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technique for efficient solution of method of moments matrix equation,

Microwave Opt Technol Lett 36 (2003), 95100.

5. R.G. Ayestaran, M.F. Campillo, and F. Las-Heras, Multiple support

vector regression for antenna array characterization and synthesis, IEEE

Trans Antennas Propag 55 (2007), 832840.

6. C. Craeye, A fast impedance and pattern computation scheme for finite

antenna arrays, IEEE Trans Antennas Propag 54 (2006), 30303034.

7. E. Lucente, A. Monorchio, and R. Mittra, An iteration-free MoM

approach based on excitation independent characteristic basis functions

for solving large multiscale electromagnetic scattering problems, IEEE

Antennas Propag 56 (2008), 9991007.

8. C. Delgado, M.F. Catedra, and R. Mittra, Application of the character-

istic basis function method utilizing a class of basis and testing func-tions defined on NURBS patches, IEEE Antennas Propag 56 (2008),

784791.

9. D.C. Ghiglia and L.A. Romero, Robust two-dimensional weighted and

unweighted phase unwrapping that uses fast transforms and iterative

methods, J Opt Soc Am A 11 (1994), 107117.

2009 Wiley Periodicals, Inc.

EXTRACTION OF EFFECTIVEPERMITTIVITY AND PERMEABILITY OFPERIODIC METAMATERIAL CELLS

Dong Hyun Lee and Wee Sang ParkDivision of Electronic and Computer Engineering, Pohang Universityof Science and Technology, San 31, Hyojadong, Namgu, Pohang,Kyungbuk, Korea 790784; Corresponding author:[email protected]

Received 14 November 2008

ABSTRACT: The complex permittivity and permeability of various pe-

riodic metamaterial (MTM) cells are extracted by using a fictitious rect-

angular waveguide consisting of perfect electric conductor and perfect

magnetic conductor walls. The shapes of the MTM cells include a thin

wire (TW), a single split-ring resonator (SSRR), a double SRR (DSRR),

a modified SRR, and a structure combining the TW and DSRR. The TW

falls in the negative-/positive- region, the SRRs in the positive-/neg-

ative- region, and the combined structure in the negative-/negative-region. We also investigate how the permittivity and permeability are

affected by the dimension parameters of the MTM cells. Another extrac-

tion technique utilizing time domain signals is developed to overcome

some limitations that the waveguide technique cannot handle. 2009

Wiley Periodicals, Inc. Microwave Opt Technol Lett 51: 18241830,

2009; Published online in Wiley InterScience (www.interscience.wiley.

com). DOI 10.1002/mop.24468

Key words: material constant extraction; metamaterial; permittivity;

permeability

1. INTRODUCTION

Metamaterials (MTMs) are broadly defined as artificial effectively

homogeneous materials possessing unusual electromagnetic prop-

erties not found in nature. Effectively, homogeneous materials are

electromagnetic periodic structures whose periodicity is much

smaller than the guide wavelength in the material. Usually, this

periodicity is smaller than a quarter of the wavelength [1]. If the

average unit cell size is four times smaller than the wavelength, a

wave in the structure is dominantly characterized by refractive

phenomena rather than scattering or diffraction phenomena. Under

this condition, the electromagnetic properties of the structure are

determined by well-defined material constants, permittivity (),

and permeability (). Therefore, the extraction of the material

constants of a given MTM is important for predicting the electro-

magnetic properties of the MTM. In the last 5 years, several

methods for extracting the parameters have been reported, and

these methods used reflection and transmission coefficients of the

structures [25]. The extraction methods were existed before the

MTMs get interests [6]. The technique in [6] uses a coaxial

transmission line and is designed for extracting the material con-

stants of normal materials ( 0, 0). The basic extraction

scheme of the technique is similar with other techniques [25], but

the formulas in this technique include less ambiguity.

