dc analysis of nonlinear circuits - peopleee219a fall 1998 3.1.11 rate of convergence ee219a fall...
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Prof. A. Richard NewtonUniversity of California at Berkeley
Page 1Copyright © 1997, A. Richard Newton
EE219A Fall 1998 3.1.1
EE219A: Computer Analysis of Electrical CircuitsOutline
Lecture 3.1
u DC Solution of Nonlinear Equations
EE219A Fall 1998 3.1.2
DC Analysis of Nonlinear CircuitsDC Analysis of Nonlinear Circuits
Prof. A. Richard NewtonUniversity of California at Berkeley
Page 2Copyright © 1997, A. Richard Newton
EE219A Fall 1998 3.1.3
DC Analysis of Nonlinear CircuitsDC Analysis of Nonlinear Circuits
EE219A Fall 1998 3.1.4
Contraction Mapping TheoremsContraction Mapping Theorems
Prof. A. Richard NewtonUniversity of California at Berkeley
Page 3Copyright © 1997, A. Richard Newton
EE219A Fall 1998 3.1.5
Contraction Mapping TheoremsContraction Mapping Theorems
EE219A Fall 1998 3.1.6
Newton’s MethodNewton’s Method
Prof. A. Richard NewtonUniversity of California at Berkeley
Page 4Copyright © 1997, A. Richard Newton
EE219A Fall 1998 3.1.7
Newton’s MethodNewton’s Method
EE219A Fall 1998 3.1.8
Newton-Raphson MethodNewton-Raphson Method
Prof. A. Richard NewtonUniversity of California at Berkeley
Page 5Copyright © 1997, A. Richard Newton
EE219A Fall 1998 3.1.9
Rate of ConvergenceRate of Convergence
EE219A Fall 1998 3.1.10
Rate of ConvergenceRate of Convergence
Prof. A. Richard NewtonUniversity of California at Berkeley
Page 6Copyright © 1997, A. Richard Newton
EE219A Fall 1998 3.1.11
Rate of ConvergenceRate of Convergence
EE219A Fall 1998 3.1.12
Techniques for Reducing the Cost ofNewton-Raphson
Techniques for Reducing the Cost ofNewton-Raphson
u 1. Computation of J(x) by built-in derivatives(SPICE, SPLICE, RELAX)
u 2. Update J(x) every p iterations (SPLICE, RELAX)u 3. Selective Update: If value of a state variable does
not change, do not update f(x) or J(x)s Bypass (SPICE) (for digital circuits, savings up to 50%
here)s Event-driven selective-trace at the state-variable and
device level (SPLICE)
u 1. Computation of J(x) by built-in derivatives(SPICE, SPLICE, RELAX)
u 2. Update J(x) every p iterations (SPLICE, RELAX)u 3. Selective Update: If value of a state variable does
not change, do not update f(x) or J(x)s Bypass (SPICE) (for digital circuits, savings up to 50%
here)s Event-driven selective-trace at the state-variable and
device level (SPLICE)
Prof. A. Richard NewtonUniversity of California at Berkeley
Page 7Copyright © 1997, A. Richard Newton
EE219A Fall 1998 3.1.13
Potential ProblemsPotential Problems
EE219A Fall 1998 3.1.14
ImplicationsImplicationsu Device model equations must be continuous with continuous
derivatives and derivative calculation must be accurate derivativeof function (not all models do this - Poor diode models andbreakdown models don’t - be sure models are decent - beware ofuser-supplied models)
u Watch out for floating nodes (If a node becomes disconnected,then J(x) is singular)
u Give good initial guess for x(0)
u Most model computations produce errors in function values andderivatives. Want to have convergence criteria || x(k+1) - x(k) || < εsuch that ε > than model errors.
u Device model equations must be continuous with continuousderivatives and derivative calculation must be accurate derivativeof function (not all models do this - Poor diode models andbreakdown models don’t - be sure models are decent - beware ofuser-supplied models)
u Watch out for floating nodes (If a node becomes disconnected,then J(x) is singular)
u Give good initial guess for x(0)
u Most model computations produce errors in function values andderivatives. Want to have convergence criteria || x(k+1) - x(k) || < εsuch that ε > than model errors.
Prof. A. Richard NewtonUniversity of California at Berkeley
Page 8Copyright © 1997, A. Richard Newton
EE219A Fall 1998 3.1.15
Computational AspectsComputational Aspects
EE219A Fall 1998 3.1.16
Computational AspectsComputational Aspects
Prof. A. Richard NewtonUniversity of California at Berkeley
Page 9Copyright © 1997, A. Richard Newton
EE219A Fall 1998 3.1.17
Modeling a DiodeModeling a Diode
EE219A Fall 1998 3.1.18
Modeling a DiodeModeling a Diode
Prof. A. Richard NewtonUniversity of California at Berkeley
Page 10Copyright © 1997, A. Richard Newton
EE219A Fall 1998 3.1.19
MNA TemplatesMNA Templates
EE219A Fall 1998 3.1.20
MNA TemplatesMNA Templates
Prof. A. Richard NewtonUniversity of California at Berkeley
Page 11Copyright © 1997, A. Richard Newton
EE219A Fall 1998 3.1.21
Modeling a MOSFET(MOS Level 1, linear regime)Modeling a MOSFET
(MOS Level 1, linear regime)
d
EE219A Fall 1998 3.1.22
Modeling a MOSFET(MOS Level 1, linear regime)Modeling a MOSFET
(MOS Level 1, linear regime)
Prof. A. Richard NewtonUniversity of California at Berkeley
Page 12Copyright © 1997, A. Richard Newton
EE219A Fall 1998 3.1.23
DC Analysis Flow DiagramDC Analysis Flow DiagramFor each state variable in the system
EE219A Fall 1998 3.1.24
Numerical OverflowNumerical Overflow
Prof. A. Richard NewtonUniversity of California at Berkeley
Page 13Copyright © 1997, A. Richard Newton
EE219A Fall 1998 3.1.25
NonconvergenceNonconvergence
EE219A Fall 1998 3.1.26
Limiting AlgorithmLimiting Algorithm
Prof. A. Richard NewtonUniversity of California at Berkeley
Page 14Copyright © 1997, A. Richard Newton
EE219A Fall 1998 3.1.27
Improving ConvergenceImproving Convergence
EE219A Fall 1998 3.1.28
Optimization-Based ApproachesOptimization-Based Approaches
Prof. A. Richard NewtonUniversity of California at Berkeley
Page 15Copyright © 1997, A. Richard Newton
EE219A Fall 1998 3.1.29
Continuation MethodsContinuation Methods
EE219A Fall 1998 3.1.30
Continuation MethodsContinuation Methods