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Progress In Electromagnetics Research Symposium Proceedings, Moscow, Russia, August 1821, 2009 535

Near Field Coupling with Small RFID Objects

Arnaud Vena and Pascal Roux

R&D Department, ACS Solutions France SAS, France

Abstract This paper presents a study on the coupling between a reader and a contactlessobject in order to define some good working rules to deal with objects with small antennas (NFCmobile phones, key fobs. . . ). We will define a model representing the magnetically coupled systemcomposed of the reader and the RFID object in order to introduce the coupling factor which isthe key parameter. The coupling factor variation according to reading distance and antennasshapes is a must to predict the overall system performance.

1. INTRODUCTION

Today, the working group in charge of ISO/IEC 14443 standard [1] is defining new contactlessobjects antenna classes smaller than the very popular Class 1 card format. We will study suchclasses and analyze their compatibility with existing readers. In transportation sector, contactlessvalidators use antennas with a typical size of 10 cm by 10 cm to assure a good communicationrange. But with smaller classes of contactless objects, the magnetic coupling factor (and thereforethe reading range) tends to reduce. To calculate the coupling factor, we have to define each antennaloop self inductance and the mutual inductance between them. The calculation of coaxial loopsself inductances and mutual inductance can be done with analytical formulas for usual shapes. Inall other cases, we can use numerical methods like Finite elements or PEEC method [2]. In nearfield RFID, antennas are usually closed loops which can be approximated by filaments loops. Inthis case the numerical Neumann method is an alternative simple way to obtain accurate values ofmutual inductance and even self inductance with minimal computation efforts. With this methodwe will calculate the coupling factor in free space in several cases, for common readers and variousRFID object antennas in order to determine the operating volume in each situation. The theoreticalvalues will be compared to experimental coupling factor measurements.

2. MODEL OF THE SYSTEM

In near field RFID [3], we can assimilate the system composed of a reader and an RFID objectwith an RF transformer. The corresponding electrical model is shown in Figure 1.

The main difference is about the magnetic coupling factor k value which is much lower. Inproximity card systems operating at 13.56 MHz,k is usually comprised between 0.03 and 0.3. Totransmit power with such low values, the transformer primary and secondary circuits must be tunedclose to operating frequency. The transformer primary circuit represents the reader source withmatching circuit and antenna. The transformer secondary circuit represents the RFID object withits antenna associated with C2 capacitor to make a resonant circuit with a frequency generallycomprised between 13.56 and 19 MHz. The RFID object antenna inductance is chosen to get themaximum power which means several turns. For Class 1 reference card [1], the number of turns is4 and the inductance is about 2300 nH. The resistance Rload represents the IC current consumptionand also allows the load modulation of the operating field. The expression of the transfer function

Figure 1: Electrical model of a coupled system composed of a reader and an RFID object.

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536 PIERS Proceedings, Moscow, Russia, August 1821, 2009

to obtain the voltage gain at load is the following (1):

H1 = V2

V1=

Zoutj M

(Z0j C1+1)(j M)2 (Z0+ (Z0j C1+1)ZL1)(Zout+ZL2) (1)

with Z0= R0+ 1

j C0, ZL1= R1+jL1, ZL2= R2+jL2 and Zout=

1

jC2+ 1

Rload

The power transmitted to the load is simply V22 / Rload. In this system, the resistive load Rloadis variable to modulate the current I2 and by the way the voltage at the transformer primary witha value in function of both the mutual inductance and the carrier frequency (2).

V BackEMF =jMI2 (2)

The power transmitted to the RFID object and the level of its response mainly depend on themutual inductance, therefore on the coupling factor. The frequency tuning of the secondary coilbetween 13.56 and 19 MHz doesnt influence a lot the results. The expression of the transfer functionis independent from the object antenna shape thanks to the coupling factor value. So we can saythat if we keep the same self inductance value for the new smaller classes then the operating limitwill be identically determined by the same minimum coupling factor. The formula (3) gives thecoupling factor value in function of both the mutual and the two self inductances:

k= M

L1L2(3)

In this equation, we can see that the coupling factor value is not influenced by the number of turnsif the radius of each loop is identical. Only the geometrical antenna shape influences this value.The smaller the object antenna size, the closer the distance to the reader for the same couplingfactor. We will evaluate the reading range in function of the object antenna size keeping usualreader antenna shapes.

