Experimental Studies of Antenna Miniaturization Using Magneto-Dielectric and Dielectric Materials
ABSTRACT Measurement results for a meandered planar inverted-F antenna (PIFA) loaded
with magneto-dielectric and dielectric materials are presented. Figures of
merit and ways to compare antennas with different fillings materials are
discussed. The used magneto-dielectric material is described, the radiation
mechanism of the meandered PIFA is studied, and the proper position for
dielectric and magneto-dielectric filling is discussed and identified.
Identical-size antennas with dielectric and magneto-dielectric fillings are
compared at the same resonance frequency using the radiation quality factor as
the figure of merit. It is seen, that the benefit from the magneto-dielectric
filling material is moderate and strongly dependent on the positioning of the
Experimental Studies of Antenna Miniaturization Using
Magneto-Dielectric and Dielectric Materials
Antti O. Karilainen1, Pekka M. T. Ikonen2, Constantin R. Simovski1,
Sergei A. Tretyakov1, Andrey N. Lagarkov3, Sergei A. Maklakov3,
Konstantin N. Rozanov3, and Sergey N. Starostenko3
1Department of Radio Science and Engineering/SMARAD Center of Excellence,
Helsinki University of Technology (TKK),
P.O.Box 3000, FI-02015 TKK, Finland.
Email: (see http://radio.tkk.fi/en/contact/).
2TDK-EPC, P.O.Box 275, FI-02601 Espoo, Finland. Email: firstname.lastname@example.org.
3Institute for Theoretical and Applied Electromagnetics (ITAE),
Russian Academy of Sciences,
13 Izhorskya ul., 125412 Moscow, Russia.
Email: Konstantin Rozanov email@example.com.
October 21, 2009
Measurement results for a meandered planar inverted-F antenna (PIFA) loaded with magneto-
dielectric and dielectric materials are presented. Figures of merit and ways to compare an-
tennas with different fillings materials are discussed. The used magneto-dielectric material is
described, the radiation mechanism of the meandered PIFA is studied, and the proper position
for dielectric and magneto-dielectric filling is discussed and identified. Identical-size antennas
with dielectric and magneto-dielectric fillings are compared at the same resonance frequency
using the radiation quality factor as the figure of merit. It is seen, that the benefit from the
magneto-dielectric filling material is moderate and strongly dependent on the positioning of
arXiv:0910.4060v1 [physics.class-ph] 21 Oct 2009
A substrate with lossless and dispersion-free permeability µ higher than the permittivity ? could
theoretically lead to substantially wider impedance bandwidths in patch antennas . However,
new artificial and composite magnetic materials have not yet proved their expectations in patch-
antenna miniaturization. Artificial magnetic materials, such as those based on split-ring resonators,
are dispersive by nature, and in case of Lorentzian-type dispersion, patch-antenna miniaturization
in terms of improved radiation quality factor is impossible, as compared to a reference design . As
opposed to artificial materials, substrates with natural magnetic inclusions can provide reasonably
large static values of permeability with relatively low dispersion, and miniaturization is possible .
In this paper we present measurement results of a meandered planar inverted-F antenna (PIFA)
miniaturized with a magneto-dielectric material, and miniaturization using conventional dielectric
material is used as a reference for comparison.
Modern material manufacturing technology has made possible to design composite substrates
with magnetic inclusions mixed with dielectric host materials. Antennas with magneto-dielectric
materials are studied experimentally in [4–13]. Known magnetic materials tend to be lossy, and in
antenna applications the radiation efficiency becomes the main figure of merit in addition to the
unloaded quality factor or impedance bandwidth. Previous results in antenna miniaturization and
efficiency include [14–16].
When using magneto-dielectric substrates in miniaturization, miniaturization is equivalent to
a decrease of the resonant electrical size of the antenna at a given operating frequency. A question
that should be answered when using novel materials is whether the used material outperforms the
traditional miniaturization methods . If we accept that by using magnetic substrates we can, at
least in theory, miniaturize a patch antenna without decreasing noticeably the bandwidth, we also
have to challenge it against available dielectric material. Good-quality dielectric materials have
low loss, but magneto-dielectric materials are typically considerably more lossy. Therefore, both
the radiation efficiency and the measured unloaded quality factor must be used when comparing
the same antenna with magneto-dielectric and dielectric fillings. This has been done in this paper
by using the radiation quality factor as as a figure of merit, where the effect of dissipative losses
in the antenna have been normalized away from the results.
The quality factor of a small antenna depends on the operating frequency and the antenna
size in addition to effective utilization of the antenna’s volume , so one has to be careful when
comparing antennas with different fillings. When comparing an antenna with magneto-dielectric
and dielectric materials, the quality factor must be measured at the same frequency for both cases.