Unfortunately, the formulas in reference [6] are valid only for

low-loss materials, so they must be modified to apply them to

highly lossy metamaterials. This article presents the modifiedequations and uses a fictitious waveguide simulation to obtain the

reflection and transmission coefficients of unit cells. The material

constants are extracted for representative MTMs, and their char-

acteristics are analyzed. In addition, another extraction technique

is developed to overcome some limitations of the previous tech-

nique.

2. EXTRACTION OF MATERIAL CONSTANTS FOR TEMWAVE INCIDENCE

Figure 1 depicts the electric and magnetic field intensities and the

wave propagation direction when a transverse electromagnetic

(TEM) wave is normally incident on a three-region dielectric

interface. Region 1 and Region 3 are free space (0, 0) and

Region 2 is an unknown material (r, r) with thickness d. Thefields in each region can be written as follows:

Region 1

E1 xEi0ejk0z

xEr0ejk0z

H1 yEi0

0ejk0z y

Er0

0ejk0z (1)

where k0 000, 0 0/0.Region 2

E2 xE2ejk2z xE2

ejk2z

H2 yE2

2ejk2z y

E2

2ejk2z (2)

Region 1:

Air

Region 2:

Unknown material

Region 3:

Air

x

z

iE

iHik

rE

rH

rk

2E

2H2

3E

3H

ik

2E

2H

2

z = 0 z = d

00 , 00 ,rr,

Figure 1 Electromagnetic field distributions in multiple dielectric mate-

rials for an incident TEM wave. TEM: transverse electromagnetic. E :

electric field intensity (V/m), H : magnetic field intensity (A/m), k :

wavenumber vector. [Color figure can be viewed in the online issue, which

is available at www.interscience.wiley.com]

1824 MICROWAVE AND OPTICAL TECHNOLOGY LETTERS / Vol. 51, No. 8, August 2009 DOI 10.1002/mop

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where k2 22 0r0r k0rr, 2 0r/0r 0r/r.

Region 3

E3 xE3ejk0z

H3 yE3

0ejk0z. (3)

After applying boundary conditions for the electric and magnetic

fields at two interfaces z 0 and z d, the reflection and

transmission coefficients on the interfaces can be written as

S11Er0

Ei0

1z2 12

1 122 z2

T S21E3

Ei0

1 122 z

1 122 z2

(4)

where

122 0

2 01

r/r 1r/r 1

(5)

z ej2d ej w/c0 rrd (6)

Note that reference [6] assumed that Region 2 is not too lossy, so

Eq. (6) was simplified as z 1. However, MTMs are highlylossy, and the equations were modified not to use this approxima-

tion in this article.

Equation (4) can be rewritten in a more compact form as

S11122 12 1 S21

2 S11

2 S11 0 (7)

z S11 S21 12

1 S11 S21 12. (8)

The solution of Eq. (7) is followed,

12 1 S21

2 S11

2

2S11 1 S21

2 S11

2

2S11

2

1. (9)

Note that one of the solutions must be chosen to satisfy the

condition of 12 1. After 12 is determined by Eq. (9), r/rcan be obtained from Eq. (5):

rr

1 12

1 12X. (10)

rr can also be determined from Eqs. (6) and (8):

rrjc0

d lnz jarg z Y. (11)

With the relations expressed in Eqs (10) and (11), the material

constants can be expressed as

r r,realjr,imagX/Y

r r,realjr,imagX Y. (12)

Therefore, the material constants r and r of the unknown mate-

rial can be determined from S-parameters at the interfaces of the

material.

3. EXTRACTION OF MATERIAL CONSTANTS USING AFICTITIOUS WAVEGUIDE

Tangential electric and magnetic fields become 0 on perfect elec-

tric conductor (PEC) and perfect magnetic conductor (PMC) sur-

faces, respectively. Therefore, a fictitious waveguide possessing

the PEC surfaces on the top and bottom walls and the PMC

surfaces on the front and back walls can support TEM waves. If

unit cells of a periodic structure are symmetric, the field distribu-

tions in the waveguide for one unit cell are identical with those of

the infinite periodic structure. Therefore, the fictitious waveguide

can produce an infinitely periodic effect. In addition, the simula-

tion running time for obtaining the S-parameters can be dramati-

cally reduced by simulating the waveguide with one unit cell rather

than the infinite structure.

