and its temperature coefficient using a Proportional To Absolute Temperature (PTAT) voltage generation circuit. In previous designs, the relationship between the drain current I<inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">D</inf> and the gate-source voltageV<inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">GS</inf> was derived based on the threshold voltage V<inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">th</inf> from the gradual channel model of MOSFETs. However, this method led to discrepancies between theory and simulation. We propose a new approach where the I<inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">D</inf> - V<inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">GS</inf> characteristics are modeled using simulation data from a single NMOSFET, fitted to a general quadratic function. This model significantly reduces the error between theoretical calculations and simulation results. Additionally, the temperature coefficient of the reference voltage V<inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ref</inf> is improved from 498 ppm/K to 32 ppm/K.