Design of a compact MOSFET model suitable for geometric programming

The design of analog integrated circuits is a demanding task that involves many constraints and objectives. Also, the transistor models employed must consider high-order physics effects to achieve accurate solutions. Geometric Programming (GP) allows finding the global minimum in optimisation problems, but requires design equations to be in monomial or posynomial form. This work proposes a simplified model inspired on the Advanced Compact MOSFET model tailored to be used in GP problems. The proposed model considers short-channel effects and it is valid in the saturation region with all inversion levels. The equations are presented, first showing the transistor current-voltage characteristic and then the associated capacitances. The validity of the equations is proven by their capacity to fit to the simulated data, achieving a mean error of 0.4% for the main NMOS characteristic. After that, the optimal design of two basic amplifier stages is performed to demonstrate the model usability with GP. The predicted voltage gain and bandwidth of the designed amplifiers are compared with simulations, presenting mean errors of 24.7% and 31.7%, respectively. These errors are low when viewed from a logarithmic perspective and considering the wide design space covered. As GP optimisation guarantees the global minimum location and does not require the usage of a circuit simulator in the loop, the proposed GP-friendly compact model can enable fast and accurate optimisation of analog integrated circuits.