Figure 2 shows the waveguide simulation scheme for acquiring

S-parameters of an unknown material. The PEC boundary condi-

tion is applied to the upper and bottom walls at the waveguide, and

the PMC boundary condition is applied to the front and back walls.

The length and width of the material with thickness Lz

(d) are Lx

and Ly, respectively. The S-parameters of the materials interface

are obtained by shifting a phase reference plane from the ports tothe materials interfaces (Em). After the S-parameters are obtained,

the material constants can be extracted by using the formulas in the

previous section.

The extraction technique was validated by extracting the ma-

terial constants of a Lorentz material. A commercial full-wave

simulator, CST MWS ver. 2006b, was used to simulate the struc-

ture in Figure 2. The extracted r andr [Fig. 3(b)] agree well with

the original values [Fig. 3(a)].

4. MATERIAL CONSTANTS EXTRACTION OF MTM UNITCELLS

4.1. Thin Wire (TW)

A periodic thin wire (TW) is a well-known epsilon-negative

(ENG) material because of a plasma phenomenon [5, 7]. Figure 4

shows the TW unit cell with parameters and its extracted material

constants. Note that the electric field vector must be parallel with

the wire. The simulation results show that the TW has the nega-

tive-/positive- region of an ENG material [Fig. 4(b)].

E (x)

k (z)

H (y)

Lx

Ly

Lz = d

Em

Embedding

distance

Unknown Material

port 1

port 2

PEC

PMC

Figure 2 Simulation scheme for acquiring S-parameters using the ficti-

tious waveguide. PEC: Perfect Electric Conductor. PMC: Perfect Magnetic

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

available at www.interscience.wiley.com]

DOI 10.1002/mop MICROWAVE AND OPTICAL TECHNOLOGY LETTERS / Vol. 51, No. 8, August 2009 1825

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4.2. Split-Ring Resonator (SRR)

A split-ring resonator (SRR) is a well-known mu-negative (MNG)

material first reported by Pendry [8]. The studies of SRR have

variously been carried out so far [912]. By Faradays law, when

a time-varying magnetic field is applied to a conducting loop, a

current is induced on the loop. According to Lenzs law, the

magnetic moment from the induced current always opposes the

applied field, thus reducing the magnetic flux density. Therefore,

the induced magnetic moment, having opposite phase with the

excited magnetic field, does not increase the permeability. In

contrast, an SRR is capacitive at low frequency (closed loops are

inductive), so an induced magnetic moment on the SRR becomesin-phase with the applied field. The SRR acts as magnetic dipoles

and can have permeability greater than 1. A magnetic resonance

occurs due to a circular current on the SRR, and the amount of this

current is determined by the inductance of the SRR and capaci-

tance of the gap. If the quality factor of this resonator is high

enough, the permeability can be negative [9].

4.2.1. Single SRR (SSRR). Figure 5 shows the structure of a

single SRR (SSRR) unit cell and the extracted material constants,

where f0 is the resonance frequency, f1 is the frequency exhibiting

the lowest permeability, and f2 is the frequency at which the sign

ofr,real changes to positive. In the designed SSRR, f0 is 8.7 GHz,

where the electric size of the SSRR is around 0.15. SRRs are

usually considered to be magneto-dielectrics exhibiting high r,realgreater than 1. The magneto-dielectric region of the SSRR appears

from 7.5 to 8.6 GHz. Using this region can improve the input

impedance bandwidth of antennas [13, 14]. The MNG region is

observed from 8.6 to 10.2 GHz.

Table 1 shows how changes in the individual dimensional

parameters affected f0, f1, r,real at f1, and f2. When one parameter

was increased, all others remained constant. For example, when R

is increased 1 mm, f0, f1, r,real at f1, and f2 decreases 3.31, 3.30,

1.34, and 2.62 GHz, respectively. When R is increased, the equiv-

alent inductance of the SRR is increased and f0 is decreased. When

gap is increased, the decreased equivalent capacitance causes to f0increase. When w is increased, the increased equivalent inductance

causes f0 to increase. The r,real is dominantly affected by the

parameters of gap and w because the amount of the induced current

is mainly affected by the capacitance of structures gap.

