Optimization of Antenna Pair for Diversity Gain

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DEPARTMENT OF TECHNOLOGY AND BUILT ENVIRONMENT

Optimization of Antenna Pair for Diversity Gain

Irfan Mehmood Yousaf

September 2008

Master’s Thesis in Electronics/Telecommunications

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Optimisation of Antenna pair for diversity gain

Irfan Mehmood Yousaf

September 2008

Master’s Thesis in Electronics and Telecommunications

Department of Technology and Built Environment

Master’s Program in Electronics/Telecommunications

Examiner: Prof. Claes Beckman

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Abstract

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Preface

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Acknowledgements

I would like to thank all the people who have contributed in any way to complete this

thesis work. First of all I would like to thank Thomas Harju for offering me this

thesis. It was him who had full confidence and belief in me for doing this thesis work.

I would like to thank my examiner Prof. Claes Beckman for accepting the

responsibilities as examiner for this thesis work.

I am very thankful and grateful to my supervisors Göran Nilsson and Daniel

Uppström. The thesis has been completed due to their supervision, guidance and

consistent support. It was a wonderful professional and personal experience to work

with both of them.

I would also like to thank ASCOM Sweden AB for the financial support, giving me

an opportunity to work in the hardware labs and to provide a professional working

environment for the thesis work.

I am thankful to Kristian Karlsson at SP Technical Research Institute of Sweden for

his support and help for the problems faced in MPA [2]. He has been very patient and

helpful in answering my queries related to MPA

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Index

Abstract………..I

Preface………..II

Acknowledgements……….III

List of Figures……….VI

List of Tables………....VIII

List of Abbreviations………...X

1 Introduction ... 1

2 Theoretical background ... 3

2.1 Fading ... 3

2.2 Diversity ... 4

2.2.1 Space diversity ... 4

2.2.2 Polarization diversity... 4

2.2.3 Frequency diversity ... 4

2.2.4 Time diversity ... 4

2.2.5 Diversity gain ... 5

2.3 Correlation Coefficient ... 6

2.4 Dipoles ... 6

2.5 PIFA ... 7

2.6 DECT ... 8

3 Validation of MPA ... 9

3.1 Agilent EMDS ... 9

3.2 CircSim... 9

3.3 MPA ... 9

3.4 Single half wave length dipole ... 9

3.5 The dipoles ... 11

4 Simulations ... 15

4.1 Simulation models in EMDS ... 15

4.1.1 PCB ... 15

4.1.2 Shields ... 16

4.1.3 LCD ... 17

4.1.4 Speakers ... 17

4.1.5 Casing ... 18

4.2 Simulation results ... 19

4.2.1 PCB ... 19

4.2.2 Casing ... 19

4.3 MPA Results ... 20

4.4 Networks and Optimisation ... 21

4.4.1 Three reactances ... 21

4.4.2 Shunt inductors at each port ... 22

4.4.3 Shunt inductors at each port and a resistor between the ports ... 22

4.4.4 Inductor and a capacitor in series between the ports ... 22

4.4.5 λ/4 transmission line between the ports ... 23

5 Measurements... 25

5.1 Reverberation Chamber... 25

5.2 Measurements... 25

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5.2.2 Transmission line on PCB ... 26

5.2.3 Inductor and a Capacitor on PCB ... 27

5.2.4 PCB with inductors ... 27

6 Results and Conclusions... 28

7 Future Work ... 30

References………...31

Appendix A: Simulation models and results……….…...32

Appendix B: Measurement results………...43

Appendix C: Optimisation of PCB………...45

Appendix D: Optimisation of Casing………..……….54

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List of Figures

Figure 2.1 A typical Rayleigh fading envelope at 900 MHz ... 3

Figure 2.2 A typical diversity measurement results performed in the reverberation

chamber ... 5

Figure 2.3 Simulation structure of two parallel half wave length dipoles at 900 MHz 7

Figure 2.4 Inverted F-antenna ... 7

Figure 2.5 DECT parameters ... 8

Figure 3.1 Simulation structure of single half wave length dipole at 900 MHz ... 10

Figure 3.2 Return loss of single half wave length dipole at 900 MHz ... 10

Figure 3.3 Simulation structure of two parallel half wave length dipoles at 900 MHz

... 11

Figure 3.4 S-parameters of two parallel half wave length dipoles at 900 MHz ... 12

Figure 3.5 S-parameters of two parallel half wave length dipoles with 0.2 λ distance

between them at 900 MHz ... 13

Figure 4.1 3-D view of the simulation model in EMDS ... 15

Figure 4.2 Angle view of structure PCB ... 16

Figure 4.3 Angle view of structure Shields ... 16

Figure 4.4 Angle view of structure LCD... 17

Figure 4.5 Angle view of structure Speakers ... 18

Figure 4.6 Angle view of structure Casing ... 18

Figure 4.7 S-parameters of structure PCB ... 19

Figure 4.8 S-parameters of structure Casing including losses ... 20

Figure 4.9 Three resistors network in CircSim ... 21

Figure 4.10 Shunt inductors network in CircSim ... 22

Figure 4.11 Two shunt inductors and a resistor in CircSim ... 22

Figure 4.12 Inductor and a capacitor network in CircSim ... 22

Figure 4.13 Inductor and a capacitor including transmission line network in CircSim

... 23

Figure 4.14 λ/4 transmission line between the antenna ports in CircSim ... 23

Figure 5.1 Measurement results for diversity gain without shunt inductors on structure

PCB ... 26

Figure 5.2 Measurement results for diversity gain with transmission line on structure

PCB ... 26

Figure 5.3 Measurement results for diversity gain with inductor and a capacitor in

series on structure PCB ... 27

Figure 5.4 Measurement results for diversity gain with shunt inductors on structure

PCB ... 27

Figures from Appendix A:

Figure A. 1 Top view of simulation model PCB... 32

Figure A. 2Side view of simulation model PCB ... 32

Figure A. 3 Top view of simulation model shields ... 33

Figure A. 4 Side view of simulation model shields ... 33

Figure A. 5 Angle view of simulation model shields ... 34

Figure A. 6 S-parameters of simulation model shields ... 34

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Figure A. 8 Side view of simulation model LCD ... 35

Figure A. 9 Angle view of simulation model LCD ... 36

Figure A. 10 S-parameters of simulation model LCD ... 36

Figure A. 11 Top view of simulation model speakers ... 37

Figure A. 12 Side view of simulation model speakers ... 37

Figure A. 13 Angle view of simulation model speakers ... 38

Figure A. 14 S-parameters of simulation model speakers ... 38

Figure A. 15 Top view of simulation model casing ... 39

Figure A. 16 Side view of simulation model casing ... 39

Figure A. 17 Angle view of simulation model casing... 40

Figure A. 18 S-parameters of simulation model casing ... 40

Figure A. 19 Top view of simulation model casing losses ... 41

Figure A. 20 Side view of simulation model casing losses ... 41

Figure A. 21 Front view of simulation model casing losses ... 42

Figures from Appendix B:

