Robert C. Melville

Artificial parameter homotopy methods for the DC operating point problem

Efficient and robust computation of one or more of the operating points of a nonlinear circuit is a necessary first step in a circuit simulator. The application of globally convergent probability-one homotopy methods to various systems of nonlinear equations that arise in circuit simulation is discussed. The coercivity conditions required for such methods are established using concepts from circuit theory. The theoretical claims of global convergence for such methods are substantiated by experiments with a collection of examples that have proved difficult for commercial simulation packages that do not use homotopy methods. Moreover, by careful design of the homotopy equations, the performance of the homotopy methods can be made quite reasonable. An extension to the steady-state problem in the time domain is also discussed. >

Efficient multi-tone distortion analysis of analog integrated circuits

This paper introduces a novel approach to analyze distortion behavior in analog integrated circuits using a nonlinear frequency-domain method. This approach circumvents the difficulties and inaccuracies associated with device modeling required for the traditional Volterra series method and can handle circuits operating in more strongly nonlinear regimes. The efficiency of the method renders the analysis of large analog blocks practical. We present examples of multi-tone distortion analyses of industrial amplifiers and continuous time filters. The trend towards higher levels of integration, particularly for wireless applications, renders this method especially useful.

Passivity and no-gain properties establish global convergence of a homotopy method for DC operating points

Finding the DC operating points of transistor circuits is an important task in circuit simulation. The problem is equivalent to solving sets of nonlinear algebraic equations describing transistor circuits. Existing circuit simulators use Newtons method, or its variants, to achieve this task. Newtons method is local and requires a good initial guess for convergence, while its variants globally converge under restrictive conditions. Recent mathematical results guarantee the existence of constructive, globally convergent homotopy methods for finding zeros of nonlinear maps with probability one. These results are applied to the DC operating point problem by constructing various homotopies to create a simple problem that is solved before proceeding with the continuation process that will transform it into the initially stated difficult problem. It is shown that for a certain class of circuits used in the design of integrated circuits, nodal equations satisfy the conditions required by the globally convergent homotopy methods.<<ETX>>

Delivering global DC convergence for large mixed-signal circuits via homotopy/continuation methods

Homotopy/continuation methods are attractive for finding dc operating points of circuits because they offer theoretical guarantees of global convergence. Existing homotopy approaches for circuits are, however, often ineffective for large mixed-signal applications. In this paper, we describe a robust homotopy technique that is effective for solving large metal-oxide-semiconductor (MOS)-based mixed-signal circuits. We demonstrate how certain common circuit structures involving turning-point nesting can lead to extreme inefficiency, or failure, of conventional probability-one homotopy methods. We also find that such situations can lead to numerical ill-conditioning and homotopy paths that fold back upon themselves, leading to algorithm failure. Our new homotopy model for MOS devices, dubbed Arc-tangent Schichman-Hodges (ATANSH), features decoupled continuation parameters that are instrumental in avoiding these problems. ATANSH-based homotopy methods in production use have led to the routine solution of large previously hard-to-solve industrial circuits, several examples of which are presented.

Finding DC operating points of transistor circuits using homotopy methods

Finding the DC operating points of transistor circuits is one of the most important tasks in electrical circuit simulation. To resolve DC convergence difficulties that often arise when simulating bipolar and MOS transistor circuits, the authors use homotopy methods to solve nonlinear circuit equations. The authors exploit the properties of the equations and construct various homotopies that prove useful in finding their solutions. Criteria are provided for choosing homotopy parameters and a good starting point for homotopy paths. Homotopy methods are robust, accurate, and capable of finding multiple operating points. The authors present a circuit that could not be simulated using techniques available in current circuit simulators, while the solutions were successfully obtained using homotopy methods.<<ETX>>

Sufficient conditions for finding multiple operating points of DC circuits using continuation methods

A sufficient condition is given for which a continuation method is guaranteed to find at least three operating points possessed by a multistable circuit. A practical realization of this condition in a homotopy using passive components is also given and demonstrated in circuit examples.

Sframe: an efficient system for detailed DC simulation of bipolar analog integrated circuits using continuation methods

This work describes a simulation package for detailed studies of biasing networks for bipolar transistors. A sophisticated transistor model is introduced which captures many second-order effects, but which causes convergence difficulties for many existing methods used for computing an operating point. Artificial parameter numerical continuation techniques are introduced, then, as a robust and efficient means of solving bias networks employing our model. Sensitivity studies and natural parameter continuation studies based on the computed operating point (or points) are also discussed.

Homotopy techniques for obtaining a DC solution of large-scale MOS circuits

A new technique for obtaining a DC operating point of large, hard-to-solve MOS circuits is reported in this paper. Based on homotopy, the technique relies on the provable global convergence of arclength continuation and uses a novel method for embedding the continuation parameter into MOS devices. The new embedding circumvents inefficiencies and numerical failures that limit the practical applicability of previous simpler embeddings. Use of the technique in a production environment has led to the routine solution of large, previously hard-to-solve circuits.

Tools and methodology for RF IC design

We describe powerful new techniques for the analysis of RF circuits. Next-generation CAD tools based on such techniques should enable RF designers to obtain a more accurate picture of how their circuits will operate. These new simulation capabilities will be essential in order to reduce the number of design iterations needed to produce complex RF ICs.

Improving DC convergence in a circuit simulator using a homotopy method

To help resolve DC convergence difficulties in a circuit simulator, the authors constructed a homotopy suitable for solving equations describing transistor circuits. The authors describe its implementation in the ADVICE circuit simulator using a software package that implements a globally convergent homotopy algorithm. Homotopy methods proved robust, accurate, and capable of finding multiple operating points. The authors give simulation examples of various bipolar and MOS transistor circuits that could not be simulated using existing techniques, while the solution was successfully obtained using homotopy methods.<<ETX>>