4.2.2. Double SRR (DSRR). The structure and the extracted ma-

terial constants of a double SRR (DSRR) unit cell are presented in

Figure 6. The depth, which is not depicted in Figure 6(a), is the

thickness of the one SRR. Note that the external dimension is same

Figure 3 Extracted material constants of Lorentz material. (a) Original

r and r. (b) Extracted r and r. Lx 6, Ly 10, Lz 1 (mm). [Color

figure can be viewed in the online issue, which is available at www.inter-

science.wiley.com]

w

R

aX

aY

aZ

E

H

k

(a)

(b)

Figure 4 (a) TW simulation geometry. (b) Extracted material constants.

aX aY aZ 5, R 5, w 0.25 (mm). [Color figure can be viewed

in the online issue, which is available at www.interscience.wiley.com]


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as that of the SRR. A DSRR has a capacitance between the twoSRRs, so f0 is lower than that of the SRR. The electric size of

DSRR at f0 is around 0.14. The magneto-dielectric region appears

from 7.4 to 8.4 GHz, and the MNG region is observed from 8.4 to

10 GHz.

The effects of changing the dimension parameters of the DSRR

are similar with those of the SSRR (Table 2). The r,real is mainly

affected by parameter s1 (distance between SRRs).

4.2.3. Modified SRR (MSRR). The structure and the extracted

material constants of a modified SRR (MSRR) unit cell are pre-

sented in Figure 7. The MSRR is symmetric, so that this structure

is reported as a structure overcoming the bianisotropy problem

which occurs with an asymmetric structure such as the SSRR and

the DSRR [11, 12]. High capacitance occurs between the two

SRRs, so f0 is lower than that of other SRRs. The electrical size at

f0 is around 0.12. The magneto-dielectric region is from 5.5 to 6.9

GHz, and MNG region appears from 6.9 to 8.8 GHz.

The effects of changing the dimension parameters of the MSRR

are similar with those of the other SRRs. The r,real is mainly

affected by s2 (Table 3). We can design SSRR, DSRR, and MSRR

or predict their characteristics by using Tables 1, 2, and 3.

w

RaY

aX

aZ

depth

gap

E

H

k

(a)

(b)

Figure 5 (a) SSRR structure. (b) Extracted material constants. aX

aY aZ 5, R 4, depth gap w 0.25 mm: f0 8.63 GHz, f1

9.1 GHz, r,real (at f1) 5.6, and f2 10.18 GHz. [Color figure can be

viewed in the online issue, which is available at www.interscience.wiley.

com]

aY

aX

Ro

Ri

w

gap

s1

Ri = Ro 2s1 2w

(a)

(b)

Figure 6 (a) DSRR structure. (b) Extracted material constants. aX

aY aZ 5, Ro 4, depth gap 0.25, s1 0.75, w 0.25 (mm):

f0 8.42 GHz, f1 8.84 GHz, r,real (at f1) 5.9, and f2 9.9 GHz.

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

www.interscience.wiley.com]

TABLE 1 Characteristics of SSRR when the Dimensions Are

Varied

(mm) f0 (GHz) f1 (GHz) r,real at f1 f2 (GHz)

Gap 0.20 0.53 0.61 1.03 0.62

w 0.20 0.34 0.39 0.91 0.39

Depth 0.25 0.46 0.39 0.35 0.19

R 1.00 3.31 3.30 1.34 2.62

aX 1.00 0.05 0.01 1.52 0.25

aY 1.00 0.20 0.10 0.40 0.07

aZ 1.00 0.17 0.08 0.84 0.12

TABLE 2 Characteristics of DSRR when the Dimensions Are

Varied


Gap 0.20 0.50 0.57 1.17 0.58

w 0.20 0.40 0.45 1.23 0.45

Depth 0.25 0.51 0.46 0.64 0.26

s1 0.25 0.85 0.94 1.84 1.00

Ro 1.00 3.44 3.41 1.22 2.72

aX 1.00 0.05 0.01 1.60 0.24

aY 1.00 0.17 0.09 0.48 0.09

aZ 1.00 0.11 0.05 0.73 0.09


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4.3. Double Negative (DNG) MTM Composed of TW and DSRR

Figure 8 shows a double-negative (DNG) unit cell consisting of a

TW and DSRR. The DNG region where the material constants are

both negative is observed from 6.3 to 7.3 GHz [Fig. 8(b)].

