rayas-sánchez, josé e.; zhang, qi j. · 2008 ieee mtt-s international microwave symposium,...

Instituto Tecnológico y de Estudios Superiores de Occidente

2008-06

Fast parametric models for EM design using

neural networks and space mapping

Rayas-Sánchez, José E.; Zhang, Qi J.

Enlace directo al documento: http://hdl.handle.net/11117/600

Este documento obtenido del Repositorio Institucional del Instituto Tecnológico y de Estudios Superiores de

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http://quijote.biblio.iteso.mx/licencias/CC-BY-NC-ND-2.5-MX.pdf

(El documento empieza en la siguiente página)

Repositorio Institucional del ITESO rei.iteso.mx

Departamento de Electrónica, Sistemas e Informática DESI - Artículos y ponencias con arbitraje

http://www.iteso.mx

http://rei.iteso.mx

http://hdl.handle.net/11117/600

http://quijote.biblio.iteso.mx/licencias/CC-BY-NC-ND-2.5-MX.pdf

2008 IEEE MTT-S International Microwave Symposium, Atlanta, GA, June 15, 2008Tutorial on Advances in CAD Techniques for EM Modeling and Design (TSC)

Fast Parametric Models for EM Design Using Neural Networks and Space MappingQ.J. Zhang, Carleton University, Canada; José E. Rayas-Sánchez, ITESO, Mexico

Fast Parametric Models for EM Design Using Neural Networks and Space Mapping

José E. Rayas-SánchezResearch Group on Computer-Aided Engineering of Circuits and Systems (CAECAS)

Department of Electronics, Systems and InformaticsInstituto Tecnológico y de Estudios Superiores de Occidente (ITESO)

Guadalajara, Mexico, 45090

http://www.desi.iteso.mx/caecas/

Q.J. ZhangDepartment of Electronics, Carleton University

Ottawa, Canada K1S 5B6

http://www.doe.carleton.ca/~qjz

Tutorial on Advances in CAD Techniques for EM Modeling and Design (TSC) 2008 IEEE MTT-S International Microwave Symposium, Atlanta, GA, June 15, 2008

2

Outline

§ Brief introduction to ANNs

§ EM-based statistical analysis

§ Input Space Mapping

§ Linear-Input Neural-Output Space Mapping (LINO-SM)

§ LINO-SM approach to yield estimation

§ Constrained Broyden-Based Space Mapping

§ Training the Output Neuromapping

§ Example

§ Conclusions



3

Biological Neuron

(Kartalopoulos, 1996)

soma

axon

dendritic tree

axonic endingnucleus

4

Artificial Neural Networks (ANNs)

§ An Artificial Neural Network (ANN) is a massively parallel distributed processor made up of simple processing units, that is able of acquiring knowledge from its environment though a learning process

§ ANNs are also information processing systems that emulate biological neural networks: they are inspired in the ability of human brain to learn from observation and generalize by abstraction



5

Artificial Neurons

§ An artificial neuron is a simple processing unit that receives and combines signals from many other neurons

§ Common types of artificial neurons are:Linear NeuronsInner-Product Nonlinear NeuronEuclidean Distance Neuron

6

Linear Neuron

vk = [vk1 … vkn]T vector of inputs

wk = [wk1 … wkn]T vector of weighting factors

bk bias or offset term

zk activation potential or induced local field, output signal

Σ

wk1

wk2

wkn

bkvk1

vk2

vkn

zkk

Tkkk bz wv+=



7

Inner Product Nonlinear Neuron

kT

kkk bs wv+=

)( kkk sz ϕ=Σ

wk1

wk2

wkn

bkvk1

vk2

vkn

sk zk)( kk sϕ

vk = [vk1 … vkn]T inputs wk = [wk1 … wkn]T weighting factors

bk bias or offset term sk activation potential

zk output signal

ϕk(sk) activation function or squashing function

8

Typical Activation Functions

Sigmoid or logistic function

kskkk esz −+

==1

1)(ϕ

ksakkk esz −+

==1

1)(ϕ

a = 1 (), a = 0.5 (× ) and a = 2 ()

With a slope parameter

-4 -2 0 2 40

0 . 2

0 . 4

0 . 6

0 . 8

1

-2 -1 0 1 2-1

-0 .5

0

0 . 5

1

Hyperbolic tangent function

kk

kk

ss

ss

kkkk eeeessz −

−

+−=== )(tanh)(ϕ



9

Some ANN Paradigms

§ Multilayer Perceptrons

§ Radial Basis Functions

§ Recurrent Neural Networks

10

3-Layer Perceptrons (3LP)

TThh

Thh ][ 1 wwW L=

vWbs hh +=

Thh

hhh bbb ][ 21 L=b

where

)(sFWby oo +=

TTom

Too ][ 1 wwW L=

Tom

ooo bbb ][ 21 L=b

Thss ])()([)( 1 ϕϕ L=sF

zh

zh

z2

z2

z1

z1

y1

I1

I2 L1

Lmym

inputlayer

hiddenlayer

outputlayer

Ih

vn

v1

hh ℜ∈Fbs ,,mo ℜ∈by, hmo ×ℜ∈W hnh ×ℜ∈W



11

Automated Model Generation (AMG)

Fastneuralmodel

EM simulators(examples used:

Ansoft HFSS, Sonnet em,

Faustus MEFiSTo)

AMG

• Data sampling and generation

• ANN structure adaptation

• Over-learning detection

• Under-learning detection

• Other actions as needed

User-requiredaccuracy

12

AMG for Spiral Inductor

Data Generators: Sonnet em Ansoft-HFSS

εr

S W

….

