Bandwidth Enhancement of Artificial Magnetic Conductor-based Microwave Absorber Using Square

Patch Corner Cutting

Aulia Dewantari Radio Telecommunication and Microwave Laboratory School of Electrical Engineering and Informatics, ITB

Bandung, Indonesia dewantariaulia@yahoo.com

Achmad Munir Radio Telecommunication and Microwave Laboratory School of Electrical Engineering and Informatics, ITB

Bandung, Indonesia munir@ieee.org

Abstract—A method for enhancing the bandwidth of microwave absorber is proposed. The absorber which is constructed from artificial magnetic conductor (AMC) consists of an array of copper square patches printed on a grounded 3.2mm thick FR4-Epoxy dielectric substrate. The proposed method is carried out by reducing the area of square patches; in this case, it is conducted by cutting the corners of square patch yielding a patch in octagonal shape. It shows that the proposed method which yields an equilateral octahedral patch with size of 9.53mm on each edge can widen the bandwidth up to 29.5% compared to the bandwidth of square patched absorber. The method also increases the resonant frequency of microwave absorber from 2.4GHz to 2.84GHz. In addition, to improve the value of reflection coefficient, external resistors are put between adjacent patches which are parallel to the electric field excitation.

Keywords-artificial magnetic conductor; bandwidth enhancement; corner-cutting; resonant frequency; return loss

I. INTRODUCTION Starting from 50 years ago, a considerable interest in

electromagnetic metamaterials research has been initiated [1]. This research has attracted more attention in recent years due to the capability of metamaterials that can be broadly applied in microwave and higher frequency regions [2]-[3]. The term of metamaterials is usually used to describe some structures that possess characteristics which are not found in nature. Various applications of metamaterials can be widely found for microwave devices including planar periodic structures such as electromagnetic/photonic bandgaps (EBG/PBG), frequency selective surfaces (FSS), and high impedance surface (HIS) [4]-[6]. The later one is sometimes referred as artificial magnetic conductor (AMC) that can be approximately approached by use of textured surfaces technology for the implementation.

The advent of AMC based on textured surfaces has also opened up a new idea in the microwave applications such as antennas, reflectors, and absorbers [7]-[9]. In the design of absorber material, as is already known that one of approaches frequently used is the Salisbury screen method [10]. However, due to the thickness of absorber material made by the Salisbury screen method is reasonably thick as the need for quarter-wavelength spacing from a perfectly conducting metal ground

plane, therefore, AMC-based structure of doubly periodic array of square patch has been applied to reduce the thickness [11]. In spite of the absorber thickness could be reduced, unfortunately the bandwidth response is still narrow indicating the need of improvement.

In this paper, the bandwidth enhancement of microwave absorber constructed of AMC structure is investigated numerically. The AMC structure consists of cooper square patches arranged in array and deployed on FR-4 Epoxy dielectric substrate. The enhancement method is conducted by cutting 4 corners of each square patch so that the patch yields octagonal shape. As the performance indicators, in addition to the bandwidth as a primary parameter, the investigation also uses resonant frequency and reflection coefficient as supplementary parameter. In the analysis, the unit cell of AMC structure with appropriate boundary conditions will be used in the investigation. A brief overview of unit cell of AMC structure and the bandwidth enhancement method will be explained as a basis of knowledge. Then, the investigation and result analysis are reported and discussed consecutively. Some parameters such as absolute bandwidth, resonant frequency, fractional bandwidth, and reflection coefficient are analyzed in the discussion. Moreover, the improvement of reflection coefficient by using external resistors which are placed on- and connected between adjacent patches is also presented.

II. CONSIDERATION OF UNIT CELL OF AMC STRUCTURE AND BANDWIDTH ENHANCEMENT METHOD

The structure of artificial magnetic conductor (AMC) is constructed using metal copper square patches which are configured in two-doubly periodic array, i.e. x- and y-direction. Gaps between adjacent patches in both directions are 2mm, whilst the thickness of patches is set to be 0.035mm. The square patches construction is deployed on a grounded FR-4 Epoxy dielectric substrate with the relative permittivity of 4.2, the loss tangent of 0.02, and the thickness of 3.2mm. The conductive loss of metal copper and the dissipation loss of dielectric substrate are accounted for the investigation to give the accurate analysis. To conserve computational effort, a unit cell of AMC structure is taken from the square patches construction as illustrated in Fig. 1. This allows investigating the characteristics of construction thoroughly.

