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

Near Field Coupling with Small RFID Objects

Abstract This paper presents a study on the coupling between a reader and a contactless
object in order to dene some good working rules to deal with objects with small antennas (NFC mobile phones, key fobs. . . ). We will dene a model representing the magnetically coupled system composed of the reader and the RFID object in order to introduce the coupling factor which is the key parameter. The coupling factor variation according to reading distance and antennas shapes is a must to predict the overall system performance. 1. INTRODUCTION

Today, the working group in charge of ISO/IEC 14443 standard [1] is dening new contactless objects antenna classes smaller than the very popular Class 1 card format. We will study such classes and analyze their compatibility with existing readers. In transportation sector, contactless validators use antennas with a typical size of 10 cm by 10 cm to assure a good communication range. But with smaller classes of contactless objects, the magnetic coupling factor (and therefore the reading range) tends to reduce. To calculate the coupling factor, we have to dene each antenna loop self inductance and the mutual inductance between them. The calculation of coaxial loops self inductances and mutual inductance can be done with analytical formulas for usual shapes. In all other cases, we can use numerical methods like Finite elements or PEEC method [2]. In near eld RFID, antennas are usually closed loops which can be approximated by laments loops. In this case the numerical Neumann method is an alternative simple way to obtain accurate values of mutual inductance and even self inductance with minimal computation eorts. With this method we will calculate the coupling factor in free space in several cases, for common readers and various RFID object antennas in order to determine the operating volume in each situation. The theoretical values will be compared to experimental coupling factor measurements.
2. MODEL OF THE SYSTEM

In near eld RFID [3], we can assimilate the system composed of a reader and an RFID object with an RF transformer. The corresponding electrical model is shown in Figure 1. The main dierence is about the magnetic coupling factor k value which is much lower. In proximity card systems operating at 13.56 MHz, k is usually comprised between 0.03 and 0.3. To transmit power with such low values, the transformer primary and secondary circuits must be tuned close to operating frequency. The transformer primary circuit represents the reader source with matching circuit and antenna. The transformer secondary circuit represents the RFID object with its antenna associated with C2 capacitor to make a resonant circuit with a frequency generally comprised between 13.56 and 19 MHz. The RFID object antenna inductance is chosen to get the maximum power which means several turns. For Class 1 reference card [1], the number of turns is 4 and the inductance is about 2300 nH. The resistance Rload represents the IC current consumption and also allows the load modulation of the operating eld. 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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to obtain the voltage gain at load is the following (1): H1 = V2 Zout jM = 2 V1 (Z0 jC1 +1)(jM ) (Z0 + (Z0 jC1 +1)ZL1 )(Zout + ZL2 ) 1 1 , ZL1 = R1 + jL1 , ZL2 = R2 + jL2 and Zout = with Z0 = R0 + 1 jC0 jC2 + Rload (1)

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

The power transmitted to the RFID object and the level of its response mainly depend on the mutual inductance, therefore on the coupling factor. The frequency tuning of the secondary coil between 13.56 and 19 MHz doesnt inuence a lot the results. The expression of the transfer function is independent from the object antenna shape thanks to the coupling factor value. So we can say that if we keep the same self inductance value for the new smaller classes then the operating limit will be identically determined by the same minimum coupling factor. The formula (3) gives the coupling factor value in function of both the mutual and the two self inductances: M k= L1 L2 (3)

In this equation, we can see that the coupling factor value is not inuenced by the number of turns if the radius of each loop is identical. Only the geometrical antenna shape inuences this value. The smaller the object antenna size, the closer the distance to the reader for the same coupling factor. We will evaluate the reading range in function of the object antenna size keeping usual reader antenna shapes.
3. DEFINITION OF THE MINIMUM COUPLING FACTOR

The minimum coupling factor is determined by minimal power transfer from reader to RFID object and by minimum signal response from RFID object to reader. A proximity card as dened in ISO/IEC 14443 operates with minimum eld strength of 1.5 A/m. While this eld produces sucient power in Class 1 cards it produces a lower power in smaller objects because the received ux is lower and the IC embedded on such objects must works with less power. Another important point is the signal sent by the object and received by the reader. The mutual inductance depends on the object area and when this area is smaller, the signal received by the reader is smaller. By experimental measurements we determined that the minimum coupling factor with usual cards is about k = 0.03 and corresponds to eld strength of 1.5 A/m. Such a coupling factor value with a smaller RFID object is found at closer distance and therefore with higher eld strength. This fact pushes us to say that the coupling factor parameter is more representative than the eld strength value. The only way to enhance reading range or at least to keep the one that we get with Class 1 format is to have a more sensitive reader and an object which need less power. In this way, the usual coupling factor limit of k = 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 analytical equation is computed with a numerical algorithm to get value of the mutual and the self inductances of approximated laments closed loops. M= 0 4
C1C2

dr1 dr2 r1 r2

(4)

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

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

paths in order to dene a rule for choosing this parameter. A very small discretization step will increase the result accuracy but the computation time will also increase a lot. So we have to nd a compromise between accuracy and computation time. The analytic expression of the Neumann equation can be transposed into the following numerical expression (5): Mnum = 0 4
k=N11 l=N21 k=1 l=1

r1x (k )r2x (l) + r1y (k )r2y (l) + r1z (k )r2z (l) (r1x (k ) r2x (l)) + r1y (k ) r2y (l)
2 2

+ (r1z (k ) r2z (l))

(5)

