IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. 50, NO. 10, OCTOBER 2002 1433
Resonator-Based Analysis of the Combination of
Mobile Handset Antenna and Chassis
Pertti Vainikainen, Member, IEEE, Jani Ollikainen, Outi Kivekäs, and Ilkka Kelander
Abstract—In this paper, the performance of the mobile phone
handset antenna–chassis combination is analyzed based on an
approximate decomposition of the waves on the structure into
two resonant wavemodes: the antenna-element wavemode and the
chassis wavemode. A double resonator equivalent circuit model is
presented and used to estimate the impedance bandwidth and the
respective distribution of radiation losses with typical parameter
values at 900 and 1800 MHz. It is noticed that at 900 MHz, the
radiation losses by the antenna element wavemode represent typi-
cally less than 10% of the total power. Thus, the antenna element
works mainly as a matching element, which couples to the low-
resonant wavemode of the chassis. At 1800 MHz, the contribution
of the antenna element wavemode is larger. By enhancing the
coupling and by tuning the chassis resonance, it is possible to
obtain an impedance bandwidth of over 50% (6-dB return loss)
at both at 900 and 1800 MHz. The results given by the equivalent
circuit study are fully supported by those of three-dimensional
phone-model simulations, including calculation of the SAR and
efficiency values. In prototyping, the 6-dB bandwidth of 5.5% was
obtained at 980 MHz with a nonradiating coupling element with a
volume of 1.6 cm
3
on a 120-mm-long chassis.
Index Terms—Bandwidth, handset antennas, mobile communi-
cations, quality factor, resonators, small antennas.
I. INTRODUCTION
I
N MANY application areas of antennas, the effect of com-
plex platforms has been studied extensively [1]. For mobile
handsets, one of the main areas has been to investigate the prop-
erties of different antenna elements and the interaction with the
user [2]–[7]. It has also been well known that the performance,
especially the bandwidth, is largely defined by the combined
behavior of the antenna and the phone chassis. However, the
effect of the chassis is usually not analyzed, though in many
published small-antenna designs the antenna is mounted on a
phone chassis and from the large bandwidths obtained it can be
assumed that the effect of the chassis is significant [4], [8]–[12].
Due to lack of identifying the contribution of the whole struc-
ture on the radiation, in some cases it has seemed that the fun-
damental limits for the bandwidth of small antennas [13], [14]
have been exceeded especially at 900 MHz. For fairly large
portable radios, the effect of the dimensions of the chassis on
the bandwidth was studied in [15]–[17]. Recently, the effect
Manuscript received June 22, 2000; revised July 9, 2001. This work was sup-
ported in part by the Graduate School of Electronics, Telecommunications, and
Automation (GETA), by the Academy of Finland, Nokia Foundation, by the
Jenny and Antti Wihuri Foundation, and by the Finnish Society of Electronics
Engineers.
The authors are with Helsinki University of Technology, Institute of Dig-
ital Communications(IDC) Radio Laboratory, FIN-02015 HUT, Espoo, Finland
(e-mail: Pertti.Vainikainen@hut.fi).
Digital Object Identifier 10.1109/TAP.2002.802085
has been investigated for smaller devices with chassis or cir-
cuit-board length in the range of 80–150 mm, typical to current
mobile-phone handsets [18]. It was noticed that the bandwidth
for 900 MHz patch antennas had very clear dependency on the
length of the chassis. For some antenna types the maximum
bandwidth was over five-timeslarger than the minimum, and the
maximum bandwidth was obtained with chassis length of about
130 mm. These results indicate that the total radiation band-
width of the antenna–chassis combination is largely defined by
the dipole-type radiationofthechassiscurrents,whoselevel fur-
ther depends on whether the chassis is at resonance or not. It is
also obvious, especially at 900 MHz, that the typically allowed
handset-antenna element size of less than 5 cm
is clearly too
small to produce the required bandwidth if the current distribu-
tion would be restricted into the vicinity of the antenna element
[13], [17]. Therefore, it is necessary to utilize the whole metallic
structure of the handset to obtain the required bandwidth and
thus there is also an obvious connection between the bandwidth,
efficiency, and specific absorption rate (SAR) of mobile-phone
antennas.
The purpose of this paper is to study the significance of
the chassis effect with a rather simple but adequately accurate
equivalent circuit model based on an approximate modal
analysis of the fields and waves on the handset structure. For
comparison, three-dimensional (3-D) simulations of phone
models including the head of the user have been performed
to validate the model and the results obtained with it [19],
[20]. Also, experimental results are presented for prototypes
designed based on the model. Finally, based on the results given
by the equivalent circuit model, simulations, and prototyping,
guidelines are given to utilize the proposed model in the future
development of optimal solutions both in the sense of radiation
properties (bandwidth, efficiency) and user interaction (SAR).
