Cole, P.

Ranasinghe, D.

Adelaide Research & Scholarship

   The following paper posted here is not the official IEEE published version. The final published version of this paper can be found in the Proceedings of the IEEE International Workshop on Antenna Technology (2006 : White Plains, New York):pp.164-167      Copyright © 2006 IEEE.   Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE.  Extending Coupling Volume Theory to Analyze Small loop antennas for UHF RFID applications  Peter H. Cole (1), Damith Chinthana Ranasinghe (1)  (1)Auto-ID Labs, University of Adelaide, Adelaide SA 5005, Australia  {cole, damith}@eleceng.adelaide.edu.au  INTRODUCTION A simple illustration of the concept of a Radio Frequency Identification (RFID) system is provided in Fig. 1. Here a transmitter of interrogation signals which is contained within an interrogator communicates via electromagnetic waves with an electronically coded label to elicit from the label a reply signal containing useful data characteristic of the object to which the label is attached. The reply signal is detected by a receiver in the interrogator and made available to a control system. TransmitterReceiverControllerInterrogatorLabel  Fig. 1 Illustration of an RFID system.  There is a wide range of operating principles for such a system [1]. The operating principle and operating frequency are driven principally by the application of the labelling system and the constraints provided by electromagnetic compatibility regulations, environmental noise, and the ability of fields to permeate a scanned region of space or to penetrate intervening materials. Applications are found in reliable and secure data collection, object or personal identification, authentication, anti-counterfeiting, theft detection and the detection of location of the scanned objects.  In a primary category of passive systems the most common operating principle is that of RF backscatter [1] in which a powering signal or communication carrier supplies power or command signals via an HF or UHF link. However the circuits within the label operate at RF or lower, and reply via sidebands generated by modulation, within the label, or part of the powering carrier. This approach combines the benefits of relatively good propagation of signals at HF and UHF and the low power of operation of microcircuits at RF or lower. Powering at UHF is employed when a longer interrogation range (several meters) is required, and HF powering is employed when electromagnetic fields, which exhibit good material penetration and sharp spatial field confinement, are required or sometimes when a very low cost RFID system implementation is desired.  A large portion, approximately 3 – 4 cents, of the label cost is allocated to the antenna manufacture, antenna and IC assembly and packaging in the manufacture of RFID labels. Hence there is a keen interest to produce small antennas to reduce manufacturing costs. This paper presents novel method of analysing the effectiveness of small antennas for UHF RFID labels using coupling volume theory.  The subject of small antennas has been considered in the past in notable publications [2, 3, 4 and 5]. This analysis makes use of both coupling volume theory and radiating antenna theory to analyse small antennas for UHF RFID use. Radiating antenna theory, commonly used in radar calculations, is appropriate in the context in which labels are placed in the far field, and when the label antenna size is large enough for the theoretically available source power from a lossless antenna to be actually extracted, or nearly so, within the constraints imposed by the facts; there is some loss, and complete extraction of the available source power is not possible, the radiation resistance of the antenna is accompanied by a reactance which results in the fact that good transfer of power to an external load can only be accomplished over a limited bandwidth.  Coupling volume theory, first published in [6], is a powerful dimensionless analysis tool with a number of applications presented in [7 and 8] and the theory was devised for situations in which labels are placed in the near field, i.e. energy storage field of a transmitter antenna, and also in the situations in which the radiation resistance of the label antenna is small in relation to the losses in that antenna.  Operation at HF ISM band centred at 13.56 MHz, both of these conditions are normally satisfied. For the situation when labels are placed in the far field of an interrogator antenna, but the labels are so small that their own losses are large in relation to the radiation resistance of the label antenna, it is appropriate to use a hybrid version of radiating antenna theory and coupling volume theory. Radiating antenna theory is used to calculate the energy density at the label position, and coupling volume theory is used to work out what useful power the label antenna can extract from the field.  