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Figure 1. Geometry of unit cell of AMC structure

A unit cell of AMC structure shown in Fig. 1 has the periodicity of 25mm and the width of 23mm. A TE mode plane wave excitation with electric field parallel to x-axis direction and wave vector perpendicular to the surface of patch illuminates the unit cell of AMC structure at normal incidence. The computational domain of unit cell is truncated by defining the electric wall and the magnetic wall boundary conditions on the sides that are perpendicular and parallel to the electric field excitation, respectively. To form a doubly-periodic array, the boundary conditions are used for imaging a unit cell into infinite extent. Hence to achieve sufficiently accurate results, a convergence condition is determined and an adaptive meshing technique is set to automatically refine the mesh at locations where the error is large.

After conducting some investigation, the result indicates that that unit cell of AMC structure with 23mm square patch operates at the resonant frequency of 2.4GHz. The unit cell yields absolute bandwidth and fractional bandwidth of 340.9MHz and 14.2%, respectively. Here, absolute bandwidth and factional bandwidth are defined as the frequency band in which the reflection phase ranges from -π/2 to π/2, and as a ratio of the absolute bandwidth to the resonant frequency, respectively. Whilst the minimum reflection coefficient of unit cell at resonant frequency is -2.13dB.

Figure 2. Corner-cutting method to enhance bandwidth

To enhance the bandwidth of microwave absorber, the method proposed is carried out by cutting the corners of square patch of unit cell, as a result, yielding a patch in octagonal shape. The illustration of how the proposed method works is shown in Fig. 2. The corners of square patch are cut in the shape of isosceles triangle. The number of corners cut and the

length of cut, i.e. length of sides of isosceles triangle are becoming variables that will be focused in the investigation analysis to explore the influence to the bandwidth response as well as other parameters of unit cell.

III. CORNER CUTTING METHOD AND DISCUSSION The first attempt to investigate the effect of proposed

method to the characteristic of microwave absorber is by cutting the corner of square patch. This is same with removing an isosceles triangle from the corner of square patch, in which the length of triangle sides is set to be constant 2mm. The investigation is performed on patches with one, two, three, and four cuts. The investigation results are plotted in Fig. 3 for resonant frequency and minimum value of reflection coefficient. Hence in Fig. 4, the results for absolute bandwidth and fractional bandwidth are depicted.

From the result shown in Fig. 3, it is seen that increasing the number of corner cut makes the resonant frequency to be higher as well as the reflection coefficient. The absolute bandwidth and fractional bandwidth have also similar tendency as plotted in Fig. 4. It should be noted that more cuts means more patch areas are reduced. Thus it can be concluded that reducing patch area yields wider absorber bandwidth where the widest is obtained for the number of cut of 4. Therefore, the next investigation will use a square patch cut on its 4 corners.

1 2 3 4

2.4

2.5

-2.14

-2.12

-2.1

-2.08

Number of cut

Res

onan

t Fre

quen

cy (G

Hz)

resonant frequency reflection coefficient R

efle

ctio

n C

oeffi

cien

t (dB

)

Figure 3. Resonant frequency and reflection coefficient of unit cell of AMC structure for different number of corner cutting

1 2 3 4340

345

350

355

360

365

370

14.5

14.6

14.7

14.8

14.9

Abs

olut

e B

andw

idth

(MH

z)

Frac

tiona

l Ban

dwid

th (%

)

Number of cut

absolute bandwidth fractional bandwidth

Figure 4. Absolute bandwidth and fractional bandwidth of unit cell of AMC structure for different number of corner cutting

z

x

y

FR4 epoxy dielectric substrate

3.2 square patch

ground plane

25

23 1

unit in mm

FR4 epoxy dielectric substrate

patch

ground plane

isosceles triangle cutting part

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The increase of resonant frequency as the reduced size plotted in Fig. 3 can be figured out using the approximation relation of inductance (L) and capacitance (C) of square patch unit cell as expressed in (1)-(3). All variables in (2)-(3) are constant, except w which will be representative of square patch area. Reducing w will affect to decrease value of capacitance of unit cell in (3). As a result, the resonant frequency of unit cell in (1) will increase