The presented work is based on patch antenna and planar
inverted-F antenna (PIFA) -type antenna elements, but the
results can be generalized to apply to any antenna elements
as soon as the necessary parameters, especially the radiation
quality factor of the element itself, are known.
II. E
QUIVALENT CIRCUIT MODEL
A. Wavemodes of the Antenna–Chassis Combination
The maximum dimension (the length) of current mobile
handsets is less than half a wavelength at 900 MHz. The other
dimensions including those of the antenna elements are clearly
smaller. Thus, the structure can support only a few significant
wavemodes. In this paper, we divide the structure into two
significant parts: the antenna element and the chassis. In current
0018-926X/02$17.00 © 2002 IEEE
© 2002 IEEE. Reprinted with permission from IEEE Transactions on Antennas and Propagation 50, number 10, pages 1433-1444.
1434 IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. 50, NO. 10, OCTOBER 2002
Fig. 1. Current density distribution of the combination of a patch antenna
and phone chassis. The concentration of the current for the antenna-element
wavemode is clearly seen, as well as the sinusoidal distribution and edge
maxima for the dipole-type wavemode of the chassis.
mobile handsets the antenna element is usually self-resonant
and has some characteristic wavemode, which is typically a
slow-wave mode like in normal mode helices or a reactively
loaded quasi-TEM mode like in patch antennas (or PIFAs).
The fields and currents of this wavemode are concentrated in
the vicinity of the small antenna element and for this mode
the chassis acts as a groundplane with confined currents
creating the mirror-image effect for the antenna element. The
length of the handset chassis or circuit board is clearly larger
than the width, or especially the thickness, and therefore the
structure supports also single-wire or thick-dipole type current
distributions. Here, the fields and currents are distributed over
the whole structure and thus, the distribution is clearly less
concentrated spatially than the antenna-element wavemode. An
example of a typical current distribution of the antenna–chassis
combination is shown in Fig. 1, where the distributions of
the patch-antenna element and chassis wavemodes are clearly
distinguished. Due to the small electrical size of the antenna
and the chassis, the frequency response of the wavemodes
is characterized by lowest order resonances including one to
three standing wave “lobes.” The basic idea presented here is
that while considering its radiation and circuit properties, the
antenna–chassis combination can be described by combining
the separate radiation and impedance characteristics of the
wavemodes of the antenna element and the phone chassis.
These characteristics are defined by the respective current
distributions and resonant responses. Furthermore, as is well
known, the impedance and the surface field distribution of an
antenna are connected through a surface integral relationship
[21]. Thus, it is also possible to study the relationships between
impedance properties and radiated fields, especially what
comes to resistive components of the impedance and the radi-
ated power. The contributions of each part of the combination
to radiated power, near fields, and bandwidth are largely
defined by the relative amplitudes of the wavemodes, which
can be selected by tuning the coupling between the wavemodes.
Accurate determination of the radiation properties of the
antenna–handset combination requires, of course, a complete
analysis of the combined wave distribution with, for instance,
Fig. 2. Circuit model of the combination of a single-resonant antenna and
chassis.
numerical methods; but the modal analysis presented here can
be used to identify main aspects of the radiation, especially in
cases where either one of the wavemodes dominates clearly. As
the impedance bandwidth, which is also defined by the coupling
and the radiation quality factors of the wavemodes, is often
the most critical design parameter of a handset antenna; the
coupling between the modes and thus also many properties of
the radiation are largely defined by the bandwidth requirement
as seen below.
B. Equivalent Circuit
When investigating a small antenna element located on a
phone chassis, it can be noticed that the currents flowing on
the chassis are induced there through electromagnetic coupling
from the antenna element, which is further excited by its feed.