Figure B. 1 Measurement results for diversity gain without shunt inductors on

structure Casing ... 43

Figure B. 2 Measurement results for diversity gain with shunt inductors on structure

Casing ... 43

Figure B. 3 Measurement results for diversity gain with transmission line on structure

Casing ... 44

Figures from Appendix E:

Figure E. 1 Drawing of structure in Agilent EMDS ... 61

Figure E. 2 Assignment of material in Agilent EMDS ... 61

Figure E. 3 Definition of radiation boundaries in Agilent EMDS ... 62

Figure E. 4 Definition of voltage sources in Agilent EMDS ... 62

Figure E. 5 Set up of simulation in Agilent EMDS ... 63

Figure E. 6 Frequency set up in Agilent EMDS ... 63

Figure E. 7 Post processing in Agilent EMDS ... 64

Figure E. 8 Antenna parameters in Agilent EMDS ... 64

Figure E. 9 Import of s-parameters in CircSim ... 65

Figure E. 10 Conversion of s-parameters to z-parameters ... 65

Figure E. 11 Antenna ports in CircSim ... 66

Figure E. 12 Computation of parameters in CircSim ... 66

Figure E. 13 Interface of MPA with Agilent EMDS ... 67

Figure E. 14 An example of radiation intensity .txt file ... 67

Figure E. 15 Array computations in MPA ... 68

Figure E. 16 Multi port computations in MPA ... 68

Figure E. 17 Radiation efficiency calculations in MPA... 69

Figure E. 18 Correlation calculations in MPA ... 69

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List of Tables

Table 3.1Comparison of S11 and power radiated between EMDS and MPA for single

dipole at 900 MHz ... 11

Table 3.2 Comparison of S11 and power radiated between EMDS and MPA for two

parallel dipoles at 900 MHz ... 12

Table 3.3 Comparison of S12 between EMDS and MPA with 0.5λ and 0.2λ distance

between two parallel dipoles at 900 MHz ... 13

Table 3.4 MPA results for different antenna parameters for 0.5λ and 0.2λ distance

between two parallel dipoles at 900 MHz ... 13

Table 3.5 Different networks between the two antenna ports optimised for low

correlation and high antenna efficiency ... 14

Table 4.1 Summary of s-parameters for EMDS simulations ... 20

Table 4.2 Correlation, diversity gain and port efficiencies from MPA for simulations

in EMDS ... 20

Table 4.3 Comparison of antenna parameters of structure PCB and Casing with and

without shunt inductors ... 21

Table 4.4 Optimised results for three resistors case for structure PCB and Casing ... 22

Table 4.5 Optimisation results for various different networks for structure PCB ... 23

Table 4.6 Component values after optimisation various different networks for

structure PCB ... 24

Table 4.7 Optimisation results for various different networks for structure Casing .. 24

Table 4.8 Component values after optimisation various different networks for

structure Casing ... 24

Table 6.1 Comparison of simulation and measurement results for optimised networks

... 28

Table 6.2 Comparison of measurements for hardware with and without shunt

inductors ... 28

Tables from Appendix C:

Table C. 1 Optimisation 1 for 3 resistors case for structure PCB ... 45

Table C. 2 Optimisation 2 for 3 resistors case for structure PCB ... 45

Table C. 3 Optimisation 3 for 3 resistors case for structure PCB ... 46

Table C. 4 Optimisation 4 for 3 resistors case for structure PCB ... 46

Table C. 5 Optimisation 5 for 3 resistors case for structure PCB ... 46

Table C. 6 Optimisation 1 for two inductors case for structure PCB... 47

Table C. 7 Optimisation 2 for two inductors case for structure PCB... 47

Table C. 8 Optimisation 3 for two inductors case for structure PCB... 47

Table C. 9 Optimisation 4 for two inductors case for structure PCB... 48

Table C. 10 Optimisation 5 for two inductors case for structure PCB ... 48

Table C. 11 Optimisation 6 for two inductors case for structure PCB ... 48

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Table C. 16 Optimisation 2 for inductor and a capacitor case for structure PCB ... 50

Table C. 17 Optimisation 3 for inductor and a capacitor case for structure PCB ... 50

Table C. 18 Optimisation 4 for inductor and a capacitor case for structure PCB ... 51

Table C. 19 Optimisation 5 for inductor and a capacitor case for structure PCB ... 51

Table C. 20 Optimisation 6 for inductor and a capacitor case for structure PCB ... 51

Table C. 21 Optimisation 1 for λ/4 line case for structure PCB ... 52

Table C. 22 Optimisation 2 for λ/4 line case for structure PCB ... 52

Table C. 23 Optimisation 3 for λ/4 line case for structure PCB ... 52

Table C. 24 Optimisation 4 for λ/4 line case for structure PCB ... 53

Table C. 25 Optimisation 5 for λ/4 line case for structure PCB ... 53

Tables from Appendix D:

Table D. 1 Optimisation 1 for 3 resistors case for structure Casing ... 54

Table D. 2 Optimisation 2 for 3 resistors case for structure Casing ... 54

Table D. 3 Optimisation 3 for 3 resistors case for structure Casing ... 55

Table D. 4 Optimisation 4 for 3 resistors case for structure Casing ... 55

Table D. 5 Optimisation 1 for two inductors case for structure Casing ... 55

Table D. 6 Optimisation 1 for two inductors and a resistor case for structure Casing 56

Table D. 7 Optimisation 1 for two inductors and a resistor case for structure Casing 56

Table D. 8 Optimisation 1 for inductor and a capacitor case for structure Casing ... 57

Table D. 9 Optimisation 2 for inductor and a capacitor case for structure Casing ... 57

Table D. 10 Optimisation 3 for inductor and a capacitor case for structure Casing ... 57

Table D. 11 Optimisation 4 for inductor and a capacitor case for structure Casing ... 58

Table D. 12 Optimisation 5 for inductor and a capacitor case for structure Casing ... 58

Table D. 13 Optimisation 1 for λ/4 line case for structure Casing ... 59

Table D. 14 Optimisation 2 for λ/4 line case for structure Casing ... 59

Table D. 15 Optimisation 3 for λ/4 line case for structure Casing ... 59

Table D. 16 Optimisation 4 for λ/4 line case for structure Casing ... 60

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List of Abbreviations

CDF : Cumulative Distribution Function

DECT : Digital Enhanced Cordless Telecommunications

EMC : Electro Magnetic Compatibility

LOS : Line of Sight

MIMO : Multi input multi output

MPA : Multi port Antenna evaluator

PIFA : Planar inverted F antenna

TDD : Time Division Duplex

TDMA : Time Division Multiple Access

TRP

: Total Radiated Power

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1 Introduction

This thesis aims at the optimisation of antenna pair for diversity gain. For this purpose

a case of receiver antenna diversity was developed by a pair of orthogonal PIFA

antennas.

