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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
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
)[email protected]@[email protected]@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
References
[1] H. A. Wheeler, “Small antennas,” IEEE Transactions on Antennas andPropagation, vol. 23, pp. 462–469, Jul. 1984.
[2] R. M. Fano, “Theoretical limitations on the broadband matching of arbi-trary impedances,” Journal of the Franklin Institute, vol. 249, pp. 57–83,139–154, 1950.
[3] J.-E. Mueller, T. Bruder, P. Herrero, N. Norholm, P. Olesen, J. Rizk, andL. Schumacher, “Requirements for reconfigurable 4G front-ends,” in IEEEMicrowave Symposium, 2013, pp. 1–4.
[4] C. A. Balanis, Antenna Theory: Analysis and Design. John Wiley & Sons,1997.
[5] W. L. Stuzman and G. A. Thiele, Antenna Theory and design. John Wiley& Sons, 2013.
[6] J. D. Kraus and R. J. Marhefka, Antennas for All Applications. New York:McGraw-Hill Companies, 2002.
[7] K. Fujimoto and H. Morishita, Modern Small Antennas. Cambridge Uni-versity Press, 2013.
[8] K.-L. Wong, Planar Antennas for Wireless Communicaiatons. John Wiley& Sons, 2003.
[9] J. Rahola and J. Ollikainen, “Optimal antenna placement for mobile ter-minals using characteristic mode analysis,” in European Conference on An-tennas and Propagation (EuCAP 2006), Nice, 2006.
[10] E. Antonino, C. A. Suárez, M. Cabedo, and M. Ferrando, “Wideband an-tenna for mobile terminals based on the handset PCB resonance,” Mi-crowave and Optical Technology Letters, vol. 48, Jul. 2006.
[11] M. Cabedo, E. Antonino, A. Valero, and M. Ferrando-Bataller, “The theoryof characteristic modes revisited: A contribution to the design of anten-nas for modern applications,” IEEE Antennas and Propagation Magazine,vol. 49, pp. 52–68, Oct. 2007.
[12] J. J. Adams and J. T. Bernhard, “A modal approach to tuning and band-width enchancement of an electrically small antenna,” IEEE Transactionson Antennas and Propagation, vol. 59, pp. 1085–1092, Apr. 2011.
71
References
[13] H. Li, Y. Tan, B. K. Lau, Z. Ying, and S. He, “Characteristic mode basedtradeoff analysis of antenna-chassis interactions for multiple antenna ter-minals,” IEEE Transactions on Antennas and Propagation, vol. 60, pp.490–502, Feb. 2012.
[14] R. Martens and D. Manteuffel, “Systematic design method of a mobilemultiple antenna system using the theory of characteristic modes,” IETMicrowaves, Antennas & Propagation, vol. 8, pp. 887–893, Sep. 2014.
[15] E. Safin and D. Manteuffel, “Manipulation of characteristic wave modesby impedance loading,” IEEE Transactions on Antennas and Propagation,vol. 63, pp. 1756–1764, Apr. 2015.
[16] P. Vainikainen, J. Ollikainen, O. Kivekäs, and I. Kelander, “Resonator-based analysis of the combination of mobile handset antenna and chassis,”IEEE Transactions on Antennas and Propagation, vol. 50, pp. 1433–1444,Oct. 2002.
[17] A. Cabedo, J. Anguera, C. Picher, M. Rib’o, and C. Puente, “Multibandhandset antenna combining a PIFA, slots, and ground plane modes,” IEEETransactions on Antennas and Propagation, vol. 57, pp. 2526–2533, Sep.2009.
[18] Z. Miers, H. Li, and B. K. Lau, “Design of bandwidth-enhanced and multi-band MIMO antennas using characteristic modes,” IEEE Antennas andWireless Propagation Letters, vol. 12, pp. 1696–1699, 2013.
[19] B. A. Kramer, C.-C. Chen, M. Lee, and J. L. Volakis, “Fundamental limitsand design guidelines for miniaturizing ultra-wideband antennas,” IEEEAntennas and Propagation Magazine, vol. 51, pp. 57–69, Aug. 2009.
[20] D. F. Sievenpiper, D. C. Dawson, M. M. Jacob, T. Kanar, S. Kim, J. Long,and R. G. Quarfoth, “Experimental validation of performance limits anddesign guidelines for small antennas,” IEEE Transactions on Antennasand Propagation, vol. 60, pp. 8–19, Jan. 2012.