As the antenna is self-resonant and the length of the chassis is
often close to some multiple of half wavelength, the obvious
lumped-component equivalent circuit model of the combination
is that of coupled parallel and series resonators as shown in
Fig. 2. In Fig. 2, resonator 1 represents the antenna element and
resonator 2 the phone chassis. While studying the performance
of the circuit, the type of the resonators is insignificant except
that there must be both a parallel and a series resonator as
normally in the case of electromagnetically coupled resonators
[22]. However, it is known that the impedance behavior of a
shorted probe-fed patch antenna (or PIFA) is close to that of
a parallel resonant circuit and thus in this paper the circuit in
Fig. 2 was selected. For a PIFA also, the inductance of the
probe can be included in the model but it is not significant
from the main results point of view. Furthermore, resonator 1
can also be considered to be a nonradiating matching circuit
providing only coupling to the radiating chassis resonance. The
input impedance
of the circuit model in Fig. 2 is
(1)
C. Parameters of the Resonators
In (1), the chassis resonant frequency is
defined by the length of the chassis as
(2)
VAINIKAINEN et al.: RESONATOR-BASED ANALYSIS OF THE COMBINATION OF MOBILE HANDSET ANTENNA AND CHASSIS 1435
Here, is the multiple number of half wavelengths for the
resonant mode (order of the resonance)
m/s and
is the open-end extension of electrical length of the chassis
causing the shift of
of from the nominal value. It must
be noticed here that the antenna element may also have an effect
on the resonant frequency of the chassis wavemode as some
part of the currents of this wavemode may flow in the antenna
element. Typical examples are monopole-type antennas, which
are usually located at the end of the chassis and thus increase
the electrical length of the chassis as well.
The unloaded quality factor
of the
chassis represents all losses of the chassis wavemode. In
addition to the radiation, these also include conductive losses,
which should be minor and dielectric losses from possible lossy
dielectrics in the phone structure and especially those from the
user’s body. The contribution of each loss mechanism can be
described with the respective quality factor and the total
is obtained in the standard manner as the inverse of the sum
of inverses of individual quality factors. In the circuit model,
the different quality factors are described by splitting
into
several loss resistors in series. The conductive and dielectric
quality factors can be found by using the well-known analysis
methods for resonant cavities [23]. The radiation quality
factor depends on the transversal dimensions so that for larger
equivalent radius of the dipole-type chassis structure the quality
factor is lower [21]. By simulations, it was found out that for
a thin (
) metal plate with length mm
and width
mm, the first-order ( ) resonance at
the 1-GHz range has
and the
unloaded quality factor
. The respective values
for the second-order resonance close to 2 GHz were found
to be
and . According
to the simulations, the increase of the chassis thickness to
mm, which is typical for modern handsets, has only
minor effects on
and . From these values it can be seen
that the lumped-element single-resonator model of the chassis
is somewhat inaccurate, due to the overlapping of the low-
resonances; better accuracy would be obtained with a lumped
dual-resonant or lossy transmission line model. However,
over a relative bandwidth of about
25% around the chassis
resonances, the response is fairly close to that of the single
resonator circuit model and thus the main features of
can
be assumed to be correct.
The unloaded quality factor
of the antenna
element alone represents again all losses of the respective
wavemode: radiation, conductive, and dielectric losses and
similar approach as in the case of the chassis wavemode can
be used. For high-
antenna elements the internal dielectric and
conductive losses may be significant. The separate radiation
quality factor of the antenna element is somewhat difficult to
determine as the chassis effect is so significant in all typical
implementations. Based on the fact that the radiation of an
antenna is defined by its current distribution it can be claimed
that the radiation quality factor of the wavemode of the planar
antenna alone can be obtained by investigating the respective
antenna situated on a large ground plane [17]. The basis for this
estimation is that the current distribution inside and close to the
planar antenna does not change very much when the antenna
is located on a phone chassis. Another way to get insight to
this question is to study the bandwidth of the antenna–chassis
combination as a function of the length of the chassis as done
laterinthispaper. Thechassislengthsatwhichthebandwidthhas
its minimums can be assumed to represent the cases, where the
contribution of the chassis radiation is small and the bandwidth
obtained is that given by the antenna element alone. It is also
useful to study the ultimate limit for the radiation quality factor
of a small antenna [13], [14], because it is typical for many
antenna types like PIFAs that their radiation quality factor is
approximately inversely proportional to volume and thus, it has
almost constant ratio to the smallest possible radiation quality
factor. For a typical mobile handset, the maximum value for
the radius of the sphere enclosing the antenna element and
thus, also the major parts of its wavemode, is around 15 mm.
This gives the minimum radiation quality factor of around
50 at 900 MHz, and around 7 at 1800 MHz for a lossless
single-mode antenna. The quality factor of practical handset
antenna elements is several times higher than the theoretical
limit [13], [17]. Based on all this information it can be assumed
that the practical minimum values are
for 900 MHz
and
for 1800 MHz. For the case where the first
resonator is a nonradiating matching circuit, the quality factor
is in the ideal case infinite (
) and also in practice values
on the order of
can be obtained below 2 GHz. The
resonant frequency
of the antenna element can
be tuned rather simply to the required frequency of operation
(often, however, at the expense of
) by using methods like
dielectric or reactive loading or meandering [8], [10], [12],
[18], and [24]. The ideal case would be
, but this is
more and more difficult to achieve at 900 MHz as the phones
get smaller and the typical chassis length is clearly less than
120–130 mm, which would give
MHz.
