Journal of Electromagnetic Analysis and Applications, 2013, 5, 302-311 Published Online July 2013 (
A Novel Methodology to Design Miniaturized Regular
Planar Inverted-F Antennas Based on Parametric
Abdelhakim Elouadih1, Ahmed Oulad-Said2, Moha Mrabet Hassani1
1Department of Physics, Semlalia University of Sciences (FSSM), Marrakesh, Morocco; 2Department of Electrical and Telecommu-
nications Engineering, Royal Air Academy (ERA), Marrakesh, Morocco.
Received June 10th, 2013; revised July 10th, 2013; accepted July 17th, 2013
Copyright © 2013 Abdelhakim Elouadih et al. This is an open access article distributed under the Creative Commons Attribution
License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
This paper describes a novel methodology to design PIFA (Planar Inverted-F Antenna) antennas based on parametric
simulations. The parameters considered in the parametric design are ground plan dimensions, height of radiating plate,
feeding point position, shorting plate width and position. The choice of the parameters that must be varied independ-
ently or simultanously is important to design optimized antenna. The author studied two scenarios in precedent works
[1,2]. He exposes here a third scenario of varing antenna parameters to design and simulate by HFSS (High Frequency
Simulator Structure) simulator a probe-fed dual band PIFA for the use in GSM 850 band (824 MHz - 894 MHz) and
PCS 1900 band (1850 MHz - 1990 MHz). The author compares the three scenarios and establishes a novel methodology
to design optimized and miniaturized antennas mounted on mobile handsets.
Keywords: PIFA; HFSS; Design; Methodology
1. Introduction
With the development of mobile networks and wireless
applications, the handset should be more miniature, while
working in different bands and supporting different ap-
plications. A small mobile device currently supports
GSM services, high speed mobile internet access and
allows connection via WiFi and blue tooth capabilities.
For this purpose, antennas are vowed to achieve minia-
turization while maintening function requirements. The
planar antennas are so compliant and their use in wireless
local and wide networks increases.
For optimum system performance, the antennas must
have high radiation efficiency, small volume, isotropic
radiation characteristics, small backward radiation, sim-
ple and low-loss impedance matching to patches. The
major types of configurations of low-profile antennas
with enhanced bandwidth performance include Planar
Inverted-F Antennas.
The PIFA consists in general of a ground plane, a top
plate element, a feed wire attached between the ground
plane and the top plate, and a shorting wire or strip that is
connected between the ground plane and the top plate.
The antenna is fed at the base of the feed wire at the
point where the wire connects to the ground plane. The
PIFA is an attractive antenna for wireless systems where
the space volume is quite limited. It requires simple
manufacturing, since the radiator must only be printed.
The addition of a shorting strip allows good impedance
match to be achieved with a top plate that is typically less
than λ/4 long. The resulting PIFA is more compact than a
conventional half-wavelength probe-fed patch antenna
The miniaturization can affect radiation characteristics,
bandwidth, gain, radiation efficiency and polarization
purity. The miniaturization approaches are based on ei-
ther geometric manipulation (the use of bend forms, me-
andered lines, PIFA shape, varying distance between
feeder and short plate [4]) or material manipulation
(loading with a high-dielectric material, lumped ele-
ments, conductors, capacitors, short plate [5]) or the en-
vironment characteristics (ground plane dimensions,
coupling, measurement and fabrication errors [4]). In this
case, the bi-band designed antenna is shorted to the
ground plane by a plate, uses regular shapes and uses a
high dielectric thin substrate under the radiating plate not
above the ground plane).
Copyright © 2013 SciRes. JEMAA
A Novel Methodology to Design Miniaturized Regular Planar Inverted-F Antennas
Based on Parametric Simulations
If all precedent works are concentrated on studying the
effects of these elements (material, geometry, environ-
ment), the choice of a PIFA element was so improvised
in the design. There are some recent works to to make
algorithms or parametric simulations but they use some
models concerning the traditional patch antennas [6] or
they deliver the thoretical frequency from predefined
parameters [7,8]. The author worked on parametric simu-
lations by varing sequently the antenna parameters (sce-
nario 1) [1] or simultanously of some parameters (sce-
nario 2) [2]. In this paper, the author will expose a third
scenario and he will compare the three scenarios before
concluding about efficient methodology to design PIFA
single or multiband.
