efficient antenna design of inductive coupled

8/8/2019 Efficient Antenna Design of Inductive Coupled

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Efcient Antenna Design of Inductive CoupledRFID-Systems with High Power Demand

Christian Reinhold / , Peter Scholz / , Werner John , Ulrich Hilleringmann

*University of Paderborn, Department of Electrical Engineering, Sensor Technology Group, Germany**Fraunhofer IZM, Departement Advanced System Engineering, Paderborn, GermanyEmail: {reinhold, peter.scholz, john }@pb.izm.fraunhofer.de, [email protected]

Abstract In contrast to pure identication labels, passiveinductive coupled RFID transponders with enhanced func-tionality have an increased power consumption. A non-optimized antenna design for high power transponders maylead to a poor efciency and high magnetic eld emissions.Therefore, in this work, the energy transmission of induc-tive coupled systems is investigated, enabling an optimizedsystem design. The RFID system is modeled by networkelements in order to optimize the energy transmission. Nextto a brief review of different methods for the antennaparameter determination, a new modication of the PEECmethod is derived enabling an accelerated and accuratecomputation of the mutual coupling of the reader and thetransponder antenna. Along with the simplication of thetransformed transponder impedance and the investigation of the reader matching, consecutive design steps are deduced.The inuence of the location-dependent antenna couplingon the energy transmission is characterized. Two casestudies are carried out showing a successful transmissionof 80 mW over a distance of up to 7.6cm by 275 mW readeroutput power. This system demonstrates an efcient energysupply of a high power transponder while keeping the eldemissions low.

Index Terms RFID System, Antenna Design, InductiveCoupling, Wireless Energy Transmission, Quality Factor,Inductance Calculation, PEEC

I. INTRODUCTION

RFID (Radio Frequency IDentication) systems suc-ceed in replacing bar code systems in the supply chainmanagement. Besides of the ability to read out tag in-formation without a line of sight, other applications ariserequiring additional functionality of the tag. Especiallyinductive coupled RFID systems turn out to be adequatebecause of their potential for an efcient energy transmis-sion.

There is a growing interest in monitoring object relatedinformation like temperature, acceleration or pressure [1],[2]. Other applications aim to enhance the label function-ality by optical devices like image sensors [3] and displays[4]. Compared to pure identication applications, theenergy demand of these so called smart label applicationsis higher. However, the emission of the electromagneticeld has to stay below regulation boundaries. In order toguarantee an efcient and reliable energy supply while

fullling the regulations, the energy transmission via theinductive coupled antenna system has to be understood.

Signicant work on this topic has been done in the areaof medical implants. In [5] the inductive energy trans-

mission was investigated in order to provide energy toan auditory prosthesis taking displacement tolerances intoaccount. In [6] the power transmission for an implantedbiomedical device is enhanced in terms of optimizing thecoupling coefcient of two spiral coils.

In contrast to medical implants, the situation regardingRFID smart labels is different. The variation of theinductive coupling of the coils of a smart label systemcaused by changes in the alignment is stronger com-pared to medical implants in most cases. For this reason,[7] presents an adaptive matching network providing anadequate matching of the reader for varying couplingconditions in order to maximize the power transmissionwhile neglecting efciency aspects.

In this paper a design approach on the bases of [8],[9] is presented which enables efcient and emissionminimized antenna design. The focus of this contribution

is on modeling, analyzing and optimizing of the energytransmission via the inductive coupled link.In section II an overview of the RFID system model is

given. For a correct model, it is essential to extract the net-work element parameters accurately. Different approachesare presented in section III allowing for the computationof the antenna parameters for different scenarios. Anadaptation of the PEEC (Partial Element Equivalent Cir-cuit) method is derived which enables a fast and accurateextraction of the positional and angular varying mutualinductance for typical RFID antenna setups.

In order to optimize the energy transmission, a holisticapproach is carried out taking the reader and the transpon-der into account as well as the interaction between eachother. In order to give an intuitive interpretation of thesystem behavior, the transformed transponder impedanceis introduced in section IV and simplied by introductionof the frequency deviation. The maximization of thequality factor and the optimization of the coupling arediscussed. The matching of the reader antenna is analyzedrevealing a single turn reader antenna to be optimum withrespect to the data transmission. The gained ndings aresummarized in a consecutive system design approach.

In section V the inuence of the varying couplingcoefcient on the energy transmission is analyzed. Case

studies are investigated in section VI in order to provethe applicability of the presented concepts by diversemeasurement setup scenarios. The key ndings of thework are nalized by a conclusion.