As mentioned in the abstract we want to optimize the antenna pair for high diversity

gain. The problem is that antennas are designed for certain specifications but when

these antennas are integrated in the system for example in a mobile hand set they do

not have the same characteristics for which they were designed due to the other

components and objects surrounding the antennas. For example in a mobile handset

there are different objects in the surroundings of the antennas like different speakers,

LCD and the casing or the body of the handset which can degrade the antenna

performance or create a shift in the resonance frequency. Also there are now multiple

antennas in the handset for different standards such as Bluetooth and wireless in very

close proximity of the main antennas which cause interference and coupling between

the antennas. Because of high coupling the diversity is decreased. To overcome these

problems one way is to simulate the whole system and try to adjust the antennas so

that interference and coupling is minimized. These 3-D simulations are very time

taking. A much faster and easier solution would be to find a network which is

connected between the antenna ports to reduce coupling and increase isolation. This

thesis simulates a system, tests different networks between the antenna ports,

optimizes those networks to achieve higher diversity gain and antenna efficiencies

and finally implement those networks and measure the hardware to compare with the

results of simulations.

The first part of the report deals with the objectives and introduction of the thesis.

Chapter 2 explains the basic theoretical concepts and background related with the

thesis. It explains how fading and multi path environment affects the communication.

There are different types of fading. Diversity is one of the solutions in practice to

overcome these challenges. There are further different types of diversity techniques

that can be implemented. There is a brief introduction of the different type of antennas

used in this thesis work.

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The next chapter starts with introduction of DECT phones. It provides the simulation

details of the structures. The s-parameter results from the simulations are also given.

The use of MPA for calculating correlation coefficients, diversity gains and radiation

efficiencies is described. Five different networks were used in between the two ports.

The results due to these networks are given. These networks are then optimised for

different goals such as maximum efficiency or minimum correlation or combination

of both.

The next chapter give details about the reverberation chamber, hardware built based

on the results from the previous chapter and the result from the measurements

performed in reverberation chamber at Bluetest AB.

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2 Theoretical background

Due to fast advancements made in the field of telecommunications and increasing

requirements of consumer market to have more communication possibilities with

higher data rates antenna designing is becoming difficult and challenging. At the same

time the tendency of electronics getting smaller in size it becomes much more

difficult to fit in multiple antennas on the same device with out interference and

mutual coupling. There are other factors such as fading and multi path propagation

which put constraints and limits on capacity and signal to noise ratio in a typical

environment.

2.1 Fading

The propagation of radio waves in a changing environment can affect the overall

performance of the system badly. There are three generalised wave propagation

mechanisms known as reflection, diffraction and scattering. In mobile environments

most of the time line of sight (LOS) is not available. The signal radiated from the

source can take different paths while reaching the receiver. These multiple signals

reaching the receiver can have different amplitude and phase as compared to the sum

due to fading and shadowing. As the receiver travels away from the source the signal

strength decreases. This is known as large scale fading. If there are very fast

variations in the signal over a very short time or small distances then it is called small

scale fading. Figure 2.1 shows a Rayleigh distributed signal envelope as a function of

time [5].

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2.2 Diversity

There are three techniques which can be used independently or at the same time to

enhance and improve the received signal strength over a short time or small distances.

Diversity, equalization and channel coding [5].

Diversity utilizes the random nature of propagating waves because all of them have

independent paths. Diversity can be defined as if one of the radio paths is deeply

faded and the antenna receives a very weak signal the other antenna at the same time

may have a received very strong signal. Small scale fading can be overcome by

selecting the best signal of the two antennas. There are four types of diversity.

2.2.1 Space diversity

Space diversity is also known as antenna diversity. In this type of diversity different

antennas are present on the receiver or transmitter with a number of wavelengths

distance between them. The antennas should have large distance between them so that

there is decorrelation between them. There are four combining techniques used for

this kind of diversity. In this thesis selection combining is used. In this technique the

receiver at the start of each burst analyses the signal strength at both antennas and

selects the one with the stronger signal. The antenna selected is used for uplink and

downlink for the burst. Before sending the next burst it again evaluates the signal

strength at both antennas.

2.2.2 Polarization diversity

In this type of diversity the signal is transmitted using different polarizations. It has

been seen that when the path is obstructed, polarization diversity dramatically reduces

the multipath delay spread keeping the received power high. Different polarizations

normally used are vertical, horizontal and circular. We can receive decorrelated

signals at the receiver caused by multiple reflections in the channel between the

transmitter and the receiver [6] and [7].

2.2.3 Frequency diversity

Frequency diversity is implemented by sending the same information on more than

one carrier frequency. So that if one frequency channel undergoes some kind of

fading we can use the other frequency having the same information. It should be taken

care of the fact that the frequencies should be separated by more than the coherence

bandwidth of the channel.

2.2.4 Time diversity

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2.2.5 Diversity gain

In the previous section different diversity techniques have been discussed. We get a

gain by combining the received signal which has travelled different paths. We can

increase the performance using diversity. In a diversity system the most important

parameter is the diversity gain.

Different diversity schemes have been explained above. Using these diversity

schemes the performance of the system can be improved. Diversity gain can be

defined as the difference between a combined CDF (cumulative distribution function)

as compared to a reference CDF at a certain level of CDF [9]. This level of CDF is

normally considered to be 1%. There are two important definitions related to diversity

gain depending on different references of CDF. If the reference CDF is the strongest

average signal level of the two antennas then it is apparent diversity gain. If the

reference CDF is of an ideal single antenna it is Effective diversity gain. In this thesis

diversity gain is referred to apparent diversity gain. Figure 2.2 shows a typical graph

for the diversity measurements done in reverberation chamber.

Figure 2.2 A typical diversity measurement results performed in the reverberation chamber

Mathematically apparent diversity gain can be expressed as:

P

G

branch div div

=

There is another approximate approach to obtain diversity gain. The relation between

diversity gain and correlation coefficient can be also approximately given by the

following approximate formula [10]:

Effective Diveristy gain

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p app

e

G

=

10 .

with

e

_p

=

1 −

ρ

2

Where

e

_p

is correlation efficiency and

ρ is correlation coefficient. In the expression

P

div

is the power level after diversity and P

branch

is the power level of the reference

branch. Following is the expression for effective diversity gain

(

)

branch radeff branch div div

e

P

G

=

Where (e

radeff

)

branch

is the radiation efficiency of the reference branch. In this thesis the

reference CDF level is 1%. The maximum effective diversity gain theoretically is

approximately 10 dB at 1% probability level using selection combining [11].

