Symbolic Analysis of Analog Circuits with Hard Nonlinearity

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Symbolic Analysis of Analog Circuits with Hard
Nonlinearity

• Alicia Manthe, Zhao Li, and Richard Shi
• Department of Electrical Engineering
• University of Washington, Seattle WA
• Orora Design Technologies, Inc.
• Redmond, WA 98195

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Overview

• Symbolic Circuit Analysis
• Nonlinearity Analysis
• Piecewise-Linear Concepts and Modeling
• Mixed Linear Complementarity Problem (MLCP)
• Explicit Solution to LCP
• Experimental Results
• Conclusion

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Simulators

• Numerical Simulators SPICE, Spectre
• Symbolic Simulators SCAPP, ISSAC

Numerical Simulator
Symbolic Simulator
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Nonlinearities

• Strongly/Hard
• Power Amplifiers
• Nonlinear PAs used to increase power efficiency
  leading to increased battery life
• Digital logic controlling the operations of
  analog/RF front-ends
• Leads to abrupt behavior changes
• Behavioral models for system-on-chip simulation
  characterized by PWL models
• Weakly
• Most systems operate in some way weakly nonlinear
• Small excursions around the quiescent point

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Symbolic Strongly Piecewise Linear Circuit
Analysis

• Model strongly nonlinear behavior
• Switching operating regions
• Sudden changes of device physics
• Model any piecewise linear function
• I-V characteristics

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PWL Concepts

• New Orthoator
• u ? 0
• j ? 0
• uj 0.
• Used to model
• PWL behavior

Polarity opposite of an ideal diode
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Modeling PWL function
Leenaerts Bokhoven, Piecewise Linear Modeling
and Analysis, Kluwer Academic Publishers, 1998.
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MNA Stamping Rule

• Compact macro circuit
• Constitutive Equation

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MNA Formulation

• What about j and u?

Mixed Linear Complementarity Problem!?!
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Explicit Solution toLinear Complementarity
Problem

• An orthoator
• State Equation

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Complementarity Decision Diagram

• Need an efficient diagram to represent the
  explicit solution to LCP
• 1-D

Sharing _at_(n-2)
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Symbolic PWL Analysis on Strongly Nonlinear
Circuits
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?a741 Behavioral Model
Normalized Harmonic Distortion
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Effects of Smoothing

• Modulus to Smoothing
• Lazaro et al. Circuits Systems 2001

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Conclusions

• Modeled circuits with hard nonlinearities using
  PWL functions in terms of orthoators
• Implemented
• DDD-based procedure for converting MLCP to LCP
• Efficient graph-based form of LCP (CDD)
• Tested on several different circuits
• ?a741, mixer, etc.

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Thank you!

• Questions?