3. DEFINITION OF THE MINIMUM COUPLING FACTOR

The minimum coupling factor is determined by minimal power transfer from reader to RFID ob-ject and by minimum signal response from RFID object to reader. A proximity card as defined

in ISO/IEC 14443 operates with minimum field strength of 1.5 A/m. While this field producessufficient power in Class 1 cards it produces a lower power in smaller objects because the receivedflux is lower and the IC embedded on such objects must works with less power. Another importantpoint is the signal sent by the object and received by the reader. The mutual inductance dependson the object area and when this area is smaller, the signal received by the reader is smaller. Byexperimental measurements we determined that the minimum coupling factor with usual cards isabout k = 0.03 and corresponds to field strength of 1.5 A/m. Such a coupling factor value with asmaller RFID object is found at closer distance and therefore with higher field strength. This factpushes us to say that the coupling factor parameter is more representative than the field strengthvalue. The only way to enhance reading range or at least to keep the one that we get with Class 1format is to have a more sensitive reader and an object which need less power. In this way, theusual coupling factor limit ofk= 0.03 will decrease.

4. MAGNETIC COUPLING FACTOR CALCULATION METHOD

The method used to calculate the coupling factor is based on Neumann Formula (4). The analyticalequation is computed with a numerical algorithm to get value of the mutual and the self inductancesof approximated filaments closed loops.

M= 0

4

C1

C2

dr1 dr2r1 r2 (4)

This method presents an interest for the simplicity of its implementation in any kind of program-ming language or dedicated numerical calculation software [4] and for its performances in terms ofcomputation efforts. To validate the numerical Neumann method we will compare its results withthe analytical formulas ones. We will use several value of discretization step to build loop antenna

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Progress In Electromagnetics Research Symposium Proceedings, Moscow, Russia, August 1821, 2009 537

paths in order to define a rule for choosing this parameter. A very small discretization step willincrease the result accuracy but the computation time will also increase a lot. So we have to finda compromise between accuracy and computation time. The analytic expression of the Neumannequation can be transposed into the following numerical expression (5):

Mnum= 0

4

k=N11

k=1

l=N21

l=1

r1x(k)r2x(l) + r1y(k)r2y(l) + r1z(k)r2z(l)

(r1x(k) r2x(l))

2

+

r1y(k) r2y(l)2

+ (r1z(k) r2z(l))2

(5)

In this expression,r1and r2represent the two loops, defined in Cartesian coordinates as a discretizedparametric equation. We have N1 elements to compose C1 path and N2 elements to compose C2path. The value represents the discretization step and is determined in order to obtain a goodapproximation of the mutual or self inductance value. To get a self inductance value with thismethod we have to take C2 = C1 + Z [5]; this means that C2 path is located on the wireboundary to avoid any singularities. If the wire is round, Zwill be equal to the wire radius a. Ifthe wire is rectangular, we have firstly to approximate it by a round wire with the same perimeteras defined by the expression (6):

a=(e + w)

(6)

with e, the wire thickness and w, its width.In this way, the external surface of this equivalent round conductor will be equal to the initialrectangular conductor one. Therefore the current density will be nearly equivalent if we considerthat the current mainly flows in the conductor surface because of the skin effect. To be moreaccurate, the intrinsic inductance value must be taken into account. It only depends on the looplength, i.e., the perimeter in case of closed loop. Finally the analytical equation becomes (7):

L= 0

4

d

2+

C1

C2

dr1 dr2r1 r2

(7)

with d, the path lengthAnd using the expression of mutual inductance (5), the equivalent numerical expression be-

comes (8):

Lnum= 0

4

1

2

k=N11k=1

(r1x(k))

2 +

r1y(k)2

+ (r1z(k))2 + Mnum (8)

In order to evaluate this method we use the analytical expression described byT. Thompson [6] asa reference. We find that to get an accurate value of the round wire self inductance for any shape,we have to define a discretization step equal to the wire radius. In the same way, to get an accuratevalue of the mutual inductance between two loops, the discretization step must be less than orequal to minimum distance between the two loops. Obviously the step has to be small enough todescribe the geometrical shape with precision. In case of a circular shape, the discretization stephas to be much smaller than the loop radius.

5. EXPERIMENTAL RESULTS

In this section, we evaluate the communication capability with usual readers in function of theobject antenna size and shape. We measure the coupling factor in free space taking the followingcoupling factor expression (9):

k= V L2

V L1

L1

L2(9)

Knowing values ofL1 and L2, we have just to measure the voltage at any coil. For our study wehave defined two new smaller classes, the Class S1 (e.g., for key fobs) and the Class S2 (e.g., formobile phones) with new dimensions as shown in Figure 2. The usual Class 1 dimensions of 72 mmby 42 mm are given for reference.

