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Analog Performance Space Exploration by FourierMotzkin Elimination with Application to Hierarchical

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Analog Performance Space Exploration. by Fourier-Motzkin Elimination ... New: Approximation to performance space by polytope ('polytopal approximation' ... – PowerPoint PPT presentation

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Title: Analog Performance Space Exploration by FourierMotzkin Elimination with Application to Hierarchical


1
Analog Performance Space Explorationby
Fourier-Motzkin Eliminationwith Application to
Hierarchical Sizing
  • Guido Stehr, Helmut Graeb, Kurt Antreich
  • Institute of Electronic Design AutomationProf.
    Dr. Ulf SchlichtmannTU Munich
  • November 10, 2004

2
Outline
  • Introduction
  • Motivation and basic concepts
  • State of the art
  • Performance space exploration by Fourier-Motzkin
    Elimination
  • General Idea
  • Algorithmic details
  • Geometric interpretation
  • Applications
  • Topology selection
  • Hierarchical sizing
  • Conclusions

3
Performance Space Exploration
  • Analog circuits in mixed-signal systems
  • Signal conversion, clock generation, data
    acquisition, ...
  • Example operational amplifier
  • Topology, technology given
  • Performance capabilities?
  • Parameters p (W,L) varied extensivelyperformanc
    es f from simulation
  • Efficient determination for large number of
    performances?

4
Formalization of Design Knowledge
  • Hierarchy of basic building blocks with certain
    functionalities
  • e.g.

transistor
  • Geometric requirements

e.g. minimum feature size
  • Electric DC requirements

e.g. saturation
  • Automatic sizing results according to good design
    practice

5
Feasible Performance Space
  • Constraints on performance space

Feasible parameter space
Feasible performance space
6
State of the Art
  • Nonlinear performance space exploration
  • Based on symbolic equations
  • Hershenson, Boyd, Lee 2001
  • Harjani, Shao 1996
  • Based on circuit simulation
  • de Smedt, Gielen 2003
  • Stehr, Graeb, Antreich 2003
  • High computational costs ? restricted to a low
    number of performances
  • New Approximation to performance space by
    polytope(polytopal approximation)
  • Based on linear description of circuit behavior
  • Applicable to high-dimensional performance spaces

7
Outline
  • Introduction
  • Motivation and problem description
  • Performance space exploration by Fourier-Motzkin
    Elimination
  • General Idea
  • Algorithmic details
  • Geometric interpretation
  • Applications
  • Topology selection
  • Hierarchical Sizing
  • Conclusions

8
Basic Idea Linear Approximation
nonlinearproblem
?
lineardescription
9
Algorithm Overview (1/2)
from simulation
from calculation
  • F has full rank

10
Algorithm Overview (2/2)
?
by Fourier-Motzkin Elimination (FME)
11
Fourier-Motzkin by Example
all combinations from (1) and (2) are valid
sophisticated redundancy detection critical
12
Geometric Interpretation of FME
  • coordinate transformation
  • number of dimensions unchanged
  • orthogonal projection along parameter coordinate
    axes
  • number of dimensions reduced

13
Outline
  • Introduction
  • Motivation and problem description
  • Performance space exploration by Fourier-Motzkin
    Elimination
  • General Idea
  • Algorithmic details
  • Geometric interpretation
  • Applications
  • Topology selection
  • Hierarchical Sizing
  • Conclusions

14
Topology Selection
  • Fast identification of performance capabilities
  • Topology selection
  • automatic in high-dimensional spaces
  • by inspection in 3D

15
Bandpass Filter
16
Sizing Task
17
Introduction of Hierarchy
2 levels of abstraction
system level
block level
18
Iterative Hierarchical Sizing (1/4)
Idea Iteration makes up for linearization
inaccuracies
First iteration system sizing constraints
19
Iterative Hierarchical Sizing (2/4)
First iteration sizing
system performances
system parameters /
block performances

OTA1
OTA2
20
Iterative Hierarchical Sizing (3/4)
Second iteration system sizing constraints

block parameters
21
Iterative Hierarchical Sizing (4/4)
Second iteration sizing
system performances
system parameters /
block performances

OTA1
OTA2
22
Experimental Sizing Run (1/2)
1) a) System sizing constraints
b) Sizing
?
23
Experimental Sizing Run (2/2)
2) a) More accurate system sizing constraints
based on 1b
b) Sizing
?
Final validation simulation of entire filter at
block level
24
Conclusions
  • Performance space exploration by Fourier-Motzkin
    Elimination
  • Calculation of polytopal feasible performance
    space
  • High efficiency suited for high-dimensional
    performance spaces
  • Hierarchical sizing
  • Polytopal block performance spaces (system level
    sizing constraints) link abstraction levels
  • Iteration compensates for linearization
    inaccuracies

Thank you!
25
Supplementary Slides
26
Approximation Quality
  • Reasonable approximation accuracy
  • sizing constraints only leave small feasible
    parameter space
  • circuit behavior usually weakly nonlinear if
    constraints met

27
Approximation Quality contd
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