CAD WITH TOLERANCES

John W. Bandler

SOS-98-02-V

March 12, 1998

© John Bandler 1998

CAD WITH TOLERANCES

John W. Bandler

Simulation Optimization Systems Research Laboratory

and Department of Electrical and Computer Engineering

McMaster University, Hamilton, Canada L8S 4L7

Email bandler @ mcmaster.ca

URL http :// soya.sos.mcmaster.ca

presented at

WORKSHOP ON COMPUTER-AIDED DESIGN FOR MANUFACTURABILITY

1998 IEEE MTT -S Int. Microwave Symposium, Baltimore, MD, June 12, 1998

Introduction

design with tolerances, yield-driven design, design centering :

methodologies indispensable for today's RF, wireless and microwave CAD

suitably integrated design methodologies take into account manufacturing tolerances and model uncertainties

microwave designers continue to use different CAD systems to address different aspects of their designs; may be tedious and time consuming because of incompatible user interfaces and data formats

we suggest a flexible approach to mixed-domain, multi- simulator yield-driven design

we integrate time-domain, frequency-domain and EM simulations into a versatile optimization environment with tolerances

Yield Interpretation in the Parameter Space

Increasing Sophistication of Design Methodology

with Tolerances

DCTT : Design Centering, Tolerancing and Tuning using mathematical optimization ( 1970s )

deterministic ( Bandler et al., 1976)

performance-driven design

fixed tolerance worst-case design

variable tolerance worst-case design

full DCTT

statistical (see Bandler and Chen, 1988)

fixed tolerance yield-driven design

correlated tolerances

variable tolerance cost-driven design

CAD goal: first-pass success design, however...

role of tuning: tunable designs may be considered in which tunable variables are assigned possible ranges at the design stage; followed by postproduction testing and tuning

Overview of Presentation

historical perspective (early work at Bell Labs, Karafin 1971)

the need for physics-based yield optimization of integrated circuits

the role of electromagnetic (EM) optimization

yield optimization of a distributed attenuator using distributed (parallel) computations

mixed-domain multi-simulator yield-driven design using SPICE, OSA90 /hope, and Sonnet's em

tolerance optimization of waveguide multiplexers

Space Mapping (SM) optimization

SM optimization using hybrid mode-matching (MM) /network theory and finite-element ( FEM ) models

Monte Carlo analysis of manufacturing tolerances using SM

Physics-Based Yield Optimization of MMICs

random variations in manufacturing process may lead to some circuits failing to meet design specifications

production tuning of MMICs is restricted

component replacement is not possible

circuits are manufactured in batches rather than individually

the cost is directly affected by yield

the ability to predict and enhance production yield is critical

accurate EM simulations of passive elements and physical simulations of active devices enhanced by Space Mapping optimization

Yield Optimization of a Three-Stage MMIC Amplifier

( Bandler et al., 1992)

the three-stage X-band MMIC amplifier is based on the circuit topology and fabrication layout originally designed by Thomson-Semiconductors ( Kermarrec and Rumelhard , 1988)

intended as a gain block for phased-array antennas

the amplifier contains three GaAs MESFETs using an interdigitated structure with two gate fingers of dimensions 150 m × 1.0 m

all passive elements are realized using lumped MMIC elements: spiral inductors, MIM capacitors and bulk resistors

37 statistical variables with correlations and 16 design variables

yield optimization carried out by OSA90 /hope

yield is improved from 26% at the nominal design to 69%

Circuit Schematic and Layout of the Three-Stage Amplifier

Predictable Yield-Driven Circuit Optimization

( Bandler et al., 1992)

usefulness of yield-driven design depends on the accuracy of yield estimated using the statistical model

yield predicted by Monte Carlo simulation using the model should be consistent with the yield predicted directly from the device measurement data

the advantage of a statistical model over the measurement data is that the model provides for convenient interpolation

the selection of device parameters for yield optimization can be assisted by yield sensitivity analyses

the yield can be significantly increased by simultaneous circuit- device optimization

design of a small-signal broadband amplifier is investigated using OSA90 /hope with the KTL model w.r.t. a number of specifications

the predicted yield is verified using the device data

YIELD VERIFICATION

Before Yield	After Yield

Optimization	Optimization

Predicted	Verified	Predicted	Verified

Yield (%)	Yield (%)	Yield (%)	Yield (%)