RS11 IS11 RS12 IS12

w s ε f

0.85%Advanced AMG(KAMG-PKI)

2.34%AMG

6.25%Conventional training

Testing Error

ANN Training TechniqueAMG uses data sampling algorithm to

sample data at critical locations. With the same amount of training data, AMG obtains better model accuracy than conventional training techniques.

Model accuracy under limited training data



13

Inverse Modeling by Neural Network

(Waveguide Filter Example, H. Kabir, Y. Wang, M. Yu and Q. Zhang, 2006)

Data Generator: Ansoft-HFSS (3D EM)

I/O coupling iris

Coupling screws

Tuning screws

Internal coupling iris

I/O coupling iris

Input neurons: electrical parametersOutput neurons: geometrical parameters

14

Filter Dimensions By Neural Net vs Measurement

-0.0011.8641.865Cavity length

0.0040.1150.111M12/M34 coupling screws

0.0020.1350.133M22/M33 tuning screws

-0.0400.0050.045M11/M44 tuning screws

0.0040.2160.212M14 iris

-0.0020.2970.299M23 iris

00.4050.405I/O irises

Difference(inch)

Measurement(inch)

Neural Model(inch)



15

Time-Domain Modeling by Neural Networks

Location of conducting posts (d ) controls

pass band behavior

Data Generator: MEFiSTo 3D Professional

WR-28 Rectangular Waveguide Ka-band (26.5 to 40Ghz)

u(t)

τ

….

f(t)

y(t-τ ) y(t-2τ) x(t-τ ) x(t-2τ)

τ τ τ

d

Recurrent neural network (RNN)

(With see thru top)1

2a = 280 mil

a

b

b = 140 mil

d

d

16

EM and RNN Transient Responses

t (ns)

f1

0 0.2 0.4 10.6 0.8

d = 3.88 mm

d = 5.17 mm

d = 4.53 mm

f21

0 0.2 0.4 10.6 0.8

d = 3.88 mm

d = 5.17 mm

d = 4.53 mm

10

-10

0

1

-1

0

… EM test data (MEFiSTo)RNN



17

EM-based Interpolating Surrogates

for Yield Estimation using

Neural Space Mapping Methods

18

EM-based Statistical Analysis

§ Statistical analysis and yield prediction are crucial for manufacturability

§ Reliable yield prediction typically requires massive amount of high-fidelity simulations (full-wave EM simulations)

§ Performing Monte Carlo yield analysis by directly using EM simulations is not feasible for most practical problems

§ Using an interpolating surrogate based on linear-input neural-output space mapping can be a solution



19

Input Space Mapping

coarsemodel

xcP

finemodel

Rf (xf ,ψ)ψ

xf

Rc(P(xf),ψ)

finemodel

Rf (xf ,ψ)ψxf coarse

modelxc

ψRc(xc,ψ)

Rf (xfSM,ψ) ≈ Rc(xc

*,ψ)

L Rc(P(xfSM)) can not

accurately estimate the fine model yield around xf

SM

☺

20

Linear-Input Neural Output Space Mapping

coarsemodel

xcP

finemodel

Rf (x f ,ψ)ψ

xf

w

QANN

Rc(P(x f),ψ)

Q(Rc(P(xf),ψ), xf,ψ, w)

),(),,),,(( * ??? ffffc xRwxcBxRQ =+for all xf and ψ in the training region



21

LINO-SM approach to Yield Estimation

Calculate xf SM and P through

input space mapping

Generate learning and testing data around xf

SM according to tolerances

Start

End

Obtain xc* by optimizing

the coarse model

Obtain Q by training an output neuro mapping

Calculate yield using Q(Rc(P(xf),ψ),xf,ψ))

22

Constrained Broyden-Based SM

(2) 2

21minarg)( T

pT

cf ee

xxP …=

),(),()( jccsjffsfj ?? xRxRxe −=

(1) )),((minarg* ?U cc

cc xR

xx =

xfSM = x f

(i ) cBxxP += ff )(

where B = B(i ) and c = xc* − Bxf

SM

Begin find xc

* solving (1) i = 0, xf

(i) = xc*, B(i) = I, δ = 0.3

*)()( )( cif

i xxPf −= using (2)

repeat until stopping_criterion solve )()()( iii fhB −= for h(i)

)()()( iif

testf hxx +=

while max)(min)(f

testff

testf xxxx f≺ ∨

)()( ii hh δ= )()()( ii

ftestf hxx +=

end )()1( test

fif xx =+

*)1()1( )( cif

i xxPf −= ++ using (2)