[21] J. Villanen, J. Ollikainen, O. Kivekäs, and P. Vainikainen, “Coupling el-ement based mobile terminal antenna structures,” IEEE Transactions onAntennas and Propagation, vol. 54, pp. 2142–2153, Jul. 2006.
[22] R. Martens, E. Safin, and D. Manteuffel, “Inductive and capacitive ex-citaion of the characteristic modes of small terminals,” in LoughboroughAntennas & Propagation Conference, 2011, pp. 1–4.
[23] R. Valkonen, M. Kaltiokallio, and C. Icheln, “Capacitive coupling elementantennas for multistandard mobile handsets,” IEEE Transactions on An-tennas and Propagation, vol. 61, pp. 2783–2791, May 2013.
[24] J. Anguera, A. Andújar, and C. Garcia, “Multiband and small coplanarantenna system for wireless handheld devices,” IEEE Transactions on An-tennas and Propagation, vol. 61, pp. 3782–3789, Jul. 2013.
[25] A. Cihangir, F. Sonnerat, F. Ferrero, R. Pilard, F. Gianesello, D. Gloria,P. Brachat, G. Jacquemod, and C. Luxey, “Neutralisation technique appliedto two coupling element antennas to cover low LTE and GSM communica-tion standards,” Electronics Letters, vol. 49, Jun. 2013.
72
References
[26] J. Ilvonen, R. Valkonen, J. Holopainen, and V. Viikari, “Design strategy for4G handset antennas and a multiband hybrid antenna,” IEEE Transac-tions on Antennas and Propagation, vol. 62, pp. 1918–1927, Apr. 2014.
[27] R. Valkonen, Impedance matching and tuning of non-resonant mobile ter-minal antennas. Ph.D thesis, Aalto University, 2013.
[28] J. Ilvonen, Multiband and environment insensitive handset antennas.Ph.D thesis, Aalto University, 2014.
[29] M. Pelosi, M. Bergholz, and G. F. Pedersen, “Multiple antenna systemswith inherently decoupled radiators,” IEEE Transactions on Antennas andPropagation, vol. 60, pp. 503–515, Feb. 2012.
[30] J. Holopainen, O. Kivekäs, J. Ilvonen, R. Valkonen, C. Icheln, andP. Vainikainen, “Effect of the user’s hands on the operation of lower UHF-band mobile terminal antennas: Focus on digital television receiver,” IEEETransactions on Electromagnetic Compatibility, pp. 831–841, Aug. 2011.
[31] A. Morris, S. Caporal, J. Shin, V. Steel, and G. F. Pedersen, “Tunable an-tennas for mobile devices: Achieving high performance in compelling formfactors,” in IEEE Microwave Symposium, 2014, pp. 1–4.
[32] P. Bahramzy, O. Jagielski, S. Svendsen, and G. F. Pedersen, “Compact agileantenna concept utilizing reconfigurable front end for wireless communi-cations,” IEEE Transactions on Antennas and Propagation, vol. 62, pp.4554–4563, Sep. 2014.
[33] L. J. Chu, “Physical limitations of omnidirectional antennas,” Journal ofApplied Physics, vol. 19, pp. 1163–1175, Dec. 1948.
[34] R. E. Collin and S. Rothschild, “Evaluation of antenna Q,” IEEE Transac-tions on Antennas and Propagation, vol. 12, pp. 23–27, Jan. 1964.
[35] W. Geyi, P. Jarmuszewski, and Y. Qi, “The Foster reactance theorem forantennas and radiation Q,” IEEE Transactions on Antennas and Propaga-tion, vol. 59, pp. 401–408, Mar. 2000.
[36] A. D. Yaghjian and S. R. Best, “Impedance, bandwidth, and Q of antennas,”IEEE Transactions on Antennas and Propagation, vol. 53, pp. 1298–1324,Apr. 2005.
[37] A. D. Yaghjian and H. R. Stuart, “Lower bounds on the Q of electri-cally small antennas,” IEEE Transactions on Antennas and Propagation,vol. 53, pp. 3114–1321, Oct. 2010.
[38] G. A. E. Vandenbosch, “Simple procedure to derive lower bounds for radi-ation Q of electrically small devices of arbitrary topology,” IEEE Transac-tions on Antennas and Propagation, vol. 59, pp. 2217–2225, Jun. 2011.
[39] M. Capek, P. Hazdra, and J. Eichler, “A method for the evaluation of radi-tation Q based on modal approach,” IEEE Transactions on Antennas andPropagation, vol. 60, pp. 4556–4567, Oct. 2012.
