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2936IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. 51, NO. 10, OCTOBER 2003

Microstrip Antennas Integrated With Electromagnetic

Band-Gap (EBG) Structures: A Low Mutual

Coupling Design for Array Applications

Fan Yang, Member, IEEE, and Yahya Rahmat-Samii, Fellow, IEEE

Abstract—Utilizationofelectromagneticband-gap(EBG)struc-

tures is becoming attractive in the electromagnetic and antenna

community. In this paper, a mushroom-like EBG structure is ana-

lyzed using the finite-difference time-domain (FDTD) method. Its

band-gap feature of surface-wave suppression is demonstrated by

exhibitingthenearfielddistributionsoftheelectromagneticwaves.

The mutual coupling of microstrip antennas is parametrically in-

vestigated, including both the E and H coupling directions, dif-

ferent substrate thickness, and various dielectric constants. It is

observed that the E-plane coupled microstrip antenna array on a

thick and high permittivity substrate has a strong mutual coupling

duetothepronounced surfacewaves.Therefore, anEBGstructure

is inserted between array elements to reduce the mutual coupling.

This idea has been verified by both the FDTD simulations and ex-

perimental results. As a result, a significant 8 dB mutual coupling

reduction is noticed from the measurements.

Index Terms—Electromagnetic band-gap (EBG), finite-differ-

ence time-domain (FDTD) method, microstrip antennas, mutual

coupling, surface wave.

I. INTRODUCTION

I

the electromagnetic and antenna community. The EBG ter-

minology has been suggested in [1] based on the photonic

band-gap (PBG) phenomena in optics [2] that are realized by

periodical structures.There are diverseforms ofEBG structures

[1], [3], and novel designs such as EBG structures integrated

with active device [4] and multilayer EBG structures [5] have

been proposed recently. This paper focuses on a mushroom-like

EBG structure, as shown in Fig. 1. Compared to other EBG

structures such as dielectric rods and holes, this structure has

a winning feature of compactness [6], [7], which is important

in communication antenna applications. Its band-gap features

are revealed in two ways: the suppression of surface-wave

propagation, and the in-phase reflection coefficient. The fea-

ture of surface-wave suppression helps to improve antenna’s

performance such as increasing the antenna gain and reducing

back radiation [8]–[11]. Meanwhile, the in-phase reflection

feature leads to low profile antenna designs [12]–[14].

This paper concentrates on the surface-wave suppression ef-

fect of the EBG structure and its application to reduce the mu-

N RECENT years, there has been growing interest in

utilizing electromagnetic band-gap (EBG) structures in

Manuscript received January 29, 2002; revised November 25, 2002.

The authors are with the Department of Electrical Engineering, University

of California at Los Angeles, Los Angeles, CA 90095-1594 USA (e-mail:

ygfn@ee.ucla.edu; rahmat@ee.ucla.edu).

Digital Object Identifier 10.1109/TAP.2003.817983

tual coupling of microstrip antennas, as shown in Fig. 1. To ex-

plorethesurface-wavesuppressioneffect,thepropagatingfields

of an infinitesimal dipole source with and without the EBG

structurearesimulatedandcomparedusing thefinite-difference

time-domain (FDTD) method [15], and a frequency stopband

for the field propagation is identified. Furthermore, the prop-

agating near fields at frequencies inside and outside the band

gap are graphically presented for a clear understanding of the

physics of the EBG structure. It is worthwhile to point out that

this band-gap study is closely associated with specific antenna

applications such as microstrip antennas and arrays.

Applications of microstrip antennas on high dielectric con-

stant substrates are of special interest due to their compact size

and conformability with the monolithic microwave integrated

circuit (MMIC). However, the utilization of a high dielectric

constant substrate has some drawbacks. Among these are

a narrower bandwidth and pronounced surface waves. The

bandwidth can be recovered using a thick substrate, yet this

excites severe surface waves. The generation of surface waves

decreases the antenna efficiency and degrades the antenna

pattern. Furthermore, it increases the mutual coupling of the

antenna array which causes the blind angle of a scanning array.

Several methods have been proposed to reduce the effects of

surface waves. One approach suggested is the synthesized

substrate that lowers the effective dielectric constant of the

substrate either under or around the patch [16]–[18]. Another

approach is to use a reduced surface wave patch antenna [19].

The EBG structures are also used to improve the antenna

performance. However, most researchers only study the EBG

effects on a single microstrip antenna element, and to the best

of our knowledge there are no comprehensive results reported

for antenna arrays.

The FDTD method is developed to analyze the mutual

coupling of probe-fed microstrip patch antenna arrays. The

simulated results agree well with the experimental results in

[20]. Then, the mutual coupling of microstrip antennas is para-

metrically investigated, including both the E- and H-coupling

directions, different substrate thickness, and various dielectric

constants. In both coupling directions, increasing the substrate

thickness will increase the mutual coupling. However, the

effect of the dielectric constant on mutual coupling is different

at various coupling directions. It is found that for the E-plane

coupled cases the mutual coupling is stronger on a high

permittivity substrate than that on a low permittivity substrate.