2.3 Correlation Coefficient

The signals received in a diversity system can be correlated to some extent.

Correlation coefficient can be calculated from scattered parameters or radiation

patterns. As the antennas are not uncorrelated therefore different kind of networks are

added between them to minimize the correlation. For two ports it can be calculated as

normalised coupling between the corresponding embedded element radiation patterns

[12]. Mathematically:

∫∫

Ω

=

π π π

ρ

4 4 2 2 1 1 4 2 1

*

d

G

total total total total total total

The relationship of the correlation coefficient is that the lower the correlation

coefficient the higher will be the diversity gain. In this thesis one of the major

objectives was to have it as low as possible. Different networks were optimised to

achieve low correlation coefficient.

2.4 Dipoles

The dipole is a basic antenna that is theoretically easy to understand. Therefore for the

validation purposes of MPA two cases of dipole antennas were used. The first case

included a single dipole antenna and in the second case two parallel dipole antennas

were used. The dipole antenna is a basic wired structure with a certain radius. The

antenna is normally fed with a source at the gap at the centre of the antenna. The total

length of the antenna is λ/2. Each antenna element is of quarter wavelength. Figure

2.3 shows the structure from EMDS used for the simulation.

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Figure 2.3 Simulation structure of two parallel half wave length dipoles at 900 MHz

2.5 PIFA

PIFA stands for planar inverted F antenna. The antenna structure is of the shape of

rotated alphabet F. The antennas normally used in mobile terminals are IFA because

of their compact size. Due to narrow bandwidth of the IFA antennas a modification is

made by connecting to a ground plane rather than wire at the shorter leg of the

antenna so basically PIFA are modification of IFA. The other leg is used for the

feeding of the antenna. This antenna can be treated as a small loop inductor

[13].Figure 2.4 describes the structure.

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2.6 DECT

In 1992 a standard for telecommunication was defined in Europe known as DECT. It

stands for Digital Enhanced Cordless Telecommunications. DECT is a cordless

technology used in Europe without requiring a licence. Other countries like USA have

slightly different standards.

In Europe DECT is assigned a frequency band of 1880-1900 MHz. DECT uses

TDMA (Time Division Multiple Access) in combination with TDD (Time Division

Duplex) meaning that communication is done on the same carrier. With in this 20

MHz of bandwidth DECT has 10 channels and each channel is further divided into 24

slots. Out of these 24 slots 12 are used to transmit and 12 to receive. It can be

concluded that each channel can carry 12 calls simultaneously and due to TDD same

frequency is used for transmission and reception. Figure 2.5 summarizes the details of

the DECT standard [14].

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3 Validation of MPA

There are programs that have been used in this thesis work.

Agilent EMDS

CircSim

Mutli Port Antenna evaluator (MPA)

The description and details of each of the softwares is given below.

3.1 Agilent EMDS

Agilent EMDS version 2006C was used as full wave simulator for generating 3-D

simulations of the dipole and DECT phone structures [4]. There are certain steps that

are to be followed to simulate a structure. These steps can be found in Appendix E.

3.2 CircSim

CircSim is a Circuit Simulator Program based on modified nodal analysis developed

by Professor Jan Carlsson in house at Chalmers, Sweden. The setup details for

CircSim are in Appendix E.

3.3 MPA

MPA stands for Multi-Port Antenna evaluator developed by Kristian Karlsson within

the CHASE project at SP Technical Research Institute of Sweden [3]. MPA is still

under development and has not been evaluated completely. Final version of MPA is

expected at the end of the CHASE project. MPA can analyse and evaluate multi port

antenna systems very efficiently and in very less time when used in combination with

circuit simulator and a full wave simulator. MPA is based on the concept that once a

full wave simulation is performed. It imports the resulting s-parameters and the

embedded element pattern. From the port currents calculated in the circuit simulator

and by weighing the previous embedded element pattern it can generate the far field

radiation pattern. It is based on this principle that we can have any feeding networks

and can instantly observe the results without generating the time consuming full wave

simulations. MPA is compatible with five full wave simulators. WSAP, CST, EMDS,

IE3D and Microstripes. The steup details of MPA are in Appendix E.

The validation of MPA can be done with comparing a single dipole and two parallel

dipole parameters from EMDS with MPA results.

3.4 Single half wave length dipole

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f

c

=

λ

=

6 8

10

900

10

3 ×

×

= 0.333 mm

Total length of dipole =

2 λ

= 166.66 mm

Length of each antenna element =

4 λ

= 83.33 mm

Figure 3.1 Simulation structure of single half wave length dipole at 900 MHz

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The calculations were also performed in MPA for comparison purposes. In Agilent

EMDS 1W by default enters each port. The comparison of results is summarized in

the following table.

Parameters

EMDS

MPA

S11

-21 dB

-21.93 dB

Power radiated (watts)

0.988

0.975

Table 3.1Comparison of S11 and power radiated between EMDS and MPA for single dipole at 900 MHz

3.5 The dipoles

Two parallel half wave length dipoles were designed at resonance frequency of 900

MHz. The distance between the dipoles was kept to be half wave length. The radius of

each dipole was kept 2 mm. The gap between the elements of each dipole was 2 mm.

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Figure 3.4 S-parameters of two parallel half wave length dipoles at 900 MHz

The calculations were also performed in MPA for comparison purposes. For

comparison purposes two special cases were also tested and compared. Source for

port 2 was made zero and shorted. Results from EMDS and MPA were compared.

Parameters

EMDS

MPA

S11

-21.5 dB

-20.96 dB

Power radiated (watts)

0.997

0.992

0.989

0.979 Source 2 = 0

0.994

0.999 Source 2 Short

0.996

0.989

Table 3.2 Comparison of S11 and power radiated between EMDS and MPA for two parallel dipoles at 900 MHz

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Figure 3.5 S-parameters of two parallel half wave length dipoles with 0.2 λ distance between them at 900 MHz

The above statement was verified by comparing S12 of the simulation of distance

between 0.5 λ and 0.2 λ.

EMDS

Distance between dipoles

0.5 λ

0.2 λ

S12

-14.88

-7.04

Table 3.3 Comparison of S12 between EMDS and MPA with 0.5λ and 0.2λ distance between two parallel dipoles at 900 MHz

The calculations for different antenna parameters were performed in MPA

Parameters

MPA

Distance between dipoles

0.5 λ

0.2 λ

Correlation

0.356

0.89 Apparent diversity gain

9.71 dB

6.74 dB

Effective diversity gain

9.68 dB

6.65 dB

Table 3.4 MPA results for different antenna parameters for 0.5λ and 0.2λ distance between two parallel dipoles at 900 MHz

It can be seen that from the above results that the mutual coupling is increased as the

distance between the dipoles is decreased. Due to high mutual coupling the

correlation has also increased consequently decreasing the apparent and effective

diversity gains.