[40] H. L. Thal, “Q bounds for arbitrary small antennas: A circuit approach,”IEEE Transactions on Antennas and Propagation, vol. 60, pp. 3120–3128,Jul. 2012.
73
References
[41] S. C. D. Barrio, A. Tatomirescu, G. F. Pedersen, and A. Morris, “Novel archi-tecture for LTE world-phones,” IEEE Antennas and Wireless PropagationLetters, vol. 12, pp. 1676–1679, 2013.
[42] H. R. Stuart, S. R. Best, and A. D. Yaghjian, “Limitations in relating qual-ity factor to bandwidth in a double resonance small antenna,” IEEE An-tennas and Wireless Propagation Letters, vol. 6, pp. 460–463, 2007.
[43] O. B. Vorobyev, “Quality factor of an antenna with closely spaced reso-nances,” IEEE Antennas and Wireless Propagation Letters, vol. 10, pp.1216–1219, 2011.
[44] M. Gustafsson and B. L. G. Jonsson, “Antenna Q and stored energy ex-pressed in the fields, currents, and input impedance,” IEEE Transactionson Antennas and Propagation, vol. 63, pp. 240–249, Jan. 2015.
[45] M. D. Estarki and R. G. Vaughan, “Theoretical methods for the impedanceand bandwidth of the thin dipole,” IEEE Antennas and Propagation Mag-azine, vol. 55, pp. 62–81, Feb. 2013.
[46] J. Rahola, “Bandwidth potential and electromagnetic isolation: Tools foranalysing the impedance behaviour of antenna systems,” in European Con-ference on Antennas and Propagation (EuCAP 2009), Berlin, 2009, pp.944–948.
[47] A. R. Lopez, “Rebuttal to "Fano limits on matching bandwidth",” IEEEAntennas and Propagation Magazine, vol. 47, pp. 128–129, Oct. 2005.
[48] ——, “Rebuttal to "Correct impedance-matching limitations",” IEEE An-tennas and Propagation Magazine, vol. 51, pp. 162–166, Oct. 2009.
[49] J. P. Doane, K. Sertel, and J. L. Volakis, “Matching bandwidth limits forarrays backed by a conducting ground plane,” IEEE Transactions on An-tennas and Propagation, vol. 61, pp. 2511–2518, May 2013.
[50] C. Pfeiffer and A. Grbic, “A circuit model for electrically small antennas,”IEEE Transactions on Antennas and Propagation, vol. 60, pp. 1671–1683,Apr. 2012.
[51] J. J. Adams and J. T. Bernhard, “Broadband equivalent circuit models forantenna impedances and fields using characteristic modes,” IEEE Trans-actions on Antennas and Propagation, vol. 61, pp. 3985–3994, Aug. 2013.
[52] A. Ghorbani, R. A. Abd-Alhameed, N. J. McEwan, and D. Zhou, “An ap-proach for calculating the limiting bandwidth-reflection coefficient prod-uct for microstrip patch antennas,” IEEE Transactions on Antennas andPropagation, vol. 54, pp. 1328–1331, Apr. 2006.
[53] J. Holopainen, R. Valkonen, O. Kivekäs, J. Ilvonen, and P. Vainikainen,“Broadband equivalent circuit model for capacitive coupling element-basedmobile terminal antenna,” IEEE Antennas and Wireless Propagation Let-ters, pp. 716–791, 2010.
[54] A. Ghorbani, M. Ansarizadeh, and R. A. Abd-Alhameed, “Bandwidth lim-itations on linearly polarized microstrip antennas,” IEEE Transactions onAntennas and Propagation, vol. 58, pp. 250–257, Feb. 2010.
74
References
[55] R. Valkonen, J. Ilvonen, and P. Vainikainen, “Naturally non-selectivehandset antennas with good robustness against impedance mistuning,”in European Conference on Antennas and Propagation (EuCAP 2012),Prague, 2012, pp. 2839–2842.
[56] D. M. Pozar, Microwave Engineering. John Wiley & Sons, 2005.
[57] A. Lehtovuori and R. Valkonen, “Strategies for finding a bandwidth-optimal topology for impedance matching,” in 21st European Conferenceof Circuit Theory and Design, Dresden, 2013.
[58] J. Ollikainen, Design and implementation techniques of wideband mobilecommunications antennas. Ph.D thesis, Helsinki University of Technol-ogy, 2004.
[59] R. M. Foster, “A reactance theorem,” Bell Systems Technical Journal, vol. 3,pp. 259–267, Apr. 1924.
[60] H. W. Bode, Network Analysis and Feedback Amplifier Design. D. VanNostrand Co., New York, 1945.