Spec. 1	17 .5	15 .7	67	57 .9

Spec. 2	21	20	83	75 .7

Spec. 3	44	37 .1	98	93 .6

Spec. 1: 7.5dB < | S21 | < 8.5dB , | S11 | < 0.5, | S22 | < 0.5

Spec. 2: 6.5dB < | S21 | < 7.5dB , | S11 | < 0.5, | S22 | < 0.5

Spec. 3: 6.0dB < | S21 | < 8.0dB , | S11 | < 0.5, | S22 | < 0.5

200 Monte Carlo outcomes are used for predicted yield, 140 for verified yield

Gain After Optimization from Model and from Data

Physics-Based Cost-Driven Design

( Bandler et al., 1995)

yield optimization maximizes the yield by adjusting the nominal values of the design variables keeping tolerances fixed

the cost for obtaining small tolerances may be very high

there is a trade-off between the yield and the cost

cost-driven design minimizes the cost while maintaining the required yield

cost-driven optimization

x vector of parameter tolerances

Y design yield

YS specified yield

C(x) cost function, e.g.,

10 dB Distributed Attenuator Design

( Bandler et al., 1995)

built on a 15 mil thick substrate with relative dielectric constant of 9.8

metallization of a high resistivity (50 /sq)

the feed lines and the grounding pad are assumed lossless

Statistical Design of the Attenuator

design specifications (from 2 GHz to 18 GHz )

9.5 dB ≤ insertion loss ≤ 10.5 dB

return loss ≥ 10 dB

the structure, treated as a whole, has 8 geometrical parameters

designable : 4 parameters describing the resistive area

statistical: 8 parameters (with a standard deviation of 0.25 mil)

em simulation at a single frequency requires about 7 CPU minutes on a Sun SPARCstation 1+

Distributed (Parallel) Computing

nominal design: 30 em analyses with an average of 3.8 analyses run in parallel

about 168 minutes on the network of Sun SPARCstations 1+

time is reduced by 75%

statistical design: additional 113 em analyses with an average of 2.5 analyses run in parallel

time is reduced by 60%

Monte Carlo Sweeps of the Attenuator Responses

yield (estimated from 250 Monte Carlo outcomes) is increased from 82% to 97%

Space Mapping

( Bandler et al., 1994)

optimization or "coarse" model:	Ros( xos )

EM, validation or "fine" model:	Rem( xem )

Space Mapping:	xos = P( xem )

such that	Ros(P( xem )) Rem( xem )

Space Mapped solution:

fast response evaluation

for tolerance analysis:	Ros(P( xem ))

The Concept of Space Mapping

( Bandler et al., 1994)

we wish to find a mapping P( xem ) from the EM space Xem to the optimization space Xos such that

where Ros and Rem are the circuit responses simulated by the OS and EM simulators, respectively

starting from the optimal design (in Xos ) we use SM to find the mapped solution in Xem as

assuming that P is invertible

Aggressive Space Mapping

( Bandler et al., 1995)

new algorithm aggressively exploits every EM simulation

avoids upfront EM analyses at many base points

applies the classical Broyden update to the mapping

quasi-Newton iteration

Broyden update:

where

Space Mapping Optimization

to avoid direct optimization of computationally intensive models

the multi-simulator approach is particularly relevant and suitable for Space Mapping

automatic alignment of two distinct models of different accuracy and computational efficiency

such models would normally be facilitated by two disjoint simulators

two different EM simulators are used here

EM space or "fine" model - 3D FEM -based field simulator Maxwell Eminence ( Ansoft Corporation)

optimization space (OS) or "coarse" model - the RWGMM library of waveguide mode-matching (MM) models connected by network theory (Fritz Arndt )

Tolerance Simulation Using SM

first, the mapping is established during nominal SM optimization

statistical outcomes in the EM space are mapped to the corresponding points in the OS space

we are able to rapidly estimate the effects of manufacturing tolerances, benefitting from

the accuracy of the FEM model

the speed of the hybrid MM/network theory simulations

the CPU time required for the Monte Carlo analysis is comparable to just a single full FEM simulation

