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Automated Synthesis and Modeling of Analog and Mixed-Signal Systems

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### Automated Synthesis and Modeling ofAnalog and Mixed-Signal Systems

### Towards Creative Analog Synthesis: A Symbolic Representation for Exploring Circuit Operation Principles

Alex Doboli, PhD

Associate Professor

Department of Electrical and Computer Engineering

State University of New York, Stony Brook, NY 11794

Email: adoboli@ece.sunysb.edu

Mixed-Domain Embedded Systems Laboratory(http://www.ece.sunysb.edu/~vsdlab)

- Analog and mixed-signal synthesis:
- Heuristic optimization algorithms (many kinds)
- Integer linear and nonlinear programming
- Synthesis from VHDL-AMS
- Automated modeling for design:
- Automated modeling of analog circuits and systems
- Modeling of process parameter variations
- Linear and nonlinear symbolic methods
- Statistical modeling
- Compiled code simulation
- Neural networks and PWL modeling

Mixed-Domain Embedded Systems Laboratory(http://www.ece.sunysb.edu/~vsdlab)

- Synthesis of analog and mixed-signal circuits with

high degree of innovation:

- Understand the difference between human designed circuits and automatically synthesized circuits
- Understand the level of innovation of new design solutions
- Representation of design knowledge for innovation:
- Classification scheme to show commonalities and differences
- Management and reuse of existing IP
- Synthesis method using the representation:
- Process more similar to human design process (i.e. combination of existing design features)

integ

DAC

m

m

m

Automated synthesis of analog and mixed-signal systemsTopology generation and

system architecture selection:

VHDL-AMS

specifications:

entity aaa is

…

end entity;

Performance

evaluation

Obtained

performance

Circuit and

interconnect

models

Constraint transformation,

floorplanning and global routing

Performance

evaluation

(simulation)

Application-specific DS modulator topologies

- H. Tang, A. Doboli, "High-Level Synthesis of Delta-Sigma Modulators Optimized for Complexity, Sensitivity and Power Consumption", IEEE Transactions on CAD of Integrated Circuits and Systems, Vol. 25, No. 3, pp. 597-607, 2006.
- Automatically synthesize DS modulator topologies optimized for a given application (specification)
- Novelty:
- Synthesis methods for topology (no general method available)
- New theoretical formulation

- Advantages:
- Global optimal solution is guaranteed (new topologies invented)
- The methodology is scalable
- The methodology could be fully automated

Generic topology for 3rd order modulator

Chain of Integrators with

Feedforward Summation

Chain ofIntegrators with Distributed

Feedback, Distributed Feedforward

and Local Feedback

Generic topology

Chain of Integrators

with Distributed Feedback

Sensitivity cost function values are 1.723 and 2.250 respectively, with all (good case)

L. Huelsman, “Active and Passive Analog Filter Design”, McGraw Hill, 1993

Optimal topology

Minimum sensitivity

Topology from Toolbox

Sensitivity cost function values is 4.454, with some terms larger than 1.0, e.g.

R. Schreier, “The Delta-Sigma Toolbox 6.0”, www.mathworks.com/matlabcentral/fileexchange, Nov 2003.

Design

Specifications

Synthesis of Reconfigurable DS ModulatorsY. Wei, H. Tang, A. Doboli, "Systematic Methodology for Designing Reconfigurable Delta Sigma Modulator Topologies for Multimode Communication Systems", invited paper, IEEE Transactions on CADICS, Vol. 26, No. 3, March 2007.

A cell phone chip

works for CDMA,

GSM, UMTS … …

Reconfigurable DS modulator topologies

Topology opt1

Experiments

- Compare the triple-mode modulator with three single-mode modulators obtained with DS toolbox
- Design effort can be less than 1/3
- Complexity can be as less as 40%
- Power saving can be as large as 24.2%
- More robust to circuit nonidealities

SNR degradation due to circuit noise

Improvement as compared to the state-of-art design:

3dB for the case of -60dB noise level

5dB for the case of -50dB noise level

Algorithms for Analog Synthesis

H. Tang, H. Zhang, A. Doboli, "Refinement based Synthesis

of Continuous-Time Analog Filters Through Successive Domain

Pruning, Plateau Search and Adaptive Sampling",

IEEE Transactions on CAD of Integrated Circuits and Systems,

Vol. 25, No. 8, pp. 1421-1440, 2006.

3rd order elliptic lowpass filter

- Synthesis problem:
- Find circuit constraints and system parameters so that functionality isachieved, and multiple performance attributes are optimized

Cost=6

plateau

Plot 2

Convex region

Plot 3

Plot 1

oscillation

Large sampling steps

(20,20 sec)

Cost=3000

Small sampling steps

(5,000,6hours)

- Plot 1: smaller variable ranges is good
- Plot 2: different types of regions: convex regions mixed with plateaus
- Plot 3: adaptive sampling for buried optima

Automated Macromodeling

Y. Wei, A. Doboli, "Structural Macromodeling of Analog

Circuits through Model Decoupling and Transformation",

IEEE Transactions on CADICS, Vol. 27, No. 4, April 2008.

- Produced macromodels:
- Structural
- No feedback dependencies (decoupled)
- Symbolically characterized nonlinear current sources
- Extensible, accuracy is controllable
- Insight into circuit
- Reusable

Structural nonlinear macromodel

Circuit netlist

(R2,C2)

vin

vout

f(vin)

Black-box macromodel

Automated MacromodelingProcess Variation Modeling

H. Zhang, A. Doboli, "A Scalable Sigma-Space Based Methodology for Modeling Process Parameter Variations in Analog Circuits", Microelectronics Journal, Elsevier, February 2009.

