A General Approach to Reciprocal of Posynomials in Geometric-Programming Based CMOS Design

Geometric Programming (GP) enables fast design and exploration of trade-offs in CMOS circuits. However, the main challenge is to put all design functions in a specific format, whether monomial or posynomial. In the formulation of the problem, an unsupported structure that commonly appears is the reciprocal of posynomials. This article proposes a methodology to approximate this type of functions. The methodology is then applied to a CMOS inverter amplifier in 65 nm technology, spanning the bandwidth specification over several decades, between 0.8 MHz to 3.2 GHz. Gain specifications of 20 to 100 are also considered. Comparing the approximations with the exact GP model, an average error of 5.4% in gain and bandwidth is detected, thus confirming the validity of the proposed equations. The results also agree with electrical simulations across the entire explored design space.