14 JOURNAL OF COMMUNICATIONS, VOL. 2, NO. 6, NOVEMBER 2007

2007 ACADEMY PUBLISHER


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V 0

R 0

MatchingNetwork

I 1 R 1L 1

V I1 = jM (x)I 2 V I2 = jM ( x )I 1

InductiveCoupling I 2R 2

L 2

C 2 V 2 R L

Figure 1. System model of an inductive coupled RFID System

I I . M ODELING OF THE RFID S YSTEM

An RFID system can be separated into two parts: theinterrogator and the transponder. An equivalent network 1

is presented in Figure 1.The reader has to provide the power from a source to

an antenna. In the presented model the output stage of the reader is represented by a voltage source V

0with an

internal resistance R0 . To deliver maximum power to theantenna, the impedance of the source has to be matchedto the antenna impedance. The antenna can be modeledby an inductance L1 and a series resistance R1 in order totake ohmic losses into account. The transponder antennais modeled in the same way by an inductance L2 and aresistance R2 . The transponder impedance is tuned to theresonance frequency by a capacitance C 2 . The transpon-der load is modeled by a resistance RL . The quantityof the load resistance can be determined via the powerconsumption of the transponder P req and the requirementsto the DC supply voltage V DD by RL = V 2DD /P req .

The inductive coupling is represented by the mutualinductance M which induces a voltage in the transponderV I2 due to a current I 1 in the reader coil and vice versa.

I I I . I NDUCTIVE C OUPLED C OILS

In this work, the inductive coupled coils are modeledby the self inductances, mutual inductances and resis-tances. 2 This section describes the computation of theseparameters by analytical expressions as well as numericalmethods. In section III-A various analytical equations forcalculation of the antenna parameters are reviewed as well

as important coherences that are needed for this work. Abrief overview of different numerical methods is given inIII-B. Afterwards a modication of the PEEC method isderived allowing for the effective calculation of the mutualinductance between two rectangular coils. This particularapproach is compared with the software tool FastHenry[10].

A. Analytic Expressions

Several analytic equations exist for the calculation of the self inductance of simple shaped coils [11][14].

1This model does not describe the transient behavior of the transpon-der. This aspect can be taken into account by regarding the quality

factors of the resonant circuits for different load resistances.2Parasitic capacitance of the transponder coil is included in the

resonance capacitance C 2 .

Most approximation expressions are valid for circularor rectangular coils only. Even though these expressionsare not feasible for an accurate inductance calculation of complicated coil structures, a general system analysis canbe done.

r 1

r 2

I 1 x

Figure 2. Representation of two inductive coupled coils

For a circular single turn coil as presented in Figure 2,

the inductance can be calculated according to [11] by

L0 = 0 r ln2 rd

, (1)

with the permeability of free space 0 , the coil radiusr and the coil wire diameter d. This inductance can beused for the calculation of the inductance of a multi turninductor by

L = N 2 L0 , (2)

where N denotes the number of turns. This equationoffers a proper approximation for a cylindrical inductor.In the case of spiral inductors it can be used for general

parameter studies. A more precise inductance computa-tion of spiral inductors is given in [15].

Besides of the self inductance, the mutual inductanceof two coupled coils is an important gure of merit. Itcan be calculated analytically for simple coil geometries.The mutual inductance of two coupled circular coils aspresented in Figure 2 can be calculated by [11]

M = N 1 N 2 r 21 r 22

2 (r 21 + x2 )3 . (3)In this equation, N 1 and N 2 represent the number of turns of the rst and the second inductor respectively.

The coil diameters are given by r 1 and r 2 and the axialseparation is represented by x. It is important to note that(3) is valid only if the magnetic eld created by a currentI 1 in the rst coil is homogenous in the area bounded

JOURNAL OF COMMUNICATIONS, VOL. 2, NO. 6, NOVEMBER 2007 15



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by the second coil. Therefore the equation is only validif r 2 < r 1 x. A more general approach of calculatingthe mutual inductance of cylindrical coils with parallelalignment and an arbitrary position is presented in [16].

The coupling of two coils can be expressed by thecoupling factor which relates the mutual inductance tothe self inductances in the following way

k =M

L1 L2 . (4)If the coupling factor equals one, the coupling is atmaximum while a coupling factor of zero describes twouncoupled coils.

The inductance matrix can be dened in order tocalculate the induced voltages from the currents by

V I = j L I = j L1 M

M L 2I 1

I 2, (5)

with the denitions of the currents and inductances asshown in Figure 1.

The ohmic losses of a coil for DC currents are denedby

RDC =l

A, (6)

where l is the conductor length, A the conductor crosssection area and the conductivity of the conductor mate-rial. The resistance of an N -turn coil can be approximatedby R = N R 0 , where R0 is the resistance of a single-turn coil. For AC currents, the skin effect inuences the

effective area of the cross section. The skin depth isdened by

= 2 . (7)In this equation = 2 f is the angular frequency. Theconductivity and permeability are represented by and respectively. In order to compute the effective ACresistance, it can be assumed that the entire current owsin the conductor skin whose thickness is determined bythe skin depth. One has to keep in mind that the skindepth is valid only for a single conductor with a circularcross section. In case of a spiral coil, current in the

adjacent coil wires causes a magnetic eld resulting in anasymmetric current distribution. This effect is visualizedin Figure 3. In order to determine the AC resistanceaccurately, numerical methods have to be applied.

B. Numerical Methods

In case of complex geometries like coupled rectangularspiral inductors no formulas exist for calculating theinductance analytically. In this case numerical methodscan be applied.

For typical inductive coupled RFID applications theseparation of the antennas can become large in compari-

son to the dimensions of the antenna structures resultingin a small surface to volume ratio. Therefore numericalmethods requiring a discretization of the entire volumesurrounding the antennas like FDTD (Finite Difference

C u r r e n t

D e n s i t y

Figure 3. BEM-computed current density of a rectangular spiralinductor.