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For learning purpose there were few random networks selected to be optimised in

MPA. There were four different networks that were designed for optimisation in

MPA.

i.

Shunt inductor at port 1

ii.

Shunt inductor at port 1 and port 2

iii.

A resistor and inductor in parallel with a resistor and capacitor in parallel

with the two ports.

iv.

An inductor and capacitor in parallel with the two ports.

Components

Correlation

dB

Apparent

Diversity gain

dB

Optimized

Correlation

dB

Apparent

Diversity gain

dB

Shunt inductor

at port 1

0.763

8.15

0.695

8.6 Shunt inductor

at port 1 and

port 2

0.22

9.88

0.097

9.98 R+L//R+C//Port

1 and 2

0.9

6.5

0.89

6.73 L+C//Port 1 and

2

0.891

6.72

0.825

7.6

Table 3.5 Different networks between the two antenna ports optimised for low correlation and high antenna efficiency

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4 Simulations

4.1 Simulation models in EMDS

The dimensions of the DECT phone were measured from the PCB layout design. The

dimensions of the components surrounding the PCB were measured. It is important to

mention here that the structures have been very simplified to save simulation time.

The structure consisted of the following parts

PCB with the orthogonal PIFA antennas

Shields

Speakers

LCD

Casing

Figure 4.1 3-D view of the simulation model in EMDS

4.1.1 PCB

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This structure is referred as ‘

PCB’

in the rest of the report

Figure 4.2 Angle view of structure PCB

4.1.2 Shields

There are two metal boxes on the PCB for shielding purposes. The dimensions of the

shields are for the lager shield length = 25 mm,

width = 18.5 mm and height = 3 mm.

For smaller shield length = 25 mm, width = 18.5 mm and height = 3 mm.

In the following figures the blue boxes are the two shields on the PCB.

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4.1.3 LCD

At the front of the phone there is a large LCD fro display purpose. The LCD was

modelled as solid metal. The dimensions of the LCD are length = 46.5 mm, width =

36 mm and height = 3 mm.

Figure 4.4 Angle view of structure LCD

4.1.4 Speakers

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Figure 4.5 Angle view of structure Speakers

4.1.5 Casing

The casing of the phone consisted of plastic material and was modelled in a

rectangular shaped surrounding all the above mentioned structures. This structure is

referred as

‘Casing’

in the rest of the report. The dimensions of the casing are length

= 132.5 mm, width = 50.9 mm, height = 24 mm and thickness = 5 mm where as

relative permittivity Er=2.35.

(31)

4.2 Simulation results

Simplified models of the above mentioned structures were used because developing

an exact model will make the simulation complex and will increase the simulation

time significantly. Complex simulations will be time consuming and may put memory

and processing constraints. All of the above mentioned structures were simulated one

by one so as it can be observed that how much variations occur in s-parameters due to

addition of each structure.

Simulations were run for frequency range of 1.7 GHz to 2 GHz with a step of 0.5

GHz. The number of iterations performed on each simulation were 15 which are the

maximum possible using the software. The simulation results were refined at the

desired frequency i.e. 1.9 GHz using the software options. The size of the radiation

box surrounding the structure was kept to be 0.25 λ. In all the simulations except the

last one all the materials were considered to be perfect i.e. there are no losses.

4.2.1 PCB

Figure 4.7 S-parameters of structure PCB

4.2.2 Casing

Losses

There were three materials with losses which were included in this simulation.

(32)

Figure 4.8 S-parameters of structure Casing including losses

Following is a table containing the summary of the results of all the above

simulations.

Setup

S11 (dB)

S22 (dB)

S12=S21 (dB)

PCB

-16.2

-20

-5.8

Shield

-18.27

-24.4

-5.3

LCD

-26.34

-19.5

-4

Speakers

-17.22

-40.5

-3.1

Casing

-18.77

-30.8

-3.2

Losses

-20

-32.8

-3.5

Table 4.1 Summary of s-parameters for EMDS simulations

4.3 MPA Results

The results from all of the above mentioned simulations were transferred to MPA. In

MPA Total radiation efficiency 50 ohm, correlation and diversity gain was calculated.

Following were the results for the above mentioned two simulations.

MPA

Setup

Corr

Div Gain

Eff. Port1

Eff. Port 2

PCB

0.46

9.49

0.81

0.93 Shield

0.48

9.43

0.83

0.91 LCD

0.55

9.22

0.83

0.73 Speakers

0.86

7.14

0.61

0.70 Casing( loss less)

0.78

8.01

0.66

0.73 Casing

0.77

8.03

0.62

0.69

(33)

Since the models of shield, LCD and speakers were not exact so the first structure i.e.

the PCB and the last structure which includes all the structures and the casing

surrounding them were considered for further investigation. In the original design

there were two shunt inductors each at antenna ports. So in the simulations we added

the 8.2 nH shunt inductors at each port.

The parameters were again calculated after adding the inductors and the results were

compared.

PCB

Corr

Div gain

Eff. 1

Eff. 2

No induc

0.46

9.49

0.81

0.93 Inductors

0.84

7.34

0.91

0.90 Casing

No induc

0.77

8.03

0.62

0.69 Inductors

0.97

4.24

0.68

0.71

Table 4.3 Comparison of antenna parameters of structure PCB and Casing with and without shunt inductors

From the above table we see that addition of shunt inductors decreased the diversity

gain by approximately 2 dB in the PCB case and approximately 4 dB in case of

casing. Also we see that the antenna efficiency of at least one of the antenna

increases by approximately 10% in case of PCB as well as casing.

4.4 Networks and Optimisation

After the simulations and the results obtained from MPA for these simulations

different kind of networks were tested

to have better diversity gain and antenna

efficiencies. The networks further used did not include the shunt inductors.

4.4.1 Three reactances

For experimentation purposes to optimise the parameters a network was implemented.

The network consisted of 3 resistors having 0 real part and imaginary part only. R3

and R4 are shunt resistors where as R5 is a resistor between the 2 ports.

(34)

Correlation

Div gain

Eff. 1

Eff. 2

PCB

0.4

9.61

0.82

0.94 Casing

0.008

9.99

0.45

0.50

Table 4.4 Optimised results for three resistors case for structure PCB and Casing

As the practical implementation issues were not considered therefore some of the

values are not practically possible. Following were the values after optimisation

n

For PCB

n

R3 = -449.1j, R4 = -537.2j, R5 = 1138j

n

For casing

n

R3 = -813.7j, R4 = -69.9j, R5 = -255.4j

There were four other configurations optimised for better diversity gain and antenna

efficiency.

