the validity of our analysis based on the effective medium mod-

eling. Consequently, to sum up, all measurement data agree well

with the two different predictions from the computer simulation

of an entire fabricated antenna structure and from the effective

homogeneous medium approach, which has proven the accuracy

and validity of our analysis and design.

3. CONCLUSIONS

We have presented a useful method to decrease overall antenna

size using the proposed artificial magneto-dielectric metasub-

strate. We have shown that high effective permittivity and per-

meability are definitely helpful to miniaturize the antenna more

than 50% based on effective medium theory. To confirm the

effective medium approach, we have substituted the real meta-

substrate with the fictitious homogeneous material consisting of

the effective permittivity and permeability that are retrieved

from the real metasubstrate. By demonstrating that the same

patch antenna with the fictitious substrate shows very similar

properties to that with the real metasubstrate, we can success-

fully prove the usefulness of our effective medium analysis. Fur-

thermore, the good agreement between the prediction and the

experiment also confirms validity of our design approach.

REFERENCES

1. J.L. Volakis, C.C. Chen, and K. Fujimoto, Small antennas: miniatur-

ization techniques & applications, McGraw Hill, 2010, pp. 107–208.

2. H. Mosallaei and K. Sarabanki, Design and modeling of patch

antenna printed on magneto-dielectric embedded-circuit metasub-

strate, IEEE Trans Antennas Propag 55 (2007), 45–52.

3. P.B. Ikonen, S.I. Maslovski, C.R. Simovski, and S.A. Tretyakov, On

artificial magnetodielectric loading for improviing the impedance

bandwidth properties of microstrip antennas, IEEE Trans Antennas

Propag 54 (2006), 1654–1662.

4. J.K. Ji, W.K. Ahn, S.H. Park, G.H. Kim, and W.M. Seong, Minia-

turized T-DMB antenna with a low-loss Ni-Mn-Co ferrite for mobile

handset applications, IEEE Magn Lett 1 (2010), 5000104.

5. CST Microwave Studio: Workflow & Solver Overview, CST Studio

Suite 2009, CST-GmbH (2011).

6. D. Kim and J.I. Choi, Novel planar metamaterial with a negative re-

fractive index, ETRI J 31 (2009), 225–227.

7. D. Kim, W.L. Lee, and J.I. Choi, A simple design method of nega-

tive refractive index metamaterials, Appl Phys A: Mater Sci Process

97 (2009), 461–467.

8. D.R. Smith, D.C. Vier, Th. Koschny, and C.M. Soukoulis, Electro-

magnetic parameter retrieval from inhomogeneous metamaterials,

Phys Rev (E) 71 (2005), 036617.

VC 2012 Wiley Periodicals, Inc.

FULL WAVE AND ASYMPTOTICCOMPUTATION OF COUPLING LOSSBETWEEN ANTENNAS ON AIRCRAFT

Jean-Francois Legendre and C. Br�eluzeauDGA Information Superiority, TEC, route de Laill�e, Bruz 35170,France; Corresponding author: jeff.legendre@free.fr

Received 21 March 2012

ABSTRACT: This article presents how to compute the coupling lossbetween a transmitter and a receiver with full-wave electromagnetic

software. An analytical method based on asymptotic sphericaldiffraction is proposed, and results of coupling loss between antennas

on an un-named aerial vehicle are compared. Extension to other aircraftsizes is discussed. VC 2012 Wiley Periodicals, Inc. Microwave Opt

Technol Lett 54:2874–2878, 2012; View this article online at

wileyonlinelibrary.com. DOI 10.1002/mop.27171

Key words: coupling loss; electromagnetic interference; diffraction

1. INTRODUCTION

One of the missions of electromagnetic interference (EMI) and

spectrum department of DGA Information Superiority is to deal

with functional EMI compatibility that must be accurately taken

into account to obtain the expected system performance and estab-

lish the risk of interference between equipments or systems. Gener-

ally, EMI can travel by radiation from its source to a receptor that

receives the EMI. The RF power of receiver can be deduced from

source characteristics (power, spectrum, etc.), receiver characteristics

(frequency band, sensitivity, etc.), and the coupling loss between

both the antennas. SPC department is using CST Microwave Studio

software to carry out such coupling loss simulation studies on ter-

restrial vehicles and on aircrafts. We present here an example where

coupling loss on an un-named aerial vehicle (UAV) is investigated.