[61] L. Weinberg, “Explicit formulas for Tschebyscheff and Butterworth laddernetworks,” Journal of Applied Physics, vol. 28, pp. 1155–1160, Sep. 1957.
[62] H. Dedieu, C. Dehollain, J. Neirynck, and G. Rhodes, “A new method forsolving broadband matching problems,” IEEE Transactions on Circuitsand Systems, vol. 41, pp. 561–571, Sep. 1994.
[63] H. J. Carlin and P. Amstutz, “On optimum broad-band matching,” IEEETransactions on Circuits and Systems, vol. 28, pp. 401–405, May 1981.
[64] A. Andújar, J. Anguera, and C. Puente, “A systematic method to designbroadband matching networks,” in European Conference on Antennas andPropagation (EuCAP 2010), 2010.
[65] D. C. Youla, “A new theory of broad-band matching,” IEEE Transactions onCircuit Theory, vol. 11, pp. 30–50, Mar. 1964.
[66] W.-K. Chen and T. Chaisrakeo, “Explicit formulas for the synthesis of op-timum bandpass Butterworth and Chebyshev impedance-matching net-works,” IEEE Transactions on Circuits and Systems, vol. 27, pp. 928–942,Oct. 1980.
[67] J. C. Allen and D. F. Schwartz, “Best wideband impedance matchingbounds for lossless 2-ports,” SPAWAR Systems Center, Tech. Rep., 2001.
[68] H. J. Carlin, “A new approach to gain-bandwidth problems,” IEEE Trans-actions on Circuits and Systems, vol. 24, pp. 170–175, Apr. 1977.
[69] H. J. Carlin and B. S. Yarman, “The double matching problem: Analyticand real frequency solutions,” IEEE Transactions on Circuits and Systems,vol. 30, pp. 15–28, Jan. 1983.
[70] B. S. Yarman, M. Sengül, and A. Kilinc, “Design of practical matching net-works with lumped elements via modeling,” IEEE Transactions on Circuitsand Systems, vol. 54, pp. 1829–1837, Aug. 2007.
75
References
[71] M. Sengül, “Design of practical broadband matching networks withlumped elements,” IEEE Transactions on Circuits and Systems - II: Ex-press Briefs, vol. 60, pp. 552–556, Sep. 2013.
[72] D. F. Schwartz and J. C. Allen, “Wide-band impedance matching: H∞ per-formance bounds,” IEEE Transactions on Circuits and Systems - II: Ex-press Briefs, vol. 51, pp. 364–368, Jul. 2004.
[73] B. S. Yarman and A. Fettweis, “Computer-aided double matching via para-metric representation of Brune functions,” IEEE Transactions on Circuitsand Systems, vol. 37, pp. 212–222, Feb. 1990.
[74] K. Yegin and A. Q. Martin, “On the design of broad-band loaded wire an-tennas using the simplified real frequency technique and a genetic algo-rithm,” IEEE Transactions on Antennas and Propagation, vol. 51, pp. 220–228, Feb. 2003.
[75] E. H. Newman, “Real frequency wide-band impedance matching withnonminimum reactance equalizers,” IEEE Transactions on Antennas andPropagation, vol. 53, pp. 3597–3603, Nov. 2005.
[76] B. S. Yarman and H. J. Carlin, “A simplified "real frequency" technique ap-plied to broad-band multistage microwave amplifiers,” IEEE Transactionson Microwave Theory and Techniques, vol. 30, pp. 2216–2222, Dec. 1982.
[77] P. Lindberg, M. M. Sengül, E. G. Cimen, B. S. Yarman, A. Rydberg, andA. Aksen, “A single matching network for a dual band PIFA antenna viasimplified real frequency technique,” in European Conference on Antennasand Propagation (EuCAP 2006), Nice, 2006.
[78] H. J. Orchard, “Filter design by iterated analysis,” IEEE Transactions onCircuits and Systems, vol. 32, pp. 1089–1096, Nov. 1985.
[79] B. S. Yarman and A. Kilinc, “High precision LC ladder synthesis part II:Immittance synthesis with transmission zeros at DC and infinity,” IEEETransactions on Circuits and Systems, vol. 60, pp. 2719–2729, Oct. 2013.
[80] V. Iyer, S. N. Makarov, D. D. Harty, F. Nekoogar, and R. Ludwig, “A lumpedcircuit for wideband impedance matching of a non-resonant, short dipoleor monopole antenna,” IEEE Transactions on Antennas and Propagation,vol. 58, pp. 18–26, Jan. 2010.