MEASURES OF EXCITING FIELD In the analysis of the performance of RFID systems it is important to consider whether the labels are placed in the near field (energy storage) or far field (energy propagating) fields of the interrogator antenna. When the antenna is of small gain the boundary between the near and far field is expressed in the more familiar terms of radian sphere of radius r =λ/(2pi), where λ is the frees space electromagnetic wavelength at the operating frequency.  It is possible to develop two measure of field excitation for linearly polarised magnetic field described by a real r.m.s phasor H  as given in (1) and (2). -22  WmH vector Poynting ofcomponent  Radial η=rS  (1) -30 VAm  Hpower  reactive ofdensity  Volume ωµ=vW  (2) Equation (2) is ω times the peak value of stored magnetic energy per unit volume. Hence if β is the propagation constant at the frequency under consideration then volume density reactive power can be expressed as in (3) using Sr which is the radial component of Poynting vector giving the power like quantity for far field radiation. rv SW β=  (3) Equation (3) is a far field expression and there is no near field reactive energy storage field to augment Wv.  SMALL ANTENNAS FOR RFID APPLICATIONS rjXrjX+_VsTransmitter Receiver r ljX+_VsReceiver (a) (b)  Fig. 2 RFID label antenna equivalent with a (a) lossless antenna and (b) accounting for ohmic losses.  Fig. 2(a) shows equivalent circuits for an electrically small antenna, operating at the left in its transmitting role, and at the right in its receiving role.  It shows that in both cases there is a radiation resistance in series with an antenna reactance. The same resistance and reactance is found in both circuits. It has been shown that for ideal lossless and electrically small antennas, which would be enclosed completely by a sphere of radius a,(both electric and magnetic dipole antennas), the radiation quality factor scales as follows [3]. ( ) 13 )( −− += aaQrββ  (4) ( ) Ω= 4220 aRrβpi  (5) While the Qr of a practical antenna will be less than the minimum bound in (4), due to material loses, (4) does show that as the antenna becomes very small, a relatively large and increasing reactance stands between the radiation resistance and any external load to which we might wish to match. When losses are to be taken into account the antenna will also have a loss resistance Rl so its equivalent circuit becomes modified to that shown in Fig. 2(b). The optimum load impedance, previously Rr -  jX, now becomes Rr + Rl - jX, and the power which can be delivered to that load impedance is reduced. When the antenna becomes very small, the radiation resistance of a loop antenna of radius a given by (5) reduces, however Rr << Rl. It is in this situation we have the option of applying coupling volume theory to determine the circuit behaviour. In coupling volume theory, the source voltage in the above antenna circuit might as well be calculated from Faraday’s law, the radiation resistance neglected, the self inductance calculated from the magnetostatic formula, and the loss resistance be determined taking into account that conduction will only occur within a skin depth of the metal surface.  FAR FIELD RELATIONS For calculation of the power Pr coupled in the far field to a label with a lossless receiving antenna the usual approach is to derive the available source power from the label antenna from (6) where Ae and gr are the effective area of the label and gain of the label antenna, while gt is the label antenna gain. rrerrr SgASPpiλ42==  (6) The effective area for the far field is a concept unrelated to either a magnetic flux collection area or a electric flux collection area. It is unrelated to any physical area the antenna may posses, but has it has the desirable property that it is possible to imagine that the label antenna collects all of the radiated power which flows through that effective area which may be thought of as surrounding the label antenna. 22t H4ηpi==rPgS tr Wm-2. (7) Equation (7), where Pt is the power transmitted and r is the distance from the transmitter antenna to the label position assuming that the label has been placed in the direction of strongest radiation from the RFID interrogator (transmitter) antenna defines the power flow per unit defined by the radial component of the Poynting vector. Then Lorenz reciprocity theorem of electrodynamics may be used to show that the effective area of a receiving antenna is related to the gain gr it would have in a transmitting role by the equations piλ42rergA =  (8) 2224 rAArggPP erettrtrλpiλ==  (9) Equation (9) provides the result usually used to evaluate the power extracted by an RFID label in the far field when Rr >> Rl for a label antenna.  