In contrast, for the H-plane coupled cases the mutual coupling

0018-926X/03$17.00 © 2003 IEEE

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YANG AND RAHMAT-SAMII: MICROSTRIP ANTENNAS INTEGRATED WITH EBG STRUCTURES: FOR ARRAY APPLICATIONS 2937

Fig. 1.Integration of the EBG structure with microstrip antenna array for reduced mutual coupling.

is weaker on a high permittivity substrate than that on a low

permittivity substrate. This difference is due to surface waves

propagating along the E-plane direction, which can be easily

viewed from the provided near field plots.

To reduce the strong mutual coupling of the E-plane cou-

pled microstrip antennas on a thick and high permittivity sub-

strate, the mushroom-like EBG structure is inserted between

antenna elements. When the EBG parameters are properly de-

signed, the pronounced surface waves are suppressed, resulting

in a low mutual coupling. This method is compared with pre-

vious methods such as cavity back patch antennas. The EBG

structureexhibits a bettercapabilityin loweringthemutual cou-

pling than those approaches. Finally, several antennas with and

without the EBG structure are fabricated on Rogers RT/Duroid

6010 substrates (

). The measured results demonstrate

the utility of the EBG structure, and this approach is potentially

useful for a variety of array applications.

II. BAND GAP CHARACTERIZATION OF THE EBG STRUCTURE

The mushroom-like EBG structure was first proposed in [3].

It consists of four parts: a ground plane, a dielectric substrate,

metallic patches, and connecting vias. This EBG structure ex-

hibits a distinct stopband for surface-wave propagation.

The operation mechanism of this EBG structure can be ex-

plained by an LC filter array: the inductor

current flowing through the vias, and the capacitor

gap effect between the adjacent patches. For an EBG structure

with patch width

, gap width , substrate thickness

electric constant

, the values of the inductor

itor

are determined by the following formula [21]:

results from the

due to the

and di-

and the capac-

(1)

(2)

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2938 IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. 51, NO. 10, OCTOBER 2003

where

tivity of free space.

Reference [21] also predicts the frequency band gap as

is the permeability of free space and is the permit-

(3)

(4)

where

Theseformulationsareverysimple;however,theirresultsare

not very accurate. For example, this model does not consider

the via’s radius information. An accurate but complex model

using the theory of transmission lines and periodic circuits can

be found in [22]. Some other methods such as reflection phase

characterization have also been utilized to identify theband-gap

features [23].

In this paper, to accurately identify the band-gap region and

understand its properties comprehensively, the FDTD method

is used to analyze the band-gap features. The computational

code developed in UCLA is based on a Cartesian grid cell with

the perfectly matched layer (PML) boundary condition. A uni-

form 0.02

( is the free space wavelength at 6

GHz) discretization is used. An infinitesimal dipole source with

a Gaussian pulse waveform is utilized to activate the structure

in order to obtain a wide range of frequency responses.

Fig. 2(a) shows an FDTD simulation model: the infinitesimal

dipole source surrounded by the mushroom-like EBG structure.

The dipole is chosen to be vertically polarized because the E

field in microstrip antenna applications is vertical to the ground

plane. As an example, two rows of EBG patches are plotted in

Fig. 2(a). In FDTD simulations four rows, six rows, and eight

rows of EBG patches are all simulated and compared.

The EBG structure analyzed in this section has the following

parameters:

is the free space impedance which is.

(5)

The vias’ radius is 0.005

to be

at

outside the EBG structure, and the height of the reference plane

is

. For the sake of comparison, a conventional case

is also analyzed. This conventional (CONV.) case consists of a

perfect electric conductor (PEC) ground plane and a dielectric

substrate with the same thickness and permittivity as the EBG

case.

The basic idea is to calculate and compare the E field at the

reference plane. Since the EBG structure can suppress the sur-

face waves in a certain band gap, the E field outside the EBG

structureshouldbeweakerthanthatoftheconventionalcase.To

quantify the surface-wave suppression effect, an average

calculated according to the following equation:

. The ground plane size is kept

. A reference plane is positioned

distance away from the edge, where it is located

is

(6)

(a)

(b)

Fig. 2.

model and (b) ??? at the reference plane. The ??? of various EBG cases are

normalized to the ??? of the conventional case.

EBG structure is analyzed using the FDTD method: (a) simulation

where

plotted by the dashed line in Fig. 2(a).

Fig. 2(b) plots the

normalized to the

study analyzing the number of EBG rows is carried out varying

the number of rows from two to eight. It is observed that when

less rows of EBG patches are used, the band-gap effect is not

significant. When the number of rows is increased, a clear band

gap can be noticed. Inside this band gap, the average E field

in the EBG case is much lower than that in the conventional

case. To determine the band-gap region, a criteria is used that

the average E field magnitude with the EBG is less than half

of that without the EBG (the CONV. case). This is equivalent to

the-6 dB (

) levelin Fig.2(b), thus a band gap from

5.8–7.0 GHz can be identified with a minimum of four rows of

EBG patches.