Time Domain) methods generate a high computational ef-fort. In order to guarantee numerical stability, the numberof necessary FDTD time steps has to be dened by the

dimensions of the discretization requiring a huge numberof time steps. Therefore lots of computational work forlow frequency problems needs to be done [17].

A further numerical technique to determine the antennaparameters is the BEM (Boundary Element Method).This method requires the discretization of the conductorsurface instead of the entire solution space. BEM matricesare typically dense whereas FDTD approaches generatehigh order sparse matrices with a band structure enablingmemory efcient and fast computation.

The PEEC (Partial Element Equivalent Circuit) methodrepresents another numerical antenna parameter computa-

tion technique, which has proven applicable for inductivecoupled RFID systems. The method presented in [10]can be adapted in order to accelerate the computationof the antenna parameters. This will be explained in thefollowing.

In order to compute the antenna parameters, it is nec-essary to segment each coil into straight elements. Theseelements can be split up into parallel brick shaped sectionsin which a constant current density is assumed. These sec-tions are called laments in the following. Each lamentis dened as being coupled via a partial inductance to allother laments. The partial inductance can be determinedby analytical expressions for an arbitrary arrangement[18]. These partial inductances as well as the lamentsresistances are combined to an impedance matrix. Bysetting up a graph, and thereby dening the lamentsconnections, it is possible to solve the impedance matrixfor the antenna parameters. For a detailed description of the presented approach [10] can be reviewed.

Figure 4 presents two rectangular inductive coupledcoils with an arbitrary number of turns. The followingderivation will concentrate on the extraction of the mu-tual inductance M of the two coils by means of thePEEC method. Due to the computational effort, eachstraight segment is modeled by one lament only. The

rst N 1 -turn rectangular spiral inductor is represented byP = 4 N 1 branches and the second by Q = 4 N 2 branchesrespectively. The total number of branches is R = P + Q.The graph, dening the laments connections, allows for




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1

2

3

4

5 P 1 P + 1

P

. . .

. . .

I m 1

I b 1

I b 2

V b 1

V b 2

V s 1

R 1

R = P + QI m 2

V s 2

M

Figure 4. Two inductive coupled segmented inductors

the relation between the branch currents and the branchvoltages to be set up by the branch impedance matrix Z

ZI b = V b, (8)

whereI

b = [I b1 , . . . , I bP , I bP +1 , . . . , I bR ]T

is the vectorof branch currents and V b = [V b1 , . . . , V bR ]T is the vectorof branch voltages. The impedance matrix is composed as

Z = R + j L C R R . (9)

In this equation R is a diagonal matrix of the DC resis-tances of each lament according to (6) and L is a densematrix describing the partial self and mutual inductanceof the laments which may be computed by [18]. In orderto extract the impedance for both terminals, it is necessaryto set up a mesh matrix 3 M , relating the topology of thebranches to the ports. Utilizing Kirchhoffs laws yields

M V b =

V s ,

M T I m =

I b, (10)

where V s = [V s 1 , V s 2 ]T is the source voltage vector andI m = [I m 1 , I m 2 ]T the port current vector. Combining (8)and (10) results in

M ZM T I m = V s . (11)

This equation relates the port currents of the two coupledcoils to the port voltages. The mutual inductance isrepresented by element 12 or 21 of the matrix M ZM T ,which will be shown in the following.

The matrix M relating the terminal voltages to thebranch voltages for two coupled inductors in this case

simplies toM = M 11 M 1P M 1P +1 M 1RM 21 M 2P M 2P +1 M 2R

= 1 1 0 00 0 1 1. (12)

For the computation of the mutual inductance of the twoinductors, it is sufcient to set up (11) with the inductancematrix L and inserting (12)

M LM T =

P

i=1

P

j =1L ij

P

i=1

P + Q

j = P +1L ij

P + Q

i= P +1

P

j =1 L ij

P + Q

i= P +1

P + Q

j = P +1 L ij

.

(13)

3Do not mistake the mutual inductance M for the mesh matrix M .

0 2 4 6 8 10 12 14 16 18 200

1

2

3

Distance between the coils xTag

(cm)

R e l a t i v e

D e v i a t i o n ( % )

0 2 4 6 8 10 12 14 16 18 2010

-9

10-8

10-7

M u t u a l I n d u c t a n c e M ( H )

FastHenry Adapted PEEC

Figure 5. Comparison of the PEEC method implemented in FastHenryaccording to [10] with each segment separated into 8 2 laments andthe presented adaptation. Parameters are the same as in Figure 14(a).

Comparing (11) and (13) with (5) yields the mutualinductance, that is expressed by element 12 of the matrixin equation (13)

M =P

i=1

P + Q

j = P +1

L ij . (14)

The standard PEEC method presented in [10] demandsthe solving of an equation system. In contrast to this

the modied approach requires the computation of a fewpartial inductances as well as their summation accordingto (14), reducing the computational effort.

In Figure 5, the standard PEEC technique is comparedwith the presented adaptation by calculating the mutualinductance of two parallel coils. The deviation of the twomethods does not exceed 3 %.

