Differential Algebraic Equations of MOS Circuits and Jump Behavior

P Sarangapani,T Thiessen,W Mathis

doi:10.5194/ars-10-327-2012

P Sarangapani, T Thiessen + Show 1 more

Open Access

https://doi.org/10.5194/ars-10-327-2012

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Abstract

Abstract. Many nonlinear electronic circuits showing fast switching behavior exhibit jump effects which occurs when the state space of the electronic system contains a fold. This leads to difficulties during the simulation of these systems with standard circuit simulators. A method to overcome these problems is by regularization, where parasitic inductors and capacitors are added at the suitable locations. However, the transient solution will not be reliable if this regularization is not done in accordance with Tikhonov's Theorem. A geometric approach is taken to overcome these problems by explicitly computing the state space and jump points of the circuit. Until now, work has been done in analyzing example circuits exhibiting this behavior for BJT transistors. In this work we apply these methods to MOS circuits (Schmitt trigger, flip flop and multivibrator) and present the numerical results. To analyze the circuits we use the EKV drain current model as equivalent circuit model for the MOS transistors.

Highlights

In this work our focus lies on circuits which exhibit fast switching behavior (Schmitt Trigger, flip flop and multivibrator)
The transient solution will not be reliable if this regularization is not done in accordance with Tikhonov’s Theorem
In this work we apply these methods to MOS circuits (Schmitt trigger, flip flop and multivibrator) and present the numerical results

Summary

Introduction

In this work our focus lies on circuits which exhibit fast switching behavior (Schmitt Trigger, flip flop and multivibrator). When the network is -regularized (Ihrig, 1975), the jump behavior can be viewed as the limit → 0 of the solutions of the singularly perturbed system (Sastry and Desoer, 1981) This method can regularize the system, but it gives erroneous transient solutions by choosing wrongly located L’s and C’s. Another problem is due to the widely spaced time-constants, which appear because the dynamics of a regularized circuit can be divided into a slow and a fast part, leading to the so-called “time-constant problem” of circuit simulation (Sandberg and Shichman, 1968). To efficiently model the MOS circuits, the EKV drain current model has been used (Enz et al, 1995)

Geometric interpretation of jump behavior

Modelling the MOS equivalent circuit

Example 1