)()(

)()1()()1(

iTi

Tiiii

hh

hfBB+

+ += , i = i + 1

end



23

Generating Learning and Testing Points

testing base pointlearning base point

xfSM

xf 1

xf 2

xf 3

2n+1 learning base points in a star distribution2n testing base points in a rotated star distribution

24

Training the Output Neuro Mapping

Begin Generate RCL, RCT, RFL and RFT

FFLCLoldL |||| RR −=ε , FFTCT

oldT |||| RR −=ε

h = m, i = 1

FLi ||)(||minarg)( wE

ww =

FFLi

LL ||)(|| )( RwQ −=ε

FFTi

TT ||)(|| )( RwQ −=ε

while TLToldT εεεε ≥∨≥

ToldT εε = , L

oldL εε = , i = i + 1, h = h + 1

FLi ||)(||minarg)( wE

ww =

FFLi

LL ||)(|| )( RwQ −=ε

FFTi

TT ||)(|| )( RwQ −=ε end

)1(* −= iww end

),(),,),,(( * ??? ffffc xRwxcBxRQ =+ for all xf and ψ in the training region

)()( wQRwE LFLL −=



25

Microstrip Notch Filter

εr

H

W50

W50

Lc

Lp

W50

W50

Lc

Lc

W50

W50

Lp

SgSg

Lo

Lo

Lo

xf = [Lc Lo Sg]T

H = 10milW50 = 31milεr = 2.2loss tan = 0.0009(RT Duroid 5880)

Specifications:|S21| ≤ 0.05 for 13.19GHz ≤ f ≤ 13.21GHz

|S21| ≥ 0.95 for f ≤ 13GHz and f ≥ 13.4GHz

26

Microstrip Notch Filter – Fine Model

1

2

Hair

ygap

ygap

ygap

Hair = 60 milLp = ½(Lo+Lc)Ygap = Logrid = 0.5mil×0.5mil



27

Microstrip Notch Filter – Coarse Model

MclinMclin

W=W50L=LcS=Sg

Mclin

W=W50L=W50

W=W50L=LcS=Sg

outin

W=W50L=LcS=Sg

W=W50L=W50

var W50 31milvar Lp 31mil var Lzero 1e-9mil

W=W50L=Lp

W=W50L=Lp

MSub RT-Duroid-5880H=10milER=2.2TAND=0.0009LEVEL=2

var Lc 143milvar Lo 158milvar Sg 8mil

Preassigned Parameters:Optimization Variables:

L=LoW=W50 L=Lzero

W=W50

L=LoW=W50

L=LzeroW=W50

L=LoW=W50 L=Lzero

W=W50

28

Microstrip Notch Filter – Starting Point

12.7 12.8 12.9 13 13.1 13.2 13.3 13.4 13.5 13.6 13.70

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

frequency (GHz)

S21

Rc(xc*)

Rf (xc*)xc

* = [143 158 8]T (mil)



29

Microstrip Notch Filter – SM Solution

12.7 12.8 12.9 13 13.1 13.2 13.3 13.4 13.5 13.6 13.70

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

frequency (GHz)

S21

Rc(P(xfSM))

Rf (xfSM)xf

SM = [143.5 159 8]T (mil)

30

Microstrip Notch Filter – Training Q

0 1 2 3 4 5-1.6

-1.4

-1.2

-1

-0.8

-0.6

-0.4

-0.2

0

hidden neurons, h

log10

(εL)

log10(εT)

tolerance region: ±0.5mil



31

Microstrip Notch Filter – LINOSM Solution

12.7 12.8 12.9 13 13.1 13.2 13.3 13.4 13.5 13.6 13.70

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

frequency (GHz)

S21

Rc(P(x fSM

))

Rf (xfSM

)

Q(Rc(P(x fSM

)), x fSM

)

32

Microstrip Notch Filter – LISM Yield

12.7 12.8 12.9 13 13.1 13.2 13.3 13.4 13.5 13.6 13.70

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

frequency (GHz)

S21

Rc(P(x

f))

for xf around xfSM

Yield = 98 %

max dev: ±0.2mil



33

Microstrip Notch Filter – LINOSM Yield

12.7 12.8 12.9 13 13.1 13.2 13.3 13.4 13.5 13.6 13.70

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

frequency (GHz)

S21

Q(Rc(P(x

f)), x

f)

for x f around xfSM

Yield = 58 %

max dev: ±0.2mil

34

Conclusions

§ We described a method for highly accurate EM-based statistical analysis and yield estimation of RF and microwave circuits

§ It consists of applying a constrained Broyden-based linear-input space mapping, followed by a neural-output space mapping, in which the responses, the design parameters and independent variable are mapped

§ The output neuromodel is trained using reduced sets of learning and testing samples

§ The resultant interpolating surrogate model is used as a very efficient vehicle for accurate statistical analysis and yield prediction

rayas-sánchez, josé e.; zhang, qi j. · 2008 ieee mtt-s international microwave symposium,...

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