IV. S YSTEM D ESIGN

In this section a system design approach for an opti-mum energy transfer is derived. All network element def-initions are chosen according to section II and Figure 1.

Section IV-A will approximate the transformed transpon-der impedance, which describes the inuence of thetransponder on the reader circuit. This approximationallows for easy examination of the parameter inuences.In IV-B the tag quality factor is maximized by means of anoptimum number of turns for a xed coil geometry. Theantenna geometry is investigated in section IV-C in orderto achieve maximum coupling for a given coil separation.In the following section IV-D the matching network of thereader circuit is discussed. The section is concluded byfour design steps resulting in an energy efcient systemdesign.

A. Transformed Transponder Impedance

The current of the inductive coupled transponder in-duces a voltage in the reader antenna. According to [11]




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this affect can be modeled via the transformed transponderimpedance. It is dened as

Z T =2 k2 L1 L2

Z Tag=

2 k2 L1 L2R2 + jL 2 + 11 /R L + jC 2

. (15)

The reader can be optimized in terms of matching,bandwidth, transferred power etc. when this impedanceis known. The transformed impedance is related to manyparameters which do not allow an intuitive interpretation.With the following considerations, a simplication of Z Tis possible.

With the denitions according to Figure 1, the transpon-der impedance Z Tag is analyzed

Z Tag =R 2R L + j

L 2R L + jR 2 C 2 2 L2 C 2 1

1R L + jC 2

.

(16)In order to operate the tag efciently, the capacitance C 2is chosen to be resonant with L2 for = 0 by fulllingC 2 = 1 / (20 L2 ). The braces of the nominator of (16) canbe simplied in the following way

= j0

0 L2RL

+R2

0 L2= j

0

d2 , (17)

=2

20 1 =0

0

0

=0

. (18)

In (17), d2 is the damping factor which is related to thequality factor Q2 by

Q2 =1d2

=0 L2RL

+R2

0 L2

1

. (19)

In (18), = / 0 0 / is the frequency deviationas dened in [5]. Inserting (17) and (18) into (16) leads to

Z Tag =R 2R L + j

0 (d2 + j )

1R L + jC 2 0 L2 (d2 + j ) .

(20)

In the approximation of (20) it is assumed that both,R2 /R L in the nominator and 1/R L in the denominatorcan be neglected. This is valid because the load resistanceRL is far greater in comparison to the coil resistanceR2 . By inserting the approximation of (20) into (15) thetransformed transponder impedance can be simplied

Z T ,approx = 220k2 0L1d2 + j

. (21)

In order to investigate the validity of the assumptionsabove, Figure 6 presents a comparison of the simpliedformula (21) with the general expression (15) of thetransformed transponder impedance. The deviation of the approximation is negligible for optimization aspectswhere parameter inuence is examined.

For the resonance frequency ( = 0 , = 0 ) thetransformed transponder impedance from (21) becomesa real value

Z T ,approx , 0 = RT = 0 k2 L1 Q2 . (22)

The power dissipated by the tag is 4 P Tag = |I 1 |2 RT and4The currents and voltages presented in this paper are interpreted as

root-mean-square values.

-0.2 -0.15 -0.1 -0.05 0 0.05 0.1 0.15 0.2-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

Frequency deviation n

T r a n s f o r m e d T r a n s p o n d e r I m p e d a n c e ( ) W

Re{Z }TRe{Z }T,approxIm{Z }TIm{Z }T,approx

Figure 6. Comparison of (15) and the simplication (21). Parametersare the same as in Figure 11 with f 0 = 13 .56 MHz and k = 0 .03.

0 2 4 6 8 10 12 14 16 18 200

2

4

6

8

10

12

14

Secondary inductance L ( 2 H)

P o w e r ( m W )

P TagP RLP R2

1

2 3

4

N =52

6

7

89

10

N2,PRLmax

P ~ QTag 2

Q 2,max

Figure 7. Power and quality factor at the transponder. The quality factoris proportional to the tag power P Tag Q 2 . Parameters: f 0 = 13 .56MHz, R L = 10 k , R 20 = 0 .8 , k = 0 .03, I 1 = 100 mA andL 1 = 0 .53 H.

therefore linear related to RT . In order to minimize thereader coil current I 1 and the magnetic eld emission aswell as for a required power delivery, it is necessary tomaximize RT . This can be achieved by maximizing Q2as well as k2 L1 . For a reliable data transmission, Q2 isupper bounded due to the bandwidth requirement.

B. Maximization of the Quality Factor

At rst, the quality factor Q2 will be analyzed. Theproduct k2 L1 is taken into account in the next section.

The tuneable design parameters of Q2 in (19) areL2 and R2 . The load resistance RL is determined bythe current draw and the supply voltage whereas C 2 ischosen to be resonant with L2 . While maximizing thequality factor by L2 one has to keep in mind that Q2involves two resistances that both dissipate power. For

small L2 the R2 -part dominates and for large L2 theRL -part respectively (see Figure 7). One has to considerthat L2 and R2 are dependent on the number of windingsN 2 .