ANALYSIS OF A SMALL LOOP Considering a small loop antenna with a radiation resistance Rr and self inductance L with an ohmic resistance Rl, gain gd, excited by the magnetic field of an interrogator antennas has an effective area Ae of .42piλde gA =  (10) and neglecting losses the available source power Pa when the loop is in a field of Poynting vector Sr is given in (11). This is the power which a lossless loop antenna would deliver to a load RL = Rr is identical to that evaluated in (9). rda SgPpiλ42=  (11) However with electrically small antennas where the antenna is small in relations to wave length, it has been shown [9] that Rr << Rl. Hence it is possible to focus attention on Rl neglecting Rr completely. Thus a more useful and meaningful formulation of the power available from such an antenna may be expressed using the coupling volume theory.   The coupling volume Vc of a label antenna can be defined as in (12), while the coupling volume for a planar coil of N turns area A and self inductance L is given by (13)[6].  position labelat  eunit volumper density power  Reactivecircuitshort hen indcutor w label in thepower  Reactive=cV  (12) LANVc220µ= . (13) Using coupling volume theory, which can be apply when Rr is negligible with respect to the losses Rl, it is appropriate, in view of the definition in (12), to calculate the power delivered to the losses Rl without any external load yet having been added. This power Pc is given by  alrc PRRP=4 (14) Substitute for Rr, Pa and Sr from (5), (11) and (7) respectively and using the value 1.5 for gd, provides .2|| 2222lc RAHP βη=  (15) In order to manipulate this into a more familiar form, replace Rl by ωL/Q where Q is the quality factor of the antenna inductor and ηβ by ωµ0 and obtain .2)||( 2020 QLAHPc=µωµ (16) Equation (16) can be expressed using (3) and (13) into the more familiar form in (17).  cvc VQWP =  (17) Equation (17) is the standard form of the result from coupling volume theory for coils coupling to the magnetic field [6]. Thus the effective area and coupling volume formulations of loop antenna behaviour are entirely equivalent however coupling volume theory formulation emphasises the internal antenna loses of the label antenna to provide a more meaningful result for the power available from a small loop antenna in the far field.   AVAILABLE POWER FROM A SMALL LOOP When an optimum load resistor RL = Rc is added to a small loop, the power which can be delivered to that load is one quarter of that given by (15) , if Q is interpreted as defined by the loop losses and its inductance. If however redefining Q to be the new and lowered Q, determined by the sum of the loop losses and the damping of the external load, then the power that can bed delivered to a matched load is half that given by (15).  CONCLUSIONS Poynting vector-effective area foliation ad the coupling volume formulations are apparently dissimilar, however they are both equivalent and useful in different contexts. The difference between the formulations is whether they emphasise the radiation resistance or the internal losses of the label antenna.   REFERENCES [1] P. H. Cole, D. M. Hall, M. Loukine, and C. D. Werner, “Fundamental constraints on RF tagging systems”, Proceedings of the fourth annual wireless symposium and exhibition, Santa Clara, pp. 294-303, February 1995. [2] H. A. Wheeler, “Small Antennas”, IEEE Trans. Antennas and Propagat., vol. AP-23, July 1975, pp. 462-469. [3] H. A. Wheeler, “Fundamental Limitations of Small Antennas”, Proc. IRE, vol. 35, Dec. 1947, pp. 1479-1484. [4] J. S. McLean, “A Re-Examination of the Fundamental Limits on the Radiation Q of Electrically Small Antennas”, IEEE Trans. Antennas Propagat., vol. 44, no. 5, May 1996, pp.672-676. [5] L. J. Chu, “Physical Limitations of Omni-Directional Antennas”, J. Appl. Phys., vol. 19, 1948, pp. 1163-11175. [6] K. Eshraghian, P. H. Cole, and A. K. Roy, “Electromagnetic coupling in subharmonic transponders,” Journal of Electrical and Electronics Engineering, No. 2, pp. 28–35, 1982. [7] P. H. Cole, D. C. Ranasinghe and B. Jamali, “Coupling relations in RFID systems II: practical performance measurements”, Auto-ID Center workshop, Sept. 2003. [8] P. H. Cole, “Coupling and Quality Factors in RFID”, Proc. of SPIE Design, Characterisation and Packaging for MEMS and Microelectronics, vol. 4593, 2001, pp. 1-11. [9] C. A. Balanis, Antenna theory: analysis and design, John Wiley and Sons, New York, 1996. 

Extending coupling volume theory to analyse small loop antennas for UHF RFID applications

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Extending coupling volume theory to analyse small loop antennas for UHF RFID applications

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