The third scenario will be applied to design a dual
band PIFA for the use in the GSM850 and PCS1900
2. Antenna Design Following the Third
2.1. The Description of the Studied Antenna
As shown in Figure 1, the designed antenna has a rec-
tangular radiating patch length Lp = 31 mm and width Wp
= 70 mm. The patch is placed at a height h from the
ground plan. The ground plan has a length Lg and a width
Wg equal to Wp. The patch is matched to the ground plan
via a rectangular shorting plate. The shorting plate has a
width Ws and a length and it is placed in the (yz) plan at a
distance D from the edge centre. The the feeding point is
situated at p from the rear edge of the patch. The patch is
fed by a 50 wire. The volume between the radiating
plate and the ground plan is filled by air except a thin
region 0.8 mm under the radiating patch who is com-
posed of FR4_epoxy (εr = 4.4).
2.2. The Choice of the Patch Dimensions
It is very important for simulation by HFSS to estimate
the resonant frequency that help the simulator to make a
refinement mesh in a band around the resonant frequency
and then give more precise values. The resonant fre-
quency of a PIFA is approximated by the Equation (1) [9]
where Fr is the resonant frequency, C is the light veloc-
 (1)
If there is another substrate different from Air, C will
be 0r
where C0 = 3 × 108 m/s. For our case, the
space between the patch and the ground plan is essen-
tially air minus a 0.8 mm FR4 epoxy layer.
= W
= W
Figure 1. Different views of the designed antenna; (a) front
view; (b) side view; (c) perspective view.
To compute the resonant frequency, we have the fol-
lowing values: Lp = 31 mm, Wp = 70 mm, Wsmax = 3 mm.
The theoretical Fris 790 MHz. The obtained frequency is
then not far from 824 MHz the first frequency of
GSM850 band. In fact, there is no equation (not empiri-
cal) to determine the resonant frequency for a PIFA that
contains not only the patch dimensions but also the other
parameters that can affect the antenna characteristics. For
this, the author will make constant the patch dimensions
that are the mean parameters can furnish the resonant
frequency and he will vary (following the scenario 3)
firstly the height, secondly and simultanously the length
Lg, the width Ws, the distance D. Finally, the author will
vary the feeding point position p and at last and simul-
tanously undependably the other parameters (ground plan
dimensions Lg, height of radiating plate h, feeding point
position p, shorting plate Width Ws and position D).
Copyright © 2013 SciRes. JEMAA
A Novel Methodology to Design Miniaturized Regular Planar Inverted-F Antennas
Based on Parametric Simulations
Copyright © 2013 SciRes. JEMAA
2.3. The Choice of the Height h
The height h is the distance between the top plate and the
ground plane. In order to eliminate the effects of the
ground plane, the patched is placed on the edge of an
infinite ground plane (in HFSS, the choice of the infinite
ground plan can be made during the definition of boun-
daries) at a height varying from 6 mm to 13 mm.
From the simulation result shown by Figure 2, the op-
timal height h is for h = 11 mm because it gives values
S11 most important and closer to central frequencies of
both bands (859 MHz and 1920 MHz). This height is a
compliant (it will be nearly the handset thickness).
2.4. Thesimultaneous Choice of the Ground Plan
Length Lg, the Short Plate Position D and
the Width Ws
The height h is taken then equal to 11 mm. It’s an ade-
quate height because the PIFA will be mounted on a
GSM handset (the height is practically close to handset
thickness). We will vary simultaneously the ground plane
Figure 2. h-parametric simulation results for GSM850 and PCS bands. (a) for GSM850; (b) for PCS1900.
A Novel Methodology to Design Miniaturized Regular Planar Inverted-F Antennas
Based on Parametric Simulations
length Lg from 80 mm to 140 mm, D will vary from 29
mm to 34 mm and the width Ws from 1 mm to 3 mm. We
will then choose our antenna configuration from 7 × 6 ×
3 = 126 possibilities. The Figures 3(a) shows the results
Figure 3. Tri-parametric simulation results; (a) for GSM850 band; (b) for PCS1900 band.
Copyright © 2013 SciRes. JEMAA
A Novel Methodology to Design Miniaturized Regular Planar Inverted-F Antennas
Based on Parametric Simulations
tion (Lg = 90 mm, D = 30 mm, Ws = 3 mm) that is one of
the three configurations related in Figure 3. We can of
the tri-parametric simulation for GSM 850 band. From
Figure 3, there are three curves that present minimal S11
values and close to the central frequency 859 MHz. The
three configurations are as indicated in Figure 3(a) (Lg =
90 mm, D = 31 mm, Ws = 3 mm), (Lg = 90 mm, D = 30
mm, Ws = 3 mm) and (Lg = 90 mm, D = 29 mm, Ws = 2
mm). We Will now check the simulation result for the
three configurations but for PCS band. The result is
shown in Figure 3(b).