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Energy maximum

Sufficient bandwidthfor communication

S e c o n d a r y

i n d u c t a n c e

L ( H )

2

F r e q u e n c y d e v i a t i o n n

I n d u c e

d v o

l t a g e

| V | ( V )

2

Number of windings

12 3

45 6

7 89

Figure 8. Load voltage V 2 depending on the frequency deviation andthe inductance L 2 . Parameters are the same as in Figure 7.

Due to the fact that it is undesirable to deliver too much

power to the coil resistance, the power delivered to theload can be affected by increasing L2 . In order to nd themaximum power at the load, one approach is to optimizethe load voltage

V 2 =Z C 2 R L

Z Tag jMI 1

0 M I 1d2 + j

. (23)

In the approximation R2 /R L in (20) has been neglected.From the voltage V 2 , the power transferred to the load canbe directly followed by P R L = V 22 /R L . Figure 8 showsthe voltage versus L2 , whereas the results are highlightedat integers of N 2 .

In order to nd the maximum voltage at the load independence of the number of windings N 2 , one has tosolve the derivation of V 2 /N 2 = 0 . From this followsthe optimum turn conguration [8]

N 2 ,P RLmax =3 2 R20 RL20 L220 , (24)

where denotes that has to be rounded up to the nextgreater integer.

C. Maximization of the CouplingThe transformed impedance can also be optimized by

maximizing k2 L1 which is the same as maximizing themutual inductance M , when L2 is xed. This can beanalyzed by numerical methods e. g. [10] as describedabove. An example is shown in Figure 9. It can be seenthat the optimum reader antenna size varies with thedesired readout range.

In order to maximize the transformed impedance, theoptimum number of windings of the reader coil has tobe investigated as well. Increasing the number of turnsN 1 does not improve the power transfer [8]. Instead,

regarding the data transmission, it is advisable to useonly a single-turn reader antenna in order to keep QReaderas low as possible. This aspect will be discussed in thefollowing section.

0 5 10 15 20 25 300

0.01

0.02

0.03

0.04

C o u p

l i n g f a c t o r k

0 5 10 15 20 25 300

2

4

6

8

10

12

Side length of the reader square coil (cm)

M u t u a

l I n d u c t a n c e M ( n H )

xTtag = 5 cmx = 10 cmTagxTag = 15 cmxTag = 20 cm

Figure 9. Coupling factor and mutual inductance as a function of theside length of the reader square coil. The side length of the square tagcoil is 5 cm. The curves are presented for different tag coil displacements

x Tag .

D. Reader Matching

As presented in Figure 1, the reader antenna has to bematched to the source. An important gure of merit isthe quality factor of the matching network. In case of anabsent tag ( k = 0 ), the quality factor of the primary coilequals

Q10 =0 L1R1

. (25)

If a tag is present ( k = 0 ) the quality factor becomes

Q11 =0 L1

R1 + RT. (26)

Figure 10 shows the matching of the reader for two casesaccording to (25) and (26).

The total quality factor of the reader circuit is dom-inated by the Q of the reader antenna highlighted byR1 + j 0 L1 . This is because the related reection coef-cient is placed most close to the border of the Smith Chartwhich represents an innite quality factor. The antennaQ can be reduced by a parallel resistor Rp in order totransmit data reliable. For the presented example, by thisa quality factor of Q10 ,R p = 33 is achieved.

In Figure 10 it can also be seen, that a couplingcoefcient of k = 0 detunes the reader which is matchedfor the uncoupled case. This mismatch leads to a reducedoutput power of the source and it can effectuate a poorpower transfer for high coupling rates. In order to avoidthis effect, the matching network may be designed for acertain coupling factor k0 = 0 . However, this decreasesthe readout range, because coupling below k0 wouldlead to a mismatch in addition to the low transformedtransponder impedance.

In order to achieve the optimum number of windings

for the reader coil with consideration of the data trans-mission, one has to minimize Q11 . Because of L1N

21 ,

R1 N 1 and RT N 21 the derivation Q 11 /N 1 reveals

that Q11 is strictly increasing with N 1 . Therefore, in order




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10

25

50

100

200

500

25

50

100

200

500

10

R 0

C 5

C 4

C 3R p

R 1 + j 0 L 1

Q = 33

k = 0 %k = 3 %

Figure 10. Smith Chart normalized to 50 with the parameterdenitions according to Figure 11.

to keep the reader quality factor as low as possible, areader coil with N 1 = 1 windings should be chosen.

E. System Approach

Summing up the results, a straightforward system de-sign approach can be reached by successively performingthe following steps:

1. For a maximum power transfer, the size of thetransponder coil should be maximized in orderto exploit the available area and maximizing thecoupling. This allows for the corresponding baseinductance L20 and resistance R20 to be estimatedfor an adequate coil wire diameter. The size of thereader coil should be chosen in such a way thatk2 L1 = M 2 /L 20 is at a maximum for a givenspatial arrangement of the coils.

2. For given RL , L20 and R20 , an optimum N 2 canbe calculated from (24). If the resulting Q2 is toohigh for the data transmission, N 2 can be increasedat the cost of the energy range.

