Optimization

Optimization, the automatic generation of model parameters and component values from a given set of electrical specifications or measured data, is available in Star-Hspice. With a user-defined optimization program and a known circuit topology, Star-Hspice automatically selects the design components and model parameters to meet DC, AC, and transient electrical specifications.

Star-Hspice optimization is the result of more than ten years of research in both the optimizing algorithms and user interface. The optimizing function is integrated into the core of Star-Hspice, resulting in optimum efficiency. The circuit result targets are part of the .MEASURE command structure, and the parameters to be optimized are Star-Hspice-defined parameter functions. A .MODEL statement sets up the optimization.

NOTE: Star-Hspice computes the .MEASURE statements using the postprocessing output. Reducing postprocessing output by setting option INTERP=1 may lead to interpolation errors in measurement results. See Input and Output for more information on using these options.

The most powerful feature of the Star-Hspice approach is its incremental optimization technique. Incremental optimization allows you to solve the DC parameters first, then the AC parameters, and finally the transient parameters. A set of optimizer measurement functions not only makes the task of transistor optimization easy, but significantly improves cell and whole circuit optimization.

To perform optimization, create an input netlist file specifying:

Minimum and maximum parameter and component limits
The variable parameters and components
An initial estimate of the selected parameter and component values
The circuit performance goals or model-versus-data error function

Given the input netlist file, optimization specifications, component limits, and initial guess, the optimizer reiterates the circuit simulation until the target electrical specification is met or an optimized solution is found.

For improved optimization and simulation time and to increase the likelihood of a convergent solution, the initial estimate of the component values should produce a circuit with specifications near those of the original target. This reduces the number of times the optimizer reselects component values and resimulates the circuit.

Optimization Control

The length of time to complete an optimization is a function of the number of iterations allowed, the relative input tolerance, the output tolerance, and the gradient tolerance. The default values are satisfactory for most applications. Generally, 10 to 30 iterations are sufficient to get accurate optimizations.

Simulation Accuracy

Set the simulator with tighter convergence options than normal for optimization. The following options are suggested:

For DC MOS model optimizations:

absmos=1e-8
relmos=1e-5
relv=1e-4

For DC JFET, BJT, and diode model optimizations:

absi=1e-10
reli=1e-5
relv=1e-4

For transient optimizations:

relv=1e-4
relvar=1e-2

Curve Fit Optimization

Use optimization to curve fit user-defined DC, AC, or transient data. In a curve fit optimization, the desired numeric data for curves is stored in the data file as in-line data using the .DATA statement. The variable circuit components and parameter values of the netlist are specified in the .PARAM xxx=OPTxxx statement. The optimization analysis statements call the in-line data using the DATA= keyword. The .MEASURE statement uses the simulation result and compares it with the values given in the data file. The .MEASURE statement controls the comparison of simulation results to the values given in the data file. This is usually done with the ERR1 keyword. If the calculated value is not within the error tolerances specified in the optimization model, a new set of component values are selected and the circuit is resimulated. This is repeated until the closest fit to the curve is obtained, or the error tolerances set is satisfied.

Goal Optimization

Goal optimization differs from curve fit optimization in that it usually only applies to the optimization of a particular electrical specification, such as rise time or power dissipation.

Goal optimizations are specified using the GOAL keyword with a choice of relational operator in the .MEASURE statement, where GOAL is the target electrical specification being measured. This choice of relational operator is useful in multiple-constraint optimizations, when the absolute accuracy of some criteria is less important than for others.

Performing Timing Analysis

To analyze circuit timing violation, Star-Hspice uses a binary search algorithm to generate a set of operational parameters that produce a failure in the required behavior of the circuit. When a circuit timing failure occurs, you can identify a timing constraint that can lead to a design guideline. Typical types of timing constraint violations include:

Data setup time before clock
Data hold time after clock
Minimum pulse width required to allow a signal to propagate to the output
Maximum toggle frequency of the component(s)

Bisection is a method of optimization that finds the value of an input variable (target value) associated with a goal value of an output variable. The input and output variables can be of various types (for example, voltage, current, delay time, or gain) related by some transfer function. You can use the bisection feature in a pass-fail mode or a bisection mode. The process is largely the same in each case.

Understanding the Optimization Syntax

Several Star-Hspice statements are required for optimization.

.MODEL modname OPT ...
.PARAM parameter=OPTxxx (init, min, max)
A .DC, .AC, or .TRAN analysis statement with MODEL=modname, OPTIMIZE=OPTxxx, and RESULTS=measurename
.MEASURE measurename ... <GOAL = | < | > val> - note that a space is required on either side of the relational operator =, <, or >

The .PARAM statement lets you specify initial, lower, and upper bound values. The types of .MEASURE statements available for optimization are described in Specifying Simulation Output.

Output statements .PRINT, .PLOT, and .GRAPH must be associated with the analysis statements .DC, .AC, or .TRAN. An analysis statement with the keyword OPTIMIZE is used for optimization only. To generate output for the optimized circuit, another analysis statement (.DC, .AC, or .TRAN) must be specified, along with the output statements. The proper specification order is:

1. Analysis statement with OPTIMIZE

2. .MEASURE statements specifying optimization goals or error functions

3. Ordinary analysis statement

4. Output statements

Analysis Statement (.DC, .TRAN, .AC)

The syntax is:

.DC <DATA=filename> SWEEP OPTIMIZE=OPTxxx RESULTS=ierr1 ...
+ ierrn MODEL=optmod

.AC <DATA=filename> SWEEP OPTIMIZE=OPTxxx RESULTS=ierr1 ...
+ ierrn MODEL=optmod

.TRAN <DATA=filename> SWEEP OPTIMIZE=OPTxxx RESULTS=ierr1
+ ... ierrn MODEL=optmod

where:

DATA	Specifies the in-line file of parameter data to use in the optimization
OPTIMIZE	Indicates the analysis is for optimization. Specifies the parameter reference name used in the .PARAM optimization statement. All .PARAM optimization statements with the parameter reference name selected by OPTIMIZE will have their associated parameters varied during an optimization analysis.
MODEL	The optimization reference name that is also specified in the .MODEL optimization statement .
RESULTS	The measurement reference name that is also specified in the .MEASURE optimization statement. RESULTS is used to pass analysis data to the .MEASURE optimization statement.