LC

fπ2

10 = (1)

tL r ⋅= μμ0 (2)

( ) ⎟⎟⎠

⎞⎜⎜⎝

⎛+= −

gaw

C r10 cosh1 ε

πε

(3)

where f0, L, C, μ0, ε0, μr, εr, t, w, a, and g are variables of resonant frequency of unit cell, inductance of unit cell, capacitance of unit cell, permeability of vacuum, permittivity of vacuum, relative permeability of substrate, relative permittivity of substrate, substrate thickness (in mm), patch width (in mm), substrate width (in mm), and gap width (in mm) between patches.

Next, the investigations are performed for the square patch cut on its 4 corners with different length of cutting part, i.e. isosceles triangle legs, starting from 1mm to 10 mm. The length of cutting part represents the area reduced from square patch. Fig. 5 shows the investigation result for resonant frequency and minimum value of reflection coefficient. Whilst in Fig. 6, the investigation results for absolute and fractional bandwidth are plotted. It can be seen from Fig. 5 that the more patch area reduced, the better bandwidth obtained, consequently the reflection coefficient shown in Fig. 6 gets higher. The resonant frequency unit cell also increase as the wider of cutting part. Again, this can also be explained through the equation of inductance (L) and capacitance (C) of square patch unit cell mentioned above.

1 2 3 4 5 6 7 8 9 10

2.5

3

3.5

-2.2

-2.1

-2

-1.9

Length of cutting part (mm)

Res

onan

t Fre

quen

cy (G

Hz) resonant frequency

reflection coefficient

Ref

lect

ion

Coe

ffici

ent (

dB)

Figure 5. Resonant frequency and reflection coefficient of unit cell of AMC structure for different length of cutting part

1 2 3 4 5 6 7 8 9 10

350

400

450

500

14

15

16

Abs

olut

e B

andw

idth

(MH

z)

Frac

tiona

l Ban

dwid

th (%

)

absolute bandwidth fractional bandwidth

Length of cutting part (mm)

Figure 6. Absolute bandwidth and fractional bandwidth of unit cell of AMC structure for different length of cutting part

From Fig. 5, it seems that the expected resonant frequency ranges are given by patch with 5mm, 6mm, and 7mm cutting part. However, after conducting some parametrical study, the patch with cutting part between 6mm and 7mm, i.e. 6.74mm, is chosen for the next investigation as it yields the equilateral octahedral shape of 9.53mm and has acceptable performances. The patch of equilateral octahedral shape gives resonant frequency of 2.84GHz and absolute bandwidth of 441.6MHz. The achieved bandwidth is 29.5% wider than the bandwidth of original square patch unit cell.

Furthermore, as the reflection coefficient as shown in Fig. 5 is indicating high portions of reflected incoming waves by the unit cell of AMC structure, around -2 dB, therefore the attempt to improve the reflection coefficient by incorporating external resistor into the patches of AMC structure is performed in the next investigation. Here, the use of resistor is to make the impedance of structure closer to the impedance of incoming wave, 120πΩ. Due to the frequency-free characteristic of resistor, it will affect to the reflection coefficient but not for resonant frequency. By using the patch in equilateral octahedral shape, the investigation to improve the value of reflection coefficient is performed. The external resistors are incorporated into the equilateral octahedral patches by putting them between 2 adjacent patches. As illustrated in Fig. 7, there are 3 different scenarios of resistors position, i.e. Scenario#1, Scenario #2, and Scenario #3, with the electric field excitation produces incoming wave is applied on x-axis direction.