The LC model [(1)–(4)] is also used to analyze this mush-

room-like EBG structure, and a band gap of 6.37–8.78 GHz is

obtained. It has some overlap with the band gap calculated by

the FDTD method, which means this model can be used to get

an initial engineering estimation. However, the LC model result

is the vertical reference plane whose boundary is

of various EBG cases and they are

of the conventional case. A parametric

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YANG AND RAHMAT-SAMII: MICROSTRIP ANTENNAS INTEGRATED WITH EBG STRUCTURES: FOR ARRAY APPLICATIONS 2939

(a)

(b)

Fig. 3.

and (b) the CONV. case. The outside field of the EBG case is about 10 dB lower

than that of the CONV. case because of the surface-wave suppression.

Near fields at 6 GHz, which is inside the band gap. (a) The EBG case

is relatively higher than the FDTD results because it uses a sim-

plifiedlumpedelementmodel.Thisisalsothereasontodevelop

the FDTD model here.

To visualize the band-gap feature of surface-wave suppres-

sion, the near field distributions of the eight row EBG case and

the conventional case are calculated and graphically presented.

Fig. 3 plots the near field of both cases at 6 GHz, which is in-

side theband gap.The fieldlevelis normalizedto1 Wdelivered

power and is shown in dB scale. The field level outside the EBG

(a)

(b)

Fig. 4.

and (b) the CONV. case. The outside field of the EBG case has a similar level

as that of the CONV. case.

Near fields at 5 GHz, which is outside the band gap. (a) The EBG case

structure is around 10 dB. In contrast, the field level of the

CONV. case is around 20 dB. The difference of field levels is

due to the existence of the EBG structure, which suppresses the

propagation of surface waves so that the field level in the EBG

case is much lower than in the conventional case. However, the

EBG structure cannot successfully suppress surface waves out-

side its frequency band gap. For example, Fig. 4 plots the near

field of both cases at 5 GHz, which is outside the band gap. The

field distribution of the CONV. case is similar to its distribution

at 6 GHz. However, the field value outside the EBG structure is

increasedtoaround20dB,whichissimilartothatoftheCONV.

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2940IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. 51, NO. 10, OCTOBER 2003

Fig. 5.

antennas.

FDTD model to calculate the mutual coupling of probe fed microstrip

case. This means that although there are some interactions be-

tween the dipole source and the EBG structure, the field can

still propagate through the EBG structure. These results corre-

late well with the results in Fig. 2(b). From this comparison it

can be concluded that as expected, the surface-wave suppres-

sion effect exists only inside the band gap of the EBG structure.

III. MUTUAL COUPLING COMPARISON OF VARIOUS

MICROSTRIP ANTENNA ARRAYS

A. FDTD Method for Mutual Coupling Simulation

The FDTD method is used to analyze the mutual coupling

of microstrip antennas. The mutual coupling of antennas fed by

microstriplineshasbeensolvedusingtheFDTDmethodin[24],

and the probe fed antenna case is discussed herein.

Fig. 5 plots an FDTD model to calculate the mutual coupling

of two probe fed patch antennas. The reflection coefficients are

defined as

(7)

where

incidentwaveandreflectedwavesaremixedtogetherduringthe

FDTD simulation, and the voltages and currents are recorded at

the ports [15]. The relation between the waves and the recorded

data is

,, , and are the normalized voltage waves. The

(8)

(9)

(10)

(11)

where

probes.

A Gaussian pulse type of voltage source is used to excite the

structure. For simplicity, only port one is activated during the

simulation and port two is matched to 50

cident wave at port two is zero,

and are characteristic impedances of the feeding

. Therefore, the in-

. Thus, (7) becomes

(12)

(13)

Substituting (12) and (13) into (8)–(11) and dividing (8) and

(10) by (9), one arrives at

(14)

(15)

Fig. 6. E- and H-plane coupled probe fed microstrip antennas.

Fig. 7.

GHz for 5 cm (radiating edge) ? 6 cm patches on a 0.305 cm thick substrate

with a dielectric constant of 2.5.

Measured [20] and FDTD simulated mutual coupling results at 1.56

Oncethevoltagesandcurrentsareobtained,thereturnloss(

and mutual coupling (

) can be derived from (14) and (15).

The validity of these formulations has been demonstrated by

the E-plane and H-plane coupled microstrip antennas illustrated

in Fig. 6. A comparison of FDTD simulation results and ex-

perimental results [20] is shown in Fig. 7. The antenna has a

patch size of 5 cm (radiation edge)

a 0.305 cm substrate with a dielectric constant of 2.5. The mu-

tual coupling is calculated and measured at 1.56 GHz, and good

agreements are observed. This method can also be used to ana-

lyze the mutual coupling of microstrip antennas with arbitrary

orientation [25].

)

6 cm, and is mounted on

B. Mutual Coupling Comparison

The developed FDTD method is next used to analyze the

mutual coupling features of microstrip antennas at different

thicknesses and permittivities [26], [27]. Both the E-plane and

H-plane couplings are investigated, and four patch antennas are

compared as follows: