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ISBN 978-952-60-6357-7 (printed) ISBN 978-952-60-6358-4 (pdf) ISSN-L 1799-4934 ISSN 1799-4934 (printed) ISSN 1799-4942 (pdf) Aalto University School of Electrical Engineering Department of Radio Science and Engineering www.aalto.fi

BUSINESS + ECONOMY ART + DESIGN + ARCHITECTURE SCIENCE + TECHNOLOGY CROSSOVER DOCTORAL DISSERTATIONS

Aalto-D

D 12

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015

The rapid increase in the use and capabilities of mobile devices in the beginning of the 21st century pose demanding goals to antenna designers. With the current massive use of wireless data transmission, a broadband operation should be achieved with high efficiency. How can circuit elements be utilized to increase the bandwidth of the antenna? This thesis focuses on finding practical tools to facilitate the co-design of the antenna and the matching circuit.

Anu L

ehtovuori O

n wideband m

atching circuits in handset antenna design A

alto U

nive

rsity

Department of Radio Science and Engineering

On wideband matching circuits in handset antenna design

Anu Lehtovuori

DOCTORAL DISSERTATIONS

Aalto University publication series DOCTORAL DISSERTATIONS 123/2015

On wideband matching circuits in handset antenna design

Anu Lehtovuori

A doctoral dissertation completed for the degree of Doctor of Science (Technology) to be defended, with the permission of the Aalto University School of Electrical Engineering, at a public examination held at the lecture hall S1 of the school on 2 October 2015 at 12.

Aalto University School of Electrical Engineering Department of Radio Science and Engineering

Supervising professors Prof. Martti Valtonen, until August 31, 2013 Prof. Keijo Nikoskinen, as of 2014 Thesis advisor D. Sc. (Tech.) Risto Valkonen Preliminary examiners Prof. Juraj Bartolic, University of Zagreb, Croatia D. Sc. (Tech.) Marko Sonkki, University of Oulu, Finland Opponent

Aalto University publication series DOCTORAL DISSERTATIONS 123/2015 © Anu Lehtovuori ISBN 978-952-60-6357-7 (printed) ISBN 978-952-60-6358-4 (pdf) ISSN-L 1799-4934 ISSN 1799-4934 (printed) ISSN 1799-4942 (pdf) http://urn.fi/URN:ISBN:978-952-60-6358-4 Unigrafia Oy Helsinki 2015 Finland

Prof. Max Ammann, Dublin Institute of Technology, Ireland

Abstract Aalto University, P.O. Box 11000, FI-00076 Aalto www.aalto.fi

Author Anu Lehtovuori Name of the doctoral dissertation On wideband matching circuits in handset antenna design Publisher School of Electrical Engineering Unit Department of Radio Science and Engineering

Series Aalto University publication series DOCTORAL DISSERTATIONS 123/2015

Field of research Circuit Theory

Manuscript submitted 21 May 2015 Date of the defence 2 October 2015

Permission to publish granted (date) 22 July 2015 Language English

Monograph Article dissertation (summary + original articles)

Abstract Transferring the growing amount of data calls for wider bandwidths in new wireless

standards. For the mobile antennas, which have to be squeezed to a very limited space, this poses quite a challenge for impedance matching, if efficiency is not to be sacrificed. Earlier, wideband matching was studied as a rather theoretical problem, but this work takes a practical viewpoint to produce readily applicable results. The goal is to utilize circuit elements to improve the performance of handset antennas.

Because the number of matching elements is to minimized in practical designs, this work focuses particularly on three-element matching circuits. The presented efficient procedure for determining the available bandwidth with a certain matching topology, i.e., the bandwidth estimator, enable accounting for the matching circuit from the beginning of the antenna design process. Furthermore, evaluating the potential of different radiating structures becomes feasible.

In mobile systems, the desired frequency band consists of two passbands, and therefore finding methods for dual-band matching is reasonable. This work presents how any two matching circuits designed separately for frequencies f1 and f2 can be converted into a dual-band matching circuit operating both at f1 and f2. In addition, simple design equations for dual-band matching are given.

A dual-band matching can be realized also with two radiating elements. This widens the study to illustrate how bandwidth estimators can be used to design matching circuits for multiple ports. Moreover, it is shown that bandwidth estimator analysis offers a suitable starting point for practical design — the simulations and measurements are in good agreement.

Finally, the work introduces other ways to improve antenna performance with aid of circuit elements and bandwidth estimators.

Keywords impedance matching, mobile antennas, circuits, capacitive coupling element

ISBN (printed) 978-952-60-6357-7 ISBN (pdf) 978-952-60-6358-4

ISSN-L 1799-4934 ISSN (printed) 1799-4934 ISSN (pdf) 1799-4942

Location of publisher Helsinki Location of printing Helsinki Year 2015

Pages 151 urn http://urn.fi/URN:ISBN:978-952-60-6358-4

Tiivistelmä Aalto-yliopisto, PL 11000, 00076 Aalto www.aalto.fi

Tekijä Anu Lehtovuori Väitöskirjan nimi Laajakaistaisten sovituspiirien hyödyntämisestä älypuhelimien antennien suunnittelussa Julkaisija Sähkötekniikan korkeakoulu Yksikkö Radiotieteen ja tekniikan laitos

Sarja Aalto University publication series DOCTORAL DISSERTATIONS 123/2015

Tutkimusala Piiriteoria

Käsikirjoituksen pvm 21.05.2015 Väitöspäivä 02.10.2015

Julkaisuluvan myöntämispäivä 22.07.2015 Kieli Englanti

Monografia Yhdistelmäväitöskirja (yhteenveto-osa + erillisartikkelit)

Tiivistelmä Älypuhelimilla siirrettävän datamäärän kasvu näkyy uusissa standardeissa yhä laajempina

taajuuskaistoina. Pieneen tilaan mahdutettujen antennien impedanssisovittaminen tulee tällöin hyvin haastavaksi, jos hyötysuhteesta ei suostuta tinkimään. Aiemmin laajakaistasovitusta on tutkittu varsin teoreettisista lähtökohdista, mutta tässä pyritään käytännönläheisiin ja helposti sovellettaviin tuloksiin. Tavoitteena on matkapuhelinantennien suorituskyvyn parantaminen.

Tarkastelu keskittyy kolmen elementin sovituspiireihin, koska käytännön ratkaisuissa piirielementtien määrä pyritään pitämään pienenä. Esitetty tehokas menetelmä antennirakenteella saavutettavan kaistanleveyden määrittämiseen (ns. kaistanleveysestimaatti) mahdollistaa sovituspiirin vaikutuksen huomioimisen antennirakenteen suunnittelussa jo alusta alkaen. Myös erilaisten vaihtoehtoisten rakenteiden vertailu helpottuu.

Koska matkapuhelintaajuudet koostuvat kahdesta erillisestä taajuusalueesta, on mielekästä tarkastella myös kaksikaistaista sovittamista. Työssä esitetään, kuinka kaksi eri taajuuskaistoille suunniteltua sovituspiiriä voidaan muuntaa yhdeksi sovituspiiriksi, joka antaa sovituksen molemmilla alkuperäisillä taajuuskaistoilla. Kaksikaistaiseen sovitukseen esitetään myös erilliset mitoituskaavat.

Kaksikaistainen sovitus on mahdollista toteuttaa myös kahdella erillisellä elementillä ja siksi työssä havainnollistetaan, kuinka kaistanleveysestimaatteja voidaan hyödyntää sovituspiirien suunnittelussa moniporttitapauksessa. Samalla osoitetaan, että ideaalisilla piirimalleilla lasketut tulokset soveltuvat hyvin käytännön antennien suunnittelun lähtökohdaksi.

Lopuksi käydään vielä läpi muita mahdollisia tapoja, joilla piirielementtejä sekä kaistanleveysestimaatteja voisi tulevaisuudessa hyödyntää antennien suorituskyvyn parantamisessa.

Avainsanat impedanssisovitus, mobiiliantennit, piirit, kapasitiivinen kytkentäelementti

ISBN (painettu) 978-952-60-6357-7 ISBN (pdf) 978-952-60-6358-4

ISSN-L 1799-4934 ISSN (painettu) 1799-4934 ISSN (pdf) 1799-4942

Julkaisupaikka Helsinki Painopaikka Helsinki Vuosi 2015

Sivumäärä 151 urn http://urn.fi/URN:ISBN:978-952-60-6358-4

Preface

The last three and a half years have been demanding but also very re-

warding. I would like to thank Prof. Keijo Nikoskinen for his support

and for giving his valuable time to see this process to the end. For my

circuit-theoretical background built over the years, I express my grati-

tude to professor emeritus Martti Valtonen. I also remember warmly late

Prof. Pertti Vainikainen, who gave me the chance to start this work as

part of the TAFECO project.

I have had the opportunity to utilize the knowledge of talented antenna

experts. My greatest thanks go to Dr. Risto Valkonen, whose earlier re-

search has created an inspiring basis for this work. As my instructor, he

has always been ready to discuss and give critical comments, which chal-

lenged me to do more and better. Dr. Janne Ilvonen deserves thanks as

well especially for opening the world of practical antenna design. I appre-

ciate also the hospitality of the groups of professors Cyril Luxey and Dirk

Manteuffel during my visits to Nice and Kiel.

The support of collegues has been invaluable. I am grateful to Prof.

Jussi Ryynänen for encouragement and advice in the beginning of the

work. Excellent cooperation in sharing teaching duties with my long-

term office-mate Dr. Mikko Honkala has made possible to concentrate

on research. Luis Costa has proficiently proofread most of the texts that

make up this thesis. Numerous other collegues have been involved in this

project, one way or another. I hope I have been able to show you that I

appreciate your effort.

My uppermost recognition is given to my family for their great flexibility.

Espoo, September 2, 2015,

Anu Lehtovuori

1

Preface

2

Contents

Preface 1

Contents 3

List of Publications 5

Author’s Contribution 7

1. Introduction 13

1.1 Objectives of the thesis . . . . . . . . . . . . . . . . . . . . . . 14

1.2 Content and main scientific merits of thesis . . . . . . . . . . 15

2. Impedance matching as a part of antenna design 17

2.1 Challenges in studying modern antennas . . . . . . . . . . . 18

2.1.1 The Q factor and the available bandwidth . . . . . . . 19

2.1.2 Complicated load impedance of current antennas . . 19

2.2 Different perspectives to impedance matching . . . . . . . . 21

2.3 Previous studies on wideband matching . . . . . . . . . . . . 23

2.3.1 Mathematical challenge in impedance matching . . . 25

2.3.2 Real-Frequency Technique . . . . . . . . . . . . . . . . 26

2.4 Towards co-design of the matching circuit and radiating part 27

3. Wideband matching and bandwidth estimators 29

3.1 Determining bandwidth estimators . . . . . . . . . . . . . . . 29

3.2 Examples on the use of bandwidth estimators . . . . . . . . 32

3.2.1 Systematic bandwidth estimator analysis . . . . . . . 32

3.2.2 Modifying antennas to enlarge available bandwidth . 35

3.3 Utilizing simulators in wideband matching . . . . . . . . . . 37

3.3.1 Effect of impedance matching on antenna performance 39

4. Dual-band impedance matching 41

3

Contents

4.1 Dual-band transforms . . . . . . . . . . . . . . . . . . . . . . 42

4.2 Simple design equations for dual-band matching of CCEs . . 45

4.3 Comparing different methods for dual-band matching . . . . 47

5. Dual-band matching with separate feeding ports 51

5.1 Scattering parameters for multiports . . . . . . . . . . . . . . 52

5.2 Impedance matching in the case of multiple ports . . . . . . 54

5.3 Applying bandwidth estimators to two-ports . . . . . . . . . 56

6. Summary and beyond 59

6.1 Interesting topics to follow up . . . . . . . . . . . . . . . . . . 60

6.1.1 Improving isolation with lumped elements . . . . . . 61

6.1.2 Use of parasitic scatterers . . . . . . . . . . . . . . . . 63

6.1.3 Tunable circuits . . . . . . . . . . . . . . . . . . . . . . 64

6.2 Co-design of matching circuit and radiating part . . . . . . . 65

6.3 Summary of publications . . . . . . . . . . . . . . . . . . . . . 67

7. Conclusions 69

References 71

Errata 83

Publications 85

4

List of Publications

This thesis consists of an overview and of the following publications which

are referred to in the text by their Roman numerals.

I R. Valkonen and A. Lehtovuori. Determining bandwidth estimators and

matching circuits for evaluation of chassis antennas. IEEE Transactions

on Antennas and Propagation, Vol. 63, pp. 4111–4120, September 2015.

II A. Lehtovuori, R. Valkonen, and J. Ilvonen. Designing capacitive cou-

pling element antennas with bandwidth estimators. IEEE Antennas

and Wireless Propagation Letters, Vol. 13, pp. 959–962, 2014.

III A. Lehtovuori, R. Valkonen, and M. Valtonen. Improving handset an-

tenna performance by wideband matching optimization. In 7th Euro-

pean Conference on Antennas and Propagation, Gothenburg, pp. 3587–

3591, April 2013.

IV A. Lehtovuori, R. Valkonen, and M. Valtonen. Dual-band matching of

arbitrary loads. Microwave and Optical Technology Letter, Vol. 56, pp.

2958–2966, 2014.

V A. Lehtovuori, R. Valkonen, J. Ryynänen, and M. Valtonen. Design

equations for dual wideband matching of capacitive coupling element

antennas. Microwave and Optical Technology Letter, Vol. 56, pp. 236–

240, 2014.

VI A. Lehtovuori, R. Valkonen, and J. Ilvonen. On designing dual-band

5

List of Publications

matching circuits for capacitive coupling element antennas. In 8th Eu-

ropean Conference on Antennas and Propagation, The Hague, pp. 3909–

3913, April 2014.

VII A. Lehtovuori, J. Ilvonen, and R. Valkonen. Wideband matching of

handset antenna ports at noncontiguous frequency bands. In 9th Euro-

pean Conference on Antennas and Propagation, Lisbon, p. 5, April 2015.

6

Author’s Contribution

Publication I: “Determining bandwidth estimators and matchingcircuits for evaluation of chassis antennas”

The paper is a result of long-term work. Dr. Valkonen has formulated the

procedure to determine bandwidth estimators and written all computer

codes. He had the main responsibility for writing the paper. The author

has participated developing the idea, and she has contributed to writing

all sections of the paper.

Publication II: “Designing capacitive coupling element antennaswith bandwidth estimators”

The author had the main responsibility for this paper. The author car-

ried out the work: simulations, prototyping, and writing. The computer

codes used to determine bandwidth estimators have been written by Dr.

Valkonen, and he also instructed the work. Dr. Ilvonen assisted in the

prototyping.

Publication III: “Improving handset antenna performance bywideband matching optimization”

The paper is based on the work of the author. Dr. Valkonen instructed

and Prof. Valtonen supervised the work.

7

Author’s Contribution

Publication IV: “Dual-band matching of arbitrary loads”

The paper is based on author’s idea; she derived all the formulations and

was responsible for writing the publication. The work was instructed by

Dr. Valkonen, and Prof. Valtonen supervised the work.

Publication V: “Design equations for dual wideband matching ofcapacitive coupling element antennas”

The author derived all the formulations, performed the simulations, and

was responsible for writing the publication. The work was instructed by

Dr. Valkonen and Prof. Ryynänen. Prof. Valtonen supervised the work.

Publication VI: “On designing dual-band matching circuits forcapacitive coupling element antennas”

The author’s original idea was developed further with Dr. Valkonen. Dr.

Ilvonen made useful comments on the text.

Publication VII: “Wideband matching of handset antenna ports atnoncontiguous frequency bands”

The paper is based on the work of the author. Dr. Ilvonen and Dr. Valko-

nen participated in writing the paper.

8

Symbols

ai the incident wave at port i; a real coefficient

bi the reflected wave from the port i; a real coefficient

C capacitance

Eg generator voltage

f frequency

fc center frequency

G conductance

h height of the antenna element

I current

j imaginary unit

l length of the antenna element

L inductance

pi pole

P power

PA power available from the source

PL power delivered to the load

Q quality factor

RG real part (resistance) of the generator impedance

RL real part (resistance) of the load impedance

s complex frequency

w width of the antenna element

XG imaginary part (reactance) of the generator impedance

XL imaginary part (reactance) of the load impedance

zi zero of the function

ZA antenna impedance

ZG generator impedance

ZL load impedance

Zin input impedance

9

Symbols

Z0 normalization impedance

η efficiency

ρ reflection coefficient

ρ0 target level for reflection coefficient

ρin input reflection coefficient

ω angular frequency

ωl angular frequency scaling factor for a low band

ωh angular frequency scaling factor for a high band

10

Abbreviations

4G 4th generation mobile networks

CA carrier aggregation

CCE capacitive coupling element

EM electromagnetic

IC integrated circuit

LTE Long-Term Evolution communication system

MIMO multiple-input multiple-output

PCB printed circuit board

PIFA planar inverted-F antenna

RF radio frequencies

RFT Real Frequency Technique

TARC total active reflection coefficient

TPG transducer power gain

11

Abbreviations

12

1. Introduction

The development of mobile devices has not in years been driven by engi-

neers but by consumers’ aspirations. They want a stylish, slim phone with

a big screen, on which the content flows non-stop at a high data rate. In

the middle of the stream of applications, the user may forget that in the

wireless world every gadget needs an antenna to transfer signals from

a device to air and vice versa. Much space is not left for an antenna in

pressure of the expectations of consumers and requirements for 4G com-

munication systems and beyond.

In order to accomplish a competent device, an antenna should be shown

as a well-matched load for the electronics of the device. However, the

handset device poses a framework, which makes antenna design chal-

lenging from the impedance matching point of view. This is due to the

following requirements:

• Size of the antenna should be minimized. The volume allocated to an

individual antenna in a mobile device is not increasing, because devices

need more antennas than earlier to serve new applications. At the low-

est frequencies, where the wavelength is largest, design challenges of

electrically small antenna are met [1]. Impedance matching difficulties

could be avoided, if a larger volume was used for the antenna.

• Bandwidth required in recent mobile communication standards is in-

creasing to guarantee fast data transfer. Designing impedance matching

for a narrow bandwidth is much more straighforward than controlling

impedance behavior over a wide frequency range.

• Efficiency is one of the most important figures-of-merit for mobile an-

tennas. The Bode-Fano criteria [2] defines how the achievable band-

13

Introduction

width is connected to an achievable matching level depending on the

impedance at antenna input. Therefore, achieving a large bandwidth

simultaneously with high efficiency is a trade-off due to the physical

limitations. Moreover, the increasing number of functions demands the

use of multiple radiating elements in the same antenna solution, and

mutual couplings between them is a challenge for efficiency.

The rapid increase in the use and capabilities of mobile devices in the

beginning of the 21st century pose demanding goals for antenna design-

ers, and new means to tackle this challenge have to be sought. When

the size of the antenna is usually fixed, compromises are needed espe-

cially between the broadband matching requirement and efficiency. With

the current huge use of wireless data transmission and the remarkable

amount of energy needed for it, efficiency is the last factor to ignore. The

interest focuses on finding more efficient ways to control wideband opera-

tion of the antenna.

1.1 Objectives of the thesis

The ambitious goal of this work is to find ways to combine a radiating

part of an antenna to a circuit part such that they operate together in

an optimal manner. Publications often study antennas looking towards

the propagating channel and aim to modify the radiating part to produce

a better radiation pattern. This work looks rather in the opposite direc-

tion, toward the circuit. Thus, the antenna is described as an impedance,

which can be adjusted with a matching circuit. Instead of aiming to de-

sign a superior antenna for a single defined purpose, this work describes

guidelines for impedance matching of small antennas and introduces ac-

cessible methods for matching circuit design. Particularly, the objective of

the work is to produce knowledge, methods, and procedures, which can be

utilized in all kind of matching problems. Antennas have offered a good

practical and demanding example as a common and important application

field. The research relies mostly on ideal circuit elements, where a study

can be presented in the clearest form and results can be generalized to a

wide scope of applications. The recognized potential solutions offer a re-

liable starting point for practical antenna design and enable formulating

novel workable design strategies.

To outline the significance of the research in a wider context, energy

14

Introduction

issues should be considered as well. Nowadays, a significant amount of

energy is consumed in wireless devices and networks. The quality of tech-

nical solutions is significant. In [3], it is described that roughly two years

of development is required to improve power amplifier efficiency by 1 %,

which is equivalent to a 0.1-dB loss reduction in the radio frequency (RF)

front-end. In the case of a poorly matched antenna, even 85 % of RF power

is lost. A significant improvement in energy efficiency of wireless devices

can be achieved in antenna design, where improving the matching level

may produce even a 1-dB improvement in efficiency (at least over part of

the bandwidth). In addition, a good impedance matching of the antenna

supports the performance of the RF front-end by creating the impedance

level that has been assumed during the design phase.

Better antenna designs and increased efficiency emerge through several

facts. Less energy is consumed for transmitting. Secondly, fewer base sta-

tions are required to produce the same coverage when devices are able

to connect at lower power levels. In addition, more robust operation is

guaranteed in various usage situations. When the use of mobile devices

and the amount of transfered data increases at an enormous rate, the ef-

ficiencies of different devices should be taken more carefully into account,

bringing to the public’s notice the device’s energy use. Therefore, although

this work concentrates on technical details and the differences seem to be

small, the questions discussed are faced by every wireless device. A mi-

nor achievement in research may have a huge aggregate effect, when it is

repeated on a large scale.

1.2 Content and main scientific merits of thesis

First, as a form of motivation, the role of impedance matching in the

antenna design is described in Section 2. The differences of circuit and

antenna disciplines are discussed, and also explained is why wideband

matching is challenging regardless of apparent simplicity of the problem.

Section 3 explains why applying earlier efforts to the antenna design is

sometimes difficult, and this guides towards a new approach for deter-

mining bandwidth limits and matching circuits. In addition to a wide

continuous passband, dual-band matching methods presented in Section 4

have also been in the focus of this thesis. Section 5 widens the study to

more complicated impedance matching cases including multiport discus-

sion. Finally, potential research lines for the future are considered, and

15

Introduction

Section 6 describes briefly the other opportunities to utilize circuit ele-

ments as a part of the antenna design. Finally, the achievements and

observations are aggregated in the conclusion.

As a concrete achievement to overcome the described challenges, the

results of this work can be briefly listed as follows:

1. The new mathematical approach for determining practical matching

limits is justified [I]. With bandwidth estimators, recognizing the op-

timal matching circuit is possible. The concept is applicable also to a

systematic analysis [II] of different antenna structures, which makes

possible adjusting a radiating part towards wider achievable bandwidth.

2. Simple design equations for certain dual-band matching cases are de-

rived [V] as well as general transforms to replace a single-band match-

ing circuit with a dual (or triple-band) matching circuit [IV,VI].

3. The work demonstrates that the bandwidth estimators can be utilized

in dual-band matching [VI], as also for multiple ports [VII], and for prac-

tical designs producing good agreement with simulations [II,VII].

4. Different accessible procedures for an optimization-based approch to

design wideband matching circuits in one- and two-port cases are pre-

sented [III,VII].

16

2. Impedance matching as a part ofantenna design

A prerequisite to antenna design is understanding the electromagnetic

behavior of the radiating part. Several books have been written on an-

tennas both generally and specializing on mobile antennas [4, 5, 6, 7, 8].

Recently, the characteristic modes of eletromagnetic fields have been ana-

lyzed to bring better insight into radiating phenomena in different shapes

of structures [9, 10, 11, 12, 13, 14, 15]. The possibility to study the behav-

ior of antenna structures through eigenvalues instead of electrical and

magnetic waves facilitates outlining the operation. In addition, the fre-

quency derivative of fundamental mode eigenvalues gives information on

available bandwidth. Optimal ways to utilize resonances both in a ground

plane and an actual radiating part have been studied, e.g., in [16, 17], and

the gathered knowledge has been applied, e.g., in [18]. Unfortunately, the

possibilities to affect the impedance behavior directly through an antenna

structure are quite limited due to the laws of the physics. The resonances

of a structure are connected to its electrical size, which in turn depends

on its physical size, shape, and material properties. Therefore, new so-

lutions have to be sought from the less explored options. With circuit

elements, the resonances can be created independently of the physical

size. To utilize the opportunities provided by circuits, an antenna designer

should take into account the new option and understand also the reso-

nances created with the matching circuit. However, designing matching

circuits for the strongly frequency-dependent impedance over a required

wide frequency range is very demanding and restricted by the nature of

passive circuit elements. Accessible and intelligible methods to facilitate

impedance matching in antenna design are needed.

17

Impedance matching as a part of antenna design

2.1 Challenges in studying modern antennas

The basic working principles of small antennas are well known [1, 19],

and a lot of research on them is still ongoing ([20] and references therein).

Typically, the antenna operation is based on radiation around a resonance

frequency, but tightening the requirements on covering larger frequency

ranges will require multiple resonances, which makes the antenna struc-

tures rather complicated. Therefore, a lot of interest has recently focused

on so called non-resonant antennas, which can be tuned with a matching

circuit to resonate over a much wider frequency range than where they in-

herently resonate. Here, the term non-resonant means that the frequency

range where the antenna radiates is not directly determined based on the

resonant frequency of the structure.

For mobile devices, capacitive coupling element (CCE) antennas [21]

have become popular. The name CCE comes from the fact that at the

demanding low mobile frequencies (f < 1 GHz), the impedance of the ele-

ment is capacitive, i.e., the coupling to the ground plane is based on the

electric field. A non-resonant antenna can also be based on inductive cou-

pling, in which case the magnetic fields are in the main role [22].

In order to make a CCE resonate at low mobile frequencies, a separate

matching circuit is required. Thus, the matching circuit becomes an es-

sential part of antenna design [23, 24, 25, 26]. Nevertheless, matching cir-

cuits have not attrated much attention in antenna papers until recently.

This is, partly, a consequence of the fact that there has not been a prac-

tical starting point for designing the matching circuit for the complicated

impedance load over a wide frequency band. The matching circuit is not

actually thought to be a part of ordinary design but rather something self-

evident which combines the actual parts together. The matching circuit

is seldom anyone’s main interest. However, precisely for this reason, the

matching circuit design offers unused potential to improve the overall de-

sign and calls for new tricks to lead to better results.

Many practical aspects of designing CCEs are considered, e.g., in [27,

28, 29]. As a simple antenna structure, the CCE is not very sensitive to

the user [28, 30]. In addition, depending on the used matching solution,

the same structure can be used in very flexible ways. A design based on a

CCE may radiate over a wide frequency band, or it can be made equally

suitable for tunable solutions, where strong resonances in the antenna

element have to be avoided to guarantee tunability [31, 32]. Both these

18

Impedance matching as a part of antenna design

ways are relevant in current handset antenna design and demonstrated

in [23].

Next, some aspects are discussed regarding the design challenges with

CCEs, where both the antenna structure and improvement to performance

obtained with a matching circuit have to be accounted for in the design.

2.1.1 The Q factor and the available bandwidth

Traditionally, the quality factor Q is used to evaluate small antennas [33,

34]. For single-resonant antennas, the Q value offers a straigthforward

way to evaluate also their available bandwidth, because Q is inversely

proportional to bandwidth [33, 35]. However, defining the exact value

for Q is difficult, a fact made clear, e.g., in [36, 37, 38, 39, 40]. The sim-

ple definition is valid only for the single-resonance case, when the an-

tenna impedance can be described as a RLC resonator. Nonetheless, Q-

values are often used to analyze also structures, where multiple modes

are present [41, 32]. In these cases, the simple circuit is not adequate to

model the energy stored in an antenna, which is needed to determine the

exact value of the quality factor. Therefore, different approximations for

Q give different results when two closely spaced impedance resonances

are present [42]. More accurate results can be obtained with new approx-

imations based on more complex equivalent-circuit models for the load

impedance [43, 44], but still defining Q may be problematic, as illustrated

in [45]. Therefore, in this thesis, using the Q factor is avoided, and the

concept bandwidth potential [46] is used to consider the available band-

width. The first reason for this is to avoid typical misunderstandings in

determining a quality factor. Secondly, an exact value for the quality fac-

tor Q is here considered as a theoretical concept. In practical purposes, it

is more important to know what the available bandwidth is with a certain

matching circuit. As stated in [20], the antenna designer is more inter-

ested in bandwidth. Nevertheless, defining impedance-matching limita-

tions is demanding, as is evident from [47, 48].

2.1.2 Complicated load impedance of current antennas

The structures used for small antennas should be complex enough that

they are capable of multiresonance behavior, which enables achieving a

greater bandwidth [49]. Multiple resonances complicate the Q-factor def-

inition, and also modeling the impedance requires a higher order equiv-

19

Impedance matching as a part of antenna design

700M 1G 1.3G 1.6G 1.9G 2.2G 2.5G10

20

30

40

50

60

−100

−60

−20

20

60

100antenna impedance 0.7−2.5GHz

Zre

Ohm

f/Hz

Zim

Ohm

Zre Zim

0.5

−0.5

2.0

−2.0

0.0 0.2 1.0 5.0

antenna impedance 0.7−2.5GHzAPLAC Simulator

Model Sparam

Figure 2.1. The real and imaginary part of the CCE antenna load is shown on theleft. The Smith chart on the right includes also the behavior of the circuitmodel. [III]

alent circuit, because a simple RLC resonator is not adequate to model

multiple resonances. Naturally, studying the problem over a wide fre-

quency band is impossible if the model for the load is not valid over the

whole bandwidth.

With integrated circuits, ’wideband’ means covering one channel at a

time, and the load impedance can be considered as a constant over a

single frequency band. On the antenna side, a much wider passband

has to be covered. Thus, it is no longer sufficient to study matching at

a single frequency, but the impedance matching must begin by under-

standing the frequency dependence of the load over the entire desired fre-

quency range. Modeling the antenna impedance accurately with proper

frequency-dependency poses a new challenge for impedance matching.

The circuit models for an antenna become quite complicated, as, e.g.,

in [50]. Modeling a complicated impedance with sufficient accuracy over

a wide frequency band requires several degrees of freedom in the circuit

model, as illustrated in [51]. Different circuit models for antennas have

been published with few [16, 52] or numerous [53, 54, 17] circuit elements.

As an example of the impedance of a CCE antenna, Figure 2.1 shows the

real and imaginary parts of the impedance of antenna ’B’ from [55]. A

circuit with six reactive elements, as in Figure 2.2, is required to model it

with reasonable accuracy.

Classifying antennas to a few categories and giving them certain match-

ing rules becomes impossible when the load depends on the frequency in

a far more complicated way than for a simple RLC resonator. Similarly,

using a circuit model instead of exact data does not give any benefit. To

guarantee applicability and to retain generality, the antenna load is de-

20

Impedance matching as a part of antenna design

1.07n

45.46

3.70p

9.76n1.18p

3.27n 6.30p 50.42

Figure 2.2. The behavioral circuit model for the antenna load [III].

scribed using a general S parameter file, which can be studied over a wide

frequency range, and the simplifications are concentrated on the circuit

side.

2.2 Different perspectives to impedance matching

Circuit theory traditionally formulates the matching problem via the com-

plex generator impedance ZG = RG + jXG and complex load impedance

ZL, as shown in Figure 2.3. With a generator voltage Eg, the maximum

power available from the generator is

PA =|Eg|24RG

(2.1)

and the power delivered to the load is

PL = �e {ZL} |I|2 =RL|Eg|2

|ZG + ZL|2 , (2.2)

where the current I is shown in Figure 2.3.

The maximum value for PL can be determined by requiring the deriva-

tive with respect to RL and XL to be zero resulting in the well-known

condition for conjugate matching: ZL = Z∗G. Hence, the ratio of powers,

the transducer power gain (TPG)

TPG =PL

PA=

4RLRG

(RL + RG)2 + (XL + XG)2, (2.3)

is maximized. With this background, every electrical engineer can design

a matching circuit at a single frequency using two elements connected in

Eg

ZG = RG + jXG

I ZL = RL + jXL

Figure 2.3. Typical circuit theoretical approach to the impedance matching.

21

Impedance matching as a part of antenna design

Figure 2.4. Possible L-section matching circuits appropriate for perfect matching in thedifferent regions of the Smith chart [IV].

an L-section. The formulas for the perfect matching at a single frequency

are presented in all basic books of the field [56]. The possible L-section

matching circuits for different impedances on the Smith chart are illus-

trated in Figure 2.4. Nevertheless, achieving impedance matching over

wider frequency range is a totally different question, when all quantities

change as a function of the frequency. Because finding an exact impedance

match is physically impossible over a wide frequency band [2], an approx-

imation is needed.

In practical wideband problems, a moderate level of mismatch is ac-

ceptable. The desired goal is not just to maximize TPG over a certain

frequency band but also to maximize the bandwidth at a certain predeter-

mined matching level (e.g., −6 dB). The generator impedance is assumed

to be real, ZG = Z0, and the input impedance Zin in Figure 2.5 should

produce the desired matching level for the reflection coefficient

|ρin| =∣∣∣∣Zin − Z0

Zin + Z0

∣∣∣∣ ≤ ρ0. (2.4)

In general, the impedance matching is studied on the Smith chart, be-

cause amplitude information alone cannot distinguish an under-coupled

resonance from an over-coupled one. In the case of lossless matching el-

ements, minimizing |ρin| is equal to maximizing TPG, because the whole

real power PL beyond reference plane B (see Figure 2.5) is dissipated in

the real part of the antenna impedance ZA.

22

Impedance matching as a part of antenna design

Eg

ρin

Z0

B

Zin

A

ZA

Figure 2.5. Antenna designers minimize the reflection coefficient ρin instead of study-ing impedances and consider the problem at a different reference plane (Binstead of A).

From a circuit theoretical stand point, the goal is to find the optimal

realizable function that gives the most accurate approximation for the

desired impedance. However, in practice, the matching circuit should be

implemented with as few elements as possible [57, 32], because the cost of

the matching circuit is directly proportional to the number of matching el-

ements, and each component introduces in reality some power loss, which

should be minimized for optimal efficiency performance. In addition, the

benefit gained through extension of bandwidth decreases as the number

of matching components increases [58]. On the whole, investing effort to

improve the accuracy of the result is pointless, because the existence of ac-

tual manufacturing tolerance and nonidealities of the matching elements

will make void all decimals beyond the second one in the ideal solution.

Naturally, in this final phase, the losses have to be taken into account,

and maximizing TPG is the final design goal also in antenna design.

Due to the acceptable mismatch and emphasis on wideband operation,

the optimal conjugate matching as a starting point appears not to be ob-

viously the best one and may even lead to a nonoptimal solution. When

a clear starting point is missing, presenting exact results becomes quite

difficult. Actually, exact equations are not given even for a simple RLC

resonator load, and even now, there is no practical starting point for de-

signing a matching circuit over a wide frequency band. Answers even to

the simplest questions are not known: What is the best topology? Should

a matching circuit start with a series or shunt component? Inductance or

capacitance? Novel approaches to this whole problem are required.

2.3 Previous studies on wideband matching

In the field of circuit theory, the methods for determining physical limits

for obtainable bandwidth in practical form have been studied since the

23

Impedance matching as a part of antenna design

L

C

L

C

L 2.3

1.2 1

Figure 2.6. The classic wideband matching problem studied in circuit theory: a low-passtype matching circuit and a circuit model for the load.

1950’s. The famous paper by Fano in 1950 [2] states the basic principle

in impedance matching: using a lossless matching circuit, perfect match-

ing can be achieved only at a number of distinct point frequencies. This

is a direct consequence of the properties of passive circuit elements. The

derivative of the reactance is always positive [59], i.e., the imaginary part

increases with frequency. Thus, for the complex conjugate of the load, the

imaginary part should decrease – which is not possible to realize with a

passive circuit. Therefore, attempts to approach a perfect match results

in a reduction of a bandwidth. The relation between mismatch and band-

width was originally shown for a parallel RC load by Bode [60].

In the early stage, determining matching circuits was closely related

to filters. However, exact solutions based on Butterworth and Cheby-

shev functions [61] are not easily applicable to antennas, because they are

limited to match only frequency independent, real loads, i.e., pure resis-

tances. Determining the limits for an arbitrary load impedance is difficult

due to the complexity of the integrals [2], and results have been presented

for simple loads including one or two reactive elements, in addition to the

resistance [62, 63, 64]. Although analytical gain–bandwidth theory has

been extended later [65] and explicit formulas have been presented for

certain types of loads [66, 54], the maximum available bandwidth for a

complex load is very demanding to evaluate [67]. Even if a corresponding

matching circuit can be determined, the theoretical starting point leads

easily to an impractical solution.

As an example, Figure 2.6 shows the wideband matching problem stud-

ied in several publications [68, 63, 62]. A simple load consists of only

two reactive elements in addition to a resistor, and a low-pass topology is

shown for the matching. This generally describes the level at which defin-

ing a wideband matching circuit is studied in circuit theory even nowa-

days [69, 70, 71]. As far as the author knows, any extensive results have

not been published for more complex loads.

24

Impedance matching as a part of antenna design

The known solutions to the problem in Figure 2.6 include quite many

elements and mutual inductances [63]. These kind of solutions are not

applicable in practice and the difference between solutions is minimal,

although three decimals are given for the element values [62]. Determin-

ing the superiority of the solution is interesting mainly from a theoretical

point of view. For engineers, a ’good enough’ solution is adequate.

The results based on H-infinity theory give the best possible perfor-

mance over all the lossless matching circuits [67, 72], but they are not

easily applicable – and they give no clue on the actual matching circuit.

However, the presented examples [72] show that the bandwidth that can

possibly be obtained with a low-pass or a high-pass filter saturates as the

order of the filter increases. The optimal H-infinity bandwidth level is not

achieved with these topologies. This observation emphasizes the impor-

tance of studying an extensive group of circuit topologies.

2.3.1 Mathematical challenge in impedance matching

The large number of research articles on the broadband matching prob-

lem shows that finding the theoretical bandwidth limit for an arbitrary

frequency-dependent impedance is impossible in a reasonable form, which

has led to optimization-based approaches. Thus, a circuit model for a

load impedance is not required, because the load can be characterized

by samples. Often the solution is sought by choosing an appropriate ap-

proximation for impedance Z∗A (see Fig. 2.5) in a function form. Never-

theless, this does not eliminate the mathematical challenge. Wideband

impedance matching is known as a difficult numerical optimization prob-

lem, because the wideband transducer power gain is a nonlinear, nondif-

ferentiable, badly scaled multivariable function [67]. To clarify this in

practice, a three-element matching circuit is studied. For simplicity, a

purely resistive load is assumed, and thus the impedance function can be

represented, e.g., in the following forms:

Zin(s) =a0 + a1s + a2s

2 + a3s3

b0 + b1s + b2s2=

a3(s + z1)(s + z2)(s + z3)(s + p1)(s + p2)

, (2.5)

where s is a complex frequency and coefficients ai and bi are real and

positive. Alternatively, the form with the poles pi and zeros zi are used to

characterize the behavior.

Through the scattering parameter

S11(s) =Zin(s) − Z0

Zin(s) + Z0, (2.6)

25

Impedance matching as a part of antenna design

the actual goal, the transducer power gain TPG = 1 − |S11|2, can be de-

fined. This quantity is quadratic, which leads to doubling the order of

nonlinearity. In addition, the load impedance ZA has at least sixth-order

frequency-dependence corresponding a circuit such as in Figure 2.2, and

thus, TPG may depend on s18. The challenges and difficulties concerning

the design of a matching network over a wide frequency band has been

described widely in [70].

2.3.2 Real-Frequency Technique

Several ways to formulate the wideband matching problem mathemat-

ically have been tested. For example in the Real-Frequency Technique

(RFT) [68, 63, 73, 74, 75], the unknowns used in the optimization can be

chosen in various ways:

1. The coefficients of the rational function describing the ideal solution,

impedance Z∗A [63], can directly be used as unknowns, but if all the

coefficients ai and bi in Eq. (2.5) are used as the unknowns, the solution

is probably non-physical, i.e., impossible to realize with a passive circuit.

In addition, the number of unknowns is large.

2. The poles pi of the latter impedance rational function in Eq. (2.5) can be

used as unknowns [73]. Thus, ensuring the realizability is more straigh-

forward.

3. The coefficients of the function describing power transfer (|S21|2) may

be chosen as well [76].

After solving the unknowns of the function, a circuit realization of the

function is sought. Searching for the solution in a general function form is

so laborious that typically the form of the optimized function is restricted

in order to simplify the mathematics of the problem through decreasing

the number of unknowns. This also limits the set of possible matching

circuit topologies realizing the function. For example, requiring that all

transfer zeros of the function are at infinity limits the corresponding cir-

cuit solution to a low-pass type ladder network [70, 71, 77]. This kind of

choice can often lead to loss of the optimal solution, as discussed in [63]

and demonstrated in [62]. On the other hand, in the case of a bandpass-

type function, the realization of the obtained function depends on the or-

26

Impedance matching as a part of antenna design

Figure 2.7. A wireless system consists of several blocks which should be designed to-gether to obtain the optimal performance [V].

der in which the transmission zeros are realized, whereupon the choice

of the best configuration requires considerable skill and experience [78].

In [79], the realization order has been fixed, which may lead the loss of

the optimal solution. Analyzing the full sphere of topologies would be im-

portant instead of just a fixed ladder topology [80]. In spite of all this, the

RFT is a standard method for wideband impedance matching and demon-

strated to work for antennas [81, 77].

To summarize, seeking general solutions requires a strong simplifica-

tion of the problem, e.g., modeling a load with a simple circuit model or

analyzing the situation at a single frequency. These kind of assumptions

make the obtained results impractical in real design problems. In prac-

tice, the study has to be turned the other way around: the matching circuit

should be simple while the antenna load may be very complex.

2.4 Towards co-design of the matching circuit and radiating part

Reaching optimal antenna performance requires co-design of the antenna

and the impedance matching circuit [82, 83] to link different blocks to-

gether as illustrated in Figure 2.7. Due to the challenge of mastering

the interdisciplinary entirety, such an approach has not been used widely.

However, circuit theoretical multiport concepts can be used to retain the

consistency between the physics of electromagnetic (EM) fields and the

mathematical world of signal and information theories [84]. In addition,

if a part of the complexity of an antenna block can be described and an-

alyzed based on circuit theory, electromagnetic simulations are replaced

with circuit simulations. Thus, the simulation effort decreases, which en-

ables utilizing circuit optimization [85] as an efficient tool in the antenna

design process. However, the more computational power and possibili-

ties are available, the more important it is to understand the basic laws

and limitations, and to identify the essential phenomena in the jungle of

details.

27

Impedance matching as a part of antenna design

In a typical antenna design process, the radiating part is designed first

and the desired operation frequencies are left to be realized by the match-

ing circuit afterwards. However, the possibility to adjust afterwards a

predetermined antenna impedance with a simple passive matching cir-

cuit is quite limited over a wide frequency range. Therefore, it is reason-

able to search for simple practical design rules and methods for matching

circuits, so that they can be easily used to choose the best antenna con-

figuration or to modify an antenna structure. As stated in [II], the proper

design process for a CCE antenna involves accounting for the potential of

the matching circuit performance as well as the possibility to revise the

antenna geometry based on the outcome of the analysis. The best perfor-

mance cannot be found without analyzing all the aspects.

28

3. Wideband matching and bandwidthestimators

The problem of broadband matching can been divided in two distinct prob-

lems: 1) finding a bandwidth limit for an arbitrary load impedance and

2) determining a matching circuit that gives the best result with certain

restrictions considering the type and complexity of the circuit. Lot of theo-

retical work has been done during past decades to study the first problem,

but the results are not practical from an antenna design point of view due

to the significant simplifying assumptions regarding the type of the load.

The question of determining a corresponding circuit has been discussed

less. Neverheless, the lack of methods to evaluate the potential of match-

ing circuits makes the comparison of different antennas difficult. Without

accurate analysis, finding an optimal solution is impossible. Therefore, ef-

ficient and reliable tools to analyze the effect of a matching circuit are im-

portant, because they bring reliable information on the operation, which

enables adapting a structure towards better performance.

3.1 Determining bandwidth estimators

A rough idea of the achievable bandwidth in different frequency ranges

can be obtained using the bandwidth potential [46], which represents the

maximum relative bandwidth1 obtained with optimal L-section matching

around any given center frequency fc. The bandwidth potential bwL can

be used as a tool for comparing different load impedances. Nevertheless,

matching with L-section does not reveal the whole truth, and ranking of

clearly different antennas remains difficult. In [I], the concept is widened

also to three- and four-component matching circuits, and the term ’band-

1In [46], the bandwidth potential was introduced without a requirement for sym-metry, but later, starting from [86], the bandwidth potential has been defined asthe maximum arithmetically symmetric relative bandwidth.

29

Wideband matching and bandwidth estimators

width estimator’ is used to generalize the concept. These bandwidth esti-

mators produce an efficient way to estimate the matching potential more

precisely, and they often provide considerably better bandwidths than the

L-section matching, like we demonstrated in [57]. The bandwidth estima-

tors can be used to find the best matching topology in a certain frequency

range or for a certain type of load. In particular, the approach is general

in the sense that the load can have an arbitrary frequency dependence.

Moreover, the in-house software Match-i2 gives the element values for a

circuit which produces the largest bandwidth.

Figure 3.1 shows the complete set of matching circuits that can possibly

be created with three elements. In addition to the well-known Π and T

topology, the ’F’, ’Γ’, and ’D’ topologies are also labelled. The four most

relevant matching topologies for CCE antennas correspond to the band-

width estimators bwΠ, bwT, bwF, and bwΓ, where the last two refer

to topologies F1 and Γ1. It is worth noticing that the Π and T topologies

include all alternative L-section circuits, and therefore bwΠ ≥ bwL and

bwT ≥ bwL.

Bandwidth estimator algorithm in a nutshell

In a typical nonlinear optimization, the number of unknowns defines how

rapidly and reliably the procedure converges to the desired solution start-

ing from arbitrary initial values. Therefore, the challenge in wideband

impedance matching crystallizes to the number of unknowns: how to for-

mulate the optimization problem described in Section 2.3.1 with a mini-

mum number of unknowns so as to guarantee finding a solution but si-

multaneously having all possible solutions involved in the optimization.

A novel insight of the procedure in [I] is to describe the problem with

only one unknown optimization variable in the case of the L-section. Be-

cause in practical engineering problems the desired matching level is

known, the maximum absolute value for the reflection coefficient is fixed,

and only the phase angle of the reflection coefficient has to be optimized.

For every phase angle value, the impedance is known, and the correspond-

ing matching circuit can be generated when the problem is studied one

frequency at a time. Equations producing an L-section matching in the

center of the Smith chart, Z0 = 50 + j0, are well-known, and similar equa-

tions leading to the impedance Z = R + jX are straightforward to derive

and are given in [I].

2Authored by Dr. Valkonen.

30

Wideband matching and bandwidth estimators

Π T

F1 F2

F3 F4

Γ1 Γ2

Γ3 Γ4

D1 D2

D3 D4

Figure 3.1. All possible three-element topologies. An antenna is assumed to be on theright throughout the thesis.

In a computational algorithm, the starting frequency of the band is

fixed, and the goal is to maximize the end frequency for the band. The op-

timization goal is well-defined. Thus, an extensive, complicated nonlinear

optimization problem is replaced with the simplest possible formulation

for the optimization and with a large amount of coarse and straightfor-

ward computation. Accordingly, finding the optimal solution is guaran-

teed.

31

Wideband matching and bandwidth estimators

110

60

60

6

w

ground corner

ground centerelement center

element corner

10

h=1.5

Figure 3.2. The studied antenna structure. The width of the coupling element w is variedand alternative feeding positions are studied. All dimensions are in millime-ters. [II]

3.2 Examples on the use of bandwidth estimators

An efficient algorithm for determining the available bandwidth opens the

way to evaluate the potential of different antenna structures. Next, the

use of bandwidth estimators is demonstrated by performing a systematic

analysis. The second example shows how the bandwidth estimators can

be used to find the best antenna modification. More examples are shown

in [I].

3.2.1 Systematic bandwidth estimator analysis

Bandwidth estimators facilitate estimating the potential of different an-

tenna structures. As an example, the antenna structure in Figure 3.2 is

analyzed systematically.

The properties of the same structure depend greatly on the feeding po-

sition. Typically, the feed in the corner of the ground plane excites the

wavemodes with stronger resonances than an excitation at the edge [22],

as shown in Figure 3.3.

Evaluating the available performance with a matching circuit is difficult

0.5 1 1.5 2 2.5 3−12

−10

−8

−6

−4

−2

0

Frequency (GHz)

|S11

| (dB

)

corner fedcenter fed

Figure 3.3. S11 of the 48-mm wide coupling element with two different feeding positions.

32

Wideband matching and bandwidth estimators

0.5 1 1.5 2 2.50

0.1

0.2

0.3

0.4

0.5

0.6

Frequency (GHz)

Rel

ativ

e ba

ndw

idth

bwT centerbwΠbwF

0.5 1 1.5 2 2.50

0.1

0.2

0.3

0.4

0.5

0.6

Frequency (GHz)

Rel

ativ

e ba

ndw

idth

bwT cornerbwΠbwF

Figure 3.4. Bandwidth estimator results for the same antenna with two different feedingpositions: center (top) and corner (bottom).

when relying only on the S11 of the structures. The bandwidth estimators

offer a practical tool to clarify the situation. For example, the results

presented in Figure 3.4 show the following:

• At 800 MHz, the F topology gives the largest relative bandwidth, 0.28,

and the position of the feed does not have essential importance. This

is natural, because at low frequencies the ground plane itself is in the

main role.

• At 2.0 GHz, the bwF value 0.4 indicates the bandwidth of 800 MHz with

center feeding, whereas for a corner feed, the maximum value is 0.17,

corresponding to 340 MHz available with the T topology.

• The T topology clearly gives the widest bandwidth for a corner-fed struc-

ture at high frequencies, but the F topology is more suitable with a cen-

ter feed.

The extracted observations aim to demonstrate that bandwidth estima-

tors give concrete values for the available bandwidth, facilitate choosing

33

Wideband matching and bandwidth estimators

0.5 1 1.5 2 2.5 3−12

−10

−8

−6

−4

−2

0

Frequency (GHz)

|S11

| (dB

)T@0.8GHzF@0.8GHzT@2.0GHzF@2.0GHz

Figure 3.5. Matching results for a center-fed antenna with T and F matching circuits at0.8 and 2.0 GHz.

the best structure, and reveal the best matching topology. Also the corre-

sponding matching circuit with element values is obtained by Match-i.

The matching results for a center-fed antenna at 0.8 and 2.0 GHz are

presented in Figure 3.5. A comparison of the T and F topologies shows

that the F topology gives a wider band at both frequencies, as was ex-

pected based on bandwidth estimator results. On top of that, the F topol-

ogy also produces a very small S11 over most of the other frequencies. If

the T circuits are used, the S11 is at a clearly lower level at many frequen-

cies outside the desired passband. In some cases, a strict passband may

be an advantageous feature for the matching circuit, as will be discussed

in Section 5.

The results here and in [II] illustrate that although the |S11| for the two

antennas without a matching circuit are greatly different, the obtainable

bandwidth at low frequencies may be almost identical at a −6-dB match-

ing level. By looking at S11 only, wrong conclusions may be drawn on the

feasibility of the structure as antennas. A radiating structure alone may

seem promising, but the improvement obtained with a matching circuit

is insignificant. On the other hand, a structure with bland behavior may

produce excellent performance united with a matching circuit.

In [II], these novel bandwidth estimators are systematically applied to

analyze a set of CCE antenna structures in order to demonstrate the use

of bandwidth estimators. By carrying out a large set of such analyses,

several guidelines for an optimal antenna structure have been found to

give clues to designers to choose promising antenna solutions.

A representative set of simple rectangular coupling elements on a printed

circuit board (PCB) ground plane have been studied. Based on the sys-

34

Wideband matching and bandwidth estimators

tematic bandwidth estimator analysis for the set of single-element struc-

tures shown in Figure 3.2, some relevant aspects and observations, es-

pecially regarding the best matching topologies, are highlighted. The

goal was to find guidelines to choose a capable structure in the studied

framework. After systematic studies, the following conclusions to find the

optimal elements for a low band (0.698–0.96 GHz) and for a high band

(1.71–2.69 GHz) were drawn [II]:

• In low-band matching, the F topology is recommended for structures of

all studied sizes.

• For a low band, about a 48-mm wide coupling element gives the required

matching potential.

• To create a high band, the optimal choice is a small 6 to 12-mm ele-

ment which is placed in the corner. The T topology gives the largest

bandwidth.

• Based on the good performance of large elements at low frequencies and

small elements at high, an attractive option is to combine the two.

These guidelines offer a solid basis for designing a one-element antenna

and facilitate combining several radiating elements to the same design as

well. The new challenges posed on several elements will be described in

Section 5.

3.2.2 Modifying antennas to enlarge available bandwidth

In addition to determining the size of antenna element, the bandwidth

analysis can be used also as a tool to modify the antenna structure it-

self. It is well-known that at low frequencies, the size of the element has

a very dominant effect on the available bandwidth. However, at higher

frequencies, small modifications in the antenna geometry may have a sig-

nificant effect on the available bandwidth. For example, different feeding

positions create different wave modes, and this affects remarkably the

operation of the antenna. However, estimating the available bandwidth

based only on the S11 curve is not easy. The following illustrative study is

done for antenna D from [V].

Figure 3.6 shows how S11 of the antenna changes when the feeding po-

35

Wideband matching and bandwidth estimators

0.5 1 1.5 2 2.5 3−10

−8

−6

−4

−2

0

Frequency (GHz)

|S11

| (dB

)

S11 f28S11 f26S11 f24

Figure 3.6. S11 for antenna D with feeding positions 28, 26, and 24 mm.

0.5 1 1.5 2 2.5 30

0.1

0.2

0.3

0.4

0.5

0.6

0.7

Frequency (GHz)

Rel

ativ

e ba

ndw

idth

bwF f28bwF f26bwF f24

Figure 3.7. Bandwidth estimator bwF for feeding positions 28, 26, and 24 mm.

sition is adjusted in 2-millimeters steps to find the optimal position for

the feed. The change in the S11 curve is at around 2.2 GHz, but it is not

evident which one of the alternatives is the right choice if the goal is to

obtain the largest bandwidth around 2 GHz.

Bandwidth estimators in Figure 3.7 show clearly the frequency range in

which the achieved improvement in S11 is possible with an F topology. At

center frequency 2 GHz, the position 26 mm gives the largest bandwidth

and not position 24 mm, which could have been the choice based on Fig-

ure 3.6. A similar study could also be done for other topologies.

The bandwidth estimator calculation gives the corresponding matching

circuits as well. Thus the matching results in Figure 3.8 can be shown

to confirm that, at center frequency 2 GHz, the largest symmetrical band-

width with an F topology is achieved with feed at position 26 mm. Recog-

nizing the modification, which gives the largest bandwidth with a match-

ing circuit, is impossible without an efficient tool for calculating matching

circuits.

The examples in [I] show that bandwidth estimators can be used both to

analyze the available bandwidth with different matching circuits and to

36

Wideband matching and bandwidth estimators

0.5 1 1.5 2 2.5 3−12

−10

−8

−6

−4

−2

0

Frequency (GHz)

|S11

| (dB

)

f28 f=2 GHzf26 f=2 GHzf24 f=2 GHz

Figure 3.8. Matching results for feeding positions 28, 26, and 24 mm with an F matchingcircuit designed for center frequency 2 GHz.

synthesize a radiating structure with better performance. Furthermore,

the following sections of this thesis will introduce some versatile and more

advanced approaches to utilize the concept.

3.3 Utilizing simulators in wideband matching

Another popular approach nowadays is, naturally, to utilize a circuit sim-

ulation software with its built-in optimization algorithms. Thus, the el-

ement values of a matching circuit are the unknowns, but a topology

with the types of the matching circuit elements has again to be defined

beforehand. The optimization problem is still highly nonlinear with re-

spect to element values. Accordingly, good initial values for elements are

necessary to ensure the convergence to the global minimum solution of

the problem. Furthermore, in the case of a strongly frequency-dependent

load, the definition of the frequency band may significantly affect the final

solution, and the norm used in error calculation determines how errors at

different frequencies have been weighted. In addition, the choice of topol-

ogy is a very important decision, as discussed earlier, because it limits the

type of the solutions that can possibly be found.

As a response to the challenge of wideband impedance matching, [III]

presents an easily adopted procedure to design wideband matching cir-

cuits for an arbitrary, frequency-dependent, real-life load through opti-

mization using a commercial circuit simulator. The impedance is de-

scribed with an S-parameter file, and thus the method does not set any

limitations to the frequency dependence of the load. The key factors of

the method are 1) choosing a versatile topology, 2) finding initial values

37

Wideband matching and bandwidth estimators

L3 C3

L2C2

L1 C1 Z

3 2 1

Figure 3.9. Matching circuit topology divided into three resonators [III].

for unknowns, and 3) minimizing the number of unknowns used at a time.

Versatile matching topology

First, the bandpass type of topology shown in Figure 3.9 is a natural

choice when the goal is to obtain matching over some pass band. In ad-

dition, this choice does not strictly fix the topology beforehand, because it

includes both a low-pass and a high-pass topology as special cases when

some of the components can be ignored due to impractically low or high

component values.

The chosen topology produces transmission zeros both at the origin and

at infinity, which makes it very versatile in the sense that it can be used

to match a wide selection of load impedances when every resonator has

a different resonance frequency. Actually, the same topology has already

been introduced in [2]. In addition, the chosen topology makes frequency

reconfigurability an option through tuning of the capacitance values, as

demonstrated in [87].

Initial values for unknowns

Secondly, as a consequence of the strong nonlinearity of the problem, good

initial values for the component values are a necessity to finding a desired

solution. Despite efficient computers and large amounts of available cal-

culation effort, the optimization algorithm will probably not find a good

solution for a wideband matching problem with arbitrary initial values

for the components. Nonlinearity means, in practice, that the optimiza-

tion error function has several local minima. As a result, the optimization

procedure drifts easily to a local minimum near the starting point and

stagnates there instead of proceeding toward the desired solution. There-

fore, optimization is a useless tool for designing wideband matching cir-

cuits if there is no indication about the right values for the components.

Nevertheless, the challenge presented by nonlinearity is avoided if the

problem can be divided into subproblems such that only one or two op-

timization variables exist at a time. Then, the optimization has a much

38

Wideband matching and bandwidth estimators

better chance of finding an optimal solution. However, this requires that

the optimization goals at every phase are determined so that the whole

optimization proceeds toward the global minimum of the problem.

Dividing optimization into subproblems

Finally, the proposed optimization algorithm is based on dividing the op-

timization problem into three smaller parts. Starting from the load end,

only two component values are adjusted at a time. An important fact ex-

ploited in this optimization procedure is the losslessness of the matching

circuit. The lossless shunt components do not affect the real part of the

admittance, and the series components do not change the real part of the

impedance. Thus, with the chosen topology (Figure 3.9), the resonators 1

and 2 already fix the real part of admittance, and the remaining resonator

3 can improve only the matching of the imaginary part. Also, in general,

presenting a clear method for determining element values is easier if the

problem can be solved in parts, as done in [88].

3.3.1 Effect of impedance matching on antenna performance

Several examples for demanding CCE antenna loads demonstrate the fea-

sibility of the proposed optimization procedure [III]. Because the antenna

impedance depends strongly on the frequency, the frequency bandwidth

used in optimization has a significant effect on the obtained result. At

some frequencies the load may be well-matched even without a matching

circuit while at others it is difficult to match. Similarly, the optimal result

does not necessarily yield an equiripple response as in filter theory. In

addition, the solution is not unique, but more matching circuits working

almost equally well can be found depending on the frequency band used

in the optimization. The ranking of alternatives can differ when their be-

havior due to losses, sensitivity to load variation, or tunability is studied.

Choosing and defining the matching level and target bandwidth for a

real-life problem can significantly affect the final performance of an an-

tenna in practice. This is demonstrated by designing an ultra-wideband

matching over 0.79–2.56 GHz for the CCE antenna ’B’ from [55]. The ref-

erence circuits have been designed using Optenni Lab [89].

In Figure 3.10, the red and blue solid lines present the ultra-wideband

matching in free space, and the corresponding dashed lines show the

matching when the presence of the user’s hand in the vicinity of the an-

tenna (CTIA talking-grip hand) is taken into account. The results show

39

Wideband matching and bandwidth estimators

800M 1.25G 1.7G 2.15G 2.6G−12

−9

−6

−3

0matching 0.8−2.6GHz

|S11|dB

f/Hz

Circuit VI Circuit VI

Circuit I Circuit I

Circuit II Circuit II

Figure 3.10. Matching results with different matching circuits for an original antennaload (—) and with the effect of the hand (- - -).

0.5

−0.5

2.0

−2.0

0.0 0.2 1.0 5.0

matching 0.8−2.6GHz

Circuit VI with hand

0.5

−0.5

2.0

−2.0

0.0 0.2 1.0 5.0

matching 0.8−2.6GHz

Circuit II with hand

Figure 3.11. Robust (on the left) and sensitive (on the right) matching with the handeffect presented on the Smith chart.

that with the hand effect, the matching is improved in the entire fre-

quency band.

If a narrower matching (green curves) for the bandwidth 0.75–1.5 GHz is

compared to the wideband results, then in contrast the bandwidth shrinks

remarkably, by about 30 %, due to the hand effect. Figure 3.11 shows

the same results on the Smith chart. The study reveals that designing a

matching circuit for an over-wide bandwidth can improve the performance

of the antenna in practical use. A similar advantage of smooth and wide

matching compared to a more resonant one has been reported also in [90,

91]. The effects of the user on a CCE antenna have been considered more

thoroughly in [30, 92, 55, 28]. Recent results of user effects for hand-held

device antennas can be found also from [29, 93, 94, 95].

40

4. Dual-band impedance matching

In today’s mobile systems, the desired frequency band consists of two

passbands, as illustrated in Figure 4.1: a low band at 0.698–0.96 GHz

and a high band at 1.71–2.69 GHz1. Therefore, it is logical to search for

dual-band matching solutions and different solutions have been presented

in dozens of recent publications. For example, multiband filtering tech-

niques are actively studied [96, 97], but in the case of normal filters the

load does not have frequency dependence. Many earlier studies for com-

plex load impedances [98, 99, 100] seek a matching circuit at point fre-

quencies with a constant load value, ignoring bandwidth considerations

and avoiding studying matching over a wide frequency band. As stated

before, for integrated circuits, the load impedance can be considered as a

constant, because only one rather narrow channel has to be covered at a

time. However, a much wider passband has to be studied on the antenna

side, and modeling the antenna impedance with proper frequency depen-

dency poses a new challenge for impedance matching at several wide pass-

bands simultaneously.

700 960 1700 2200 MHz

-6 dB

|S11|

Figure 4.1. The desired frequency band in mobile systems consist of two passbands.

A single-feed antenna can be designed to operate at two frequency bands

in several ways by utilizing matching circuits as presented in [VI]:

1Sometimes in other references, the frequencies 1.71–2.17 GHz are labeled asmid-band, and the term high-band is reserved for frequencies above 2.3 GHz.

41

Dual-band impedance matching

1. An ultra-wideband matching circuit allows the simultaneous matching

of all frequencies from low-band to high-band (see [III]).

2. A matching circuit can be used to broaden the two passbands of self-

resonant antennas [77] or to create the missing second band of a single-

band antenna without destroying the operation at the self-resonant

band [26].

3. A diplexer can be used as a matching circuit [23], and simple design

equations based on the well-known Butterworth filters have been intro-

duced in [V].

4. Single-band matching circuits can be converted into a dual-band match-

ing circuit using the dual-band transforms presented in [IV].

Methods 3 and 4 are discussed in more detail in the following.

4.1 Dual-band transforms

Dual-band impedance matching is so fundamental a problem that one

could imagine it to have been solved already dozens of years ago. In fact,

the published results on this topic are quite recent. Dual-band matching

at point frequencies has been represented in [101] based on basic circuit

theory and resonance frequencies. The results contain five to six circuit el-

ements. Just a few years ago, in [102] and [103], single matching elements

were replaced with higher order LC circuits to produce a perfect match-

ing of two complex impedances at two point frequencies. In addition, the

problem has been studied in [98] for a limited group of loads. Multireso-

nant circuits have also been used in [99], but emphasizing transforms for

open or short circuits leads to an unnecessarily large number of elements

in the obtained matching circuit.

A straightforward way to design a dual-matching circuit for impedance

loads having an arbitrary frequency dependence is presented in [IV]. The

presented transforms produce the realization with a minimum number of

elements and can be applied to any kind of load impedance with arbitrary

frequency dependence. The basis of this approach is two matching cir-

cuits designed separately for the desired passbands. One example of this

kind of matching circuit pairs is presented in Figure 4.2. If a matching

42

Dual-band impedance matching

Lp

Ls

ZL

at f1

Cp

Cs

ZL

at f2 Lp(ω22−ω2

1)

ω22(1+ω2

1LpCp)

1+ω22LpCp

Lp(ω22−ω2

1)

Ls(ω22−ω2

1)

ω22(1+ω2

1LsCs)

1+ω22LsCs

Ls(ω22−ω2

1) ZL

at f1 and f2

Figure 4.2. One possible dual-band matching transform producing a four-element circuitand relying on the transformation L1 → C2 [VI].

element is an inductance L1 at frequency f1 and a capacitance C2 at f2

(f2 > f1), a parallel resonator can describe both the values. Exact trans-

form equations convert the obtained single-band matching circuits into a

dual-band matching circuit, and Figure 4.2 shows also the dual-band im-

plementation with equations for the element values. The transformation

in the figure is denoted in the following by L1 → C2.

The transforms are based on the properties of reactance functions [59,

60, 104]. By replacing a single reactive element with a higher-order re-

active circuit, a desired functionality can be achieved at two or more fre-

quencies. The starting point for the process of dual-band matching is a

suitable matching circuit designed independently for each of the desired

passbands, which are then converted into a dual-band matching circuit

transforming one element at a time. Because the matching circuits are

first designed separately, design goals can be adapted flexibly based on

the requirements of the problem. A desired matching level and band-

width can be determined individually for each passband. In addition, the

impedance level can be different for both passbands, i.e., it can also differ

from the 50-Ω level.

Transform equations

Figure 4.3 summarizes the simplest LC-circuits which are used in a dual-

band circuit to replace one element in a single-band circuit. The simplest

transforms (e.g., L1 → C2 and C1 → L2) can be realized using the two-

element circuits I and II. Three elements are needed in more complicated

cases (e.g., L1 → L2). Transforms for open and short circuits (see [IV])

enable extending the approach for using different topologies in the pass-

bands as the starting point. An extensive set of transforms with equa-

tions is presented in [IV]. The solutions have a smaller number of ele-

43

Dual-band impedance matching

Transform Circuit realization

L1 → C2

L1 → L2, L1 < L2

C1 → C2, C1 < C2

L→ open

open→ C

I

CA LA

C1 → L2

L1 → L2, L1 < L2

C1 → C2, C1 < C2

C→ short

short→ L

II

LA

CA

L1 → L2, L1 > L2

C→ open

open→ L

III

LB

CA LA

LA

CA

LB

C1 → C2, C1 > C2

L→ short

short→ C

IV

LA

CA

CB

CB

CA LA

Figure 4.3. Simple reactive circuits that realize combinations of different reactive ele-ments at f1 and f2 [IV].

ments with equal or even better performance than in recently published

papers [98, 99].

The L sections appropriate for perfect matching in different regions of

the Smith chart were shown in Figure 2.4. For a CCE load, the type of

possible L sections is limited, especially if the goal is to use the simplest

transformations leading to a final dual-band realization with four ele-

ments. At low frequencies, where the load is capacitive, the first matching

element from the load is an inductor, and vice versa for higher frequencies.

Figure 4.2 presented one such solution and another typical dual-band re-

alization is shown in Figure 4.4. In the latter case, the original single-

band matching circuits often have a dual-band nature for CCE loads, pre-

senting an opportunity for wideband operation. In addition, this realiza-

tion does not produce a reject band between the passbands. A parallel

capacitance close to an antenna load makes this circuit appropriate also

for tuning purposes as demonstrated in [105].

Naturally, the single-band circuits used as the basis of transformation

44

Dual-band impedance matching

L1

C1

ZL

at f1

C2

L2

ZL

at f2

1+ω22L2C1

C1(ω22−ω2

1)

C1(ω22−ω2

1)

ω22(1+ω2

1L2C1)

L1(ω22−ω2

1)

ω22(1+ω2

1L1C2)

1+ω22L1C2

L1(ω22−ω2

1)

ZL

at f1 and f2

Figure 4.4. A dual-band matching circuit appropriate for tuning purposes [VI].

affect the final result, and choosing a reasonable pair of them requires

some consideration from the designer. If a wider bandwidth is desired, a

more intricate matching circuit yielding a wider bandwidth can be cho-

sen as the basis of a dual-band matching. For example, the alternatives

obtained with the bandwidth estimators in Section 3 can be used.

The examples presented in [IV] cover a wide range of applications, from

antennas to integrated circuits and sensors, illustrating that the approach

is directly applicable for various purposes. Additionally, examples for

coupling-element antennas demonstrate that also wide bandwidths can

be achieved. Moreover, the presented equations facilitate designing multi-

band matching circuits and are feasible also for solving double matching

problems where also the generator impedance has frequency-dependence.

Such impdance matching is needed for harmonic transponders [106, 107,

108] used to detect objects. The simplest harmonic transponder consists of

an antenna connected to a nonlinear element, e.g., a diode, as illustrated

in Figure 4.5. The radar detecting the objects operates at frequency f0,

and the transponder transmits at the first harmonic frequency 2f0. Thus,

the complex impedances of an antenna and a diode have to be matched at

both frequencies. We discuss this application more in [109, 110].

4.2 Simple design equations for dual-band matching of CCEs

Determining a dual-band matching circuit would be even easier, if design-

ing a single-band matching circuit were not necessary first separately for

both bands. By applying the design equations presented in [V], element

values for the final dual-band matching circuit are directly obtained. The

mathing circuit topology is the same as in Figure 4.2, but the element

45

Dual-band impedance matching

V (f0)

R(f) jX(f)

matching

circuit G(f) jB(f) I(2f0)antenna

diode

Figure 4.5. The equivalent circuit of an antenna matched to a diode. The antenna isrepresented with a Thévenin equivalent circuit and the diode with a Nortonequivalent circuit. [IV].

Rg L2 C2

L1

C1

ZA

Figure 4.6. Two branches of the filter: L1 and C2 constitute a low-pass and C1 and L2 ahigh-pass filter [V].

values are derived based on Butterworth filters.

The design formulas for Butterworth low-pass filters for arbitrary real

load resistor values [111] were already derived in the 1950s. The formulas

are valid only for resistors, i.e., real, constant, and frequency-independent

loads. Therefore, the formulas are not directly applicable to more compli-

cated loads. Although appyling filter theory is not straightforward, they

offer a reliable starting point to design filters and some such attempts

have been made in [V]. The novel matching solution is based on com-

bining a low- and high-pass filter in parallel and utilizing Butterworth

prototypes as the starting point.

In the case of CCE antennas, the real part of the impedance is usually

smaller than the generator impedance RG = 50 Ω. Therefore, the filter

prototype for the case RL < RG has been chosen. Figure 4.6 shows a sim-

ple diplexer, where a second-order low- and high-pass filter are combined.

C2 and L1 belong to the low-pass branch, and L2 and C1 form a high-pass

filter.

The element values are not very sensitive to changes in the load re-

sistor value. A load resistance value change of 10 Ω causes an element

value change of only 5–10 %. Therefore, determining the frequency scal-

ing terms ωl and ωh for the prototype filters is the crux of the method.

The simple equations were derived in [V] and presented in a more com-

pact form in [VI]. Despite the large number of equations, only solving

46

Dual-band impedance matching

110

60

10

5

60

100

60

10

5

50

130

60

50

10

5

3

Figure 4.7. The CCE antennas used in the examples: antenna B, antenna D with sym-metric (30 mm) and asymmetric (26 mm) feeding positions, and antenna E.Dimensions are in millimeters. [VI]

a second-order equation and a number of substitutions are required to

obtain the element values of a diplexer producing a dual-band matching

circuit. The examples in [V] demonstrate that matching circuits for real

CCE antennas can be designed with these straighforward calculations,

and wide bandwidths within practical frequency ranges are obtained us-

ing the matching circuit consisting of only four elements. Fast design of a

matching circuit enables evaluating different antenna designs efficiently,

which promotes finding more effective antenna structures for dual-band

usage.

4.3 Comparing different methods for dual-band matching

Evaluation of the different techniques for dual-band matching with a sin-

gle feeding port has been presented in [VI]. The suitability of the different

example antennas in Figure 4.7 is analyzed using the bandwidth esti-

mators [I]. The bandwidth estimators are defined for one passband at a

time, but does it still give a useful ranking of antennas also for dual-band

matching?

Figure 4.8 compares the obtainable bandwidths for the studied anten-

nas B, D (with symmetric and asymmetric feeding) and E using band-

width potential (bwL). Antenna E, with its long ground plane, is the best

alternative in the lowest frequency range below 1 GHz, and, especially in

the high band (1.6–2.3 GHz), the achievable relative bandwidth is clearly

47

Dual-band impedance matching

1 1.5 2 2.5

0.1

0.2

0.3

0.4

0.5

0.6

Frequency (GHz)

Rel

ativ

e ba

ndw

idth

BDDasymE

Figure 4.8. The bandwidth potential for antennas B, D, Dasym, and E. [VI]

the largest, which indicates its good matching potential for dual-band us-

age.

Bandwidth estimators bwF and bwG for antennas Dasym and E are

also analyzed in [VI]. Three methods are compared there: method I is

based on equations from [V], and methods IIA and IIB are based on the

transforms from [IV], corresponding to Figures 4.2 and 4.4, respectively.

The circuit used in method I and IIA reduces to an ’F’ matching circuit

in the passbands when the resonance frequency of the first resonator is

between the passbands. Similarly, for the circuit in Figure 4.4, bandwidth

estimator bwG gives a reasonable merit.

The dual-band matching results for antenna D show that methods I and

IIA yield almost identical bandwidths, which is interesting, because the

premises of the methods are totally different: Method I gives the exact

equations for element values of the low and high-pass filter whereas in

method IIA, the original matching circuits are sought through optimiza-

tion after which the results are transformed into the final dual-band cir-

cuit. Based on [IV], the exact equations only at single frequencies can be

presented as done in [VI], whereas [V] gives clear equations to determine

a dual-band matching circuit for a wide band. However, [IV] produces

more general results which can be applied to a wide range of applications,

and, based on them, deriving design equations for different special pur-

poses may be possible.

As an example of the use of design equations, the different feeding po-

sitions for antenna D have been compared in [V]. Especially at the high

band, the upper limit of the passband depends substantially on the feed-

ing position. The conclusion in [V] was that a wider passband for high

frequencies can be achieved with the asymmetric position of the feed. Fig-

48

Dual-band impedance matching

600M 1.1G 1.6G 2.1G 2.6G−12

−9

−6

−3

0|S11|dB

f/Hz

Method I Method IIA

Method IIB

Figure 4.9. Dual-band matching for antenna D with asymmetric feeding with differentmethods [VI].

ure 4.9 shows the results for the configuation with the asymmetric feed,

and passbands achieved with method IIA confirm the result. Accordingly,

the fast methods to determine the matching circuit promote modifying the

antenna structure appropriately.

Even if the bandwidths obtained with these methods do not cover all the

LTE-A frequencies, the presented configurations can offer a basis for de-

signing tunable matching-circuit solutions [105] and can be used to eval-

uate the potential of different antennas.

49

Dual-band impedance matching

50

5. Dual-band matching with separatefeeding ports

Earlier sections have discussed impedance matching at one port. Band-

width estimators offer a solution for recognizing a promising antenna

structure with a corresponding matching circuit, and Section 4 and [VI]

discussed cases where one radiating element was utilized to create dual-

band performance. However, this covers only a part of the opportunities

to create a dual-band operation by utilizing circuit elements.

Figure 5.1 gathers different configurations to implement a dual-band

operation. Utilizing the whole antenna volume for low frequencies would

be favorable in order to improve efficiency at the lowest frequencies, and

thus, only one radiating element is used in alternative a) and is dis-

cussed in the previous section. Several antenna solutions have been pre-

sented also using tunable matching circuits or a constant-valued diplex-

ing matching circuit [105, 23]. Moreover, one antenna element can be

used with many feeds [23], and such a multi-feed single-element antenna

is desribed as case b) in Figure 5.1.

On the other hand, the optimal shapes of the radiating elements are con-

tradictory at the low and high bands, as shown, e.g., in [26]. Compromises

can be avoided by utilizing separate radiating elements, as illustrated in

case c) in Figure 5.1. Usually, separate matching circuits are designed for

all antenna feeds, as in [112, 113, 24] and [II]. Alternatively, in case d),

the antenna elements are connected to one common input [114].

Two (or more) radiating elements placed in the same, small volume

causes mutual coupling between the different excited ports. Thus, iso-

lation becomes then a new aspect to consider and designing multiport

matching is necessary. The design principles for wideband matching cir-

cuits of two-ports in case c) are presented in [VII] and are discussed in the

following.

51

Dual-band matching with separate feeding ports

matching

circuit

radiating

partLOW

HIGH

matching

circuit

matching

circuit

radiating

part

radiating

partLOW & HIGH

c)

a)LOW

HIGH

LOW

HIGH

b)

d)

matching

circuit

matching

circuitLOW

HIGH

LOW & HIGHmatching

circuit

radiating

part

radiating

part

LOW

HIGH

radiating

partLOW

HIGH

Figure 5.1. Different ways to construct an antenna solution operating at two passbands.

5.1 Scattering parameters for multiports

Understanding multiport theory is necessary to design matching circuits

for a system consisting of many radiating elements [115]. The existence

of multiple ports makes the problem remarkably more challenging — one

port can be described with one parameter, whereas two ports require a

2 × 2 matrix with four parameters1, and the complexity increases rapidly

when the number of ports increases. The fundamental property of the

scattering parameters of a passive multiport [116, 117, 118] is obvious

from the conservation of energy:

N∑j=1

|Sij |2 ≤ 1 (5.1)

for each row i of the scattering matrix. The equility sign holds for a loss-

less system, in which power is conserved. In this context, the radiated

power is also seen as power lost from the system. Therefore, it becomes

immediately clear that in the case of a two-port both the reflection coef-

ficient (S11) and the transducer power gain (S21) are equally important

when aiming to maximize the radiated power. The power lost in a two-

port is 1 − |S11|2 − |S12|2, which consist of radiation, substrate, and ohmic

1For reciprocal systems, such as antennas, this naturally reduces to three un-equal parameters.

52

Dual-band matching with separate feeding ports

Z1 Z2

MC1 ANT

S

MC2

Figure 5.2. Studying a matching problem at port 1 in the case of two ports.

losses. In practice, far-field measurements are the only reliable way to

determine the exact division between them, as demonstrated in [119].