3. The primary coil should only have one turn in orderto keep the Q1 low. Additionally, the coil resistanceR1 may be increased, for example by thinner circuitwires so as to reduce Q1 . However, this increasesthe power loss by the coil and decreases the ef-ciency.

4. If the readout range is the main objective, thereader matching network should be designed forzero coupling ( RT = 0 ). In this case, scenarios with

high coupling ( RT 0) would lead to a mismatch

and a poor power transfer. This effect is also knownas resonance circuit detuning. Another approach isto design the reader matching network for a certain

coupling coefcient k0 . Thus, the efciency will beat an optimum for this special case, but the bordersof functionality will be reduced.

V. R EADER N ETWORK M ATCHING FOR VARYINGT RANSPONDER C OUPLING

The antenna impedance of the reader depends on thecoupling coefcient. The resistive part can be expressedwith (22) according to Figure 1 as

R1 (k) = R1 + 0 k2 L1 Q2 . (27)

If the system is designed for a coupling coefcient k0 , thesystem is matched for a load R1 (k0 ). Since the reactiveelements of the matching network ideally do not dissipatepower, the power delivered to R1 (k0 ) is

P R 1 (k0 ) = P 0 =V 20

4R0. (28)

If the transponder coupling k differs from the matchedcoupling k0 a mismatch occurs. The mismatch can becharacterized by the reection coefcient

(k) =R1 (k) R1 (k0 )R1 (k) + R1 (k0 )

. (29)

Inserting (27) and (25) gives

(k) =k2 k202

Q 10 Q 2 + k2 + k20

. (30)

The power delivered to the antenna load and to thetransponder can be calculated using the the reectioncoefcient and the power divider rule by

P R 1 (k) = P R 1 (k0 ) 1 2 (k) , (31)P Tag (k) = P R 1 (k)

RTRT + R1

. (32)

The power dissipated by the resistive elements for twotest scenarios is presented in the following section.

VI. C AS E STUDIES

A test setup according to Figure 11 was utilized inorder to verify the results. The challenge was to transmit80 mW at about V 2 = 4 .9 V to the load RL . Following thefour design rules as presented in the previous section, it isnecessary to maximize the available area for the tag coilrst. In this example, the given size of the tag coil was6.9 cm 5.4 cm. According to the numerical simulation,a side length of 12 cm for the reader coil was chosenso as to reach a power range of less than 10 cm. Thearrangement of the test setup is visualized in Figure 14.

Subsequently, the optimum number of windings N 2 andthe width of the wires of the tag had to be determined.Since the load RL = (4 .9 V)2 / 80mW = 300 is smallin comparison to standard RFID systems, the quality

factor of the tag in (19) turns low except if R2 and L2are also small. This was realized by a trace width of w2 = 4 mm. By usage of FastHenry [10], L20 = 168 nHand R20 = 30m were deduced. Referencing to (24),




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RL=300 WC 2=820 pF

R2=30 mW

L1=530 nH

R1=240 mW

V 2

I 2

C 3=120 pF

C 4=170 pF R0=50 W I 1

V =0 7.4 V

M(r)

C 5=730 pF

L2=168 nH

R P =1.8 k W

Figure 11. Test setup for transmitting 80 mW to the load R L at V 2 = 4 .9 V.

0 5 10 15 20 250

0.05

0.1

0.15

0.2

0.25

0.3

Distance between the coils xTag

(cm)

P o w e r ( W ) P Source,sim

PRL,sim

PRL,meas

PR1,sim

P RP,sim

Figure 12. Simulation compared to the measurement for the arrange-ment of Figure 14(a).

0 2 4 6 8 10 120

0.02

0.04

0.06

0.08

0.1

0.12

0.14

Distance between the coils x Tag (cm)

P o w e r ( W )

P RL,simP RL,meas

Figure 13. Simulation compared to the measurement for the arrange-ment of Figure 14(b).

xy

zx

5 .4 c m

6 . 9

c m

1 2 c m 1 2

c m 4 mm

1 mm

(x ,0,0)Tag

(a) Parallel Arrangement

xy

z

(x ,0,0)Tag x

5 . 4 c m

6. 9 c m

1 2 c m 1 2 c m

4 mm

1 mm

(b) Rectangular Arrangement

Figure 14. Depiction of the spatial arrangements of the reader andtransponder coils.

N 2 = 1 was chosen. Thus the tag quality factor isQ2 = 20 .

In accordance to the third design step, a single windingwas chosen for the primary coil. With the trace width of w1 = 1 mm, L1 = 530 nH, R1 = 240m and a qualityfactor of Q1 = 188 were computed [19]. This high qualityfactor is unfeasible in respect to a data transmission andcould be reduced by thinner trace width of the primarycoil. Another possibility to increase the bandwidth is toadd a parallel resistor, which is less sensitive towardsvariations during the manufacturing process. The parallelresistor R p = 1 .8 k reduced the quality factor to

Q10 ,R p = 33 .The reader matching was realized by a -matchingnetwork consisting of three capacitors ( C 3 , C 4 and C 5 ),in order to be able to easily match the primary load to a

50 source. The matching network was designed for theuncoupled system k0 = 0 , where RT = 0 [7].