[81] O. M. Ramahi and R. Mittra, “Design of a matching network for an HF an-tenna using the real frequency method,” IEEE Transactions on Antennasand Propagation, vol. 37, pp. 506–509, Apr. 1989.
[82] F. Gianesello, “Innovate in a 4G world: RFIC designers discovering an-tennas,” in European Conference on Antennas and Propagation (EuCAP2013), Gothenburg, 2013, pp. 1302–1306.
[83] M. Kaltiokallio, R. Valkonen, K. Stadius, and J. Ryynänen, “A 0.7–2.7-GHzblocker-tolerant compact-size single-antenna receiver for wideband mobileapplications,” IEEE Transactions on Microwave Theory and Techniques,vol. 61, pp. 3339–3349, Sep. 2013.
[84] M. T. Ivrlac and J. A. Nossek, “Toward a circuit theory of communication,”IEEE Transactions on Circuits and Systems, pp. 1663–1683, Jul. 2010.
76
References
[85] R. E. Massara, Optimization Methods in Electronic Circuit Design. Long-man Scientific & Technical, England, 1991.
[86] R. Valkonen, J. Ilvonen, J. Rahola, and P. Vainikainen, “Symmetrical band-width potential as a performance measure for reconfigurable antennas,”Feb. 2010, presented at COST IC0603 Working Groups Workshop, Lisbon,Portugal.
[87] R. Whatley, T. Ranta, and D. Kelly, “CMOS based tunable matching net-works for cellular handset applications,” in 2011 IEEE MTT-S Int. Mi-crowave Symp. Digest, 2011.
[88] H. Yang and K. Kim, “Ultra-wideband impedance-matching technique forresistively loaded vee dipole antenna,” IEEE Transactions on Antennasand Propagation, vol. 61, pp. 5788–5792, Nov. 2013.
[89] Optenni Lab, http://www.optenni.com.
[90] M. Sonkki, M. Berg, E. Antonino-Daviu, M. Cabedo-Fabrés, M. Ferrando-Bataller, and E. T. Salonen, “User effect comparison between metal bezelantenna and planar inverted F-antenna for mobile terminal,” Microwaveand Optical Technology Letters, vol. 55, pp. 316–322, 2013.
[91] P. Bahramzy and G. F. Pedersen, “Head and hand detuning effect study ofnarrow-band against wide-band mobile phone antennas,” Electronics Let-ters, vol. 50, pp. 1040–1042, Jul. 2014.
[92] R. Valkonen, J. Ilvonen, K. Rasilainen, J. Holopainen, C. Icheln, andP. Vainikainen, “Avoiding the interaction between hand and capacitive cou-pling element based mobile terminal antenna,” in European Conference onAntennas and Propagation (EuCAP 2011), Rome, 2011, pp. 2781–2785.
[93] S. Zhang, K. Zhao, Z. Ying, and S. He, “Adaptive quad-element multi-wideband antenna array for user-effective LTE MIMO mobile terminals,”IEEE Transactions on Antennas and Propagation, vol. 61, pp. 4275–4283,Aug. 2013.
[94] H. Li, Z. T. Miers, and B. K. Lau, “Orthogonal MIMO handset antennasbased on characteristic mode manipulation at frequency bands below 1GHz,” IEEE Transactions on Antennas and Propagation, vol. 62, pp. 2756–2766, May 2014.
[95] Y. Chen, R. Martens, R. Valkonen, and D. Manteuffel, “Evaluation of adap-tive impedance tuning for reducing the form factor of handset antennas,”IEEE Transactions on Antennas and Propagation, vol. 63, pp. 703–710,Feb. 2015.
[96] A. García-Lampérez and M. Salazar-Palma, “Single-band to multiband fre-quency transformation for multiband filters,” IEEE Transactions on Mi-crowave Theory and Techniques, vol. 59, pp. 3048–3058, Dec. 2011.
[97] X. Sun and E. L. Tan, “Novel dual-band dual-prototype bandpass filter,”Microwave and Optical Technology Letters, vol. 56, pp. 1496–1498, 2014.
[98] N. Nallam and S. Chatterjee, “Multi-band frequency transformations,matching networks and amplifiers,” IEEE Transactions on Circuits andSystems, vol. 60, pp. 1635–1647, Jun. 2013.
77
References
[99] F. G. S. Silva, R. N. de Lima, R. C. S. Freire, and C. Plett, “A switch-less multiband impedance matching technique based on multiresonant cir-cuits,” IEEE Transactions on Circuits and Systems - II: Express Briefs,vol. 60, pp. 417–421, Jul. 2013.