We have realized measurements with two different reader antennas and for each one with Class 1,Class S1 and Class S2 RFID objects. For each reader antenna we have made several measures,

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varying Zdistance to get k values while keeping loops coaxial and therefore parallel to each other.In Figure 3, we can see the coupling factor evolution in function of Zdistance respectively witha circular loop reader antenna and with a rectangular loop reader antenna for each defined RFIDobject class. With the circular loop, we can see that the maximum range which correspond toa coupling factor k = 0.03 is respectively 37 mm for Class S1 and 5mm for Class S2. With therectangular reader antenna, results are similar and the maximum range for Class S1 is 43 mm and5 mm for class S2. In comparison, the Class 1 antenna range is greater than 50 mm with the two

reader antennas.The theoretical values are close to the experimental results. We notice an error of approximately

10%, probably due to imperfection in voltage V L1 measurement and position of RFID object. The

Class S1 Class S2

72 mm

36 mm

42 mm 24 mm

Class 1

Figure 2: Dimensions of usual Class 1 and smaller classes S1 and S2 used for experiments.

Coupling factor with circular loop reader antenna

0,00

0,01

0,02

0,03

0,04

0,05

0,06

0,07

0,08

0,09

0,10

5 10 15 20 25 30 35 40 45 50Z (mm)

K

Class 1 Meas.

Class 1 Theo.

Class S1 Meas.

Class S1 Theo.

Class S2 Meas.

Class S2 Theo.

K limit

Coupling factor with rectangular loop reader antenna

0,00

0,01

0,02

0,03

0,04

0,05

0,06

0,07

0,08

0,09

0,10

5 10 15 20 25 30 35 40 45 50Z (mm)

K

Class 1 Meas.

Class 1 Theo.

Class S1 Meas.

Class S1 Theo.

Class S2 Meas.

Class S2 Theo.

K limit

(a) (b)

Figure 3: Coupling factor as a function of Z distance when loops are coaxial. (a) With a 6.5cm radiuscircular reader loop, (b) with a 12 cm by 13 cm rectangular loop. Dashed lines are the theoretical values andplain lines are measured values.

(a) (b)

Figure 4: coupling factor 2D map at a distance Zof 5 mm, between RFID object Class S2 (bold blue loop)and reader antenna (bold green loop). (a) 12 cm by 13 cm rectangular reader antenna, (b) 13 cm by 9 cmoval reader antenna. Note: The coupling factor is maximal in the red zone.

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Progress In Electromagnetics Research Symposium Proceedings, Moscow, Russia, August 1821, 2009 539

theoretical and measured curves shapes are very similar. The major difficulty in the measurementmethod is to get the real value of V L1 voltage because with a high Q antenna the voltage canreach 100 V and the matching is very sensitive to the probe capacity. This is why we set a highimpedance resistive voltage divisor in parallel of the antenna and we use a differential active probeto realize the measurement. Another way consists in measuring the reader antenna current loop todeduce voltage V L1. The main interest of this calculation method is to gain time in determiningif any shape of new RFID object is able to work with a usual reader antenna. The must is to

determine the communication volume by representing the coupling map in 2D at any Z distance.With experimental measurements this task is very long and difficult. In Figure 4(a), we can seethe calculated coupling factor 2D map between the rectangular loop reader antenna and the RFIDobject Class S2.

We notice that the maximum coupling is obtained when the RFID object is in a corner of thereader antenna. And this was experimentally verified. In Figure 4(b), the calculation method isapplied for an unusual shape like a 13 cm by 9 cm oval loop reader antenna. This last antennais better for smaller Class S2 thanks to its smaller size. Further simulations with various readerantennas confirm that smaller class RFID objects benefit from a smaller reader antenna size.

6. CONCLUSION

The numerical Neumann method is very efficient to calculate the coupling factor in every positionand for every shape. The experimental measurements have validated theoretical values with anerror of 10%. The results show that new smaller classes of card have a loss in range at center ofantennas of 40% for Class S1 and 90% for Class S2 with usual reader antennas. Globally, suchnew classes of RFID object need smaller reader antennas and interoperability with usual readersis not guaranteed. A way to increase interoperability with these small objects is to develop readerantennas which combine both a good reading range with present cards, e.g., by keeping their usualsize, and a zone of high coupling for smaller RFID objects, e.g., in a corner of a rectangular loop.

REFERENCES

1. ISO/IEC 14443-1, 2008.2. Reinhold, C., P. Scholz, W. John, and U. Hilleringmann, Efficient antenna design of inductive

coupled rfid-systems with high power demand, Journal of Communications, Vol. 2, No. 6,November 2007.

3. Finkenzeller, K.,RFID Handbook: Fundamentals and Applications in Contactless Smart Cardsand Identification, Wiley, April 2003.4. Kiusalaas, J., Numerical Method in Engineering with Matlab, Cambridge University Press,

2005.5. Gardiol, F., Traite delectricite, Electromagnetisme, T3, Presses Polytechniques et Universi-

taires Romandes, 2001.6. Thompson, T. and M. Phd, Inductance calculation technique, Part II: Approximations and

handbook methods, Power Control and Intelligent Motion, December 1999.