In this expression, r1 and r2 represent the two loops, dened in Cartesian coordinates as a discretized parametric equation. We have N1 elements to compose C1 path and N2 elements to compose C2 path. The value represents the discretization step and is determined in order to obtain a good approximation of the mutual or self inductance value. To get a self inductance value with this method we have to take C2 = C1 + Z [5]; this means that C2 path is located on the wire boundary to avoid any singularities. If the wire is round, Z will be equal to the wire radius a. If the wire is rectangular, we have rstly to approximate it by a round wire with the same perimeter as dened by the expression (6): (e + w) a= (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 initial rectangular conductor one. Therefore the current density will be nearly equivalent if we consider that the current mainly ows in the conductor surface because of the skin eect. To be more accurate, the intrinsic inductance value must be taken into account. It only depends on the loop length, i.e., the perimeter in case of closed loop. Finally the analytical equation becomes (7): dr1 dr2 0 d L= + (7) 4 2 r1 r2
C1C2

with d, the path length And using the expression of mutual inductance (5), the equivalent numerical expression becomes (8): Lnum 0 1 = 4 2
k=N11 k=1

(r1x (k ))2 + r1y (k )

+ (r1z (k ))2 + Mnum

(8)

In order to evaluate this method we use the analytical expression described by T . Thompson [6] as a reference. We nd that to get an accurate value of the round wire self inductance for any shape, we have to dene a discretization step equal to the wire radius. In the same way, to get an accurate value of the mutual inductance between two loops, the discretization step must be less than or equal to minimum distance between the two loops. Obviously the step has to be small enough to describe the geometrical shape with precision. In case of a circular shape, the discretization step has 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 the object antenna size and shape. We measure the coupling factor in free space taking the following coupling factor expression (9): V L2 L1 (9) k= V L1 L2 Knowing values of L1 and L2 , we have just to measure the voltage at any coil. For our study we have dened two new smaller classes, the Class S1 (e.g., for key fobs) and the Class S2 (e.g., for mobile phones) with new dimensions as shown in Figure 2. The usual Class 1 dimensions of 72 mm by 42 mm are given for reference. We have realized measurements with two dierent 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 Z distance 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 Z distance respectively with a circular loop reader antenna and with a rectangular loop reader antenna for each dened RFID object class. With the circular loop, we can see that the maximum range which correspond to a coupling factor k = 0.03 is respectively 37 mm for Class S1 and 5 mm for Class S2 . With the rectangular reader antenna, results are similar and the maximum range for Class S1 is 43 mm and 5 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 1 Class S1 Class S2 24 mm

42 mm

36 mm 72 mm

Figure 2: Dimensions of usual Class 1 and smaller classes S1 and S2 used for experiments.
Coupling factor with circular loop reader antenna
0,10 0,09 0,08 0,07
Class 1 Mea s.

Coupling factor with rectangular loop reader antenna

0,06 0,05 0,04 0,03 0,02 0,01 0,00 5 10 15 20 25 30 Z (mm) 35 40 45 50 K

Class 1 The o. Class S1 Me as. Class S1 Theo. Class S2 Me as. Class S2 Theo. K lim it

0,06 K 0,05 0,04 0,03 0,02 0,01 0,00 5 10 15 20 25 30 Z (mm) 35 40 45 50

Class 1 The o. 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 6.5 cm radius circular reader loop, (b) with a 12 cm by 13 cm rectangular loop. Dashed lines are the theoretical values and plain lines are measured values.

(a)

(b)

Figure 4: coupling factor 2D map at a distance Z of 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 cm oval reader antenna. Note: The coupling factor is maximal in the red zone.

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

theoretical and measured curves shapes are very similar. The major diculty in the measurement method is to get the real value of V L1 voltage because with a high Q antenna the voltage can reach 100 V and the matching is very sensitive to the probe capacity. This is why we set a high impedance resistive voltage divisor in parallel of the antenna and we use a dierential active probe to realize the measurement. Another way consists in measuring the reader antenna current loop to deduce voltage V L1 . The main interest of this calculation method is to gain time in determining if 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 dicult. In Figure 4(a), we can see the calculated coupling factor 2D map between the rectangular loop reader antenna and the RFID object Class S2 . We notice that the maximum coupling is obtained when the RFID object is in a corner of the reader antenna. And this was experimentally veried. In Figure 4(b), the calculation method is applied for an unusual shape like a 13 cm by 9 cm oval loop reader antenna. This last antenna is better for smaller Class S2 thanks to its smaller size. Further simulations with various reader antennas conrm that smaller class RFID objects benet from a smaller reader antenna size.
6. CONCLUSION

The numerical Neumann method is very ecient to calculate the coupling factor in every position and for every shape. The experimental measurements have validated theoretical values with an error of 10%. The results show that new smaller classes of card have a loss in range at center of antennas of 40% for Class S1 and 90% for Class S2 with usual reader antennas. Globally, such new classes of RFID object need smaller reader antennas and interoperability with usual readers is not guaranteed. A way to increase interoperability with these small objects is to develop reader antennas which combine both a good reading range with present cards, e.g., by keeping their usual size, 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, Ecient antenna design of inductive coupled rd-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 Cards and Identication, Wiley, April 2003. 4. Kiusalaas, J., Numerical Method in Engineering with Matlab, Cambridge University Press, 2005. 5. Gardiol, F., Trait e d electricit e, Electromagn etisme, T3, Presses Polytechniques et Universitaires Romandes, 2001. 6. Thompson, T. and M. Phd, Inductance calculation technique, Part II: Approximations and handbook methods, Power Control and Intelligent Motion, December 1999.