A tool based on asymptotic diffraction between two monopoles on

a cylinder has been developed by SPC to evaluate such coupling

loss without computer aided design (CAD) model.

2. FULL WAVE COMPUTATION METHOD OF COUPLING LOSS

The process to compute coupling loss with finite-difference

time-domain (FDTD) electromagnetic full wave software can be

divided into several steps.

Figure 6 Comparison in measured and predicted radiation patterns of

the antenna shown in Figure 1 at 2.5 GHz (a) an E-plane and (b) an H-

plane. [Color figure can be viewed in the online issue, which is available

at wileyonlinelibrary.com]

2874 MICROWAVE AND OPTICAL TECHNOLOGY LETTERS / Vol. 54, No. 12, December 2012 DOI 10.1002/mop

2.1. Structure GenerationThe structure generation is performed starting from paper plans

of the UAV, which have been digitalized thanks to a CAD soft-

ware (red lines in Fig. 1). The different shapes of the UAV

model are created using 3D primitives (sphere, brick, elliptical

cylinder, etc.) and more advanced operations such as lofting

(creating new shapes between profiles). Each shape of this

model is assigned to a material that is by default an electrically

perfect conductive (PEC) material. In reality, only the load, the

batteries, and the engines of the UAV can be considered as

PEC. A second model is created by assigning dielectric material,

namely, Plexiglass (relative permittivity ¼ 3.6 and electrical

conductivity ¼ 0.02 S/m). The dielectric parts of the UAV are

illustrated in yellow color in Figure 1.

2.2. Antennas IntegrationTwo k/4-monopole antennas working at 4.5 GHz are integrated

on the main cylinder that represents the UAV load. They are

modeled by two short PEC cylinders that are separated by an

axial distance of 28.4 cm. A discrete edge port is used as feed-

ing point source for each antenna. This port realizes an input

power of 1 W under 50 X and enables the calculation of corre-

spondent S-parameter, based on the incoming and outgoing time

signals. The S12 parameter between both ports will give the cou-

pling loss between both the monopoles.

2.3. Mesh Settings and Solver SetupThe electromagnetic software is based on a transient (time do-

main) solver that calculates the development of fields through

time at discrete locations and at discrete time samples by the

‘‘Leap Frog’’ updating scheme. The whole 3D structure needs to

be rendered to a discrete geometric form, by creating a suitable

mesh system made of many small grid cells. One has to specify

spatial sampling rate connected to the wavelength of the highest

frequency set for the simulation (here 4.5 GHz). A good com-

promise between calculation time and the achievable accuracy is

the default value of 8, which means a spacing distance less than

k/8 � 8 mm. This leads to 73 millions of grid cells, because

automatic meshing performs refinement of small shapes of the

structure. Using the subgridding option with topologically irreg-

ular grids, the amount of grid cells can be reduced by a factor

of 10. This improves the computation speed, and less RAM

memory is needed. Another factor that has a strong influence on

the calculation time is the accuracy of the frequency domain

signals that are calculated by Fourier transformation of the time

signals. The amplitudes of the time signals as well as the total

energy inside the calculation domain are computed during the

simulation. The simulation stops when the defined accuracy

level is reached. This accuracy factor is set to �30 dB.

2.4. Postprocessing: Exploitation of [S] ParameterThe transient solver allows the simulation of a structure’s behav-

ior in a wide frequency range in just a single computation run.

The S-parameters are defined as the quotient between the output

Figure 1 Creating UAV 3D model from plans and antennas integration. [Color figure can be viewed in the online issue, which is available at

wileyonlinelibrary.com]

Figure 2 Coupling loss computed by FDTD. [Color figure can be

viewed in the online issue, which is available at wileyonlinelibrary.com]

DOI 10.1002/mop MICROWAVE AND OPTICAL TECHNOLOGY LETTERS / Vol. 54, No. 12, December 2012 2875

signal spectrum and the input signal spectrum, deduced from

time signals using discrete Fourier transform. Considering port

no. 1 for the first antenna and port no. 2 for the second one, S12

parameter corresponds to the coupling loss between both anten-

nas placed on the UAV structure.