The limitation of the SA Method

- “Statistical Modeling for Computer-Aided Design of MOS VLSI Circuits”, Christopher Michael and Mohammed Ismail, Kluwer Academic Publishers, 1993

Modeling and Fast Simulation of Nonlinear Systems

H. Zhang, S. Doboli, H. Tang, A. Doboli, "Compiled Code Simulation of Analog and Mixed-Signal Systems Using Piecewise Linear Modeling of Nonlinear Parameters", Integration the VLSI Journal, Elsevier, Vol. 40, No. 3, pp. 193-209, 2007.

- At the system-level, the method uses symbolic descriptions of ADCs
- Building blocks are macromodels, which include circuit non-idealities and nonlinear behavior.
- Non-linear parameters are expressed using PWL models, which are created automatically through model extraction from trained neural networks (NN) .
- Method is more accurate than simulation of behavioral models
- Method is significantly faster than numerical simulation (two orders of magnitude)
- Accuracy is not traded-off for speed
- Simulator code can be optimized to avoid convergence problems

Level selection

Connection pattern

recognition

Modified nodal

analysis

PWL segment control

flow generation

Code optimization

Code generation

Lazy generation of

symbolic expression

Simulation Methodology - overviewTopology

GIT

library

PWL MM

library

DDDs

APTs

Terminal block analysis

Middle block analysis

Code generation and optimization

Compiled-code simulator

Spectre + VerilogXL(s)

Symbolic (s)

Speed-up

1

507.1

3.5

144.88

2

533.9

5.88

90.79

3

852.3

8.24

103.43

4

1284.9

10.69

120.19

5

1752.0

12.91

135.70

Simulation ResultsComment: Because of the extreme values of some parameters, we had severe convergence problems in Cadence Mixed-Signal Simulation Environment (Spectre + Verilog A).

Conclusions

- Automated synthesis of analog and mixed-signal synthesis:
- Heuristic optimization algorithms (all kinds)
- Integer linear and nonlinear programming
- Stochastic methods (Markov chains, dynamic programming)
- Automated modeling for design:
- Automated modeling of analog circuits and systems
- Modeling of process parameter variations
- Linear and nonlinear symbolic methods
- Statistical modeling
- Compiled code simulation
- Neural networks and PWL modeling

cferent@ece.sunysb.edu

Cristian Ferent and Alex Doboli

Motivation, Goals, and Contributions

- Systematically characterize a collection of designs:
- Implement performance specific circuit models
- Highlight common & different features between circuits
- Identify advantages & limitations of a circuit compared to others
- Derive conditions under which design alternatives exhibit similar performance

Motivation, Goals, and Contributions (II)

- Model to characterize transconductor linearity
- Illustrate mechanisms which can enhance circuit performance: extended operating range and/or device non-linearity compensation

Motivation, Goals, and Contributions (III)

- Automatically produce circuit classification schemes:
- Build a model to express main similarities & differences between a set of circuits implementing the same functionality
- Based on topological structures of features that influence the performance of a design
- Produce compact classification – minimum of separation criteria

Problem Description: concept representation

Coupling between nodes

Classification along curve D1

Features related to performance

Circuit node

Similar node features

Distinguishing criteria curves

C. Ferent, A. Doboli, "A Symbolic Technique for Automated Characterization of the Uniqueness and Similarity of Analog Circuit Design Features", DATE 2011

Proposed Method: automated generation of classification schemes

- Produce the separation criteria for a given performance
- Determine best separation criteria
- Construct hierarchical classification scheme

Algorithm Details

- Build performance-based circuit models

2) Group nodes with similar behavior:

- Minimize total number of matched groups (N )
- Minimize matching error within groups of nodes
- Identify constraints under which matching is valid

Algorithm Details (II)

3) Sort matched groups:

- Signal path tracing and model decoupling algorithms

4) Use entropy to rank similarities and differences between circuits:

- N – number of circuits represented in cluster Ck
- pi – probability a circuit from cluster Ck is associated with matched group Gj

5) Produce hierarchy with maximum matching at higher levels

AC Domain Model Matching: amplifier circuits hierarchical classification

Increasing entropy

value

Similar behavior

Common structures

Different structures

Different behavior

Classification correlation with performance

- Also identify number of terms that differ between node structures
- Indication of topology’s flexibility to satisfy performance (e.g. setting pole and zero positions)

Linearity Model Matching: transconductors hierarchical classification

Common structures

Identical Processing Path

Additional Processing

Different structures

Linearity Model Matching: (II)transconductors hierarchical classification

Identical Control Path

Additional Control

Additional Control Voltages

Current Developments

- Apply the proposed methodology for a set of 10 state-of-the-art amplifier designs
- Derive topological and performance classification schemes

Conclusions

- Develop new symbolic technique for automated generation of circuit classification schemes
- Produce the set of separation criteria
- Based on performance specific circuit models
- Sort separation criteria based on their capability to distinguish between different structures
- Proposed metric based on entropy
- Build hierarchical classification
- Highlight similarities and differences with impact on performance
- Offer insight through symbolic expressions
- Identify common & dissimilar circuit node structures
- Relate symbolic differences and similarities to performance attributes
- Suggest design’s flexibility for achieving certain performance

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