Optimization of Components using Sensitivity and Yield Information

Transcription

1 Optimization of Components using Sensitivity and Yield Information Franz Hirtenfelder, CST AG CST UGM 2010 April 10 1

2 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. CST UGM 2010 April 10 2

3 Introduction 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? CST UGM 2010 April 10 3

4 CST UGM 2010 April 10 4 Introduction to Sensitivity Matrix to solve: Q E K [K]: symmetric, complex, contains geometry, material, frequency xi, yi Example: Linear Shape functions for a 2D element in xy j k ijk k j ijk k j k j ijk k j i k j i k j i x x c y y b x y y x a c c c b b b a a a y x N ; ; ;., 1, 2 1 xj, yj xk, yk k j i k j i z z z N N N z ],, [ zi [E]: unkowns z [Q]: Sources k j i m n dxdy x N x N x N x N k n m y n m xy x n m,,, ; ) (, Example: electrostatic

5 Introduction to Sensitivity S-Parameters: 3D Fieldsolution S(, p) 1 j 0 E T (, p) K T (, p) E(, p) [K] left hand side, E (Fields at ports, p any parameter Sensitivity of S-parameter vs. parameter change: j 0 S p E T K p E Direct analytical derivation of K-matrix elements via e.g. [N] Same 3D Fieldsolution CST UGM 2010 April 10 5

6 Introduction to Sensitivity Numerical calculation of gradients is expensive and unstable Here: Sensitivity of S-parameter vs. parameter change j 0 S p E T K p E 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 CST UGM 2010 April 10 6

7 Introduction to Sensitivity 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 : S( x p) S( x) p S p. p (Approximated by 1st order Taylor expansion) S Snm Snm(3D MWS). p CST UGM 2010 April 10 7 exact computation of the Sensitivity The various sensitivities are used in an optimizer to solve for p as variables to best fit the S-parameter goals. p p p face constraints

8 What is the Yield Analysis For every product, there are: Technical specifications Fabrication tolerances The fabrication tolerances will lead to some products not fulfilling the specifications Yield: # Passed yield # Total Gaussian Uniform CST UGM 2010 April 10 8

9 Typical Approach vs. CST Approach 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 threedimensional structures CST UGM 2010 April 10 9

10 Example 1: 2-Post Bandpass Filter Rel Bandwidth:0.9 % CST UGM 2010 April 10 10

11 Definition of Face Constraints I variation of resonator s lengths CST UGM 2010 April 10 11

12 Definition of Face Constraints II variation of input coupling lengths CST UGM 2010 April 10 12

13 Sensitivity of facedistances S linear > S1,1 arg(s) > S1,1 CST UGM 2010 April 10 13

14 Optimization using Sensitivity Data Dummy 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 S 11 S 11_3 D _ MWS sens p. p p CST UGM 2010 April 10 14

15 Optimization using Sensitivity Data S 11 S 11_3 D _ MWS sens p. p p PostProcessing Templates CST UGM 2010 April 10 15

16 Perform e.g. Parameter Sweeps Shift of the input coupling CST UGM 2010 April 10 16

17 Perform e.g. Parameter Sweeps + - Shift the resonator s lengths CST UGM 2010 April 10 17

18 Perform Optimizations : 0D Results New desired band: MHz CST UGM 2010 April 10 18

19 Perform Optimizations : Simplex Inital parameters Goal 0 CST UGM 2010 April Initial -----optimized

20 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. CST UGM 2010 April 10 20

21 Second Iteration The sensitivity data is fed back again into the optimizer model to run a 2nd loop: CST UGM 2010 April 10 21

22 Results of the 2 nd opt. loop Simplex optimizer Opt.results 3D CST UGM 2010 April 10 22

23 3rd Iteration Centering f-band ---- Initial -----optimized Opt.results 3D CST UGM 2010 April 10 23

24 S-Parameter Results: Comparison Several iteration steps are required since the linear sensitivity approach is applied to a nonlinear system (3D-filtermodel) CST UGM 2010 April 10 24

25 Yield Analysis Yield-Specifications: < -25dB In 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. CST UGM 2010 April 10 25

26 Yield Analysis Another yield specification: S11 < -26dB Yield Result: only 0.71% CST UGM 2010 April 10 26

27 Example 2: 7-Post Filter *) Center frequency: 7.55 GHz Bandwidth: 100 MHz Rel Bandwidth: 1.3 % Insertion Loss: db Return Loss: 26 db Best results obtained by Group delay Tuning *) By courtesy of MESL Microwave Limited, Edinburgh CST UGM 2010 April 10 27

28 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) CST UGM 2010 April 10 28

29 Method of InvChirpZ: final results Final results by individually tuned posts CST UGM 2010 April 10 29

30 Opimization using Sensitivity Data I Note high magnitude! Results of the lin. optimization ---- Initial -----optimized Note small dimensional changes! (µm) CST UGM 2010 April 10 30

31 Opimization using Sensitivity Data I Modifying the geometry according to the found Delta-Ps of the lin. Opt. system: Result of the new 3D simulation CST UGM 2010 April 10 31

32 Opimization using Sensitivity Data II Perform a 2nd optimisation loop Result of new δp ---- Initial -----optimized CST UGM 2010 April 10 32

33 Opimization using Sensitivity Data II Result of the new 3D simulation CST UGM 2010 April 10 33

34 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 CST Studio Suite 2011: New Optimization Strategy (based on sensitivity information) initial design final design 10 design parameter CST UGM 2010 April Only 16 solver runs (FD TET), i.e. almost a factor 100 faster compared to the current method!