Figure 7. External resistors positions to improve reflection coefficient

z

x y

Scenario#2 resistor

equilateral octahedral patch

equilateral octahedral patch

Scenario#1

resistors

equilateral octahedral patch

Scenario#3

resistor

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2.6 2.7 2.8 2.9 3 3.1-40

-30

-20

-10

0

Ref

lect

ion

Coe

ffici

ent (

dB)

Resonant Frequency (GHz)

without resistor perpendicular parallel parallel and perpendicular

Figure 8. Reflection coefficients of equilateral octahedral patch unit cell for 3 different scenarios of resistors position (resistance value is 500Ω)

It is shown in Fig. 8 that external resistors connecting equilateral octahedral patches in Scenario#2, i.e. perpendicular to the electric field excitation, have no impact on return loss and have the same responses as the patches without resistor. Meanwhile, the external resistors connecting the patches in Scenario #3, i.e. parallel to the electric field excitation, yield much better response of reflection coefficient and reach more than -30dB with the resistance value of 500Ω. The result of Scenario#3 is also coincided with Scenario#1; therefore for the better component efficiency, the external resistors should be placed between adjacent patches only in the same direction with electric field excitation.

Moreover, to find the resistance value of resistors which yields the best value of reflection coefficient, the investigation is performed for equilateral octahedral patch. Similarly, the investigation to obtain the resistance value of resistors yields the best value of reflection coefficient is also carried out for square patch. From the investigation results, it is found that the resistance values of resistor are 430Ω and 528Ω for square patch and equilateral octahedral patch, respectively. Whilst, the absolute bandwidths with both resistance values achieve 235.9MHz and 299.1MHz for equilateral octahedral patch and square patch, respectively. Different with the absolute bandwidth definition used in previous investigation, here it is defined as the frequency band around resonant frequency in which the value of reflection coefficient is less than -10dB.

The bandwidth comparison of investigation results with and without external resistor is tabulated in Table 1. From the result, it is shown that incorporation of external resistor into the patch evokes to the narrowing absolute bandwidth both for square patch and equilateral octahedral patch. This can be understood that there is a trade-off between bandwidth and quality factor represents as reflection coefficient value. As mentioned before that the external resistor will make the impedance of structure closer to the impedance of incoming wave affecting to the increase of absorbed power from the incoming wave by the unit cell of AMC structure, or in other word, it is increase the quality factor. This can be seen from the increase of reflection coefficient vlue. However, since the bandwidth is inversely proportional to the quality factor, thus the increase of reflection coefficient should be paid by the narrower bandwidth. Nevertheless, the absolute bandwidth of

equilateral octahedral patch unit cell with the optimum resistance value of external resistor is wider than of the square patch unit cell. It can be concluded that the proposed bandwidth enhancement method with incorporating external resistors has successfully widen the bandwidth of square patch unit cell up to 26.8%.

TABLE I. BANDWIDTH COMPARISON OF UNIT CELL WITH AND WITHOUT EXTERNAL RESISTORS

External resistors

Absolute bandwidth (MHz) Bandwidth enhancement

(%) square patch equilateral octahedral patch

No 340.9 441.6 29.5

Yes 235.9 299.1 26.8

IV. CONCLUSION The method of bandwidth enhancement for microwave

absorber constructed based on artificial magnetic conductor (AMC) structure has been successfully investigated. The AMC structure consisted of square patches as unit cells arranged in array and deployed on FR-4 Epoxy dielectric substrate. The enhancement method was conducted by cutting 4 corners of square patch yielding an equilateral octahedral patch with size of 9.53mm on each edge. From the investigation result, it has been demonstrated that the proposed method has successfully enhanced the bandwidth of microwave absorber. The bandwidth of unit cell of equilateral octahedral patch could be enhanced up to 29.5% from the unit cell square patch; hence the resonant frequency has increased from 2.4GHz to 2.84GHz. The improvement of reflection coefficient value of microwave absorber has also been investigated numerically by incorporating external resistors into the unit cell patches. It has been shown that the external resistors should be placed between adjacent patches only in the same direction with electric field excitation. Although the bandwidth achievement of patches with external resistors has been narrower than of patches without external resistors, however, the proposed method has been also successfully implemented with the achievement of bandwidth enhancement up to 26.8% compared to the bandwidth of square patch unit cell.

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