UNTIL recently, power consumption has been almost last

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1 IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS I: REGULAR PAPERS, VOL. 51, NO. 7, JULY Optimal Transmission Frequency for Ultralow-Power Short-Range Radio Links David C. Yates, Student Member, IEEE, Andrew S. Holmes, Member, IEEE, and Alison J. Burdett, Senior Member, IEEE Abstract Analysis determining the optimal transmission frequency for maximum power transfer across a short-range wireless link is introduced, including a comparison of near-field transmission with far-field transmission. A new near-field power transfer formula has been derived, which allows direct comparison with the well-known far-field Friis transmission formula. Operating charts are presented, which provide the designer with the preferred transmission frequency as a function of distance and antenna dimensions, together with surface plots which show the power transfer for this frequency. The analysis, performed for loop antennas, has been used to evaluate the oscillator transmitter as a low-power topology. It is shown that the requirement of a high-q factor to realize a low-power oscillator need not be contradictory to achieving optimal far-field radiation characteristics. Based on this fact an approach to sizing loop antennas for low-power oscillator transmitters is suggested. Index Terms Antennas, far-field, near-field, oscillator transmitters, ubiquitous computing, ultralow power, wireless communications. I. INTRODUCTION UNTIL recently, power consumption has been almost last on the list of specifications for designers of wireless communications systems. Instead, designers have been preoccupied with factors such as data rate, reliability, and spectral efficiency. However, the explosion in the development and popularity of portable devices such as cellular phones, laptops and personal digital assistants (PDAs), has led to a general increase in the demand for low-power circuits and systems. One important emerging application area for lightweight portable technologies is ubiquitous computing. The ubiquitous computing paradigm envisages devices being embedded in everyday objects, and also being worn or carried by (and possibly even implanted in) users. The devices concerned are capable of forming ad hoc networks, and exist to gather, process and route data. Typical applications may range from office environment control [1] to human health monitoring [2]. Central to this vision is the apparent invisibility of many of these devices to the user, who is aware of, but not inconvenienced by their presence. This places stringent limits on de- Manuscript received May 21, 2001; revised November 29, This work was supported by the U.K. Engineering and Physical Sciences Research Council and by the European Commission. This paper was recommended by Associate Editor D. Czarkowski. D. C. Yates and A. S. Holmes are with the Department of Electrical and Electronic Engineering, Imperial College London, London SW7 2BT, U.K. ( david.yates@imperial.ac.uk; a.holmes@imperial.ac.uk). A. J. Burdett is with Toumaz Technology Ltd., Oxfordshire OX14 3DB, U.K. ( alison.burdett@toumaz.com). Digital Object Identifier /TCSI vice size, weight and power consumption. To achieve a lifetime measured in years, devices powered from small coin cells must consume no more than a few microwatts. Similar restrictions apply to small self-powered devices that scavenge energy from their surroundings [3]. One of the major barriers in realising hardware for ubiquitous computing is the absence of ultralow-power wireless transceivers that can operate at microwatt power levels. Typical off-the-shelf low-power transceivers, when operated at a sufficiently low duty cycle to achieve this power consumption, achieve data rates of only tens of bits per second [4] [6]. The same is true of devices presented in the academic literature [7] [10]. A. Achieving Ultralow-Power Operation Much of the research into low-power transceiver design has been subject to additional constraints, such as low voltage operation, a high level of integration and use of standard CMOS processes. These are not necessarily conducive to low-power operation [11], [12]. Furthermore, conventional high performance transceiver topologies have been used. However, short-range communication does not require the high performance circuits needed for longer range systems. Simpler transceiver topologies such as the oscillator transmitter [13] or the super-regenerative receiver [14] allow performance to be traded with power consumption. In order to achieve ultralow-power operation, power must become the main design criterion, and the relevant tradeoffs must be identified and investigated. This paper sheds some light on one such tradeoff. To achieve optimal far-field radiation characteristics antennas generally have to be some proportion of the wavelength. For size-constrained devices, this suggests that high frequencies should be used. However, the power dissipation in the RF processing electronics will increase with frequency. As a first step to solving this problem, we have determined the optimal frequency for particular antenna dimensions in terms of maximizing the power transfer from the transmitting antenna input to the receiver load. This minimizes the required power input to the transmitting antenna for successful demodulation at the receiver. B. Importance of the Loop Antenna The analysis presented in this paper has been performed for the loop antenna, since it is particularly suited to ubiquitous computing applications. The relatively nondirectional nature of loop antennas and monopole antennas makes them ideal for use in adhoc mobile wireless networks. The loop antenna has the /04$ IEEE

