Analysis of Antenna Coupling in Near-field RFID Systems

Yen-Sheng Chen* and Shih-Yuan ChenGraduate Institute of Communication Engineering,

and Department of Electrical Engineering,National Taiwan University, Taipei 10617, Taiwan

E-mail: sychen@cc.ee.ntu.edu.tw.b92901132@ntu.edu.tw

Introduction

Recently, the near-field RFID systems operating at either LF (125-134 kHz) or HF (13.56MHz) bands have been widely used due to the matured technology. However, the largersize of the antennas used in the LF/HF band systems limits their commercial applications.Thus, it is straight forward to reduce antenna size by designing the system in a higherfrequency band, such as the UHF (860-960 MHz) band. In addition, the near-field UHFRFID systems have other superiorities, including higher data rate, and lowermanufacturing cost, making them suitable for item-level tagging.

To successfully design a near-field UHF RFID system, it is important to investigate theantenna coupling between reader and tag. However, to our knowledge, only a fewattempts have so far been made at computing coupling of near-field RFID systems[I}·..,[3]. The power transfer function presented in [1] was confined to only the smallcircular loop antenna, and the equivalent coupling model [2] is lack of a direct relationbetween coupling and antenna spacing. In this paper, an analytic form to compute thenear-field coupling coefficient has been presented. Although it is based on theformulation from [4], its numerical complexity due to the usage of FFT and the tedioustruncation methods has been greatly reduced. The presented formulation is a near-fieldcounterpart of the Friis equation in the far zone. For verification, the near-field couplingcoefficients calculated using the presented formulation are compared with those full­wave simulated using Ansoft HFSS, and they agree well.

Near-field Coupling Coefficient

According to [3], the power absorbed by a RFID tag chip, ~hiP' can be expressed as

~hiP = ~eader per (1)

where ~eader is the output power of the reader circuitry, p and r are the powertransmission coefficients of the reader and tag between the front-end circuitry and theassociated antenna, respectively, and C is the coupling coefficient between reader and tagantennas. When the tag antenna is located in the far field of the reader antenna, thecoupling coefficient can be determined by the Friis equation:

C = GtGr (~J2 p (2)41rd

where Gt , Gr are the gains of reader and tag antennas, respectively, d is the antennaspacing, and p is the polarization mismatch loss between the two antennas. As for thenear-field case, to determine the coupling coefficient between the tag and reader antennas,let's first consider a tag placed in the near field of a reader as depicted in Fig.I (a).

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Referring to [4], the incident and emergent waveguide mode coefficients for the reader

(tag) antenna are Go,bo' (Go', bo') respectively. The reflection coefficient between tag

antenna and tag chip is r L' •

k"Z

(b)

-~

( RX, Dipole antelllla)Tag antelllla withnormalized far field f(-k)

"z

(a)

"~-"JII-+ Yer antelllla with

1, i4 normalized far field f(k)ao bo ( TX, Loop antelllla)

Fig. 1. (a) Arbitrarily oriented tag antenna in the near field of a reader.(b) Orientation of tag antenna in terms of spherical coordinate system (OR'¢R).

Now, define the coupling quotient bo' / Go as the coupled signal received by the tag

antenna when a unit signal is incident to the reader antenna, which is equal to 821 when

considering the tag-reader system as a two-port network. Recall from (1), the coupling

coefficient C = lbo' / Goris the amount of power accepted by the tag antenna when a unit

power is transmitted from the reader antenna.

From [4], the coupling quotient between the reader and tag antennas can be written as

b~ (r)=- C' II f'(-k)ef(k) eikordK=-C'xT(r) (3)Go k K<k r

where 1/C' = Zo1]~ (1- r L ') is the mismatch constant, Zo is the intrinsic impedance of free

space, 1]~ is the admittance of the tag antenna, and j' and j are the normalized vector far­

field patterns for tag and reader antennas, respectively. The propagation vector

k= kxex+ kyey+ rez = K + rez' and k = Ikl = 21i/Awith A the free-space wavelength. The

position vector of the tag antenna r = xex+ yey +dez = R +dez .T(r) is the normalized

coupling quotient as a function of r. Applying the Laplacian operator V2 to (3) yields

V 2T=.!. II f'(-k)·f(k)[V2(eikor)]dK=.!. II f'(-k)'f(k)[_k2eikor]dK (4)

k K<k r k K<k rThus, we obtain (V2 +k2

) T = 0 meaning that T (r) satisfies the scalar Helmholtz

equation, and consequently we can rewrite T ( r ) as00 n

T(r) = L L Bnmhn(I)(kr)p"m(cosBo)eimf/Jon=O m=-n

(5)

where the angles (Bo,t/Jo) are the spherical angles of r and h~l) and p"m are the spherical

Hankel functions of first kind and the associated Legendre polynomials, respectively.

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Bnm are spherical wave coefficients. To determine Bnm , first, consider the near-field

coupling in Fig. l(a) when the tag antenna is placed along the z-axis, hence Bo = 0 and

R = o. Since p"m (1) is nonzero only when m = 0 , (5) can be reduced to00

T(d) = LBnh

n(I)(kd)

n=O

(6)

(9)

From [4], one can have

Bn = (2n +1)(irYl[J'(-k)ef(k)] P"(cosOo)sinOod¢odOo (7)2 0 0

Given the vector far-field patterns for reader and tag antennas, their inner product can beeasily computed and be substituted it into (7). In [4], to evaluate Bn Yaghjian exploitedan FFT algorithm, to convert the integrals into summations. However, this limits theintegration range. Therefore, we directly perform the numerical integration usingMathematica 6.0. Substituting Bn computed from (7) into (6) and multiplying T(d) by

C' yieldbo' / Go • Although T (d) is an infinite series, it has been observed that only less

than ten terms ofBn are needed for the series to converge.