[100] Y. Liu, Y. Zhao, S. Liu, Y. Zhou, and Y. Chen, “Multi-frequency impedancetransformers for frequency-dependent complex loads,” IEEE Transactionson Microwave Theory and Techniques, vol. 61, pp. 3225–3235, Sep. 2013.
[101] Y. Salomatov, V. Pan’ko, and V. Ovechkin, “Multifrequency matching forwide-band antennas,” in Proceedings of the IEEE-Russia Conference onHigh Power Microwave Electronics: Measurements, Identification, Appli-cations, Novosibirsk, 1999, pp. IV13–IV14.
[102] Y. Liu, Y. J. Zhao, and Y. G. Zhou, “Lumped dual-frequency impedancetransformers for frequency-dependent complex loads,” Progress In Electro-magnetics Research, vol. 126, pp. 121–138, 2012.
[103] A. Dutta, K. Dasgupta, and T. K. Bhattacharyya, “Parasitic-aware robustconcurrent dual-band matching network for a packaged LNA,” IET Mi-crowaves, Antennas & Propagation, vol. 3, pp. 1094–1101, Jul. 2009.
[104] M. E. V. Valkenburg, Introduction to Modern Network Synthesis. JohnWiley & Sons, 1960.
[105] J. Ilvonen, R. Valkonen, J. Holopainen, and V. Viikari, “Multibandfrequency reconfigurable 4G handset antenna with MIMO capability,”Progress In Electromagnetics Research, vol. 148, pp. 233–243, 2014.
[106] B. G. Colpitts and G. Boiteau, “Harmonic radar transceiver design: Minia-ture tags for insect tracking,” IEEE Transactions on Antennas and Propa-gation, vol. 52, pp. 2825–2832, Nov. 2004.
[107] D. Psychoudakis, W. Moulder, C. Chi-Chih, Z. Heping, and J. L. Volakis,“A portable low-power harmonic radar system and conformal tag for in-sect tracking,” IEEE Antennas and Wireless Propagation Letters, vol. 7,pp. 444–447, 2008.
[108] V. Viikari, J. Song, and H. Seppä, “Passive wireless sensors platform utiliz-ing a mechanical resonator,” IEEE Sensors Journal, vol. 13, pp. 1180–1186,Apr. 2013.
[109] K. Rasilainen, J. Ilvonen, A. Lehtovuori, J.-M. Hannula, and V. Viikari,“On design and evaluation of harmonic transponders,” IEEE Transactionson Antennas and Propagation, vol. 63, pp. 15–23, Jan. 2015.
[110] ——, “Harmonic transponders: Performance and challenges,” Progress InElectromagnetics Research M, vol. 41, pp. 139–147, 2015.
[111] L. Weinberg, Network Analysis and Synthesis. McGraw-Hill Book Com-pany, Inc., 1962.
[112] J. Villanen, C. Icheln, and P. Vainikainen, “A coupling element-based quad-band antenna structure for mobile terminals,” Microwave and OpticalTechnology Letters, vol. 49, pp. 1277–1282, Jun. 2007.
78
References
[113] P. Ikonen, J. Ellä, E. Schmidhammer, P. Tikka, P. Ramachandran, andP. Annamaa, “Multi-feed RF front-ends and cellular antennas for next gen-eration smartphones,” Tech. Rep., 2011.
[114] F. Sonnerat, R. Pilard, F. Gianesello, R. L. Penenc, C. Person, and D. Gloria,“Innovative LDS antenna for 4G applications,” in European Conference onAntennas and Propagation (EuCAP 2013), 2013, pp. 2696–2699.
[115] J. W. Wallace and M. A. Jensen, “Termination-dependent diversity perfor-mance of coupled antennas: Network theory analysis,” IEEE Transactionson Antennas and Propagation, vol. 52, pp. 98–105, Jan. 2004.
[116] V. Belevitch, “Elementary applications of the scattering formalism in net-work design,” IRE Transactions on Circuit Theory, vol. 3, pp. 97–104, Jun.1956.
[117] E. S. Kuh and R. A. Rohrer, Theory of Linear Active Networks. San Fran-cisco, California, Holden-Day, Inc., 1967.
[118] B. S. Yarman, Design of Ultra Wideband Power Transfer Networks. JohnWiley & Sons, 2010.
[119] C. Volmer, M. Sengül, J. Weber, R. Stephan, and M. A. Hein, “Broad-band decoupling and matching of a superdirective two-port antenna ar-ray,” IEEE Antennas and Wireless Propagation Letters, vol. 7, pp. 613–616,2008.