5. EXTRACTION OF MATERIAL CONSTANTS USING TIMEDOMAIN SIGNALS

5.1. S-parameters from Time Domain Signals

The extraction technique in the previous section can quickly ex-

tract the material constants of an infinite periodic structure. How-

ever, this technique cannot simulate finite structures and cannot be

verified by experiments because of the fictitious waveguide. In

addition, it cannot construct perfect periodic structures because

the PEC and PMC walls mirror the fields instead of transfer-

ring those. So this technique can make the perfect periodic effect

only for symmetric structures. Note that the extraction errors of the

SSRR, DSRR, and MSRR unit cells are disregardable even though

their structures are asymmetric. In this section, a new extraction

technique that can handle the above problems of the waveguide

technique is introduced and verified.

Figure 9 shows a procedure of extracting the S-parameters of an

unknown material from time domain signals. To obtain an input

signal (a reference signal), first, a configuration without the mate-

rial is simulated [Fig. 9(a)]. Here, the probe P1(t) measures only

the input signal a(t). Next, the reflected and transmitted signals,

b(t) and c(t), are obtained by simulating the configuration with the

material [Fig. 9(b)]. The transmitted signal is measured by a probe

inserted behind the material. Then, the signals P2(t) and P3(t) are

a combined signal a(t) b(t) and the transmitted signal c(t),

respectively. Note that P1(t), P2(t), and P3(t) are all time domain

signals, so the reflected signal b(t) can be obtained by simply

subtracting P1(t) from P2(t). Applying Fast Fourier Transform to

gap

w

depthR

aX

aY

aZs2

(a)

(b)

Figure 7 (a) MSRR structure. (b) Extracted constitutive parameters.

aX aY aZ 5, R 4, depth gap 0.25, s2 1, w 0.25 (mm):

f0 6.92 GHz, f1 7.34 GHz, r,real (at f1) 6.11, and f2 8.76 GHz.

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

www.interscience.wiley.com]

w

Rw

aX

aY

aZ

Rs

gap

depth

s1

s3

(a)

(b)

Figure 8 (a) DNG unit cell composed of a TW and DSRR. (b) Extracted

constitutive parameters. aX aY aZ 5, Rs 4, Rw 5, depth

gap 0.25, s1 0.2, s3 1.75, w 0.25 (mm). [Color figure can be


com]

TABLE 3 Characteristics of MSRR when the Dimensions Are

Varied


Gap 0.20 0.39 0.46 1.04 0.45

w 0.20 0.18 0.17 0.68 0.10

Depth 0.25 0.68 0.69 0.19 0.50

s2 0.35 1.66 1.85 7.40 2.23

R 1.00 2.82 2.75 1.64 1.85

aX 1.00 0.04 1.59 0.33

aY 1.00 0.11 0.01 0.78 0.22

aZ 1.00 0.20 0.13 1.30 0.14


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a(t), b(t), and c(t), gives the frequency domain signals A(f), B(f),

and C(f). Then, S11 B(f)/A(f) and S21

C(f)/A(f) at the location

of probes can be calculated. Finally, S-parameters on the material

interfaces are obtained by shifting the phase reference plane (Em).

Then, the material constants can be extracted by using the equa-

tions in section 2.

5.2. Verification of the Code

This extraction technique was verified by the extractions for two

materials, a material ofr 10 j0, r 1 j0, and the Lorentz

material in Figure 3(a). The results are plotted in Figure 10. The

extracted material constants show good agreement with the orig-inal material constants.