The Figure 3(b) shows a S11 peak for the configura-
consider the triplet (Lg = 90 mm, D = 30 mm, Ws = 3 mm)
a very interesting trade-off configuration for both bands.
2.5. The Choice of the Feeding Point Position p
We have then chosen the parameters h, Lg, D and Ws. We
can now look for the effect of the feeding point position
p to enhance the bandwidth or the input impedance. It is
calculated from the rear edge of the patch. We will vary
the p parameter from 2 mm to 16 mm (the centre). The
value p = 1 can’t be taken because the feeding point is
theoretically a circle that has a radius. The result is
shown on Figure 4. We can consider the peak for p = 3
mm an interesting position for feeding for PCS band. We
will see for GSM band as shown in Figure 5. It is an
adequate position because it gives a S11 peak very closely
to the central frequency of the GSM850 band.
2.6 The Third Scenario Results
The results of parametric simulations are exposed in the
following. We can see in Figure 6 two peaks of S11 pa-
rameter, one is around 860 MHz (very close to the
GSM850 central frequency 859 MHz), the second peak is
around 1922 MHz (very close to the PCS central fre-
quency 1920 MHz). Also, the S11 values out of both
bands are near 0, that means the designed antenna can’t
interfere with other radiations. We can also run the
simulation by refining the sweep interval for more preci-
sion. As given exactly by simulations tables, we note S11
= 14.04 dB for 824 MHz (the low frequency of the
GSM850 band), S11 = 14.89 dB for 894 MHz (the high
frequency of the GSM band), S11 = 2.7 dB for 1850
MHz (the low frequency of the PCS band), S11 = 6.09
dB for 1990 MHz (the high frequency of the PCS band).
2.6.1. The Bandwidth and VSWR
We obtain as shown in Figure 7(a) for GSM850 band a
VSWR = 1.49 for 824 MHz (the lowest frequency),
VSWR min = 1.03 for 860 MHz (the resonant fre-
quency), VSWR = 1.43 for 894 MHz (the highest fre-
quency). The VSWR is at its minimum, it’s very interest-
ing result. Also, The GSM bandwidth (70 MHz) is for
the designed antenna a 1:1.5 VSWR bandwidth and the
antenna presents a presents a 1:2 bandwidth equal to 120
MHz. It is considered a very interesting result.
Also, we obtain as shown in Figure 7(b) for PCS band
Figure 4. Feeding point position parametric simulation results for PCS1900 band.
Copyright © 2013 SciRes. JEMAA
A Novel Methodology to Design Miniaturized Regular Planar Inverted-F Antennas
Based on Parametric Simulations
Figure 5. The selected configuration in GSM850 band.
Figure 6. S11 depending on frequency for (0 - 2400 MHz).
a VSWR = 6.47 for 1850 MHz (the lowest frequency),
VSWR min = 1.00 for 1922 MHz (the resonant fre-
quency), VSWR = 1.00 for 1990 MHz (the highest fre-
quency). The VSWR is at its minimum, it’s a very inter-
esting result. Also, The PCS bandwidth (140 MHz) is for
the designed antenna a 1:6.47 VSWR bandwidth and the
antenna presents a 1:2 bandwidth equal to 63 MHz.
2.6.2. The Impedance in the Feeding Point
The Figure 8 shows a regular impedance smith chart
with interesting parameters of reflection, impedance,
VSWR and Q. We can see very close values between the
impedances (input and port). The feeding point position
is then confirmed that is very adequate because it pre-
sents a very interesting adaptation.
2.6.3. The Antenna Parameters
The simulations results are summarized in Table 1. The
obtained gain G is 1 dBi and the radiation efficiency is
2.6.4. The Diagram Pattern
We can confirm by the Figure 9 that (xz) is the E-plane.
Also, by the tables the E-field has its maximum in (phi =
0 deg and theta = 36 deg).
3. Comparison between the Three Scenarios
The mean results are shown by Table 2. We can detect
that the second scenario gives more intersting results, the
simultanous parametric simulations increas the pro-
bability to find an optimized configuration.
4. The Selected Methodology
By the precedent comparision, the author concluded
about the following methodology that is improvement of
the second scenario. To design antenna, we must group
by the parameters that have the same order of magnitude
to make simultanous parametric simulation and also
varying successively the parameters wich have different
order of magnitude. For this, the following methodology
is efficient to design optimized mulibandes PIFAs:
Choose the patch dimensions and shape by applying
the theoretical formula of resonnant frequency.
