Douglas Frey

A state-space formulation for externally linear class AB dynamical circuits

The state-space description of externally linear class AB dynamical systems is explored. Motivated by recent work in the area of log domain filtering, a definition for a generic class AB dynamical system is proposed. Following this, a more useful differential state-space formulation is proposed which is intuitively consistent with the nonlinear electronic circuits that implement class AB systems. A discussion of static and dynamic constraints which imply class AB operation, along with a basic theorem, leads to more practical constraints on the state space formulation which will allow class AB externally linear behavior of a system. Next, the results are used to explain the operation of several already-existing basic class AB log domain and exponential state-space filters. Finally, a new generalization to existing class AB circuit topologies is offered.

State-space synthesis and analysis of log-domain filters

The general state-space synthesis of linear filters is reviewed including the use of linear transformations. Then the use of time-varying nonlinear mappings on the state variables is shown to produce equations for the synthesis of linear, linear companding, and log-domain filters. Formulas are developed which underlie the realization of log-domain filters. Design issues relating to realizability, noise, and nonideal performance are discussed using the state-space mathematical formulation.

A Study of Different Class AB Log Domain First Order Filters

Several different class AB log-domain/translinear filters are compared in terms of their noise and distortion behavior using both analytical and simulation results. A few of the circuit topologies shown have not been considered before and are derived using a new theory for class AB dynamical circuits recently proposed. The study, although approximate, suggests ways in which both noise and distortion performance may be optimized by appropriate choice of circuit topology. Other practical aspects of the designs are also discussed.

An adaptive analog notch filter using log filtering

An adaptive analog notch filter is proposed for applications requiring high frequency adaptive signal processing. Based on a log filter circuit topology, this filter design suggests new circuitry for the implementation of analog adaptive filters. Simulation results demonstrate that the filter is capable of rejecting a sinusoid, and with a second notch filter section attached, is capable of rejecting a pair of sinusoids. The circuit design and the adaptation method are described.

An integral equation approach to the periodic steady-state problem in nonlinear circuits

The problem of efficiently determining the periodic steady-state solution of a lightly damped nonlinear circuit is treated using an integral equation formulation, which is reduced to a vector nonlinear equation. A highly efficient way of generating the vector equations is also given. The resulting solution vector, which is a set of uniformly distributed time samples, is found by iteration. The vector equation formulation amounts to solving for the steady-state solution directly, as in frequency-domain techniques, but the solution vector does not have to be transformed repeatedly between the time and frequency domains. Several efficient iteration schemes are identified that further improve the speed of the method. Several examples are given, including a circuit exhibiting bifurcation, to demonstrate the robustness and general applicability of the method. Comparison of this method to other methods shows its superiority in solving this class of problems. >

On log domain filtering for RF applications

The design concept of log filters is reviewed. A new second order filter topology which is particularly useful for RF signal processing is introduced with a discussion of its features which meet the needs of RF design.

Syllabic-companding log domain filters

A general theory for companding log domain filters is proposed which combines not only exponential mappings, but also a new translational mapping approach which guarantees suitable operating conditions in any log domain filter. The filter equations resulting from the use of the theory ultimately contain translinear terms which are known to be realizable using translinear techniques. A discussion of the design of the companding filters, regarding the economical use of translinear loops and the convenient selection of system parameters, is offered which leads to first- and second-order circuit designs. Finally, the noise performance of an example design is investigated using a carefully crafted large-signal simulation technique, showing clearly the advantage of the companding filter approach.

State space synthesis of Log Domain filters

The general state space synthesis of filters is reviewed and the mathematics is modified to include the mapping concepts crucial to the synthesis of Log Domain filters. Formulae are developed which underlie the realization of these filters. Design issues relating to realizability, noise, and distortion performance are discussed using the mathematical formulation. Finally, class AB filters are given a state space formulation.

Continuous-time to discrete-time conversion via a novel parametrized s-to-z-plane mapping

A parametrized s-to-z-plane map is introduced, where the conventional bilinear map and backward and forward Euler rules appear as special cases. Time and frequency-domain characteristics of the map are discussed, along with a simple technique for applying this map to adaptively reduce truncation error in the continuous-time to discrete-time conversion problem. An example illustrates the method and its potential for yielding more accurate discrete-time models over conventional approaches.

On adaptive chaotic encoding

Chaotic digital encoders are enhanced to improve their complexity and correlation properties. A new adaptive chaotic encoder (ACE) is proposed which combines a chaotic encoder with an adaptive filter, producing a more complex and, potentially, more useful encoder. An inverse system approach is proposed that not only specifies the inverse of the ACE, but also shows an interesting way to understand synchronization in chaotic communications systems. Finally, simulation results are offered, showing the performance of the new encoder and synchronization of an IIR digital chaotic communications system.