The developed extraction method requires longer simulation

times because the structure is simulated twice, but it can construct

the perfect periodic structure and can be applied on finite struc-

tures.

6. CONCLUSIONS AND FUTURE WORKS

The material constant extraction technique using the fictitious

waveguide was reviewed, and the material constants were ex-

tracted for representative MTM unit cells: TW, SSRR, DSRR,

MSRR, and combined TW/DSRR. The TW had a negative-/

positive- region, the SRRs a positive-/negative- region, and

the combined structure a negative-/negative- region. We also

investigated how the material constants are affected by the dimen-

sion parameters of the SSRR, DSRR, and MSRR cells, which

should be helpful for designing SRRs and predicting their charac-

teristics. To overcome some limitations of the waveguide tech-

nique, an extraction technique utilizing time domain signals was

developed and verified by extracting the material constants of

known materials.

Here, the material constants of infinite structures are consid-

ered. By using the technique of using time domain signals, we are

investigating the material constants of finite structures and cou-

pling effects between different layers.

REFERENCES

1. C. Caloz and T. Itoh, Electromagnetic metamaterials, Wiley-Inter-science, Hoboken, NJ 2006.

2. D.R. Smith, S. Schulz, P. Markos, and C.M. Soukoulis, Determination

of effective permittivity and permeability of metamaterials from re-

flection and transmission coefficients, Phys Rev E 71 (2002), 195104.

3. Richard W. Ziolkowski, Design, fabrication, and testing of double

negative metamaterials, IEEE Trans Antennas Propag 51 (2003),

15161529.

4. 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.

5. P.D. Imhof, Metamaterial-based Epsilon negative [ENG] Media: Anal-

ysis & designs, Master Thesis, Electric and Computer Engineering at

the University of Arizona, February 2006.

6. C.C. Courtney, Time-domain measurement of the electromagnetic

properties of materials, IEEE Trans Microwave Theory Tech 46

(1998), 517522.

7. J.B. Pendry, A.J. Holden, D.J. Robbins, and W.J. Stewart, Low fre-

quency plasmons in thin-wire structure, J Phys Condens Lett 10

(1998), 47854809.

8. J.B. Pendry, A.J. Holden, D.J. Robbins, and W.J. Stewart, Magnetism

from conductors and enhanced nonlinear phenomena, IEEE Trans

Microwave Theory Tech 47 (1999), 20752084.

9. S. Maslovski, P. Ikonen, I. Kolmakov, and S. Tretyakov, Artificial

magnetic materials based on the new magnetic particle: Matasolenoid,

Prog Electromagn Res 54 (2005), 6181.

10. M. Kafesaki, TH Koschny, R.S. Penciu, T.F. Jundogdu, E.N. Econo-

mou, and C.M. Soukoulis, Left-handed metamaterials: Detailed nu-

Source

Air

P1(t)

a(t)

Em

probe

(a)

Source

Material

Em

P2(t)

b(t)a(t) c(t)

P3(t)

Em

(b)

Figure 9 S-parameters acquisition scheme from time domain signals. (a)

Without material. (b) With material. [Color figure can be viewed in the

online issue, which is available at www.interscience.wiley.com]

Figure 10 Extracted material constants. (a) Material ofr 10 j0,

r 1 j0. (b) Lorentz material in Figure 3(a). [Color figure can be


com]


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merical studies of the transmission properties, J Opt A 7 (2005),

S12S22.

11. R. Marques, F. Medina, and R. Rafii-El-Edrissi, Role of bianisotropy

in negative permeability and left-handed metamaterials, Phys Rev B

65 (2002), 1440/11440/6.

12. I. Bulu, H. Caglayan, and E. Ozbay, Experimental demonstration of

labyrinth-based left-handed metamaterials, Opt Exp 13 (2005).

13. P.M.T. Ikonen, S.I. Maslovski, C.R. Simovski, and S.A. Tretyakov,

On artificial magnetodielectric loading for improving the impedance

bandwidth properties of microstrip antennas, IEEE Trans Antennas

Propag 54 (2006), 16541662.

