Optimization of Components using Sensitivity and Yield ... › franz_hirtenfelder › UGM2010...ijk j k j k ijk j k ijk k j i j k i j k i j k a x y y x b y y c x x c c c b b b a a

www.cst.com | CST UGM 2010 | April 10 | 1

Optimization of Components using

Sensitivity and Yield Information

Franz Hirtenfelder, CST AG

[email protected]


Abstract

Optimization is a typical component of any design engineer’s workflow. With the introduction of

new global (genetic, particle swarm) and local (Nelder-Mead) optimizers, CST addressed this issue

with release 2009 of CST STUDIO SUITE™. With version 2010 CST goes one step further: CST MWS

2010 features a sensitivity analysis algorithm which is capable of evaluating the s-parameter

dependencies on various model parameters after a single 3D electromagnetic simulation run.

This means that all further evaluations for different model parameter sets and optimization runs

based on sensitivity data can be derived without restarting the full-wave simulation.

The efficiency of this new sensitivity analysis approach now makes Monte-Carlo based yield analysis

feasible even for complex multi-parametrical three-dimensional structures. This is due to the s-

parameter results being available at virtually no additional effort or computational cost.


Optimization: a typical task in a workflow CST Studio Suite 2009

Global (Genetic, Swarm)

Local (Nelder-Mead, Quasi-newton)

CST Studio Suite 2010 Sensitivity

Yield

How can sensitivity data be used in an optimization?

Introduction


Introduction to Sensitivity

Matrix to solve: QEK

[K]: symmetric, complex, contains geometry, material, frequency

xi, yi

Example: Linear Shape functions for a 2D element in xy

jkijkkjijkkjkjijk

kji

kji

kji

xxcyybxyyxa

ccc

bbb

aaa

yxN ;;;.,,12

1

xj, yj

xk, yk

k

j

i

kji

z

z

z

NNNz ],,[

zi

[E]: unkowns z

[Q]: Sources

kjinmdxdyx

N

x

N

x

N

x

Nk nmy

nm

xy

xnm ,,,;)(,

Example: electrostatic


),(),(),(1

),(0

pEpKpEj

pS TT


S-Parameters:

[K] …left hand side, E (Fields at ports, p… any parameter

Ep

KE

p

Sj T0

Sensitivity of S-parameter vs. parameter change:

Direct analytical derivation of

K-matrix elements via e.g. [N]

3D Fieldsolution

Same 3D Fieldsolution


Numerical calculation of gradients is expensive and unstable

Here: Sensitivity of S-parameter vs. parameter change

no additional 3D solution required (only another S-Parameter computation)

Very efficient computation of sensitivities

Result: S-parameter ranges for tolerant parameters

Currently available for FD-Tet solver


Ep

KE

p

Sj T0


pp

SSS

p

MWSDnmnm .)3(

What is it good for?

The sensitivity helps estimate „new“ S-parameters due to the (small) change of the

parameter, at no extra cost

Suppose the parameter p changes by a quantity ∆p :

exact computation of the Sensitivity

(Approximated by 1st order Taylor expansion)


The various sensitivities are used in an optimizer to solve for ∆p as variables to

best fit the S-parameter goals.

∆p … face constraints

pp

SxSpxS

p

.)()(


For every product, there are:

Technical specifications

Fabrication tolerances

The fabrication tolerances will lead to

some products not fulfilling the

specifications

Yield:

What is the Yield Analysis

Total

Passedyield

#

#

Gaussian

Uniform


How is yield calculated typically?

Parameters vary according to a known probability curve

Repeat

Change the value of all parameters

Simulate

Check if specification (in our case for S-params.) is met

Until the number of simulations is statistically relevant

This is a large number of EM simulations - typicaly hundreds or thousands!!!

Knowing the sensitivity, there is no need to perform 3D simulations, at least if the parameters vary in a small range.

