Presentation by Jiri Ocenasek at the Optimization by Building and Using Probabilistic Models (OBUPM 2008) workshop at the Genetic and Evolutionary Computation Conference (GECCO-2008)

1. +
July 2008
Jiri Ocenasek, Magwel NV, Belgium 1

2. Robust circuit sizing:
EDA for EDA
Jiri Ocenasek, Magwel NV, Belgium 2

3. Company Overview

MAGWEL was founded in April 2003

Spin­off from IMEC in Belgium
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Initially focused on 3D device­EM simulation

With acquisition of Kimotion Technologies
− Expanding into Robust Design and Verification of Analog
and RF circuits
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Customers: TI, NXP, IMEC, UCL ….

Participant in EU research projects
Jiri Ocenasek, Magwel NV, Belgium 3

4. Robust sizing of Analog & RF building blocks
Design variables Specifications Process and Environment
EldoTM
SpectreTM
HspiceTM
KtModels
ADVanceMSTM
…
Performance models Optimized netlist Specification corners
Jiri Ocenasek, Magwel NV, Belgium 4

5. Example: Gain­boosted op. amplifier
* [M.Waltari, “circuit techniques for low-voltage and high-speed A/D converters, PhD.]
Jiri Ocenasek, Magwel NV, Belgium 5

6. Terminology I

Design variables D
− The designer can prescribe them within some accuracy
− Example: W and L of transistors, bias current, …

Operational variables O
− The circuit has to work under all operational conditions within
specified limits
− Example: Temperature, Supply voltage, …

Technology variables T
− Variation of manufacturing process, statistically distributed
− Example: Doping parameters of substrate
Jiri Ocenasek, Magwel NV, Belgium 6

7. Terminology II

Mismatch variables M
Mismatch in T
+
Mismatch in D
IDS1 IDS2 Transistors are not
identical !
VGS1 VGS2
Jiri Ocenasek, Magwel NV, Belgium 7

8. Terminology III

Response variables R
− Extracted from simulator’s output: r = simulate(d,o,t,m )
− Example: Noise, Gain, Power, Die area, ...
 Constraint cost for i­th constraint Ci(r)
­ Ci(r) ≥ 0 if satisfied, Ci(r) < 0 if violated
­ Example: Power is below 100 mW: “100mW ­ Power”
 Goal cost for j­th goal Gj(r)
Jiri Ocenasek, Magwel NV, Belgium 8

9. Yield explanation

Probability density function ρ(t,m )
­ Typically normal or uniform

Advanced manufacturing processes ­ the design d
has to be robust against variations of t and m
­ yield(d) = ∫t,m F(d,t,m) ρ(t,m) dt dm
where F(d,t,m) indicates whether all constraints Ci are
satisfied under all permissible operational conditions o:
 F(d,t,m)=1 if ∀i, ∀ο ϵΟ : Ci(simulate(d,o,t,m))≥0

F(d,t,m)=0 otherwise
Jiri Ocenasek, Magwel NV, Belgium 9

10. Optimization target
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First stage: nominal optimization
− find d such that ∀i: Ci(simulate(d,o=nominal,t=0,m=0))≥0
− can be replaced by user­provided solution

Second stage: yield maximization
− find/improve d such that yield(d) is maximized

Third stage: when yield( d ) > 0.997
− minimize sum of goals ∑j Gj(d,o=nominal,t=0,m=0,r)
while keeping the yield
Jiri Ocenasek, Magwel NV, Belgium 10

11. Results: gain­boosted amplifier
# devices 56
# design variables 22
# constraints 63
# tech.+mm. variables 30
# operational variables 4
starting point none
# simulations 12626
runtime 251 min
total yield 99.8%
goal 1 area = 7970 μm2
goal 2 power = 13.7 mW
Jiri Ocenasek, Magwel NV, Belgium 11

12. Results: gain­boosted amplifier
Number of fitness evaluations
Jiri Ocenasek, Magwel NV, Belgium 12

13. Jiri Ocenasek, Magwel NV, Belgium 13

14. Why are Estimation of Distribution
Algorithms suitable?

Decomposability of the problem
− the circuit is composed of sub­blocks

Complicated fitness landscape
− multimodality: several local optima
− nonlinearities: responses are hard to be modeled
− discontinuities: simulator switches modes
− missing data: regions where simulation fails
Jiri Ocenasek, Magwel NV, Belgium 14

15. Conclusion

Robust Optimizer
− Can handle tough circuits where others fail
− Capable of handling fairly large blocks

Produces quality results with high yield
− 3 step approach, does not require user intervention
− Provides insight: yield distributions, sensitivities, trade­offs

Integration
− Cadence design environment
− Simulators: Spectre, Eldo, Hspice (others can be added)
− Supports LSF for distributed simulation
Jiri Ocenasek, Magwel NV, Belgium 15

16. Thank you
Jiri Ocenasek, Magwel NV, Belgium 16