Design and optimization of continuous-time filters using geometric programming

This paper is concerned with the design and optimization of continuous-time active-RC and g
_m
-C filters. We demonstrate how we can maximize the filters' dynamic range (DR) for a given voltage swing, area and power consumption. Using closed-form symbolic expressions, the optimization problems are formulated as geometric programs (GPs) and mixed-integer GPs (MIGPs) that can be quickly solved to find the globally-optimal solution. The techniques developed in this paper are applied to the design and optimization of an active-RC filter with 1 MHz bandwidth, and a g
_m
-C filter with 30 MHz bandwidth, both of which implement a 5
^th
order elliptic transfer function. The proposed design flow is general, and can be extended to any filter topology or any set of specifications in order to find a low-noise, linear, low-area, and low-power circuit solution.