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© CADFEM 2015

Optimization of a Dual Band Antenna

using `Statistics on Structures`

Marc Vidal, Sebastian Wolff, Christian Römelsberger

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© CADFEM 2015

Internet of Things and Antennas

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• Number of connected devices

growing rapidly

• ca. 30,000,000,000 devices by 2020!

• Automotive, Households, Industrial,

Consumer, Communications, …

• Wearable and mobile devices

wirelessly connected

© CADFEM 2015

Challenges in Antenna Design

3

• Communication of wireless devices

through various frequency bands

using different technologies and

standards

• NFC

• WLAN

• Bluetooth

• ZigBee

• …

• Wearable and mobile devices should

be small

• Save space by using multiple band

antennas

Source: Wikipedia:

Nicolas Sadoc, Nick Pitsas, CSIRO

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Engineering Task:

Design antenna structure that works at

the given frequency bands and fits into

a given small space!

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HFSS – High Frequency Structure Simulator

• 3D Field Solver

• 3D Finite Element Method (FEM)

• Boundary Integral (IE)

• Mesh Process: Adaptive

• Advanced Boundary Types

• Radiation and Perfectly Matched Layers

• Symmetry, Finite Conductivity, Infinite Planes, RLC, and Layered Impedance

• Advanced Material Types

• Frequency dependent

• Anisotropic

• Post Processing and Report Type

• SYZ parameters

• Field display

• Near Field/Far Field

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Simulation Model – Dual Band Slot Antenna

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• Need to move minima of return loss

to the right frequencies

• Make 5.8GHz minimum deeper

FR4 Substrate

Slot

GND plane

Microstrip feed

on the back side

© CADFEM 2015 7

• Which parameter shall be taken for a manual variation?

Simulation Model – Dual Band Slot Antenna

lf

wf 50Ω

ws

hs

w1

w2

gap1

gap2

dd

dd

gap1 gap2

ws w2 hs w1

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The Optimization Goal

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• Return Loss at 2.4GHz and at 5.8GHz minimal

• Find out after calculating 100 Designs:

• COP not good enough for optimization!

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Use of SoS

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• Better:

• Get signals from DOE and construct an F-MOP (Field Metamodel of Optimal

Prognosis)

• Be able to define optimization goal after DOE!

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Field Meta Model

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• Expand a signal in terms of ‘shape functions’

• ‘Shape functions’ are determined from the DOE of signals in order to capture

the most important characteristics of the signals

• ‘Regular’ MOP for the expansion coefficients z1, z2, z3,…

≈ *z1+ *z2+ *z3+ *z4+… +

Mean value of DOE

at each frequency

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Field Meta Model

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Determine

‘shape functions’

Calculate MOP

for coefficients

Reassemble

signals

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Plan / Workflow

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DOE

(optiSLang) SoS

Optimization

(optiSLang)

Validation

(HFSS)

Signals

F-MOP

for

Signals

Better

Design

•Fully

automated

sampling

•‘Shape

Functions’ for

signals

•F-MOP

•F-CoP

•Decide on

optimization

goal

•Use F-MOP as

raw data

© CADFEM 2015

F-CoP

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• Bad F-CoP for return loss

Due to dB-Scale of

The Return Loss

(Singularity)

Bad explainability due

to little variation and little

correlation in frequency domain

combined with nonlinear effects

Good F-CoP

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F-CoP

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• But Return Loss is expressible in terms of complex S-parameters

• With good F-CoP for the S-parameters

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Reformulation of the Optimization Goal

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• Extract positions and values of the

minima of a given signal

(from F-MOP)

• Optimization Goal:

• Minimize Max(Min24,Min58)

• Constraints:

• Pos24=2.4

• Pos58=5.8

Pos24 Pos58

Min24

Min58

Range 1 Range 2

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Optimization using ARSM on F-MOP

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MOP for

Coefficients zi

Use ‘shape functions’

to generate F-MOP

Extract scalar

quantities as

optimization goals

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Optimization

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• Good agreement between F-MOP and calculated Return Loss

Validation

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Best Design

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Summary

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• Good quality of prognosis for full

signals (e.g. Return Loss) using F-

MOP:

• No new simulations

• Possibility for plausibility checks of

solutions before validation using FE-

analysis

• Discover new possibilities (e.g. third

frequency band)

• CoP for signals over frequency (F-

CoP)

• Explain Relations

• Advantage for the engineer:

• Can define optimization goals after

DOE has been done and signals have

been understood.

• Generate F-MOP once and then look at

behavior of signals under optimization.

• No re-evaluation of DOE

F-CoP

© CADFEM 2015

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