Comparisons between the Formulation and HFSS Simulations

In order to verify the capability of the presented formulation, three commonly-seenscenarios are considered. The associated coupling coefficients between the reader and tagantennas are computed and are compared to those simulated using Ansoft HFSS. Please

note that, in the HFSS simulations, the corresponding quantity is IS2112 by assuming that

the antennas are perfectly matched. Also, all the antennas are designed in the UHF bands.

Scenario 1: Half-wavelength dipole - half-wavelength dipole in parallelAlthough dipole antennas are not used as reader antenna in most RFID applications andtag antennas are in most cases arbitrarily oriented, this is the simplest scenario forverification purpose. The normalized far-field patterns of the half-wavelength dipole, ofwhich the dipole axis is parallel to the y-axis, can be written as

(1rsin Bsin ffJ) (1rSin Bsin ffJ)cos cos

fo oc 2 cosOsintp, 1, oc 2 costp (8)1- sin2Bsin2ffJ ffJ 1- sin2Bsin2ffJ

Substituting (8) into (7) yields Bn • The computed spherical wave coefficients Bn diminish

in only seven terms leading to fast convergence of (6). The near-field couplingcoefficients computed by presented method and those obtained via HFSS are shown inFig. 2(a). The result shows good consistence between two methods.

Scenario 2: Half-wavelength dipole - half-wavelength dipole inclined by 20°Since the tag antenna is often randomly oriented, consider the receiving tag dipole, whichis rotated about the z-axis by an angle of 20°. To facilitate evaluating the innerproduct1.1' , the normalized vector far-field patterns I andI' are transformed into therectangular coordinate system using

[Ix] [-Sin¢R COSORC~S¢R][/fjJ]Iy = COS¢R cosBRsln¢RJz 0 -sinOR fo

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-40

_-10

~U -15

"5~ -20

oo -25.5§--30oU

-35

- Presented method-S21 simlated by HFSS -5

- ...........- ..... 5'

_-10~

~U -15~aJ

~ -20aJ00 -25.5§--300U

-35

Y-40

- Presented method-S21 simlatedb 'HFSS -5

where OR and t/JR are defined in Fig. 1(b). For computing the tag antenna pattern f in this

scenario, take OR =200 '¢R =90° . Substituting (9) into (7) yields Bn , which converge in nineterms. The coupling coefficients thus obtained are plotted in Fig. 2(b). The couplingcoefficients in this scenario are much smaller than those in the preceding scenariobecause of the orientation of the tag antenna.000

-40

-5

X-45 X -45 X -45 +--r.....,.....,.~~~"T""""""T""-r-r.....,.....,.---r-'1(a) 0 50 100 150 200 250 300 350 400 (b) 0 50 100 1?0 2~0 250 300 350 400 (c) 0 50 100 1?0 2~0 250 300 350 400

Separation distance (mm) SeparatIon dIstance (mm) SeparatIon dIstance (mm)

Fig. 2. Coupling coefficients versus separation distance for (a) two dipoles in parallel,(b) two dipoles with the receiving one inclined by 20 degrees, (c) a square loop and a

dipole with matched polarization.

_-10

~U -15

5~ -20

o0-25

.r!1-30oU

-35

Scenario 3: Square loop - half-wavelength dipole with matched polarizationHere, a square loop with perimeter ofA is used as the reader antenna. Its normalized co­polarized component of its far-field pattern can be represented as an array composed oftwo parallel dipoles a quarter wavelength apart. The radiation patterns of the readerantenna can be approximated using the principle of pattern multiplication. The computedcoupling coefficients are shown in Fig. 2(c). The agreement between the computedresults and those simulated by HFSS for all the three scenarios indicates that thepresented method can be utilized to determine the near-field coupling coefficients as thefar-field patterns of the reader and tag antennas are known.

Conclusion

A simple formulation has been presented for computing the coupling coefficientsbetween two antennas that are placed in the near field of each other and are arbitrarilyoriented. Although the formula is complicated to some extent, it could be regarded as anear-field counterpart of the Friis transmission formula. Based on the presented formula,the near-field coupling phenomenon has been investigated, and the result thus obtainedmay be useful for the design and optimization of the near-field RFID systems.

References

[1] K. Fotopoulou, B. Flynn, "Optimum antenna coil structure for inductive powering ofpassive RFID tags," IEEE International Conference on RFID, pp. 71-77, Mar. 2007.

[2] P. Cole, "Coupling relations in RFID systems," white papers, 2003[3] P.V. Nikitin, K.V.S. Rao, and S. Lazar, "An overview of near field UHF RFID,"

IEEE International Conference on RFID, pp. 167-174, Mar. 2007.[4] A.D. Yaghjian, "Efficient computation of antenna coupling and fields within the

near-field region," IEEE Trans. Antennas Prop., vol. AP-30, pp. 113-128, Jan. 1982.

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