2 1406 IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS I: REGULAR PAPERS, VOL. 51, NO. 7, JULY 2004 advantage of being electrically larger in a given volume than a monopole or dipole antenna, resulting in greater radiation efficiency. Furthermore, the loop antenna is used in all systems where wireless power delivery is required, such as the powering of biomedical implants [15] and radio-frequency identification (RFID) [16]. The ability to receive wireless power may well prove essential for true autonomy in many ubiquitous computing systems. The charging of batteries or the providing of initial power for the energy scavenging electronics are two strong reasons for requiring this facility. As an example, an electrostatic vibration-to-electrical energy converter requires an initial charge [3]. If this charge is dissipated, then, the device will cease to generate. A fourth advantage of the loop antenna is that it can be used in simple low-power short-range transmitters such as those presented in [13] and [17]. These oscillator transmitters use the inductance of the loop antenna in the oscillator resonant tank to define the transmission frequency. In this way the oscillator also becomes the output stage. This is acceptable for short-range transmission where no power amplifier is required. II. ANTENNA FIELD REGIONS The electromagnetic field surrounding a transmitting antenna can be divided into two separate regions the reactive nearfield and the radiating field. Energy is stored in the former, while energy propagates as electromagnetic waves in the latter [18]. The boundary between the two regions is generally accepted to be at a distance,, from the antenna, where being the wavelength [16]. For an electrically large antenna, a further distinction becomes significant. The radiating field can be split into two regions the radiating near-field and the radiating far-field. The commonly used distance to the boundary between the radiating near-field and the radiating far-field is where is the largest dimension of the antenna. In the following section, we review methods for calculating power transfer in the far-field and derive an equivalent analysis for the reactive near-field. III. MODELING POWER TRANSFER A certain amount of signal power must be received for accurate demodulation to take place in the presence of noise and interference. The mathematical relationships governing the power transfer from transmitter to receiver differ substantially depending upon whether the receiver lies in the near-field or the far-field. The aim of the analysis presented here is to determine the optimal frequency in terms of power transfer for a certain transmission distance, given particular constraints on the maximum allowable antenna dimensions. (1) (2) Fig. 1. Equivalent circuit model of multiturn loop antenna using lumped parameters. Fig. 2. Basic method of driving loop antenna [18]. A. Modeling the Loop Antenna A coil or loop can be modeled with lumped components as shown in Fig. 1 [18]. Here, is the radiation resistance, which represents the power radiated as electromagnetic waves in the far-field. is the real part of the internal impedance of the conductor, L is the inductance and is the parasitic inter-turn capacitance. For a single turn loop can be modeled using standard theory [19], [20]. The multiturn loop presents a more complex problem, which was solved for the electrically small case by Butterworth, whose analysis is summarized in [21]. Alternatively [22] claims to present a more accurate method but does not cover as wide a range of coil dimensions. The radiation resistance of an electrically small -turn coil of radius,, is given by [23] where and is the impedance of free space. The radiation resistance of an electrically large coil is a much more complex matter because a uniform current distribution can no longer be assumed. The most common analytic approach has been to assume a certain current distribution (see [24] [28] for further details). However, these methods tend to lack accuracy unless the antenna is driven in a particular manner, such as coupling to a transmission line as described in [26] and [29]. If the antenna is driven in the natural manner depicted in Fig. 2, then, modern well-referenced texts such as [18] and [23] agree that the best approach to evaluating the antenna parameters is the method described in [30]. Instead of assuming a particular current distribution the electromagnetic problem is solved rigorously for a single-turn loop of thin wire. This approach results in the current being represented as a fourier series, from which the antenna impedance can be easily evaluated. The method has been shown to agree very well with experiment [18]. The and components of the electric field are readily obtainable from the fourier components of the current distribution [31]: (3) (4)