Vary h from some millimeters to the maximun ac-
Copyright © 2013 SciRes. JEMAA
A Novel Methodology to Design Miniaturized Regular Planar Inverted-F Antennas
Based on Parametric Simulations
Figure 7. The VSWR depending on the frequency for both bands.
cepted thickness of the handset (in the hypothesis of
an infinite ground plan that can be chosen in the
simulation by HFSS). The height h is then selected.
for multiband antenna, the optimal value should be a
trade-off for different bands.
Vary the ground plan dimensions regarding the maxi-
mum dimensions of the PCB card where the antenna
will be mounted. The ground plan dimensions are
then chosen.
Make a simultanous parametric simulations for the
parameters concerning the feeding point and the
shorting plate (as Ws, D, p). This step is compliant for
Copyright © 2013 SciRes. JEMAA
A Novel Methodology to Design Miniaturized Regular Planar Inverted-F Antennas
Based on Parametric Simulations
Figure 8. The impedance smith c har t for both bands.
Table 1. The design antenna parame ter s and dime nsions.
Antenna parameter Value of the parameter
GSM850 PCS1900
Patch Length Lp 31 mm
Patch width Wp 70 mm
Ground plan length Lg 90 mm
Ground plan width Wg 70 mm
Height h 11 mm
Short plate width Ws 3 mm
Short plate position D 30 mm
Feeding point position 3 mm
Resonnat frequency 860 MHz, 1922 MHz
Peak S11 36 dB, 56 dB
1:2 VSWR bandwith 63 MHz, 40 MHz
Peak Gain 1 dB
Peak directivity 1 dB
Radiation efficiency 85%
E total max Phi = 0 deg, Theta = 36 deg
Table 2. Comparision of the three scenarios.
Scenario 1
Single Band
Scenario 2
First Second
band band
First Second
band band
bandwith 140 70, 170 70, 140
10 db
bandwith > 140 MHz >70 MHz, 65
>70 MHz
40 MHz
1:1.5 VSWR
bandwith 130 MHz (93%)
>90 MHz
40 MHz
70 (100%), 35 MHz
Peak S11 65 dB 55 dB, 23 dB 36 dB, 56 dB
Peak gain1.16 dB 12.9 dB 1dB
directivity 1.15 dB 15.2 dB 1 dB
efficiency 1.0085 0.84 1dB
1920 MHz 925 MHz,
859 MHz,
1920 MHz
frequency 1924 MHz 926 MHz,
1804 MHz
860 MHz,
1922 MHz
Copyright © 2013 SciRes. JEMAA
A Novel Methodology to Design Miniaturized Regular Planar Inverted-F Antennas
Based on Parametric Simulations
Figure 9. The E-field polar diagram pattern; (a) in 2D; (b) in 3D.
Copyright © 2013 SciRes. JEMAA
A Novel Methodology to Design Miniaturized Regular Planar Inverted-F Antennas
Based on Parametric Simulations
both antenna feeding ways (probe or plate). Make a
trade off choice of the optimal configuration for dif-
ferent bands.
This methodology is interesting not only to design
PIFA with regular shape (as studied here), but also
PIFAs with bent and meandered shapes by modifing
an initial regular PIFA.
5. Conclusions
To design a dual band (or multibands) PIFA, the author
exposed a methodolgy based on parametric simulations.
The parameters variations are simulated successively or
simultanously by group that have the same order of mag-
nitude. The methodogy is a formalism of precedent pub-
lished works of the author concerning the parametric si-
mulations to design PIFAs. The results are interesting and
the methodogy can be used lonely or can be also com-
bined with other design algorithms of PIFA literature.
Also, the methodology is a trade-off between differ-
ents band of the antenna because enhancement in a band
affects negatively the other bands. The methodology has
as goal to search an effective solution that respects the
requirements and not necessary the optimal one. In com-
parison with precedent designed PIFAs [4,5] for different
frequency bands, the methodology allows the design of
antennas presenting a very high gain and directivity and
also an interesting radiation efficiency for different band.
The use of methodology in designing antenna is so inter-
esting to optimize the antenna characteristics and per-
formance. This research field is in progress and the an-
tenna design methodology can be combined with algo-
rithms as genetic algorithms to make more optimized
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Copyright © 2013 SciRes. JEMAA