[120] M. Manteghi and Y. Rahmat-Samii, “Broadband characterization of thetotal active reflection coefficient of multiport antennas,” in 2003 IEEE AP-S International Symposium, 2003, pp. 20–23.
[121] ——, “Multiport characteristics of a wide-band cavity backed annularpatch antenna for multipolarization operations,” IEEE Transactions onAntennas and Propagation, vol. 53, pp. 466–474, Jan. 2005.
[122] A. Lehtovuori and R. Valkonen, “Efficient matching circuit design pro-motes terminal antenna development,” Sep. 2013, presented at COSTIC0603 Working Groups Workshop, Ghent, Belgium.
[123] Z.-M. Wang and W.-K. Chen, “Broad-band matching of multiport net-works,” IEEE Transactions on Circuits and Systems, vol. 31, pp. 788–796,Sep. 1984.
[124] J. P. Doane, K. Sertel, and J. L. Volakis, “Bandwidth limits for lossless, re-ciprocal PEC-backed arrays of arbitrary polarization,” IEEE Transactionson Antennas and Propagation, vol. 62, pp. 2531–2542, May 2014.
[125] D. Nie, B. M. Hochwald, and E. Stauffer, “Systematic design of large-scalemultiport decoupling networks,” IEEE Transactions on Circuits and Sys-tems, vol. 61, pp. 2172–2181, Jul. 2014.
[126] A. Andújar and J. Anguera, “Coplanar non-resonant elements for multi-band operation,” in European Conference on Antennas and Propagation(EuCAP 2013), 2013, pp. 1843–1847.
[127] R. Valkonen, A. Lehtovuori, and D. Manteuffel, “Capacitive coupling ele-ments – changing the way of designing antennas,” in European Conferenceon Antennas and Propagation (EuCAP 2014), 2014.
79
References
[128] S. A. Bassam, W. Chen, M. Helaoui, and F. M. Ghannouchi, “Transmitterarchitecture for CA: Carrier aggregation in LTE-advanced systems,” IEEEMicrowave Magazine, pp. 78–86, Jul. 2013.
[129] R. Valkonen, A. Lehtovuori, and C. Icheln, “Dual-feed, single-CCE antennafacilitating inter-band carrier aggregation in LTE-A handsets,” in Euro-pean Conference on Antennas and Propagation (EuCAP 2013), Gothen-burg, 2013.
[130] A. Diallo, C. Luxey, P. L. Thuc, R. Staraj, and G. Kossiavas, “Study and re-duction of the mutual coupling between two mobile phone PIFAs operatingin the DCS1800 and UMTS bands,” IEEE Transactions on Antennas andPropagation, vol. 54, pp. 3063–3074, Nov. 2006.
[131] H. Li, J. Xiong, and S. He, “Compact planar MIMO antenna system for fourelements with similar radiation characteristics and isolation structure,”IEEE Antennas and Wireless Propagation Letters, vol. 8, pp. 1107–1110,2009.
[132] B. K. Lau and J. B. Andersen, “Simple and efficient decoupling of com-pact arrays with parasitic scatterers,” IEEE Transactions on Antennas andPropagation, vol. 60, pp. 464–472, Feb. 2012.
[133] Y. Wang and Z. Du, “A wideband printed dual-antenna with three neutral-ization lines for mobile terminals,” IEEE Transactions on Antennas andPropagation, vol. 62, pp. 1495–1500, Mar. 2014.
[134] S. N. Venkatasubramanian, A. Lehtovuori, C. Icheln, and K. Haneda, “Onthe constrains to isolation improvement in multi-antenna systems,” in Eu-ropean Conference on Antennas and Propagation (EuCAP 2015), 2015.
[135] S.-C. Chen, Y.-S. Wang, and S.-J. Chung, “A decoupling technique for in-creasing the port isolation between two strongly coupled antennas,” IEEETransactions on Antennas and Propagation, vol. 56, pp. 3650–3658, Dec.2008.
[136] C.-H. Wu, G.-T. Zhou, Y.-L. Wu, and T.-G. Meng, “Stub-loaded reactive de-coupling network for two-element array using even-odd analysis,” IEEEAntennas and Wireless Propagation Letters, vol. 12, pp. 452–455, 2013.
[137] K. Wang, L. Li, and T. F. Eibert, “Comparison of compact monopole an-tenna arrays with eigenmode excitation and multiport conjugate match-ing,” IEEE Transactions on Antennas and Propagation, vol. 61, pp. 4054–4062, Aug. 2013.
