Exponential state space filters: a generic current mode-design strategy

TLDR

The paper proposes a generic current‑mode analog filter design that incorporates nonlinear active components while maintaining an overall linear transfer function. The authors introduce Exponential State Space (ESS) filters, derived by mapping the state space of a linear filter using exponential, tanh, and sinh functions, and compare their implementation to a standard transconductance‑C filter via band‑pass simulation. The ESS filters yield realizable log, tanh, and sinh designs, with sinh filters behaving as class‑AB devices, and all variants achieve 100:1 tunability, stable frequency response up to 5 MHz, and favorable IMD and noise performance even with 300 MHz cutoff transistors.

Abstract

A new method of analog filter design is proposed where nonlinear active components are a natural part of a filter realizing an overall linear transfer function. This approach to design is articulated in the generation of the class of so-called "Exponential State Space" (ESS) filters. An outgrowth of "log filters", ESS filters are created via a mapping on the state space of a linear filter. Specifically, the state variables are equal to simple functions of exponentials or node voltages. The use of exponential, hyperbolic tangent, and hyperbolic sine mappings is shown to produce realizable nodal equations that result in "log", "tanh" and "sinh" filters, respectively. Aspects of interpretation and realization of the transformed state equations are discussed. It is shown that sinh filters are class AB filters, which is an intriguing extension of a concept introduced by Seevinck (1990). The different filter types are compared to an analogous standard transconductance-C filter via simulation of a band-pass filter with a Q of 5. All filters demonstrate tunability over a 100 to 1 range with excellent frequency response stability and accuracy over the tuning range, which extends to 5 MHz. These results and IMD and noise performance are given using both ideal transistors and transistors whose cutoff frequency equals approximately 300 MHz.