4.4.2 Shunt inductors at each port

Figure 4.10 Shunt inductors network in CircSim

4.4.3 Shunt inductors at each port and a resistor between the

ports

Figure 4.11 Two shunt inductors and a resistor in CircSim

4.4.4 Inductor and a capacitor in series between the ports

(35)

To connect the inductor and capacitor between the ports on the board it was seen that

on the PCB it was convenient to use already present transmission line on the board at

one of the ports therefore its affect was also added in the simulation.

Figure 4.13 Inductor and a capacitor including transmission line network in CircSim

4.4.5 λ/4 transmission line between the ports

Figure 4.14 λ/4 transmission line between the antenna ports in CircSim

The last column of the table represents the value of diversity gain in dB added to the

value of antenna with lower efficiency in dB. The optimisation was performed to

achieve a maximum of overall efficiency.

Following is a table of results performed for the optimisation of the PCB.

Configuration

Corr

Div

Eff1

Eff2

Net

Original with

inductors

0.84

7.34 -0.4

-0.45

6.89 3 reactances

0.4

9.61 -0.86

-0.26

8.74 Two inductors

0.15

9.94 -1.19

-0.36

8.75 2 shunt inductors

and resistor

0.09

9.97 -0.91

-0.04

9.06 Ind and cap inseries

0.44

9.54 -0.96

-0.36

8.58 λ/4 line

0.05

9.99 -0.08

-0.75

9.23

Table 4.5 Optimisation results for various different networks for structure PCB

(36)

Configuration

Values

Net

Original with inductors

L1 and L2 = 8.2 nH

6.89 3 reactances

R3=-449.1j,R4=-537.2j,

R5 = 1138j

8.74 Two inductors

R3=-205.7j and R4=-180.3j

8.75 Two shunt inductors and

resistor

R3=-394j,R4=-101j

R5 = -473-153j

9.06 Ind and cap in series

L1=55.9pH C1= 0.02pF

8.58 λ/4 line

50 ohms, 0.0289m

9.23

Table 4.6 Component values after optimisation various different networks for structure PCB

Following is a table of results performed for the optimisation of the casing.

Configuration

Corr

Div

Eff1

Eff2

Net

Original with

inductors

0.97

4.24 -1.67

-1.48

2.75 3 reactances

0.008

9.99 -3.46

-3

6.99 Two inductors

0.78

8 -2.07

-1.61

5.93 2 shunt inductors

and resistor

0.65

8.81 -2.83

-2.29

5.98 Ind and cap inseries

0.7

8.53 -2.29

-1.8

6.24 λ/4 line

0.53

9.27 -1.13

-1.36

7.91

Table 4.7 Optimisation results for various different networks for structure Casing

Following were the values after optimisation.

Configuration

Values

Net

Original with inductors

L1 and L2 = 8.2 nH

2.75 3 reactances

R3 = -813.7j, R4 = -69.9j

R5 = -255.4j

6.99 Two inductors

L1=1E-6 and R4=-1E-6

5.93 Two shunt inductors and

resistor

L1= 9.4E-7, L2 = 5.9E-7

R3= 380-400j

5.98 Ind and cap in series

L1=0.93pH C1= 0.08pF

6.24 λ/4 line

50 ohms, 0.0316m

7.91

Table 4.8 Component values after optimisation various different networks for structure Casing

(37)

5 Measurements

5.1 Reverberation Chamber

There are different measurement setups that can be used to measure diversity gain

[15]. The measurements for diversity gain and radiation efficiencies were performed

in reverberation chamber at Bluetest AB. Mostly reverberation chambers are used for

EMC (ElectroMagnetic Compatibility) measurements but they can be very effectively

used to measure different parameters on handsets because of the reflections of the

waves inside the chamber which forms a multipath environment as it is in reality. The

reverberation chamber is also known as mode-stirred chamber due to the reason that

the chamber is supposed to stir different resonant modes so that many independent

field distributions are created to have a real multipath environment which after

averaging over different positions creates a uniform distribution of the incoming

waves.

The dimensions of the chamber used were 1m x 1.6m x 1.6m. The chamber has well

shielded metal walls so that there are no external interferences. The stirring of the

resonant modes can be done in four different ways, frequency stirring, mechanical

stirring, platform stirring and polarization stirring [16].

The measurement results for apparent diversity gain at 1% probability and the

radiation efficiencies from the chamber will be measured with the simulation results.

5.2 Measurements

For measurement purposes the DECT phones were connected to a computer through a

cable to the software developed for testing purposes of these DECT phones. It was

needed to manually select each antenna and set the antenna in continuous transmitting

mode. After optimisation it was decided to have 5 prototypes built and measured.

Following were the configurations:

n

No inductors on PCB

n

No inductors with casing

n

Transmission line on PCB

n

Transmisson line on casing

n

Inductor and Capacitor in series on PCB

(38)

5.2.1 No inductors on PCB

Figure 5.1 Measurement results for diversity gain without shunt inductors on structure PCB

5.2.2 Transmission line on PCB

Transmission line impedance = 50 ohms, Transmission line length = 0.022m

Correlation = 0.04, Diversity gain = 9.99, Efficiency antenna 1 = 0.99,

Efficiency antenna 2 = 0.89

(39)

5.2.3 Inductor and a Capacitor on PCB

L = 04.6e-9, C = 8.2e-12, Correlation = 0.66, Diversity gain = 9.99

Efficiency antenna 1 = 0.79, Efficiency antenna 2 = 0.77

Figure 5.3 Measurement results for diversity gain with inductor and a capacitor in series on structure PCB

(40)

6 Results and Conclusions

Following is the table comparing the results from the simulations and measurements

made in the reverberation chamber for the five configurations.

Simulation

Measurements

Corr

Div

TRP1

TRP2

Div

TRP1

TRP2

No inductors

PCB

0.46

9.49

23.08

23.68

5

22.69

24.45 No inductors

Case

0.77

8.03

21.92

22.38

5

19.26

23.01 TL PCB

0.04

9.99

23.95

23.49

5

18.5

17.3 TL casing

0.30

9.79

22.97

4

17.45

21.58 Inductors and

Capacitor

PCB

0.06

9.99

22.97

22.86

5

21.49

18.88

Table 6.1 Comparison of simulation and measurement results for optimised networks

From the table above we see that the diversity gain did not increase in any of the cases

as expected in all of the five configurations. The simplest of the cases which just

required removal of already shunt inductors on the PCB did not make any change in

the diversity gain. It was expected from the simulations results an increase of

approximately 2 dB gain in case of PCB and 4 dB gain in case of casing. The total

radiated powers (TRP in dBm) also do not agree with the simulations. In the case of

transmission lines a significant increase of diversity gain was expected, more than 3

dB in case of PCB and more than 4 dB in case of the Casing. There was no change in

the diversity gain. The TRPs were also expected to be very high around maximum 24

dBm. In contrast of improvement they were decreased. In the last case an inductor

and capacitor was added on the PCB between the ports and was optimised for zero

correlation only. It also did not affect the diversity gain at all.