In order to compare the taken measurements withthe simulations, both coils were arranged in a paralleldirection, with each center points being at y = 0 andz = 0 (Figure 14(a)). The separation between the tagand the reader coil, indicated by the x-coordinate, wasincreased from zero to xTag , max = 25 cm, while mea-surements were taken at the maximum separation of 1 cmper measurement step. The voltage V 2 was measured andthe appropriate power was calculated by P RL = V 22 /R L .

Figure 12 shows that the measurements match thepredicted computations very closely. The power of 80 mWis transmitted at about 1 cm up to 7 .6 cm. For large dis-tances, the transformed transponder impedance convergesto zero. In this case, the power of the source offered toa 50 load, which is about 275 mW, is parted into theperfectly matched R p and R 1 . If the tag is moved closertowards the reader coil, the transformed impedance risesas well as the power at RL . The transformed transponderimpedance creates a mismatch that leads to a reducedpower output of the source. This effect causes a relativelypoor power transfer for small distances.

A second measurement scenario is presented in Figure14(b). It illustrates the power transmission for a rectan-

gular orientation of the reader and tag. The tag coil wasrotated by 90 and moved by xTag . In Figure 13 simu-lation results are plotted against measurements. Again, aclose correlation is achieved, except for small distances,




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where the uncertainty of the position and rotation hasa big impact on the coupling factor and therefore onthe transmitted power. These errors might be minimizedby a more accurate positioning system of the coils. Thepower of 80 mW can be transferred at up to 2.7 cm fora rectangular alignment of the coils. The range can beincreased by boosting the power of the source, whichresults in a shift of the power curve.

With the presented equations, the resulting current I 1can be calculated. This allows for the computation of thecorresponding eld strength by numerical eld calculationsoftware, in order to show its compliance with EM-eldemission boundary legislation.

VII. C ONCLUSION

The presented work focuses on optimizing the antenna

system of an inductive coupled RFID system. For this it isimportant to estimate the antenna parameters. For simplegeometries, analytic expressions for the self and mutualinductance as well as the resistance are given. Numericalmethods, which can be used for complicated structuresare presented and a simplication of the PEEC methodfor two coupled antennas is developed. The functionalityof the simplication is tested by comparing it with themutual inductance of two coupled rectangular coils for atypical RFID application example. The simplied methodresults deviate only slightly from the results generated bythe original PEEC computation by less than three percent.

In order to give an intuitive interpretation of the in-uence of the parameters on the energy transmission,the transformed transponder impedance is presented andsimplied. Based on this an equation for the optimum turnnumber is derived. The inuence of the coil geometry onthe coupling factor is investigated revealing a correlationbetween the optimum coil geometry and the separationbetween the reader and the transponder. The presentedreader matching considerations result in a single turnreader coil being optimum for the data transmission.The results are summarized in a straightforward stepby step design approach. Finally, the inuence of avarying transponder coupling on the energy transmission

is investigated.Case studies are carried out to show the power trans-

mission of 80 mW to a transponder. This power can beachieved by a 275 mW reader for a rectangular and aperpendicular orientation. The measurement results are inclose alignment to the computations based on the systemmodel.

ACKNOWLEDGMENT

The reported R+D work was carried out in the frame of the R+D project PARIFLEX. This particular research was

supported by the BMBF (Bundesministerium f ur Bildungund Forschung) of Republic of Germany under grant 16SV 2240/16 SV 2239/16 SV 2236. The responsibility forthis publication is held by the authors only.

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[1] H. M. Lu, C. Goldsmith, L. Cauller, and J.-B. Lee,MEMS-based inductively coupled RFID transponder forimplantable wireless sensor applications, IEEE Transac-tions on Magnetics , vol. 43, no. 6, pp. 24122414, June2007.

[2] H.-P. Huang, C.-S. Chen, and T.-Y. Chen, Mobile diag-nosis based on RFID for food safety, in Proceedings of the IEEE International Conference on Automation Scienceand Engineering , October 2006, pp. 357362.

[3] M. Schwarz, R. Hauschild, B. Hosticka, J. Huppertz,T. Kneip, S. Kolnsberg, W. Mokwa, and H. Trieu, Singlechip CMOS image sensors for a retina implant system,in Proceedings of the IEEE International Symposium onCircuits and Systems (ISCAS) , vol. 6, May 1998, pp. 645648.

[4] W. John, P. Scholz, C. Reinhold, and G. St onner, Papier-infotr ager haben bald ausgedient, Funkschau , vol. 3/2007,pp. 3941, March 2007.

[5] E. S. Hochmair, System optimization for improved ac-curacy in transcutaneous signal and power transmission, IEEE Transactions on Biomedical Engineering , vol. BME-31, no. 2, pp. 177186, February 1984.

[6] S. Atluri and M. Ghovanloo, A wideband power-efcientinductive wireless link for implantable microelectronicdevices using multiple carriers, in Proceedings of the IEEE International Symposium on Circuits and Systems(ISCAS) , May 2006, pp. 11311134.

[7] B. Jiang, J. R. Smith, M. Philipose, S. Roy, K. Sundara-Rajan, and A. V. Mamishev, Energy scavenging for in-ductively coupled passive RFID systems, in Proceedingsof the IEEE Instrumentation and Measurement TechnologyConference , vol. 2, May 2005, pp. 984989.