.PARAM Statement

The syntax is:

.PARAM parameter=OPTxxx (initial_guess, low_limit, upper_limit)

.PARAM parameter=OPTxxx (initial_guess, low_limit, upper_limit,
+ delta)

where:

OPTxxx	Specifies the optimization parameter reference name, referenced by the associated optimization analysis. This must agree with the OPTxxx name given in the analysis command associated with the keyname OPTIMIZE.
parameter	Specifies the parameter to be varied, the initial value estimate, the lower limit, and the upper limit allowed for the parameter. If the best solution does not exist within these constraints, the optimizer attempts to find the best solution.
delta	The final parameter value is the initial guess ± (n·delta). If delta is not specified, the final parameter value can be anything between low_limit and upper_limit. This is useful for optimizing transistor drawn widths and lengths, which must be quantized.

Example

.PARAM vtx=OPT1(.7,.3,1.0) uox=OPT1(650,400,900)

In the above example, the parameters uox and vtx are the variable model parameters to optimize a model for a given set of electrical specifications. The parameter vtx is given an initial value estimate of 0.7 volts and can be varied within the limits of 0.3 and 1.0 volts for the optimization procedure. The optimization parameter reference name, OPT1, is used to reference the associated optimization analysis statement (not shown).

.MODEL Statement

For each optimization within a data file, specify a .MODEL statement to allow for more than one optimization per simulation run to be executed. The optimization .MODEL statement defines the convergence criteria, number of iterations, and derivative methods.

The syntax is:

.MODEL mname OPT <parameter=val ...>

You can specify the following OPT parameters in the .MODEL statement:

mname	Model name. Elements refer to the model by this name.
CENDIF	Represents the point at which more accurate derivatives are required. When the gradient of the RESULTS functions are less than CENDIF, the more time-consuming derivative methods are used. Values of 0.1 to 0.01 are suitable for most applications. If too large a value is used, the optimizer requires more CPU time. If too small a value is used, it might not find as accurate an answer. Default=1.0e-9.
CLOSE	The initial estimate of how close the parameter initial value estimates are to the final solution. CLOSE multiplies the changes in the new parameter estimates. A large value for CLOSE causes the optimizer to take large steps toward the solution and a small value causes the optimizer to take smaller steps toward the solution. CLOSE should range from 0.01 for very close parameter estimates to 10 for rough initial guesses. Default=1.0. If CLOSE is greater than 100, the steepest descent part of the Levenburg-Marquardt algorithm dominates. For CLOSE less than 1, the Gauss-Newton method dominates. For further details, see L. Spruiell, "Optimization Error Surfaces," Meta-Software Journal, Vol. 1, No. 4, December 1994.
CUT	Modifies CLOSE, depending on how successful the iterations toward the solution become. If the last iteration was successful, descent toward the solution CLOSE is decreased by CUT. If the last iteration was not a successful descent to the solution, CLOSE is increased by CUT squared. CUT drives CLOSE up or down depending on the relative success in finding the solution. The CUT value must be greater than 1. Default = 2.0.
DIFSIZ	Determines the increment change in a parameter value for gradient calculations ( Δx = DIFSIZ · max(x, 0.1) ). If delta is specified in a .PARAM statement, then Δx = delta. Default = 1e-3.
GRAD	Represents a possible convergence when the gradient of the RESULTS function is less than GRAD. Values of 1e-6 to 1e-5 are suitable for most applications. If too large a value is used, the optimizer could stop before the best solution is found. Too small a value requires more iterations. Default=1.0e-6.
ITROPT	Sets the maximum number of iterations. Typically no more than 20-40 iterations are needed to find a solution. Too many iterations can imply the values for RELIN, GRAD, or RELOUT are too small. Default=20.
LEVEL	Selects the optimizing algorithm to use. Currently, the only option is LEVEL=1, a modified Levenburg-Marquardt algorithm.
MAX	Sets the upper limit on CLOSE. Values greater than 100 are recommended. Default=6000.
PARMIN	Allows better control of incremental parameter changes during error calculations. This produces more control over the trade-off between simulation time and optimization result accuracy. Star-Hspice calculates parameter increments using the relationship: Δ`par_val` = DIFSIZ · MAX(`par_val` , PARMIN) Default=0.1.
RELIN	Specifies the relative input parameter variation for convergence. If all the optimizing input parameters vary by no more than RELIN from one iteration to the next, then the solution is declared convergent. Since RELIN is a relative variance test, a value of 0.001 implies that the optimizing parameters are varying by less then 0.1% from one iteration to the next. Default=0.001.
RELOUT	Represents the relative output RESULTS function variance for convergence. For RELOUT=0.001, the difference in the RMS error of the RESULTS functions should vary less than 0.001. Default=0.001.

Star-Hspice Manual - Release 2001.2 - June 2001