3 YATES et al.: OPTIMAL TRANSMISSION FREQUENCY FOR ULTRALOW-POWER SHORT-RANGE RADIO LINKS 1407 Fig. 3. system. Geometry of the circular loop antenna using the spherical coordinate (5) where are the Fourier coefficients. The spherical coordinate geometry used is shown in Fig. 3. The radiation intensity (measured in ) can be calculated from the electric field using [23] Fig. 4. Maximum directivity versus circumference to wavelength ratio (for wire radius equal to one twentieth of the coil radius). (6) The power radiated is then given by (7) where is the solid angle element, which is equal to. The radiation resistance is, by definition, given by (8) The directivity is another important far-field parameter, which is needed to evaluate the power transfer. The maximum directivity, i.e., the directivity in the direction of maximum radiation intensity, is given by The maximum directivity and radiation resistance for the loop antenna are shown as a function of electrical size in Figs. 4 and 5 respectively. These graphs were derived numerically by evaluating the electric field at points around the antenna using (4) and (5), and then applying (6), (7), (8) and (9). The directivity and radiation resistance are functions only of the electrical size and the loop radius to wire radius ratio, which in this case was taken to be 20. Graphs similar to Figs. 4 and 5 have been published previously [18], [23], [32], but not covering the range of circumference to wavelength ratios required for our analysis. Furthermore, the maximum directivity is not normally plotted. B. Modeling Far-Field Transmission The receivers in most wireless transmission systems will lie in the radiating far-field either because of the large distance in- (9) Fig. 5. Radiation resistance versus circumference to wavelength ratio (for wire radius equal to one twentieth of the coil radius). volved such as for typical AM radio broadcasting or because of the high frequencies involved such as for Bluetooth. In this case, the power transfer from the input to the transmitting antenna to the receiver load is given by the well-known Friis formula dealt with in standard antenna texts such as [18], [23] (10) where represents the directivity, is the wavelength, is the distance between the transmitting and receiving antennas. The subscripts TX and RX denote transmitter and receiver parameters, respectively. is a factor taking into account misalignment of the antennas. The radiation efficiency describes the fraction of antenna input power radiated in the far-field (11)

4 1408 IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS I: REGULAR PAPERS, VOL. 51, NO. 7, JULY 2004 Fig. 6. Near-field transmission equivalent model. C. Modeling Near-Field Transmission Fig. 6 shows the equivalent circuit for modeling near field transmission [16], [33]. In this circuit, the transmitter and receiver radiation resistances are represented by and, respectively, while the loss resistances are represented by and. The total coil resistances have been combined as follows: Fig. 7. Mutual inductance versus coil radius and number of turns. The nodal equations can be obtained from the equivalent circuit using Kirchhoff s laws (12) (13) From these equations, the current and voltage gains can be easily evaluated. The power transferred from the input to the antenna to the receiver load can then be determined. In order to increase the power transfer near-field transmission systems, such as those used in RFID devices and for implanted medical devices, use one of the four possible combinations of series or parallel tuned resonant coils in the transmitter and receiver [15], [16]. Analysing these topologies using the standard nodal equations is tedious and does not facilitate intuitive insight. Fortunately, the analysis can be simplified for the kinds of applications we are considering, because the mutual inductance (see Fig. 7) will always be small. A general equivalent circuit for a poorly coupled system is given in Fig. 8. It should be noted that this equivalent circuit could equally well represent any one of the four tuned resonant coil topologies. Using this equivalent circuit we can derive a formula expressing the power transfer from transmitter to receiver, allowing direct comparison with the far-field Friis transmission formula. On the transmit side, we assume is chosen to resonate with the antenna inductance,, enabling the maximum current flow, i.e., where (14) The real input power under these conditions is given by (15) Fig. 8. Near-field transmission equivalent model assuming poor coupling. The resulting magnetic field at the receiver antenna can be obtained using the Biot Savart law [16], [33] (16) where is the transmission distance and the transmitting antenna is a coil of turns and radius. The antennas are assumed to be aligned on a common central axis. By Faraday s law, the induced voltage at the receiver antenna is given by the rate of change of flux linkage (17) where is the number of turns, is the loop area, and is the permeability of free space. Equation (17) is valid only if the flux linking with the coil is uniform, which implies that the distance of separation between the transmitter and receiver must be much larger than the loop dimensions. This condition must also be met to ensure poor coupling. Combining (16) and (17), the induced voltage at the receiver can be expressed in terms of the transmitter current (18)