Moreover, the physical size of the antenna should also be the same. We discuss in this article the
necessary conditions for fair comparison between antennas with different material fillings.
Resonant antennas in general behave differently when using magnetic or dielectric materials
for filling. This can be understood easily from the field distributions inside antennas. It has been
proposed, that in some cases the optimal filling material can be determined from the radiating
fields [19,20]. We discuss how to choose and also position the used filling materials for antennas
in general, and use these guidelines for the meandered PIFA under study .
In Section 2, we describe the needed figures of merit and discuss how to compare antennas
in practice. Section 3 describes the used magneto-dielectric material and Section 4 presents the
antenna under test and the results of the measurements. The measurement results are analyzed
and discussed in Section 5 and conclusions are made in Section 6.
2Antenna Merits and Comparison
Before we start describing the measurements, we will review and discuss the measured parameters.
The obvious figure of merit for small antenna measurements is the unloaded quality factor, or the
radiation quality factor when the radiation efficiency of the antenna is included in calculations.
However, when comparing two small antennas, we must also consider the size or volume, and the
resonance frequency together.
2.1Figures of Merit for Small Antennas
First we discuss the figures of merit for antenna measurements. In other words, we define what we
want to use when comparing performance of antennas. The radiation efficiency is the ratio between
the radiated power Prand the total accepted power Ptot. Ptotis the sum of Prand the dissipated
power PLin the antenna. Using the Thevenin equivalent antenna impedance Za= Ra+ jXaand
dividing the antenna resistance as Ra= Rr+RL, where Rrcorresponds to radiated power and RL
to dissipated power, we can write the radiation efficiency as (e.g. ):
Using the Wheeler-cap method to calculate the radiation efficiency , the right-hand part of (1)
can be directly applied to find ηrfrom the measured Za.
The antenna quality factor Q and the bandwidth B of an antenna with a single resonance are
related to each other with the voltage standing wave ratios (VSWRs) as follows: If the bandwidth
criterion is VSWR < S and T is the VSWR at the resonant frequency, Q can be calculated as 
(TS − 1)(S − T)
It follows from (2), that for a certain desired matching level we should have half the reflection
coefficient for the optimal over-coupled resonance. For example, for S11= −6 dB matching level,
the reflection coefficient should be −12 dB at the center frequency of the resonance.
It has been recently proposed, that the quality factor can be approximatively solved directly
from the impedance also for antennas with lossy and dispersive materials: [24,25]
although, strictly speaking, the knowledge of only Za is not enough to find the ratio between
radiated, stored and dissipated powers.
When the quality factor is calculated from (2) or (3), the effect of dissipated power in the
antenna can be removed from Q by using the radiation quality factor
In practice, when we measure an antenna and solve Q from the S11parameter or from Za, we must
use (4) to compare antennas with different ηr.
Now that we know what to compare in antenna measurements, we must set up rules how we
compare antennas with different loading materials. When dealing with small antennas, the well-
known lower limit for the quality factor (e.g. )
can be thought to hold with ka ? 1. It is calculated from the stored average energy outside a
sphere with radius a surrounding the antenna. If we assume that a3is proportional to the volume
V of an antenna, we can write the minimum quality factor as follows:
since k = 2πf√µ?. Now, it is obvious from (6) that if we compare the quality factors of two
antennas, they should have the same volume V and the same operating frequency f. Otherwise it
is not possible to come to any conclusion which one of the antennas has e.g. the largest potential
bandwidth and comes close to the fundamental limit. In fact, the bandwidth itself is a difficult
figure of merit since both Q and the radiation efficiency affect it. Because of this, we favor the
radiation quality factor below.
The effect of material filling, partial or full, on antenna performance is not simple. Is has been
proposed in  that the most beneficial material type can be determined analyzing the radiating
currents of the antenna. Next, we summarize the steps needed for an efficient design of a small
i) Identify the radiating fields or currents. For example, in case of patch antennas, most of
the radiation is produced by the fringing electric fields at the open ends of the patch. The
surface current due to the magnetic field is canceled by the image current below the ground
plane, but the magnetic equivalent current from the electric field is doubled.
ii) Determine the fields contributing mainly to the stored energy. If either electric or magnetic
field does not provide radiation, it is safe to use dielectric or magnetic materials, respectively,
to suppress these fields and make the resonating wavelength larger, i.e. to miniaturize the
iii) Apply the filling to the right place. If possible, use the filling material only at the place where
it has the desired effect. There is no need to use dielectric or magnetic filling in places where
there is no electric or magnetic fields, respectively.
Magneto-dielectric materials have, of course, both magnetic and dielectric material responses.
If we use the material in a position with strong magnetic field but weak electric field, we use
only the magnetic properties which may be beneficial and not the harmful dielectric properties,
depending on the antenna type. When comparing miniaturization using different material types,