Figure 2 gives the simulation results of the coupling loss for

three 3D structures up to 4.5 GHz. ‘‘PEC’’ curve is obtained with

the full UAV in full PEC material, ‘‘PEC þ Plexiglass’’ is

obtained with the full UAV in PEC and plexiglass material as

shown in Figure 1. The trend of the coupling loss is similar for

the three case studies. Maximum value is about �43 dB at 4

GHz. When dielectric material is taken into account, one can

notice much more interferences in the S12 result. This may be

due to the fact that interactions with the engines and batteries are

not masked anymore by dielectric wings. Computation time rises

up to 15 h on a DELL T7400 workstation with 8 Go RAM. A

third curve is presented when we consider only PEC load shape

of the UAV. The main effect is the grazing diffraction that hap-

pens between both antennas around the PEC cylinder. There is

still a good agreement with the simulations found on the complex

structures, even if the effects on wings and engines are neglected.

As shown by this third full-wave simulation, coupling loss

on the UAV (and by extension on an aircraft) can be approxi-

mated by considering two monopole antennas placed on a PEC

cylinder. The load of the UAV is modeled by a cylinder with a

radius R (6.5 cm).

3. ASYMPTOTIC COMPUTATION OF COUPLING LOSS ON ACYLINDER

Considering the geometry of Figure 3, the coupling loss CL is

defined by the ratio of the receiver power Pr to the input power

Pt. The following equation is obtained from Friis transmission

equation [1], assuming matched vertical polarization and adding

the correction factor Q for diffraction loss of one ray around the

cylinder. One has to take into account two existing grazing rays

(one on the left side and the other on the right side of the cylin-

der), whose amplitudes have to be added (phase is neglected).

This leads to this general formula:

CL ¼ Pr

Pt

¼ ð1 � Ct2Þ � Dt � ð½A � Q�left þ ½A � Q�rightÞ

2 � Dr � ð1 � Cr2Þ

(1)

where Dt and Dr are the directivity gains of the transmitting and

receiving antennas, respectively. As we consider k/4-monopoles,

we apply by default the value 4.8 dBi obtained on a flat PEC

surface. Ct and Cr are the voltage reflection coefficients at the

input terminals of the transmitting and receiving antennas,

respectively. The factor (1 � C2) represents the reflection mis-

match efficiency of the antenna. Reflection coefficient C can be

computed knowing the characteristics impedance of the trans-

mission line Zo and the antenna input impedance Zin. If the feed-

ing line connecting to the monopole has a real impedance Zo

(typically 50 W), reflection coefficient is given by:

C ¼ Zin � Zo

Zin þ Zo

�������� ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiðZin r � ZoÞ2 þ Zin i

2

ðZin r þ ZoÞ2 þ Zin i2

s(2)

This impedance for a monopole on a flat ground can be com-

puted analytically according to Ref. 1 knowing the length (l ¼1.7 cm) and the radius (r ¼ 1 mm) of the monopole.

Zin ¼ Zin r þ jZin i � 202pkl

� �2

�j120 lnl

r� 1

� �cot

2pkl

� �(3)

Figure 4 compares the coefficient reflection of each antenna

obtained by full-wave simulation on the UAV and by this ana-

lytical formula. Good agreement is achieved and enables to get

reliable reflection efficiency. At 4.5 GHz, efficiency (1 � C2)

equals to 0 dB, because k/4-monopole shows perfectly matched

impedance. But below this frequency, the reflection mismatch

leads to large losses, about �30 dB at 1 GHz.

Factor A represents the free-space loss factor along the total

geodesic path d(h) around the cylinder between both antennas.

Let define the angle t and the axial distance dst between the

monopoles, the traveling distance along cylinder can be easily

approximated. If we consider the second grazing wave, we just

have to change h by p � h.

