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• www.cst.com | CST EuMW 2010 Presentations| September 2010 | 1

A Glimpse into Multiphysic-Analyses

using

CST STUDIO SUITE™

Accounting for thermal heating effects and mechanical

deformation in the electrical design

• www.cst.com | CST EuMW 2010 Presentations| September 2010 | 2

EM-field computation

Thermal

analysis

Stress analysis /

deformation

EM-properties of deformed geometry

can be fed into sensitivity analysis

The Motivation …

• www.cst.com | CST EuMW 2010 Presentations| September 2010 | 3

 Thermal Simulation

 Mechanical Stress Simulation

CST MPHYSICS STUDIOTM

Courtesy of Spinner GmbH, Germany

• www.cst.com | CST EuMW 2010 Presentations| September 2010 | 4

Online Demo

• www.cst.com | CST EuMW 2010 Presentations| September 2010 | 5

Example : 2-Post Bandpass Filter

Rel Bandwidth:0.9 %

• www.cst.com | CST EuMW 2010 Presentations| September 2010 | 6

1) EM (FD tet)

• www.cst.com | CST EuMW 2010 Presentations| September 2010 | 7

1D Results > |S| dB

Tchebychev Filter

===================

Order = 2

Bandwidth = 5 MHz

Center Frequency = 570 MHz

Passband ripple = 0,01 dB (1,100747 VSWR)

Return loss = -26,3828 dB

Normed g values:

-------------------------------------------

g1 = 0,4489

g2 = 0,4078

g3 = 1,1008

Corresponding coupling coefficients in MHz / (rel):

-------------------------------------------

k_E = 11,14 (0,0195413)

k1_2 = 11,69 (0,0205021)

k_out = 11,14 (0,0195413)

Group Delay Time

----------------

t_d1 = 57,153 ns

t_d2 = 51,922 ns

t_d3 = 0, ns

• www.cst.com | CST EuMW 2010 Presentations| September 2010 | 8

Power Loss Dens. > loss (f=0.575)

• www.cst.com | CST EuMW 2010 Presentations| September 2010 | 9

Power Loss Dens. > loss (f=0.575)

• www.cst.com | CST EuMW 2010 Presentations| September 2010 | 10

Current Density (f=0.575)

• www.cst.com | CST EuMW 2010 Presentations| September 2010 | 11

Export the Thermal losses

• www.cst.com | CST EuMW 2010 Presentations| September 2010 | 12

2) Thermal Solver

Import the losses from EM FD

5000

• www.cst.com | CST EuMW 2010 Presentations| September 2010 | 13

Thermal boundaries Thermal volume losses as sourceThermal boundaries

Temperature Heat flow

• www.cst.com | CST EuMW 2010 Presentations| September 2010 | 14

3) Mechanical Solver

FxKxBxM 

• www.cst.com | CST EuMW 2010 Presentations| September 2010 | 15

http://www.engineeringtoolbox.com/young-modulus-d_417.html

1 GPa = 1kN/mm2 σ=ε.E

• www.cst.com | CST EuMW 2010 Presentations| September 2010 | 16

• www.cst.com | CST EuMW 2010 Presentations| September 2010 | 17

Displacements > displacement1 Define a displacement eg at a face (xyz) directly at the WG-Port

• www.cst.com | CST EuMW 2010 Presentations| September 2010 | 18

Import a field source (from therm),

and activate it

• www.cst.com | CST EuMW 2010 Presentations| September 2010 | 19

2D/3D Results > Displacement Temperature change as source Mech. Displacements

Von Mises Stress Deformed Mesh

• www.cst.com | CST EuMW 2010 Presentations| September 2010 | 20

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 ;;;.,,1 2

1

xj, yj

xk, yk

k

j

i

kji

z

z

z

NNNz ],,[

zi

[E]: unkowns z

[Q]: Sources

kjinmdxdy x

N

x

N

x

N

x

N k nmy

nm

xy

xnm ,,,;)(,

Example: electrostatic

4) Sensitivity ( Introduction)

• www.cst.com | CST EuMW 2010 Presentations| September 2010 | 21

),(),(),( 1

),( 0

pEpKpE j

pS TT

Introduction to Sensitivity

S-Parameters:

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

E p

K E

p

S j T0

Sensitivity of S-parameter vs. parameter change:

Direct analytical derivation of

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

3D Fieldsolution

Same 3D Fieldsolution

• www.cst.com | CST EuMW 2010 Presentations| September 2010 | 22

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

Introduction to Sensitivity

E p

K E

p

S j T0

• www.cst.com | CST EuMW 2010 Presentations| September 2010 | 23

p p

S SS

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)

Introduction to Sensitivity

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

best fit the S-parameter goals.

∆p … face constraints

p p

S xSpxS

p

.)()(

• www.cst.com | CST EuMW 2010 Presentations| September 2010 | 24

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

Passed yield

#

#

Gaussian

Uniform

• www.cst.com | CST EuMW 2010 Presentations| September 2010 | 25

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

• www.cst.com | CST EuMW 2010 Presentations| September 2010 | 26

Import the displacements

4) Sensitivity (based on mech. Displacements)

• www.cst.com | CST EuMW 2010 Presentations| September 2010 | 27

Setup Sensitivity Analysis

4) Sensitivity

• www.cst.com | CST EuMW 2010 Presentations| September 2010 | 28

Display S-parameter Sensitivity

4) Sensitivity

• www.cst.com | CST EuMW 2010 Presentations| September 2010 | 29

Summary

Integrated workflow with

CST MPHYSICS STUDIO™

Ease-of-use: New solvers within

well known frontend

Accuracy of integrated solution and

solver technology

Wide application range due to tight

integration within CST STUDIO SUITE™

Thermal

Structural Mechanics

EM

• www.cst.com | CST EuMW 2010 Presentations| September 2010 | 30