D. Coupling Factors
The coupling factor
in (1), giving the impedance scaling
factor between the resonators is defined by the coupling of the
antenna to the chassis resonance. For an antenna located near
the end of the chassis, the coupling takes place mostly through
electric fields and is thus capacitive. The coupling can be tuned
by changing the mutual capacitance between the antenna and
chassis wavemodes. This in turn is affected by the height and
width of the antenna and its location versus the electric fields of
the chassis wavemode. Respectively, magnetic coupling can be
arranged with loop-type structures located close to the magnetic
field maximum of the chassis wavemode. The coupling factor
of the dual-resonant circuit to the feed line can usually be
tuned over a broad range of values, e.g., by changing the feed
location of the antenna.
III. T
HEORETICAL RESULTS WITH THE
EQUIVALENT CIRCUIT MODEL
As mentioned above, there is a connection between the ra-
diation bandwidth of the antenna–chassis combination and the
relative amplitudes of the modes. It was also shown that the ra-
diation quality factor of the antenna element is much higher than
1436 IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. 50, NO. 10, OCTOBER 2002
Fig. 3. Bandwidth as a function of power dissipated in the antenna element for
different values of
Q
.
that of the chassis. This being the case, it was interesting to use
the dual-resonant equivalentcircuitto study the following items:
• The maximum bandwidth obtained as a function of cou-
pling (
) between the two resonators. The input coupling
factor
was tuned to obtain maximum bandwidth for
each value of
.
• The distribution of power between the resonators for dif-
ferent values of bandwidth to estimate the contributions of
the wavemodes on the radiated power (if no other losses
are present) or, correspondingly, the power lost in the non-
radiating matching circuit.
• The effect of the antenna quality factor
on the band-
width and distribution of power. As shown above, the
chassis quality factor is clearly lower, and fairly constant,
and thus, an average value of
was used.
• The effect of the difference between the resonant frequen-
cies of the chassis and the antenna to investigate, espe-
cially the situation caused by a “too short” handset.
In the calculations, the matching criterion was
dB,
which is rather typical for small internal antennas [18]. Re-
sults for other matching criteria can be obtained with respec-
tive scaling factors. For example, for single-resonant antennas
the optimal 6-dB bandwidth is about 130%
and for 10-dB
bandwidth, about 70%
[17]. Thus, the scaling factor to get
the 10-dB bandwidth from the 6-dB bandwidth is about 0.5. All
frequencies and bandwidths have been normalized by defining
everywhere. In Fig. 3, the results for the normalized
bandwidth (compared to
) as a function of the power
dissipated (lost or radiated) in resonator 1 at are
shown for
or , respectively, for the best pos-
sible case when
. The basis for such values for
was described generally in Section II. The connections of the
selected values to practical implementations are as follows:
•
is the typical value obtained for a 4-mm-thick
air-filled single-resonant quarterwave patch (or PIFA) at
around 2 GHz on a large ground plane [17]. However,
at 900 MHz, this value is not possible to achieve with a
patch, PIFA, or helix, fulfilling the size requirement for a
handset-antenna element.
Fig. 4. Examples of frequency responses of the reflection coefficient with
Q
=500
for the maximum bandwidth of Fig. 3 (solid line) and for 10%
bandwidth (dashed line).
• is the estimated radiation quality factor if the
4-mm-thick antenna element mentioned above is tuned to
resonance at 900 MHz, but the volume is not changed (to
meet the volume requirement). The estimation is based on
the inverseproportionality of radiation quality factor to the
volume of a small antenna in wavelengths [13], [14] and
supported by results of simulations with different lengths
of the ground plane (see Section IV-A). This value can
also be used for a nonradiating reactive coupling element
with matching circuit consisting of high-quality lumped
elements.
•
can be estimated to be a typical quality factor
obtained with a reactive coupling element with distributed
microstrip matching circuit on high-quality substrate or
with a small self-resonant antenna/coupling element [12].