Inductors

Div

TRP1

TRP2

PCB

5

22.03

22.68 Casing

5

19.31

22.68 No inductors

PCB

5

22.69

24.45 Casing

5

19.26

23.01

Table 6.2 Comparison of measurements for hardware with and without shunt inductors

Since now we had also measured the PCB and the casing without the inductors so we

could also compare the two measurement results. From the simulations we saw that

removal of the inductors gave a great improvement in diversity gain and a very small

decrease in efficiency. But from the measurements of both the configurations we see

that the diversity does not change at all with or without inductors.

(41)

(42)

7 Future Work

This thesis was first of its kind performed under the “CHASE project” because it

included all the steps i.e. from modelling of the structures, simulation, taking the

results into MPA, designing of different networks in CircSim, optimization of the

networks for higher diversity gain and antenna efficiency, implementation of

hardware for the optimized values and finally measuring the hardware in

reverberation chamber. As from the results it was concluded that the objectives of the

thesis were achieved in the simulations but hardware measurements did not agree with

the simulation results.

(43)

References

[1]

Bluetest AB,

http://www.bluetest.se/

[2]

Sveriges Tekniska Forskningsinstitute,

http://www.sp.se/

[3]

K. Karlsson,”MPA-Mutli Port Antenna evaluator,” MPA Manual, SP

Technical Research Institute, Sweden, May 2008.

[4]

Agilent EMDS v.2006C,

http://eesof.tm.agilent.com/products/emds_main.html

[5]

T. S. Rappaport, “

Wireless Communications: Principles and practice

”,

Prentice Hall, 1996.

[6]

C. Beckman and U. Wahlberg, “Antenna systems for polarization diversity,”

Microwave Journal

, May, 1997

[7]

Beckman C., Wahlberg U. and Widell S., “The performance of polarization

diversity antennas at 1800 MHz,” in

IEEE Antennas and Propagation Society

International Symp., 1997.

[8]

M. Schwartz, W. R. Bennett, S. Stein, "Communication System and

Techniques",New York, McGraw-Hill, 1965

[9]

Kent, Rosengren, “Characterization of Terminal Antennas for Diversity and

MIMO Systems by Theory, Simulations and Measurements in Reverberation

Chamber”, Ph.D. thesis 2005.

[10] Kent Rosengren, P-S. Kildal, "Radiation efficiency, correlation, diversity gain

and capacity of a six monopole antenna array for a MIMO system: Theory,

Simulation and Measurement in Reverberation Chamber." Proceedings

IEE,

Microwaves, Optics and Antennas

, pp. 7-16, Vol. 152, No. 1, Feb. 2005.

[11] P-S. Kildal, K. Rosengren, J. Byun and J. Lee, “Definition of effective

diversity gain and how to measure it in a reverberation chamber”,

Microwave

and Optical Technology Letters

, Vol. 34, No. 1, pp. 56-59, July 2002

[12]

P-S. Kildal, Kent Rosengren, "Electromagnetic Analysis of Effective and

Apparent Diversity Gain of Two Parallel Dipoles",

IEEE antennas and

wireless Propagation Letters

, Vol.2. 2003.

[13]

A. T. Gobien, “Investigation of Low Profile Antenna Designs for Use in

Hand-Held Radios”,

MSc. In Electrical Engineering

, Virginia Polytechnic

Institute and State University, Virginia 1997.

[14]

J. D. Gibson,

The mobile communications handbook

, CRC Press and IEEE

Press, 1996.

[15]

C. Beckman

et al

., “Evaluation of antenna diversity performance for mobile

handsets using 3-D measurement data,”

IEEE Trans. Antennas and

Propagation,

vol. 47, issue 11, pp. 1736 – 1738, Nov, 1999

[16]

C. Carlsson, Characterization of mode-stirred chamber and its setups for

antenna measurement, Bluetest, 2001.

[17]

K. Karlsson, J. Carlsson, I. Belov, G. Nilsson and P-S. Kildal, “Optimization

of antenna diversity gain by combining full-wave and circuit simulations”,

EUCap 2007, Edinburgh, UK, Nov. 11-16, 2007

[18]

Laura Canizares Lozano, “Evaluating the effective diversity gain on laptop

antennas”, MSc. thesis, Chalmers University of Technology, 2008

(44)

Appendix A: Simulation models and results

PCB

Figure A. 1 Top view of simulation model PCB

(45)

Shields

Figure A. 3 Top view of simulation model shields

(46)

Figure A. 5 Angle view of simulation model shields

(47)

LCD

Figure A. 7 Top view of simulation model LCD

(48)

Figure A. 9 Angle view of simulation model LCD

(49)

Speakers

Figure A. 11 Top view of simulation model speakers

(50)

Figure A. 13 Angle view of simulation model speakers

(51)

Casing

Figure A. 15 Top view of simulation model casing

(52)

Figure A. 17 Angle view of simulation model casing

(53)

Casing losses

Figure A. 19 Top view of simulation model casing losses

(54)

(55)

Appendix B: Measurement results

No inductors with casing

Figure B. 1 Measurement results for diversity gain without shunt inductors on structure Casing

Casing with inductors

(56)

Transmission line on casing

Transmission line = 50, 0.031, Correlation = 0.30, Diversity gain = 9.79

Efficiency antenna 1 = 0.79, Efficiency antenna 2 = 0.79

(57)

Appendix C: Optimisation of PCB

Three reactances

R3 = -j320, R4 = -j320, R5 = j985

Efficiency (1, 0.6), Correlation (0, 0.6)

Freq TRP RadEff Correlation Imbalance DivGain RadEffPort [MHz] [W] [-] [-] [-] [dB] [-] 1.70E+09 0.65067 0.32543 0.93425 0.92421 5.8002 1 0.49987 2 0.37313 1.75E+09 0.14606 0.07305 0.99756 0.9104 1.9622 1 0.44324 2 0.43247 1.80E+09 0.25924 0.12966 0.98459 0.87956 3.4891 1 0.53 2 0.67996 1.85E+09 0.82304 0.41164 0.8249 0.88344 7.6127 1 0.71329 2 0.91782 1.90E+09 1.3916 0.69603 0.34749 0.94719 9.7265 1 0.81789 2 0.95168 1.95E+09 1.6309 0.81571 0.20786 0.99179 9.906 1 0.76941 2 0.8523 2.00E+09 1.619 0.80973 0.47475 0.99345 9.458 1 0.66319 2 0.72469 Table C. 1 Optimisation 1 for 3 resistors case for structure PCB