14. H. Mosallaei and K. Sarabandi, Design and modeling of patch antenna

printed on magentor-dielectric embedded-circuit metasubstrate, IEEETrans Antennas Propag 55 (2007), 4552.

2009 Wiley Periodicals, Inc.

DESIGN OF AN INTEGRATED LOOPCOUPLER AND LOOP ANTENNA FORRFID APPLICATIONS

Randy BancroftRandwulf Technologies, 2837 Perry Street, Denver, CO 80212;Corresponding author: [email protected]

Received 14 November 2008

ABSTRACT: The design of a novel planar loop antenna with an inte-

grated coupling loop for RFID applications is described. The antenna con-

sists of a center nonradiating coupling loop, which acts as a phase shifter

to produce a radiating current distribution on the outer loop. 2009

Wiley Periodicals, Inc. Microwave Opt Technol Lett 51: 1830 1833, 2009;

Published online in Wiley InterScience (www.interscience.wiley.com).

DOI 10.1002/mop.24467

Key words: microstrip antenna; RFID; loop antenna; planar antenna;

RFID sensor

1. INTRODUCTION

Currently existing sensor designs for RFID tags at 915 MHz are

generally designed to operate as either a nonradiating coupler to

drive an electrically small (low radiation) tag or as a radiating

antenna, which is optimized to couple with an electrically large

RFID tag. In many applications, it is a requirement that both

electrically small and electrically large RFID tags be addressable.

This article introduces the design of an antenna/coupler hybrid,

which is optimized to work well with both electrically small and

electrically large RFID tags.

2. NEAR FIELD AND FAR FIELD RFID TAGS

RFID tags exist in many forms. Electrically small tags are often

small loops. Some are circular and others are oval shaped as shown

in Figure 1. The average radius of the tag of Figure 1 (a ) is 6 mm.

When the loop is electrically small, the radiation resistance Rr and

ohmic resistance RCu of the loop may be estimated using Eqs. (1)

and (2) [1].

Rr 31,200a2

2 (1)

RCu 2a

Rs (2)

Rs 02f2 (3)where:

is the free space wavelength

0 is the permeability of free space

f is the frequency in Hz and

Rs is the surface resistance.

For the tag of Figure 1, the radiation resistance is only Rr

34.53 m and the copper resistance is RCu 364.23 m at 915MHz. The estimated radiation efficiency of this loop is 9.48%.

HFSS analysis indicates the radiation efficiency of this tag is only

0.53%. These small values indicate that a tag of this size must rely

on direct current inducement on the loop to provide an adequate

modulation of the driving point reflection coefficient for RFID

applications.

The backscattering from an electrically small RFID tag is

further attenuated by the reactive part of the driving point imped-

ance [2]. The desire to use both near field (direct inductive

coupling) and far field (radiative coupling) tags in industrial

applications leads to the need for an antenna which had both a

coupling region for nonradiative tags and satisfactory radiation for

radiative tags.

3. LOOP ANTENNA THEORY

The resonant and antiresonant dimensions of circular loop anten-

nas have been discussed by Schekunoff and Friis [3].

C n n 1,2,3, . . . (4)

C 2n 1

2 n 0,2,4, . . . (5)

Equation (4) gives the resonant circumferences (C) of a loop

antenna in terms of wavelength and Eq. (5) relates the antireso-

nant circumferences.

When the circumference of a loop antenna is less than /2,neither resonance nor antiresonance exists. When a loop with a

circumference which is less than one-half wavelength is fed in a

balanced manner, the current is approximately uniform around the

perimeter of the loop. The current on one side of the loop will

cancel with a current on the opposite side of the loop in the far

field. When the small loop is fed in an unbalanced manner, the two

Figure 1 HFSS model of a common electrically small RFID loop tag.

The outer length is 17.27 mm and the outer width is 8.23 mm with a

conductor width of 1 mm. [Color figure can be viewed in the online issue,

which is available at www.interscience.wiley.com]


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