14 Channel Multiplexer Tolerance Optimization

Common port return loss after nominal optimization

14 channel multiplexer

112 variable optimized

511 frequency points

14 Channel Multiplexer Tolerance Optimization

Channel insertion loss after nominal optimization

14 Channel Multiplexer Tolerance Optimization

Common port return loss with tolerances

14 Channel Multiplexer Tolerance Optimization

Common port return loss after optimization with tolerances

a total of 280 CPU hours on a SPARCstation 10

Conclusions

possibilities in microwave CAD with tolerances are presented

active and passive, linear and nonlinear, lumped and distributed, circuit-oriented and EM-oriented designs are considered

brief historical perspective of DCTT is provided

intelligent computational interfaces combine and enhance the features of otherwise disjoint simulators based on OSA's Datapipe open architecture

the role of distributed or parallel computing is exemplified

mixed time-domain, frequency-domain and EM simulations are integrated for efficient statistical design

optimization using OSA90 /hope of a broadband amplifier with microstrip components: the MESFET is simulated by SPICE and the microstrip components are analyzed by em

tolerance design of a 14 channel waveguide multiplexer is presented

Space Mapping and its advantages in design with tolerances is reviewed

further advantages of the multi-simulator approach are exemplified by Space Mapping optimization with two different EM simulators: mode-matching and finite element

References

B.J. Karafin , "The optimum assignment of component tolerances for electrical networks," Bell Syst . Tech. J., vol.50, 1971, pp. 1225-1242.

J.F. Pinel and K.A. Roberts, "Tolerance assignment in linear networks using nonlinear programming," IEEE Trans. Circuits Syst ., vol. CAS-19, 1972, pp. 475-479.

J.W. Bandler , "The tolerance problem in optimal design," Proc. European Microwave Conf. (Brussels, 1973), Paper A. 13.1.(I ).

J.W. Bandler , P.C. Liu and H. Tromp , "Integrated approach to microwave design," IEEE Int. Microwave Symp . Dig. (Palo Alto, CA, 1975), pp. 204-206.

J.W. Bandler , P.C. Liu and H. Tromp , "A nonlinear programming approach to optimal design centering , tolerancing and tuning," IEEE Trans. Circuits Syst ., vol. CAS-23, 1976, pp. 155-165.

J.W. Bandler and A.E. Salama , "Functional approach to microwave postproduction tuning," IEEE Trans. Microwave Theory Tech., vol. MTT -33, 1985, pp. 302-310.

J.W. Bandler , R.M. Biernacki , S.H. Chen, M.L. Renault, J. Song and Q.J. Zhang, "Yield optimization of large scale microwave circuits," Proc. European Microwave Conf. (Stockholm, 1988), pp. 255-260.

J.W. Bandler and S.H. Chen, "Circuit optimization: the state of the art," IEEE Trans. Microwave Theory Tech., vol. 36, 1988, pp. 424-443.

J.W. Bandler , R.M. Biernacki , Q. Cai , S.H. Chen, S. Ye and Q.J. Zhang, "Integrated physics-oriented statistical modeling , simulation and optimization," IEEE Trans. Microwave Theory Tech., vol. 40, 1992, pp. 1374-1400.

References ( cont'd )

J.W. Bandler , R.M. Biernacki , S.H. Chen, P.A. Grobelny and R.H. Hemmers , "Space mapping technique for electromagnetic optimization," IEEE Trans. Microwave Theory Tech., vol. 42, 1994, pp. 2536-2544.

J.W. Bandler , R.M. Biernacki , Q. Cai , S.H. Chen, P.A. Grobelny and D.G. Swanson, Jr., "Heterogeneous parallel yield-driven electromagnetic CAD," IEEE MTT -S Int. Microwave Symp . Dig. (Orlando, FL, 1995), pp. 1085-1088.

J.W. Bandler , R.M. Biernacki , S.H. Chen, R.H. Hemmers and K. Madsen , "Electromagnetic optimization exploiting aggressive space mapping," IEEE Trans. Microwave Theory Tech., vol. 43, 1995, pp. 2874-2882.

J.W. Bandler , R.M. Biernacki , S.H. Chen and P.A. Grobelny , "Optimization technology for nonlinear microwave circuits integrating electromagnetic simulations," Int. J. Microwave and mm-Wave CAE, vol. 7, 1997, pp. 6-28.

J.W. Bandler , R.M. Biernacki , S.H. Chen and D. Omeragić , "Space mapping optimization of waveguide filters using finite element and mode-matching electromagnetic simulators," IEEE MTT -S Int. Microwave Symp . Dig. (Denver, CO, 1997), pp. 635-638.

J.W. Bandler , R.M. Biernacki and S.H. Chen, "Mixed-domain multi-simulator statistical device modeling and yield-driven design," Proc. European Gallium Arsenide Applications Symposium (Bologna, 1997), pp. 193-200.

M.H. Bakr , J.W. Bandler , R.M. Biernacki , S.H. Chen and K. Madsen , "A trust region aggressive space mapping algorithm for EM optimization," IEEE MTT -S Int. Microwave Symp . Dig. (Baltimore, MD, 1998).