Hierarchical Performance Macromodels of Feasible Regions for Synthesis of Analog and RF Circuits

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Hierarchical Performance Macromodels of Feasible
Regions forSynthesis of Analog and RF Circuits

• Anuradha Agarwal, Ranga Vemuri
• Dept of ECECS, University of Cincinnati
• agarwala_at_ececs.uc.edu

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Outline

• Introduction and Motivation
• Static Vs Dynamic Modeling
• Problem Definition
• Proposed Synthesis and Modeling Approach
• Experimental Results
• Conclusion
• Future Work

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Introduction
Search Space
Performance Constraints
Sizes
Performance Estimator
Circuit Sizer
Un-sized Circuit Topology
Performance
Sizes and Bias W1 20u W2 10u W3 19u I1
10uA
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Motivation

• High computational complexity of Simulation-based
  approach.
• Performance estimation time using simulation 1
  sec
• Performance estimation time using Equation/Model
  1ms
• Inaccuracy of Model-based approaches
• Performance Parameters are complex functions of
  the design variables.
• Difficult to accurately model the entire design
  space.
• Failure to achieve convergence.

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Static Vs Dynamic Modeling
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Static Vs Dynamic Modeling

• Static Modeling
• Model is built once and not improved during
  synthesis.
• Cannot guarantee convergence!
• Dynamic Modeling
• Uses an initially generated model.
• Model is enhanced during sizing in case of
  inaccuracy.
• Guarantees accurate design solutions.
• Accuracy of model is constantly improved.

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Problem Definition

• Address both sizing and modeling problems at the
  same time.
• Goal of Sizing To find a design D such that the
  performance constraints are satisfied when
  validated using a simulator.
• Modeling To reduce the modeling error in
  feasible regions or regions of interest by
  placing a higher density of samples in the
  inaccurate feasible regions.

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Feasible Design Space

• Defined using Performance Parameters.
• Defines the region of synthesis and modeling
  interest.
• Occupies a small fraction of the design space.
• Idea is to model this region accurately.
• Reduces the complexity of modeling.

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Synthesis Flow
Performance Constraints
Topology
Optimization Engine
Performance Evaluator
Search Space
Spline Models
Simulator
Validate Design
Enhance Macro-model
Accurate?
No
Yes
Set Search Space
Resizing Loop
Stop
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Initial Model Generation

• Initial Model
• Initially generated model valid for entire design
  space.
• Generated prior to sizing.
• Data Generation for Initial model
• Quasi-random samples generated in the entire
  design space using Halton sequence generator.
• Uniform design space representation.
• Regressor
• Pseudo Cubic Spline
• Works well on multi-dimensional scattered data.

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Splitting the Initial Design Space

• Initial model constructed using uniform random
  samples in design space.
• Split the design space until no region contains
  more than the threshold number of samples.
• Reduces the model construction time.
• Reduces modeling error.

(0,1)
(1,1)
(0.5,1)
(1,0.5)
(0,0.5)
(0,0)
(1,0)
(0.5,0)
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Sizing

• Mapped to an unconstrained minimization problem.
• Simulated Annealing.
• Uses the performance models for estimating
  performance of designs.
• Converges when specifications are met.
• Converged design is validated using a simulator.

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Model Enhancement Steps

• Calculate Modeling Error at the design point D,
  obtained from sizing.
• Determine the category to which the error
  belongs.
• Apply sampling rule.
• Determine the box constraints of the region where
  the model needs to be improved.
• Place samples in the identified region and build
  the model.
• Update the models for the next sizing iteration.

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Dynamic Hierarchical Models
R21
R11
Parent and Child Regions R01 is the parent of
R11 and R11 is the child of R01. Box Constraints
of child regions are determined from the box
constraints of the parent region.
Hierarchy Level 2
Hierarchy Level 1
Hierarchy Level 0
R01
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Definitions

• Modeling error
• where there are m performance constraints
• Acceptable Error, AEr
• Minimum Error Threshold, Ermin
• Maximum Error Threshold, Ermax
• Modeling error is classified into three
  categories
• High (Er gt Ermax)
• Medium (Ermin lt Er lt Ermax)
• Low ( AEr lt Er lt Ermin)

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Sampling Rules

• If Er belongs to high category, place samples in
  the region D belongs to. No child regions are
  defined.
• If Er belongs to medium category, go to the next
  hierarchy level by defining a child region around
  D based on the modeling error and box constraints
  of the parent region.
• If Er belongs to low category, go to the next
  hierarchy level by defining a child region in the
  vicinity of D .

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Box Constraints of Child Region

• Input Design point (D), Modeling Error (Er)
• Output Box constraints of Child region
• Begin
• P FindParent(D)
• (XMINP, XMAXP) GetBoxConstraints(P)
• N ApplySamplingRule(Er)
• if N 1
• return (XMINP, XMAXP)
• else
• for i e 1..n
• XMINCi Di - N (XMAXPi
  XMINPi) x 0.5
• XMAXCi Di N (XMAXPi XMINPi) x
  0.5
• end for
• end if
• return (XMINC, XMAXC)
• End

• Identify region around converged design point.
• Prune the boundary of the feasible region using
  performance sensitivities.
• Limit the variation of the more sensitive
  variables.
• Helps in reducing the modeling complexity.

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Performance Evaluation
D
D
Query point belongs to a unique region. Use
corresponding model for performance evaluation.
Query point belongs to multiple regions. Use
model at highest level of hierarchy for
performance evaluation.
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Feasible Space Modeling
Region of sampling Performance of sampled
points
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Benchmarks
Two-stage Opamp OTA opamp
Single Ended LNA
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Experimental Results
Static Model Failure Statistics
Synthesis Time Comparison with Simulation Approach
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Experimentation Terminology

• Experiment
• Given a set of performance constraints, the
  process of determining the device sizes and bias
  such that the desired performance goals are
  achieved and validated using a simulator.
• Run/No. of Loops
• The number of times the performance model needs
  to be constructed/refined in order to achieve the
  desired accuracy.
• The number of times sizing needs to performed
  before convergence is achieved.

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Competing Approach
Global Model

• Dynamic technique.
• Initial model (also called global model) remains
  unchanged during synthesis.
• Creates local models in case of inaccuracy.
• Only two levels of hierarchy.
• Local model has higher precedence over global
  model in feasible regions.

D
Local Models
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Synthesis Results
Two-stage Opamp OTA Opamp
Single Ended LNA
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Validation of Synthesis Results
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Discussion of Results

• Static Model Based Approach fails to guarantee
  convergence even with a large number of samples.
• Dynamic Approach constantly improves the accuracy
  of the model.
• Dynamic Approach guarantees convergence.
• Each synthesis experiment enriches the model
  leading to possible faster convergence of
  subsequent experiments.
• The proposed algorithm should be executed with
  several sets of performance constraints to
  identify the various feasible regions.

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Conclusions

• A dynamic modeling approach was developed.
• Synthesis framework was used for identifying
  feasible regions in the design space.
• The proposed approach guarantees to obtain
  accurate simulator validated design solutions.
• Significant speedup (more than 14X) was obtained
  as compared to a simulation-based approach.
• Proposed approach yields accurate models in
  feasible regions.
• The feasible design space is less than 1 of the
  total design space.

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Future Work

• Extend the models to higher dimensional design
  space.
• Build layout-aware performance models.
• Build feasibility models.
• Explore other techniques for partitioning the
  initial design space (based on sensitivity).

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Thank you.