Also, Total Active Reflection Coefficient (TARC) [120, 121] is used to

characterize the radiation performance of multiport antennas and to de-

scribe the effectiveness of the system. A scattering matrix is defined

as [116, 117]

b = Sa, (5.2)

where by definition ai:s are the incident waves toward ports and bi:s are

the waves reflected from the ports. If the radiation is the only cause for

the lost power, TARC is the ratio of the reflected and incident powers:

TARC =

√N∑

i=1|bi|2√

N∑i=1

|ai|2. (5.3)

This definition sums the power over the all ports. If only one port is ex-

cited at a time, TARC is the square root of the summation in Eq. (5.1)

and the criteria are congruent except the TARC describes the amplitude

instead of power.

When analyzing the situation at port 1, the other ports are shown as

load impedances. Figure 5.2 presents the examination for the two-port.

The properties of passive networks hold for scattering parameters deter-

mined for the dashed or dotted range. To improve the radiation efficiency,

circuit elements can be used to decrease either S11 or S21.

A matching circuit MC1 makes S11 smaller, but due to reciprocity (S12 =

S21 for the dashed range), isolation cannot be improved with this match-

ing circuit [122]. Instead, an appropriate load Z2 prevents the power from

proceeding to port 2. However, if the antenna ports are fed at the same

frequency as in the multiple-input-multiple-output (MIMO) case, the cir-

cuits in Figure 5.2 cannot produce both matching and mismatching at the

same frequency, although utilizing an asymmetric impedance matching

53

Dual-band matching with separate feeding ports

can produce a minor benefit when studying the performance over a wider

band.

The publications included in this thesis as well as the discussion in this

section focus on cases, where the matching circuits using the format pre-

sented in Figure 5.2 can be efficiently used:

1. The antenna ports operate at different frequencies and matching cir-

cuits can be designed as filters that create the desired passbands and

stopbands.

2. The isolation of the antenna is originally sufficient, and the matching

circuits at the ports can be designed quite independently.

The next section will widen the discussion, e.g., showing how a decoupling

circuit can be used to improve the isolation in a MIMO case.

5.2 Impedance matching in the case of multiple ports

As pointed out in [VII], it is not initially clear for which impedance the

matching circuit at port 1 should be designed, because the impedance seen

at port 1 is not equal to the normalization impedance Z0, but it depends

on S21 and the relation between impedances Z2 and Z0 (see Figure 5.2):

Z1 = Z01 + ρ1

1 − ρ1, (5.4)

where

ρ1 = S11 +S2

21ρ2

1 − S22ρ2(5.5)

and

ρ2 =Z2 − Z0

Z2 + Z0. (5.6)

All impedances vary significantly with frequency, which creates quite a

challenge in the wideband matching of the multiport. The goal of imped-

ance matching is to maximize the power transferred to a desired load,

which in this case is the radiation resistance of the antenna. In the single

port case, studying power is straighforward. Power can reflect back due

to the impedance mismatch, vanish as heat in matching components, or

be absorbed into the substrate. A multiport system has several reference

planes with different impedance levels, and power can disappear to an-

other port due to some impedance mismatch and vanish as heat there,

too.

54

Dual-band matching with separate feeding ports

Although necessary and sufficient conditions for broadband matching of

multiport networks have been presented [123, 124], they do not greatly

help in designing simple practical circuits. Approaches starting from con-

jugate matching [115, 125] produce a narrowband solution, because the

conjugate matching is impossible to realize with passive circuit elements

over a wide frequency band. The unsatisfactory starting point for wide-

band antennas forces seeking a solution through optimization and makes

impossible to follow an analytical examination, whereupon giving an ex-

act method for an arbitrary load is impossible.

Guidelines for matching design

Essential aspects of multiport matching over a wide frequency band in the

case of separate frequency bands fed to ports are summarized in [VII].

The first task is finding the proper matching topologies. The chosen

topology should guarantee achieving adequate matching over the desired

passband and create a reject band at other frequencies to control isolation.

In addition, a matching circuit should also be seen as an appropriate load

such that matching the impedance at the other port according to Eq. (5.4)

is possible. Including resonators to a matching circuit increases freedom

in the final topology. Such circuits are applied in many publications [114,

24, 126] indicating that a resonator circuit is the recommended choice.

Also, bandwidth estimators can be used to evaluate promising matching

topologies, as done in [II].

After finding a promising set of matching topologies, optimization is

used to determine the element values. The number of unknowns should

be minimized to guarantee that the optimization algorithm finds a solu-

tion regardless of the used initial values, as discussed also in Section 3.3.

Splitting a problem into smaller ones is important in order to facilitate

finding a good solution. By defining the optimization goals so that all de-

pendencies are considered, good results can be found by optimizing both

matching circuits in turns such that only element values of one matching

circuit are varied at a time. The involved dependencies between matching

circuits at separate ports lead to an iterative design process.

Although the effect of the matching circuit at the unfed port may seem to

be insignificant in the final design, the dependencies have to be properly

controlled during the optimization process. Otherwise, the optimization

may proceed in a wrong direction preventing the desired operation at the

other ports and deteriorating isolation.

55

Dual-band matching with separate feeding ports

110

60

10

60

6

30

w2

w1

Figure 5.3. The studied two-element CCE antenna: the larger element with width w1 forthe low band fed at the center of the ground plane and at the small corner-fedelement with width w2 for the high band. w1 and w2 are varied. [II]

5.3 Applying bandwidth estimators to two-ports

To demonstrate the presented principles in practice, a set of prototypes

have been designed. Combining more than one closely spaced radiating

elements in the same design becomes more straighforward after survey-

ing the suitable matching topologies and determining adequate sizes for

the element (see page 35). However, in order to achieve the best total per-

formance, a systematic comparison of structures is needed. A workable

method for designing matching circuits is essential in order to find the

best alternative from several two-element structures.

A systematic study [II] has been continued for a set of alternatives, as

described in Figure 5.3. The structure is fully planar with a substrate

height of 1.5 mm, and the widths w1 and w2 were varied using the values

44, 46, 48, 50, and 52 mm for w1, and 6, 8, 10, 12 mm for w2. All reasonable

combinations of w1 and w2 were studied.

The mutual coupling between ports in two-port antennas should be min-

imized in order to achieve high efficiency. The method and principles de-

scribed in [VII] have been used to design circuit parts. Because isolation

of the final design depends on the chosen matching solution, matching

circuits and their element values have to be determined before ranking

the alternatives. From the large number of tested structures, only two

combinations fulfilled the requirements.

At this stage of the thesis, the reader is certainly eager to see a real

antenna. Figure 5.4 presents the prototype A on an FR4 substrate and

having elements of size 46 mm and 10 mm. It was measured, and the

results are reported in [II], showing good agreement with simulations.

The same structure was also manufactured on a low-loss Rogers 4003C

substrate (prototype B in [VII]) to study the effect of substrate losses,

but the difference in efficiencies was not significant, although the Rogers

56

Dual-band matching with separate feeding ports

4.7n 5.6p

12n

port 1

1.8p

4.3n

1.2p

port 2

Figure 5.4. The measured prototype with the matching circuits mounted on the PCB.

substrate was assumed to produce less losses than the FR4 substrate.

Another alternative (prototype C in [VII]) is to combine elements of size

50 mm and 6 mm, but this requires an additional matching element (seven

in total), as we described in [127]. These prototypes demonstrate that the

choices made based on the theoretical study and ideal simulations steer

towards a practical design.

57

Dual-band matching with separate feeding ports

58

6. Summary and beyond

The earlier sections have described several viewpoints to the impedance

matching of mobile antennas. Figure 6.1 collects results describing differ-

ent ways to combine a matching circuit and an antenna. For one antenna

element, a goal can be, say a contiguous passband, as a case a) in Fig-

ure 6.1 and in papers [I, II, III]. Alternatively, the passband can consist

of two parts, as shown in a case b) and in papers [V, IV, VI]. Also, an

antenna can have two feeds and two separate matching circuits, as in c)

and papers [II, VII].

In case a), the challenge with a contiguous band is achieving an ade-

quate passband, and in all probability the future will bring new frequency

bands to mobile communication. As can be observed, solution b) may pro-

duce a better matching level due to the narrower passbands, and it is an

appropriate solution for tuning, too. In case c), the available volume for

the antenna is to be divided for the two elements, and the challenge in

the matching circuit design increases when isolation is a new aspect to be

considered.

The key issues used to rank different approaches may change in the fu-

ture. For example, the losses of tunable elements will probably decrease

making a tunable narrowband matching an attractive choice from an an-

tenna point of view. On the other hand, the use of carrier aggregation

(CA) (more, e.g., in [128, 129]) requires simultaneous matching at various

combinations of frequency bands, which is not easy to implement with

a tunable solution. In addition, introducing new frequency bands, e.g.,

about 1.5 GHz, will promote the use of a contiguous band. There are also

plans to extend the bandwidth of the single bands to increase the data

rate, and thus achieving the desired relative bandwidth at the lowest fre-

quencies starts to require quite large antennas and the benefit obtained

with tuning will decrease.

59

Summary and beyond

600M 1.1G 1.6G 2.1G 2.6G

−12

−9

−6

−3

0

|S11|

dB

f/Hz

800M 1.25G 1.7G 2.15G 2.6G

−12

−9

−6

−3

0

|S11|

dB

f/Hz

700M 1.1G 1.5G 1.9G 2.3G 2.7G 3.1G

−12

−9

−6

−3

0

|S11|

dB

f/Hz

Figure 6.1. Different designs for impedance matching of antennas from this thesis.

6.1 Interesting topics to follow up

Only a small part of the potential of exploiting circuit elements in de-

signing a antenna system has been covered. These days a mobile device

includes a bundle of antennas, and Figure 6.2 shows different additional

circuit blocks which can be used to advance antenna design and to im-

prove the total performance. The grey area in the figure depicts the part

that has been discussed earlier in this thesis.

After all, in a multiport system, lumped elements placed at ports, be-

tween ports, or to extra ports will always affect both the impedance match-

matching

circuit 2

radiating

partFEED 1matching

circuit 1

Zparasitic

Zisolation

21

3

FEED 2

Figure 6.2. An antenna system including different possibilities to utilize matching ele-ments.

60

Summary and beyond

ing and the isolation through mutual dependence. As a result, they affect

also the efficiency. Although mastering the antenna entity is possible at

a single frequency, wideband operation (even divided into two separate

bands) sets an additional challenge. The final performance is a compro-

mise between several aspects; [27] describes many practical issues, which

must be considered when placing an antenna in a radio system.

Some ways to utilize lumped elements as a part of the antenna design

are discussed further in the following to give reasonable starting points

for future work in developing simple design procedures. In addition to

these, the general results presented in [I] and [IV] can be applied to

impedance matching in other fields of application as well.

6.1.1 Improving isolation with lumped elements

Nowadays, interest is concentrated on increasing the channel capacity

with a MIMO system, which intensifies the use of the limited spectrum.

Thus, the operating frequency is the same for several elements, and the

previous approach explained in Section 5.1 is not valid. To improve isola-

tion in this case, an additional isolation circuit can be connected between

ports 1 and 2, as illustrated in Figure 6.2. In addition, a parasitic element

could be used to modify the operation of the radiating part.

For mobile antennas, achieving good isolation and a low correlation at

the same frequency is a demanding task especially at the low frequencies,

where the ground plane is the main radiator. Methods for decreasing the

mutual coupling has been studied actively for long, and earlier attempts

have been collectively summarized, e.g., in [130, 29]. Decoupling methods

include the following:

1. Placing the antenna elements at optimal positions. This does not give

adequate isolation for small mobile antennas at low frequencies, where

the number of possible wavemodes is very limited [18].

2. Modifying the shape of the PCB with, e.g., slots [131], which is not

usually applicable to practical designs.

3. Designing decoupling networks, which typically produce narrowband

behavior. A comparison of narrowband and broadband decoupling and

matching networks for compact antenna arrays is presented in [119].

61

Summary and beyond

4. Utilizing parasitic elements, for which the design procedure is difficult

to outline [132].

5. Utilizing neutralization lines for compact antennas as, e.g., in [25], but

this has its own design challenges, as analyzed in [133].

Moreover, we proposed utilizing lossy elements as a part of the decoupling

circuit to produce a wider bandwidth for isolation improvement [134], but

applying this naturally requires careful consideration of efficiency issues.

The interest in the isolation studies focuses on the MIMO case. Re-

cently, even and odd mode excitations [135] have been exploited to ana-

lyze symmetrical MIMO structures. Even and odd mode excitations have

been utilized in [136] to simplify the problem and to facilitate design-

ing decoupling circuits analytically. Designing a decoupling and conju-

gate matching network is combined also in [137]. In addition, a tun-

able decoupling network for closely spaced antennas has been presented

in [138], and the idea of isolation improvement is described more analyt-

ically in [139]. The approach can be applied also with dual-frequency de-

coupling [140]. In [141], common and differential mode admittances have

been used instead of even and odd modes, but the approach is equivalent.

Moreover, a systematic examination of multiport decoupling networks is

offered in [125], leaving bandwidth as a future challenge even there.

With the even and odd mode excitations, the circuit is simplified along

the symmetry axis. The even and odd mode loads can be considered sepa-

rately, as shown in Figure 6.3, where the study is presented for a Π-type

matching circuit. An F topology could be a potential candidate as well.