The efficiency of this new sensitivity analysis approach makes Monte-Carlo based yield analysis feasible even for complex multi-parametrical three-dimensional structures

Typical Approach vs. CST Approach


Example 1: 2-Post Bandpass Filter

Rel Bandwidth:0.9 %


Definition of Face Constraints Ivariation of resonator‘s lengths

+

-

+

-


Definition of Face Constraints IIvariation of input coupling lengths

+-

+ -


Sensitivity of facedistances

|S| linear > S1,1 arg(S) > S1,1


Optimization using Sensitivity Data

A dummy model is defined using two

parameters P1 and P2,

ResultsTemplates are defined to import

sensitivity and S11 data from the 3D model.

compute S11 according to the equation

psensSSp

pMWSD ._3_1111

Dummy


PostProcessing Templates

psensSSp

pMWSD ._3_1111

Optimization using Sensitivity Data


Perform e.g. Parameter Sweeps

Shift of the input coupling


Perform e.g. Parameter Sweeps

Shift the resonator‘s lengths+ -


Perform Optimizations : 0D Results

New desired band: 570-575 MHz


Perform Optimizations : Simplex

Inital parameters

Goal

0

---- Initial

-----optimized


Check Results of the modified 3D Model

+p2

+p1

Found parameters p1

and p2 are used to

modify the new 3D

model geometry.

Frequency band has

been shifted ok.


Second Iteration

The sensitivity data is fed back again into the optimizer model to run a 2nd loop:


Results of the 2nd opt. loop

Simplex optimizer

3D

Opt.results


3rd Iteration

Centering f-band

Opt.results

3D ---- Initial

-----optimized


S-Parameter Results: Comparison

Several iteration steps are required since the linear sensitivity

approach is applied to a nonlinear system (3D-filtermodel)


Yield-Specifications: < -25dBIn the range .569 to .574, S11 is under -25dB, the 3-sigma Lines are partially above and

below -25dB

For this spec, the yield will tell us what percentage of the devices are within this limit of

< -25 dB for the given frequency band.

Yield Analysis


Another yield specification: S11 < -26dB

Yield Result: only 0.71%

Yield Analysis


Example 2: 7-Post Filter *)

Center frequency: 7.55 GHz

Bandwidth: 100 MHz

Rel Bandwidth: 1.3 %

Insertion Loss: -0.01 dB

Return Loss: – 26 dB

Best results obtained by Group delay Tuning

*) By courtesy of MESL Microwave Limited, Edinburgh


Method of InvChirpZ

Comparison of the InvChirpZ-resonse between

groupdelayed tuned filter and Theory

Resonator3

and 4

Note the high sensitivity

at resonator 3 and 4

(parameter ph3 and ph4

respectively)


Final results by individually tuned posts

Method of InvChirpZ: final results


Opimization using Sensitivity Data I

Results of the lin. optimization

Note high magnitude!

---- Initial

-----optimized Note small dimensional changes! (µm)


Modifying the geometry according to the found

Delta-Ps of the lin. Opt. system:

Result of the new 3D simulation

Opimization using Sensitivity Data I


Perform a 2nd optimisation loop

Result of new δP

Opimization using Sensitivity Data II

---- Initial

-----optimized


Opimization using Sensitivity Data II

Result of the new 3D simulation


Summary

CST Studio Suite 2010 offers

Sensitivity and Yield Analyses

S-Parameter Sensitivity is computed exactely without any meshvariation,

broadband, at no additional costs

It has been demonstrated that sensitivity data is useful to speed up optimization loops

Optimization performed on the smaller linear matrix system and runs

much faster

10 design parameter

final design

Only 16 solver runs (FD TET),

i.e. almost a factor 100 faster

compared to the current method!

initial design

CST Studio Suite 2011: New Optimization Strategy (based on sensitivity information)

Documents

Optimization of Components using Sensitivity and Yield ... › franz_hirtenfelder › UGM2010...ijk j k j k ijk j k ijk k j i j k i j k i j k a x y y x b y y c x x c c c b b b a a