Automatic Generation of Differential-Input Differential-Output Second-Order Filters Based on a Differential Pair

In this paper, the generation of differential-input differential-output second-order active filters based on a common-source differential amplifier is systematically conducted using two-port network modeling techniques which enable exploiting the power of symbolic math CAD tools. Starting from a generic two-transistor differential-pair structure, and the maximum possible number of surrounding impedances, all possible filters are derived and classified. In particular, 35 transfer functions and a total of 876 filters are found to be possible. Due to employing a $2\times 2$ transmission matrix representation of each transistor, flexibility in examining parasitic effects on the derived transfer functions is achieved and can be easily automated within the design framework. Selected filters are constructed and experimentally verified using discrete transistors. The operation of some filters is also verified with simulations using a 65-nm CMOS process.