[138] X. Tang, K. Mouthaan, and J. C. Coetzee, “Tunable decoupling and match-ing network for diversity enhancement of closely spaced antennas,” IEEEAntennas and Wireless Propagation Letters, vol. 51, pp. 268–271, 2012.
[139] L. Zhao, L. K. Yeung, and K.-L. Wu, “A coupled resonator decoupling net-work for two-element compact antenna arrays in mobile terminals,” IEEETransactions on Antennas and Propagation, vol. 62, pp. 2767–2776, May2014.
[140] H. Sato, Y. Koyanagi, K. Ogawa, and M. Takahashi, “A method of dual-frequency decoupling for two-element MIMO antenna,” in Progress in
80
References
Electromagnetics Research Symposium Proceedings, Stockholm, 2013, pp.1853–1857.
[141] A. Krewski, W. L. Schroeder, and K. Solbach, “Matching network synthesisfor mobile MIMO antennas based on minimization of the total multi-portreflectance,” in Loughborough Antennas & Propagation Conference, 2011.
[142] F. Fezai, C. Menudier, M. Thevenot, and T. Monediere, “Systematic de-sign of parasitic element antennas – application to a WLAN Yagi designimpedances,” IEEE Antennas and Wireless Propagation Letters, vol. 12, pp.413–416, 2013.
[143] K. K. Kishor and S. V. Hum, “A pattern reconfigurable chassis-mode MIMOantenna,” IEEE Transactions on Antennas and Propagation, vol. 62, pp.3290–3298, Jun. 2014.
[144] E. A. Elghannai, B. D. Raines, and R. G. Rojas, “Multiport reactive loadingmatching technique for wide band antenna applications using the theory ofcharacteristic modes,” IEEE Transactions on Antennas and Propagation,vol. 63, pp. 261–268, Jan. 2015.
[145] Y. Kabiri, P-Gardner, and C. Constantinou, “A novel approach for wide-band tunable electrically small antennas,” in European Conference on An-tennas and Propagation (EuCAP 2014), 2014, pp. 3633–3637.
[146] S. E. Sussman-Fort and R. M. Rudish, “Non-Foster impedance matching ofelectrically small antennas,” IEEE Transactions on Antennas and Propa-gation, vol. 57, pp. 2230–2241, Aug. 2009.
[147] E. Ugarte-Munoz, F. Albarracin, F. J. Herraiz-Martinez, and D. Segovia-Vargas, “Sensitivity and stability analysis of non-Foster matched two-portantennas,” in European Conference on Antennas and Propagation (EuCAP2013), 2013, pp. 2898–2901.
[148] F. Albarracin-Vargas, E. Ugarte-Munoz, V. Gonzáles-Posadas, andD. Segovia-Vargas, “Sensitivity analysis for active matched antennas withnon-Foster elements,” IEEE Transactions on Antennas and Propagation,vol. 63, pp. 6040–6048, Dec. 2014.
[149] F. C. W. Po, E. de Foucauld, D. Morche, P. Vincent, and E. Kerherve, “Anovel method for synthesizing an automatic matching network and its con-trol unit,” IEEE Transactions on Circuits and Systems, vol. 58, pp. 2225–2236, Sep. 2011.
[150] N. J. Smith, C.-C. Chen, and J. L. Volakis, “An improved topology for adap-tive agile impedance tuners,” IEEE Antennas and Wireless PropagationLetters, vol. 12, pp. 92–95, 2013.
[151] R. Valkonen, C. Icheln, and P. Vainikainen, “Power dissipation in mobileantenna tuning circuits under varying impedance conditions,” IEEE An-tennas and Wireless Propagation Letters, vol. 11, pp. 37–40, 2012.
[152] K. Rasilainen, A. Lehtovuori, J. Ilvonen, J. Holopainen, R. Valkonen, andV. Viikari, “Tunable MIMO antenna for small handsets,” in European Con-ference on Antennas and Propagation (EuCAP 2015), 2015.
81
References
[153] M. Thompson and J. K. Fidler, “Determination of the impedance matchingdomain of impedance matching networks,” IEEE Transactions on Circuitsand Systems, vol. 51, pp. 2098–2106, Oct. 2004.
[154] Q. Gu, J. R. D. Luis, A. S. Morris, and J. Hilbert, “An analytical algorithmfor Pi-network impedance tuners,” IEEE Transactions on Circuits and Sys-tems, vol. 58, pp. 2894–2905, Dec. 2011.
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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