A � k4pdðhÞ (4)

dðhÞ �ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiðRhÞ2 þ dst2

q(5)

Factor Q is the attenuation due to grazing diffraction ray along

the cylinder. The book [2] discusses the wave diffraction around

the terrestrial sphere, which is one of the oldest studied

Figure 3 Description of the geometry and definition of the parame-

ters. [Color figure can be viewed in the online issue, which is available

at wileyonlinelibrary.com]

Figure 4 Reflection coefficient and efficiency. [Color figure can be

viewed in the online issue, which is available at wileyonlinelibrary.com]

2876 MICROWAVE AND OPTICAL TECHNOLOGY LETTERS / Vol. 54, No. 12, December 2012 DOI 10.1002/mop

diffraction problems. We apply the analytical diffraction formula

[2], which comes from simplification the general expression giv-

ing the field in the form of development series, sometimes

called serial residues. Q is the ratio between diffraction field E(on a sphere of radius R) and free-space field Eo. Q equals to 1

when both antennas are installed on the same side (h ¼ 0) of

the cylinder and tends to minimum value when they are on the

opposite side (h ¼ p). If we consider vertical polarization and

PEC cylinder, asymptotic formula of Q can be reduced to a

compact form.

Q ¼ E

Eo

¼ ð1 þ 2bfþ 2pðbfÞ3Þ12 � e�1:607bf with b ¼ 0:5555

(6)

fðhÞ ¼ 2pkR2

� �1=3

ðR � hÞ (7)

If we consider the second grazing wave, we just have to change

h by p � h in the former formula.

4. RESULTS OF COUPLING LOSS ON THE UAV

Figure 4 compares the coupling loss obtained by simulation and

the coupling loss deduced from the proposed analytical model. A

very good agreement is observed. The different contributions that

are taken into account in formula (1) are also shown: the diffraction

loss Q, the free-space loss A, and the reflection mismatch loss (1 �C2), which is the same for transmitting and receiving antennas.

When the antennas are on opposite sides, the factor ‘‘A�Q’’ is same

for both the rays. This leads to 6 dB gain in the coupling loss.

At 4.5 GHz, the analytical coupling loss is about �42 dB,

compared to �49 dB simulated with the full PEC model of the

UAV. If we use only the free-space model and antennas gain,

this gives only �26.6 dB, which is far from simulated value.

The difference is mainly due to diffraction loss Q that gives

�21.3 dB for each grazing rays around the UAV load cylinder.

Reflection mismatch loss is near to 0. Below this frequency, fac-

tors Q and A become lower, because frequency is decreasing.

The main contribution is due to the mismatch reflection loss; for

example, at 1 GHz, this effect gives 80% (�60 dB, twice the

value of one monopole antenna) of the coupling loss. Above

this frequency, the main contributors of coupling loss �63 dB

are diffraction Q and free-space loss A; at 7 GHz, there are �26

dB and �40 dB. The mismatch reflection loss is about �6 dB

that tends to cancel antenna directivity gain (4.8 dB).

5. EXTENSION OF OTHER AIRCRAFT SIZES

The analytical model results are compared to simulation with

different aircraft sizes approximated by a cylinder of radius R:

UAV, missile (R � 10 cm), fighter aircraft (R < 1 m), and air-

liner aircraft (R � 2–3 m). The next figure shows the 3D model

used for simulation, where two k/4-monopoles (length l ¼ 6.2

cm, radius ¼ 4 mm) with a resonance frequency of 1.2 GHz.

The comparison with CST results shows that our analytical

model is quite accurate (standard deviation < 3 dB) around the

resonance frequency antenna (at 1 GHz). The coupling takes its

maximum value, because both antennas are perfectly matched.

At 1.7 GHz above the frequency resonance, the model is still

good. At 100 MHz (k ¼ 3 m), the error may exceed 20 dB if

the radius of the cylinder is much lower than wavelength k; for

example, when radius is 10 cm, the ratio R/k is only 0.03. The

hypothesis of two grazing waves is not suitable anymore, and

the diffraction formula becomes less accurate. In this case, simu-

lation can be achieved quickly with full-wave method.