In addition, the even and odd modes S11 parameters (or impedances) are

easy to calculate from the normal S parameters:

Se11 = S11 + S21 (6.1)

So11 = S11 − S21. (6.2)

The above equations also reveal that the fully matched and isolated case

(S11 = S21 = 0) corresponds to the case So11 = Se

11 = 0. Thus, the multi-

port matching problem can be solved by simply realizing the impedance

matching for the even and odd mode impedances. Efficient tools, such as

the bandwidth estimators, make analysis handy. The last example in [I]

already demonstrates that the bandwidth estimators have the potential

also to facilitate a decoupling circuit design. A similar approach as in [II]

62

Summary and beyond

Y4 Y2

Y3 Y1

Y4 Y2

Ys

Ys

Y4 Y2

Ys

Ze

Y4 + 2Y3 Y2 + 2Y1

Ys

Zo

Figure 6.3. Symmetrical decoupling and matching circuit for a two-element antenna (onthe left), and the examination of the for even and odd modes separately (onthe right). The figure is a modification of the figures presented in [141, 138,136].

could be used for searching an optimal structure in order to further widen

the bandwidth. Consequently, getting acquainted with the even and odd

mode operation of CCE structures would be interesting in future.

6.1.2 Use of parasitic scatterers

Adding an extra port to the design with a reactive load brings a new oppor-

tunity to improve the design. Parasitic scatterers are shown as an extra

load at an additional port. According to Eq. (5.5), the reflection coefficient

at another port is known. Therefore, at a single frequency, the optimal

loading producing zero reflection can be solved:

Zopt = Z0 · ΔS + S11

ΔS − S11, (6.3)

where ΔS = S11S22 − S221 is the determinant of the S matrix.

An analysis for a parasitic scatterer as an additional port is presented

in [132] with z parameters. Solving the problem at one frequency leads

to a rather narrowband solution. In [142], parasitic elements with reac-

tive loads have been used to modify the antenna radiation pattern, but a

similar approach could be used also to improve efficiency. The difficulty is

finding a method for placing additional ports in an optimal manner. The

theory of characteristic modes has been utilized as a tool to determine lo-

cations for the ports [143, 144]. Furthermore, in [145], an excitation at an

additional port is utilized to match another port. Also, in this approach,

the properties of the antenna mainly determine how wideband results can

be achieved.

In addition, non-Foster circuits, i.e., active circuits, have been used [146,

147] as a load at an additional port to improve the impedance match-

ing. Realizations with the active circuit are not limited to positive real

63

Summary and beyond

functions as in the case of passive elements [111]. Thus, it is possible to

achieve a wide band. However, sensitivity emerges as an important addi-

tional design parameter [148], and an efficiency consideration makes this

kind of approach currently unsuitable for mobile antennas.

Although adding an extra port with an additional reactive load creates a

new opportunity to modify the design, finding the optimal position for the

port and determining an appropriate reactive load brings a lot of freedom

to the design process. Therefore, developing a systematic design method

is challenging. Nevertheless, the bandwidth estimators give an efficient

way to determine three-element circuits producing the desired behavior

over a wide frequency band. If the complex conjugate of Zopt is used as

the normalization impedance to determine the bandwidth estimator, the

optimal reactive three-element circuit for a parasitic loading is easily de-

termined. This promotes achieving wideband results also with passive

loads. However, the price paid for the improvement is the required addi-

tional space for a parasitic element, and efficiency issues must be taken

into account. The usefulness of the approach depends on the application.

6.1.3 Tunable circuits

The matching elements as a part of the antenna design enable achieving

adequate bandwidth with a smaller structure. A step forward is utiliz-

ing tunable matching elements. Thus, covering the whole frequency band

is not needed simultaneously, and the size of the antenna structure can

be minimized further. The reduction of the antenna element volume by

a factor of four with an adaptive matching network has been reported

in [95]. On the other hand, tunable matching makes possible adjusting

the impedance matching automatically, e.g., conforming with changes in

the environment [149]. Different tunable matching circuits have been

used for the antenna matching [23, 114, 87], but the bandwidth require-

ments are still increasing, and MIMO operation is required as well [105].

From a design point of view, an adjustable element as a part of the

matching circuit brings new aspects to be considered [31]. Studying the

losses in tunable circuits is essential, as emphasized in [150, 151]. Addi-

tional losses introduced to the design with tunable circuit elements makes

achieving high efficiency difficult [23]. The low frequencies are the most

critical for component losses, as we illustrated in [152]. When tunable el-

ements with lower losses will be available, their usage is going to be more

favourable.

64

Summary and beyond

An important aspect with strongly frequency-dependent antenna loads

is achieving a sufficient tuning ratio, which is determined by the high-

est frequency. Due to the losses, only one tunable element is typically

used, and thus the position of the tunable component within the circuit is

crucial. Placing the tunable element as close to the frequency-dependent

antenna load as possible will provide the widest tuning range compared

to constant the 50 Ω impedance level. Because a parallel capacitor is of-

ten used for tuning in practical implementations, the circuit presented in

Figure 4.4 may offer a potential starting point for the design.

Tunable matching circuits have not been studied a lot from an antenna

perspective. In the circuit community, the capability of tunable circuits

has been researched based on the area of the impedances that they are

able to match on the Smith chart [153]. Especially the algorithms for ap-

plying a Π topology have been presented [154, 149], but determining the

element values require quite an extensive computation. Furthermore,

these studies concentrate on impedances at a single frequency, and the

bandwidth requirement are forgotten. As shown in [105], the behavior

of the antenna impedance provides an important figure-of-merit for the

losses. The antenna and the matching circuit cannot be designed as sep-

arate entities, but rather a co-design is needed. The antenna impedance

should perform in such a way that the matching component losses are

minimized, but improvement in the radiating structure towards this tar-

get may, e.g., decrease the tuning range.

Developing accessible design strategies for tunable antennas is still in

its infancy. Plenty of research is required so as to analyze the strengths of

different circuit topologies, to find ways to minimize losses and maximize

tuning range in the case of a complicated load. Furthermore, the prop-

erties of the chosen tuning element have to be taken into account at an

early stage of the design.

6.2 Co-design of matching circuit and radiating part

This research indicates that it seems to be extremely difficult to master

wideband impedance matching generally for all circuit topologies and for

all antenna loads. In addition, constructing an antenna with a particular

impedance behavior is challenging. Therefore, finding the most potential

solutions for mobile antennas will require co-design of the matching cir-

cuit and the radiating part.

65

Summary and beyond

Design principles in co-design

When formulating a procedure for co-design, identifying the most funda-

mental constraints and influence of details is crucial. First of all, the size

of the radiating part has the largest effect on the total performance due to

the laws of physics. No one will deny the importance of the smaller details

either: the position of the feed, width and the shape of the element, and so

on. If a matching circuit is attached to the design at this phase, the result

is a gamble: in some cases, a significant benefit is achieved and sometimes

not. A bad design cannot be redeemed with the matching circuit due to the

fundamental gain-bandwidth limitations. The first idea of increasing the

number of matching elements to find more sophisticated solutions is not

the most effective one, either. Aiming to widen the available bandwidth is

often better achieved by modifying the antenna structure.

In order to reap the full benefit, the circuit has to be a part of the process

from the first step. Formulating an efficient method to alternate both

modifications in the radiating part and seeking the values of the matching

circuit elements is essential. A significant part of the potential can be lost,

due to a lack of knowledge and the matching circuit design relying on false

starting points. A poorly matched antenna does not radiate efficiently, and

it may also deteriorate the operation of an IC.

On the circuit side, the basic principle in formulating a design procedure

is simplification. Developing efficient ways to design matching circuits

for complicated loads is challenging enough even for three-four-element

circuits. The spectrum of ways of using only a couple of lumped elements

is wide and unexplored, although some concepts [I] and approximative

equations [V] are offered in this thesis.

Examples

The co-design approach has already been applied in few papers by our re-

search group. In [26], matching circuit properties have been taken as a

guideline in the antenna design, and the structure is optimized for a cer-

tain matching solution. A dual-band mobile antenna has been designed by

choosing a high-pass type matching circuit for the low band in the begin-

ning of the design process, and then the antenna geometry is used to cre-

ate the desired operation for the high band. In addition, a pre-determined

tunable matching topology is used to compare alternative antenna designs

and to find the most promising of the set [105]. Also in [II], the intelli-

gent use of matching circuits led to a final structure. In all these cases,

66

Summary and beyond

the starting point is choosing a method for the matching circuit design,

and the radiating part is modified to obtain the best choice for the chosen

matching circuit topology. Discovering both a good structure for the ra-

diating part and an appropriate matching circuit is a necessity in order

to exploit the full potential of a non-resonant mobile antenna. Moreover,

placing an antenna in a real device brings new issues to consider, which

offers plenty of room for research and challenging work for engineers.

6.3 Summary of publications

Determining bandwidth estimators and matching circuits for eval-

uation of chassis antennas

A novel algorithm for determining the practically achievable bandwidth

of a strongly frequency-dependent load impedance is presented. The knowl-

edge obtained with the bandwidth estimators facilitate evaluating the po-

tential of different antenna structures and enable efficient co-design of an

antenna and a radiating part. The versatility of the proposed computa-

tional algorithm is illustrated with examples.

Designing capacitive coupling element antennas with bandwidth

estimators

A representative set of capacitive coupling element antennas is system-

atically analyzed. As a result, guidelines for finding the best antenna

structures is given. An example design shows that the antenna solution

found based on the systematic analysis produces a good working antenna;

measurements are in good agreement with simulated results.

Improving handset antenna performance by wideband match-

ing optimization

A new, easily adopted procedure is presented to design wideband match-

ing circuits for an arbitrary, frequency-dependent load impedance. Exam-

ples indicate the potential of wideband matching design to improve the

overall performance of handset antennas.

Dual-band matching of arbitrary loads

The paper presents how any two matching circuits designed separately

67

Summary and beyond

for frequencies f1 and f2 can be converted into a dual-band matching cir-

cuit operating both at f1 and f2. The transform is based on the properties

of reactance functions. Due to the fundamental nature of the paper, re-

sults can be applied in a very flexible way with different goals and to

different applications.

Design equations for dual wideband matching of capacitive cou-

pling element antennas

Simple design equations are introduced to determine element values

for a dual-band matching circuit appropriate for CCE antennas. The

paper also demonstrates the use of filter theory for matching of highly

frequency-dependent loads. The benefit of the equations was demonstrated

by comparing antennas having different feed positions. Choosing the most

promising antenna structure becomes efficient if the matching circuit de-

sign can be automized.

On designing dual-band matching circuits for capacitive cou-

pling element antennas

The paper discusses four different techniques for producing dual-band

matching circuit solutions for CCEs. The potential of bandwidth estima-

tors for evaluating the suitability of an antenna for dual-band usage is

demonstrated. The paper proposes a co-design approach where a match-

ing circuit is taken into account already in the antenna design.

Wideband matching of handset antenna ports at noncontiguous

frequency bands

Design principles for wideband matching of two-ports are presented. Es-

sential aspects in the optimization procedure are emphasized and demon-

strated with examples.

68

7. Conclusions

An antenna designer cannot get rid of the laws of physics. A resonance fre-

quency of a structure depends on its physical dimensions, and the avail-

able bandwidth is restricted by physical limits. In order to fulfill the ever-

challenging technical requirements and to achieve the optimal efficiency,

a matching circuit and a radiating structure have to be designed together.

The antenna impedance plays a major role, but the antenna performance

can be greatly improved with skilled circuit design. To handle this ensem-

ble, methods for designing matching circuits have been developed.

The prerequisite in combining circuit elements efficiently to a part of

the antenna design is to produce accessible tools [I] to evaluate before-

hand the obtainable benefit provided by the circuit elements. This kind of

tools make it possible to compare antenna structures and to adjust a radi-

ating part and an antenna impedance so that better total performance is

achieved with a circuit. Aiming towards co-design of the antenna and the

matching circuit requires also simple methods for a dual-band matching-

circuit design, such as the ones introduced in this thesis [V, IV]. In ad-

dition, the bandwidth estimators can be applied to systematically seek

optimal antenna structures, and they also benefit the design of multiele-

ment antennas, as demonstrated in [II]. Plenty of ideas worth developing

were left even for the future.

A part of the achievable potential can be lost if the matching circuit is

ignored when designing the radiating parts. With the design methods

introduced in this thesis, the circuit elements can be efficiently used to

exploit the capacity of an electromagnetic structure yielding a better an-

tenna performance. Also, a deeper understanding of EM fields in small

antenna structures would be welcomed, and, after all, more cooperation

between the disciplines is needed to speed up mobile antenna develop-

ment.

69

Conclusions

70

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ISBN 978-952-60-6357-7 (printed) ISBN 978-952-60-6358-4 (pdf) ISSN-L 1799-4934 ISSN 1799-4934 (printed) ISSN 1799-4942 (pdf) Aalto University School of Electrical Engineering Department of Radio Science and Engineering www.aalto.fi

BUSINESS + ECONOMY ART + DESIGN + ARCHITECTURE SCIENCE + TECHNOLOGY CROSSOVER DOCTORAL DISSERTATIONS

Aalto-D

D 12

3/2

015

The rapid increase in the use and capabilities of mobile devices in the beginning of the 21st century pose demanding goals to antenna designers. With the current massive use of wireless data transmission, a broadband operation should be achieved with high efficiency. How can circuit elements be utilized to increase the bandwidth of the antenna? This thesis focuses on finding practical tools to facilitate the co-design of the antenna and the matching circuit.

Anu L

ehtovuori O

n wideband m

atching circuits in handset antenna design A

alto U

nive

rsity

Department of Radio Science and Engineering

On wideband matching circuits in handset antenna design

Anu Lehtovuori

DOCTORAL DISSERTATIONS