R3 = -j432, R4 = -j552, R5 = j1054

Efficiency (1, 0.4), Correlation (0, 0.4)

--- Result file --- Freq TRP RadEff Correlation Imbalance

(58)

R3 = -j438.8, R4 = -j520.8, R5 = j1136

Efficiency (1, 0.2), Correlation (0, 0.2)

DivGain RadEffPort [MHz] [W] [-] [-] [-] [dB] [-] 1.70E+09 0.65696 0.32858 0.89482 0.91771 6.6646 1 0.5006 2 0.37089 1.75E+09 0.1454 0.072722 0.99676 0.89695 2.0945 1 0.44506 2 0.42953 1.80E+09 0.25509 0.12758 0.98862 0.87368 3.1206 1 0.53792 2 0.6786 1.85E+09 0.80625 0.40325 0.85271 0.89207 7.2921 1 0.72508 2 0.9179 1.90E+09 1.3568 0.67861 0.402 0.95919 9.6256 1 0.82483 2 0.9482 1.95E+09 1.5845 0.79251 0.16118 0.99889 9.944 1 0.76683 2 0.84056 2.00E+09 1.5696 0.78505 0.43739 0.99728 9.5491 1 0.65379 2 0.70667 Table C. 3 Optimisation 3 for 3 resistors case for structure PCB

R3 = -j445.8, R4 = -j539.2, R5 = j1142

Efficiency (1, 0.1), Correlation (0, 0.1)

DivGain RadEffPort [MHz] [W] [-] [-] [-] [dB] [-] 1.70E+09 0.6572 0.3287 0.89244 0.91746 6.7062 1 0.5006 2 0.37073 1.75E+09 0.14532 0.072681 0.99669 0.89619 2.1066 1 0.44514 2 0.42934 1.80E+09 0.25481 0.12744 0.9888 0.87332 3.1024 1 0.53836 2 0.67845 1.85E+09 0.80531 0.40278 0.8541 0.89255 7.2745 1 0.72575 2 0.91783 1.90E+09 1.355 0.6777 0.40482 0.95991 9.6198 1 0.82524 2 0.948 1.95E+09 1.5822 0.79134 0.15889 0.99939 9.9456 1 0.76675 2 0.83993 2.00E+09 1.5672 0.78383 0.43554 0.99768 9.5533 1 0.65337 2 0.70569 Table C. 4 Optimisation 4 for 3 resistors case for structure PCB

R3 = -j449.1, R4 = -j537.2, R5 = j1138

Efficiency (1, 0.6), Correlation (0, 0.6)

(59)

Two inductors

R3 = -j3600, R4 = -j600

Efficiency (1, 1), Correlation (0, 1)

DivGain RadEffPort [MHz] [W] [-] [-] [-] [dB] [-] 1.70E+09 0.66974 0.33497 0.91887 0.92335 6.1838 1 0.50333 2 0.37624 1.75E+09 0.15296 0.076504 0.99765 0.88985 1.9463 1 0.43995 2 0.43448 1.80E+09 0.26369 0.13189 0.98608 0.85016 3.3601 1 0.52332 2 0.68431 1.85E+09 0.80563 0.40294 0.8398 0.86389 7.4482 1 0.7056 2 0.91676 1.90E+09 1.3329 0.66667 0.39905 0.94109 9.6315 1 0.80773 2 0.93715 1.95E+09 1.5413 0.7709 0.13762 0.98275 9.9593 1 0.75078 2 0.82937 2.00E+09 1.5176 0.75903 0.39582 0.96967 9.638 1 0.63486 2 0.70283 Table C. 6 Optimisation 1 for two inductors case for structure PCB

R3 = -j3354, R4 = -j560

Efficiency (1, 0.7), Correlation (0, 0.7)

R3 = -j220, R4 = -j170

Efficiency (1, 0.5), Correlation (0, 0.5)

(60)

R3 = -j235, R4 = -j174

Efficiency (1, 0.2), Correlation (0, 0.2)

R3 = -j215, R4 = -j176

Efficiency (1, 0.1), Correlation (0, 0.1)

R3 = -j205.7, R4 = -j180.3

Efficiency (1, 0.05), Correlation (0, 0.05)

(61)

2 shunt inductors and resistor

R3 = -j360, R4 = -j60, R5 = -360-j110

Efficiency (1, 0.6), Correlation (0, 0.6)

DivGain RadEffPort [MHz] [W] [-] [-] [-] [dB] [-] 1.70E+09 0.63528 0.31774 0.74612 0.45244 8.2871 1 0.66405 2 0.40565 1.75E+09 0.20725 0.10365 0.90033 0.38475 6.5644 1 0.49862 2 0.51431 1.80E+09 0.3497 0.1749 0.76478 0.36762 8.1509 1 0.48456 2 0.74123 1.85E+09 0.98772 0.49401 0.21301 0.54394 9.9012 1 0.65353 2 0.90985 1.90E+09 1.633 0.81675 0.27916 0.8132 9.8275 1 0.81513 2 0.92402 1.95E+09 1.9183 0.95946 0.56088 0.9251 9.1995 1 0.80566 2 0.91103 2.00E+09 1.9018 0.95117 0.6893 0.91482 8.639 1 0.70525 2 0.91477 Table C. 12 Optimisation 1 for two inductors and a resistor case for structure PCB

R3 = -j365, R4 = -j84, R5 = -422-j172

Efficiency (1, 0.2), Correlation (0, 0.2)

DivGain RadEffPort [MHz] [W] [-] [-] [-] [dB] [-] 1.70E+09 0.64345 0.32182 0.78962 0.46413 7.9492 1 0.63352 2 0.44162 1.75E+09 0.18421 0.092132 0.93473 0.48864 5.7868 1 0.51254 2 0.54716 1.80E+09 0.32107 0.16058 0.8509 0.50325 7.3149 1 0.52117 2 0.79153 1.85E+09 0.94221 0.47125 0.4077 0.6285 9.6139 1 0.67463 2 0.97177 1.90E+09 1.5651 0.78278 0.13902 0.84243 9.9585 1 0.80611 2 0.96878 1.95E+09 1.8322 0.91639 0.4558 0.93469 9.5056 1 0.78647 2 0.91606 2.00E+09 1.8165 0.9085 0.60667 0.91377 9.0284 1 0.6927 2 0.87377 Table C. 13 Optimisation 2 for two inductors and a resistor case for structure PCB

R3 = -j394, R4 = -j101, R5 = -473-j153

Efficiency (1, 0.05), Correlation (0, 0.05)