6. CONCLUSIONS

The main drawback of the transient solver is long computation

time, when the size of the aircraft is high compared to

Figure 5 Analytical coupling loss on the UAV. [Color figure can be

viewed in the online issue, which is available at wileyonlinelibrary.com]

Figure 6 3D model used with different radius R. [Color figure can be

viewed in the online issue, which is available at wileyonlinelibrary.com]

Figure 7 Effect of radius R on coupling loss. [Color figure can be

viewed in the online issue, which is available at wileyonlinelibrary.com]

DOI 10.1002/mop MICROWAVE AND OPTICAL TECHNOLOGY LETTERS / Vol. 54, No. 12, December 2012 2877

wavelength. For example, simulation on airliner aircraft implies

also big RAM amount and time. The proposed analytical model

based on asymptotic diffraction loss can give a first approxima-

tion of coupling loss on aircraft (drone, fighter, and airliner),

which is better than the free-space assumption. Accuracy is sat-

isfactory during the process to carry out EMI studies, when

CAD is not available. This has been verified with full wave 3D

software and is easy to implement.

REFERENCES

1. C.A. Balanis: Antenna theory—Analysis and design, 2nd edition,

Wiley, New York, NY, 1997.

2. L. Boithias, Propagation des ondes radio�electriques dans l’environ-

nement terrestre, 2nd ed., Dunod, 1984.

VC 2012 Wiley Periodicals, Inc.

AN ULTRA-WIDEBAND CPW-FEDMONOPOLE ANTENNA WITH FAN-SHAPED STRUCTURE

Chen Wang,1 Ze-Hong Yan,1 Bo Li,1 and Sheng Li21National Key Laboratory of Science and Technology on Antennasand Microwaves, Xidian University, Xi’an, People’s Republic ofChina; Corresponding author: wangchen@mail.xidian.edu.cn2 Shaanxi Broadcast & TV Network Intermediary (Group) Co., Ltd.Hanzhong Branch, Hanzhong, People’s Republic of China

Received 27 March 2012

ABSTRACT: In this article, we present a novel ultrawideband (UWB)coplanar waveguide fed printed monopole antenna with fan-shaped

structure. Its UWB-related performances are simulated andexperimentally verified. The fabricated antenna occupies a small area,

exhibits omnidirectional radiation pattern and good gains within theoperating band, which illuminates the fan-shaped structure is also agood candidate for UWB antenna design. VC 2012 Wiley Periodicals, Inc.

Microwave Opt Technol Lett 54:2878–2880, 2012; View this article

online at wileyonlinelibrary.com. DOI 10.1002/mop.27218

Key words: monopole antenna; ultrawideband; coplanar waveguide-

fed; fan-shaped structure

1. INTRODUCTION

Wireless communications have evolved at an astonishing rate

recently. The future development of the personal communication

device will lay emphasis on the production of image, speech,

and data communications at any time, and anywhere around the

world. Ultrawideband (UWB) technology owing to its attractive

performances, such as low complexity, low cost, and extremely

high data rates, has been largely used in communication sys-

tems. In 2002, the Federal Communication Commission put out

an unlicensed 3.1–10.6 GHz frequency band with an effective

isotropic radiated power level of less than 241.3 dBm/MHz for

UWB applications, where UWB is defined as the occupied frac-

tion bandwidth >20% or larger than 500 MHz of the absolute

bandwidth. UWB technique has opened a promising door to

future wireless communication, radar applications, and other

military applications [1–5].

In this article, a novel coplanar waveguide (CPW) fed

printed monopole antenna with fan-shaped structure is proposed

for UWB operation. It is simulated, fabricated, and measured.

Its characteristics, including the VSWR, radiation pattern, gain,

and so on, are presented and discussed.

2. ANTENNA DESIGN

The configuration of the proposed antenna is shown in Figure 1.

The proposed antenna is etched on an inexpensive FR4 substrate

of dielectric constant er ¼ 4.4 and substrate thickness H ¼ 2

mm, with the dimension of 35 � 30 mm2 (L � W) and fed by a

CPW transmission-line with a fixed strip thickness W2 and a gap

distance g between the signal strip and the coplanar ground

plane.

Figure 1 Geometry of the proposed antenna. (a) Top view. (b) Side

view

Figure 2 Photograph of the proposed antenna. [Color figure can be

viewed in the online issue, which is available at wileyonlinelibrary.com]

2878 MICROWAVE AND OPTICAL TECHNOLOGY LETTERS / Vol. 54, No. 12, December 2012 DOI 10.1002/mop