[8] P. Scholz, C. Reinhold, W. John, and U. Hilleringmann,

Analysis of energy transmission for inductive coupledRFID tags, in Proceedings of the IEEE InternationalConference on RFID , March 2007, pp. 183190.

[9] , Antenna design of HF-RFID tags with high powerrequirement, in Proceedings of the 19th InternationalConference on Herzian Optic and Dielectrics (OHD) ,September 2007, pp. 9398.

[10] M. Kamon, M. J. Tsuk, and J. K. White, FastHenry: Amultipole-accelerated 3-d inductance extraction program,in Proceedings of the 30th Conference on Design Automa-tion , 14-18 June 1993, pp. 678683.

[11] K. Finkenzeller, RFID Handbook: Fundamentals and Ap- plications in Contactless Smart Cards and Identication .John Wiley and Sons, 2003.

[12] R. Dengler, Transponder - Elektrodynamik, pp. 19,April 1999.

[13] C. M. Zierhofer, Geometric approach for coupling en-hancement of magnetically coupled coils, IEEE Transac-tions on Biomedical Engineering , vol. 43, no. 7, pp. 708714, July 1996.

[14] A. Goulbourne, HF antenna design notes, technical appli-cation report, Texas Instruments, Radio Frequency Iden-tication Systems, Tech. Rep. 11-08-26-003, September2003.

[15] S. Atluri and M. Ghovanloo, Design of a widebandpower-efcient inductive wireless link for implantablebiomedical devices using multiple carriers, in Proceedingsof the 2nd International IEEE EMBS Conference on Neural Engineering , March 2005, pp. 533537.

[16] L. Hannakam, Berechnung der gegeninduktivit at achsen-paralleler zylinderspulen, Archiv f ur Elektrotechnik ,vol. 51, pp. 141154, 1967.

[17] K. S. Yee, Numerical solution of initial boundary valueproblems involving maxwells equations, IEEE Transac-




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tions on Antennas and Propagation , vol. AP-14, no. 3, pp.302307, May 1966.

[18] A. E. Ruehli, Inductance calculations in a complex inte-grated circuit environment, IBM Journal of Research and Development , vol. 16, no. 1, September 1972.

[19] Y. Sun and J. Fidler, Design of impedance matchingnetworks, in Proceedings of the IEEE International Sym- posium on Circuits and Systems (ISCAS) , vol. 5, May 1994,pp. 58.

Christian Reinhold was born in Germanyin 1978. He received the diploma degree inelectrical engineering from the University of Paderborn, Germany in 2005. Since 2006 hehas been pursuing the Ph. D. degree at the Sen-sor Technology Group, University of Pader-born. His current research interests include HFantenna design, energy transmission and neareld coupling.

Peter Scholz was born in Germany in 1980.He received the diploma degree in electricalengineering from the University of Paderborn,Germany in 2006. Since 2006 he has beenpursuing the Ph. D. degree at the Sensor Tech-nology Group, University of Paderborn. His

current research interests include localizationof resonant structures, HF antenna design andwireless energy transmission.

Werner John was born in Osnabrueck, onDecember 13, 1950. He received the Dipl.-Ing. degree from the University of Hanoverin 1980. From 1980 to 1985 he was withthe University of Paderborn (Department of Electrical Engineering) as a researcher en-gaged in electromagnetic eld theory. FromJanuary 1986 to September 1998 he was thehead of the group Physical System Design atcadlab(c-lab (joint venture of the Universityof Paderborn and Siemens Nixdorf Informa-

tionssysteme AG). Since October 1998 he has been the head of theDepartment of Advanced System Engineering at the Fraunhofer In-stitute of Reliability and Microintegration in Berlin/Paderborn. He isresponsible for the development and integration of simulation toolsand design methods for Electro Magnetic Reliability (EMR), EMCanalysis, EMC engineering, RF design, analogue simulation and designenvironments. He has 24 years of experience with the developmentof software (microwave engineering, analogue simulation, EMC anddesign environment). W. John has authored more than 90 publicationsin national and international scientic journals and conferences. Since1888 he served as member and reviewer of the program committeesof EMC Zurich, EMC Compo, EMC Europe, EMC Wroclaw, EMV

Duesseldorf and Smart Systems Integration.

Ulrich Hilleringmann was born in Germanyin 1958. He studied physics from 1978 to 1984at University of Dortmund, Germany. From1984 to 1985 he was with the Fraunhofer Insti-tute of Microelectronic Circuits and Systems,Duisburg, Germany. Afterwards Hilleringmannchanged to the Department of Electrical Engi-neering at University of Dortmund, where hewrote a thesis about Laser Recrystallizationof Silicon in 1988. In 1994 he received thevenia legendi at the same department with

the corresponding thesis Integrated Optics on Silicon. Since 1999he has been Professor at the Institute of Electrical Engineering andInformation Technology, Sensor Technology Department at Universityof Paderborn. His main interests are nanometer scale devices, organicelectronics, microsystem technologies, RFID and wireless sensors.



efficient antenna design of inductive coupled

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