In Fig. 3,thecouplingtoresonator2decreases(
decreases)
as
increases. When %, all power is radiated by the
chassis, we have the single-resonant case and the 6-dB band-
width obtained is about 130%
%. With very loose
coupling to the chassis resonance (beyond the right end of the
scale in Fig. 3) we get
%, all power is radiated by the
antenna-element wavemode, and again we have a single-reso-
nant case now with 6-dB bandwidth of about 130%
7,
0.9, or 0.3%, respectively. The maximum bandwidth seen in
Fig. 3 is obtained by optimal coupling for best dual-resonant
response, which typically gives somewhat more than double the
bandwidth compared to the single-resonant case. If the quality
factors of the two resonators are clearly different, the maximum
bandwidth does not depend much on the higher quality factor
as seen from Fig. 3. This indicates that huge bandwidths are
possible with optimal coupling also by using practically nonra-
diating coupling elements.
Examples of frequency responses with different coupling
levels to the chassis resonance are shown in Fig. 4 for
. In the case of maximum bandwidth (solid line), the
response is clearly dual resonant. For the typical bandwidth of
about 10% (dashed line), the response looks single resonant,
VAINIKAINEN et al.: RESONATOR-BASED ANALYSIS OF THE COMBINATION OF MOBILE HANDSET ANTENNA AND CHASSIS 1437
Fig. 5. (a) Bandwidth as a function of power dissipated in the antenna
element for
Q
=150
and
df
=0
;
0
:
1
, and
0
:
2
. (b) Close-up view for small
bandwidths.
though the effect of resonator 2 (chassis wavemode) is sig-
nificant as seen from Fig. 3. The reason for this result is that
the total bandwidth is clearly narrower than that of resonator
2. Therefore, the admittance seen from the resonator 1 toward
the resonator 2 is almost constant over the whole significant
bandwidth. In this case, the admittance of resonator 2 can be
described with a narrow-band approximation of the equivalent
circuit. This consists of a conductance
and susceptance
in parallel and having values, which resonator 2 represents
at the center frequency of the whole circuit. The values of
the components depend on the coupling factor
, and the
difference between the center frequencies of the resonators. It
is obvious that
has maximum at and is positive
below
and negative above it. From the whole circuit point
of view,
represents a decrease of the total effective quality
factor
and can also be considered
as the effective chassis quality factor
(not the same as ). Now the total quality factor is obtained as
. To obtain the 6-dB bandwidth of
10% requires
. Because at 900 MHz, is typically
at least 150, it is obvious that the effect of the coupling to the
chassis wavemode is significant. The narrow-band model gives
also the power distribution very simply as
(3)
Here,
is the power consumed by radiation and losses in
resonator 1 (antenna-element wavemode) and
the total
input power to the circuit. Thus, the narrow-band approxima-
tion can be used to replace the complicated calculations with
the whole circuit of Fig. 2 for the cases where
.
The main effect of susceptance
is that it shifts the
effective resonant frequency
of the whole circuit by
.
This shift is fairly small, because
inside the 3-dB
bandwidth of resonator 2, and
is typically over 10.
In Fig. 5, the respective results as in Fig. 3 are given for
, when with or . This
describes the typical situation at 900 MHz where the chassis
is too short to be in resonance at
. It can be noticed that for
the effect is small on the bandwidth or power distribu-
tion. When
, the maximum bandwidth is still high but
more problems can be expectedinachieving the required perfor-
mance. Actually, tighter coupling is required to obtain the same
bandwidth because
decreases as increases, which in
practice means a larger coupling element. The obvious result
obtained but not seen from Fig. 5, is that the center frequency
of the band is close to
for tight coupling (large bandwidth)
and close to
for loose coupling (small bandwidth).
As mentioned previously, at 900 MHz the typical bandwidth
(
dB) for a phone with an internal antenna is about
10%. Thus, the results in Fig. 3 and given also by (3), indicate
that the power radiated by the wavemode of the typical internal
antenna element (
) is less than 10% of the total ra-
diated power. In this case, it can be expected that the antenna
element has only a minor effect also on properties like the body
loss or SAR of the phone. For
, representing the situ-
ation at around 2 GHz, the contribution of the antenna element
wavemode is clearly more significant, i.e.,
% for 10%
bandwidth.
IV. S
IMULATION RESULTS AND COMPARISON WITH THEORY
A. Impedance of Phone Models in Free Space
The validity of the circuit model wasstudiedwith3-Dsimula-
tions of phonemodelsin free space by using method of moments
(MoM)-based commercial software. Simulated impedance re-
sults obtained with the software have been noticed to agree
very well with experimental ones also for complicated multifre-
quency antenna–chassis structures [24]. Simulated impedance
results for different antenna–chassis combinations are shown in
Figs. 6–8. The items studied were:
• effect of increasing the coupling between the antenna and
the chassis;
• effect of the difference between the resonant frequencies
of the antenna and chassis;
• effect of the ground-plane length on the impedance band-
width.