5 YATES et al.: OPTIMAL TRANSMISSION FREQUENCY FOR ULTRALOW-POWER SHORT-RANGE RADIO LINKS 1409 Fig. 9. Variation of near-field power transfer with frequency and the number of turns for a transmission distance of 0.5 m, a coil radius of 1 cm and a wire radius of 0.1 mm with 0.1 mm spacing between turns. Fig. 10. Variation of near-field power transfer with frequency and coil radius for a transmission distance of 1 m, a 4-turn coil and a wire radius of 0.1 mm with 0.1 mm spacing between turns. For poor coupling, the load impedance should be conjugately matched to the receiver antenna impedance to achieve maximum power transfer [34] (19) In this case, the power delivered to the receiver load is the available power, which is given by (20) Using (15), the power transfer ratio can now be expressed as Adding an antenna misalignment factor results in the following: and assuming (21) (22) where has been replaced by. Figs. 9 and 10 plot the variation of near-field power transfer with coil dimensions and frequency as predicted by (22). The resistive and radiative losses were modeled in the manner explained in Section III-A. The conductor is assumed to be copper wire, which has a conductivity of about S/m at room temperature. The wireless link is peer-to-peer, i.e., the transmitting and receiving antennas are identical. This will often be true for ubiquitous computing applications where many similar if not identical devices will be used to route and sense data. Figs. 9 and 10 show that the power transfer increases with the number of turns, the coil radius and the frequency. Both the numerator and denominator of (22) increase with these factors, but the numerator does so more quickly and hence determines the overall trend in power transfer. Fig. 11. Operating chart informing designer of preferred transmission frequency depending on antenna dimensions and transmission distance for a maximum wire radius of 2 mm. IV. OPTIMAL TRANSMISSION FREQUENCY This section presents two operating charts (Figs. 11 and 13), which indicate how the preferred transmission frequency, chosen from a selection of standard frequency bands, varies with the transmission distance and loop radius for a single-turn loop antenna. Copper wire and peer-to-peer communication are again assumed. Surface plots (Figs. 12 and 14) are also presented, showing the power transfer for the preferred frequency as a function of the same variables. The frequencies compared are the ISM bands of 40, 433, 900 MHz, and 2.4 GHz and also the mobile phone band of 1.8 GHz. Two sets of graphs are presented because the power transfer characteristics are also heavily dependent upon wire thickness. In general the wire radius is assumed to be a twentieth of the loop radius. However, a large loop radius may well be acceptable whereas a large conductor radius may not. For instance, large radius loop antennas can be unobtrusively embedded into clothes or paper as long as the conductor is sufficiently thin and flexible. This suggests that for a particular application there will also be a

6 1410 IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS I: REGULAR PAPERS, VOL. 51, NO. 7, JULY 2004 Fig. 12. Surface plot shows the power transfer for the preferred transmission frequency depending on antenna dimensions and transmission distance for a maximum wire radius of 2 mm. Fig. 14. Surface plot shows the power transfer for the preferred transmission frequency depending on antenna dimensions and transmission distance for a maximum wire radius of 0.5 mm. Fig. 13. Operating chart informing designer of preferred transmission frequency depending on antenna dimensions and transmission distance for a maximum wire radius of 0.5 mm. Fig. 15. radius. Optimum far-field frequency for maximum power transfer versus coil maximum allowable wire thickness. Therefore, two charts have been presented, one with a maximum wire radius of 2 mm, the other with a maximum radius of 0.5 mm. The frequencies represented in Figs are It was shown in Section III-C that near-field power transfer increases with frequency. 40 MHz was chosen as the near-field frequency to be used in this comparison since it is the highest ISM frequency for which suitable transmission distances are still in the near-field. Near-field transmission is shown to be preferable for large loop radii and short distances. The nearfield is superior at short distances but far-field power transfer quickly becomes preferable as distance increases since the en- ergy stored in the near-field decays with whereas the power transfer available at far-field frequencies decreases with [see (10) and (22)]. The region in which near-field transmission is superior is significantly decreased when the wire radius is limited to 0.5 mm, because the advantage of lower series loss resistance (due to operating at a lower frequency) is reduced for thinner wire. In the region where the far-field frequencies are dominant the preferred far-field frequency decreases with increasing loop radius. The boundary between preferred frequencies is determined by the crossover point of two frequency dependent factors. The radiation efficiency decreases as the electrical size of the antenna decreases but the far-field power transfer is inversely proportional to frequency squared. Figs. 12 and 14 demonstrate superior power transfer for larger antenna dimensions, which is explained by the same two factors. A. Far Field The power transfer has been evaluated for 40 discrete values of antenna radius, scaled logarithmically between 3 mm and 7

7 YATES et al.: OPTIMAL TRANSMISSION FREQUENCY FOR ULTRALOW-POWER SHORT-RANGE RADIO LINKS 1411 Fig. 16. Power transfer for optimum far-field frequency over a distance of 1 m. Fig. 18. Radiation efficiency versus electrical size for a loop antenna of radius 5 mm and a conductor radius equal to one twentieth of the loop radius. Fig. 17. Optimum circumference to wavelength ratio (in terms of maximum power transfer) versus coil radius. cm, using the Friis formula combined with the directivity and radiation efficiency analysis presented earlier. For each of these antenna radii, the power transfer was calculated for 70 logarithmically scaled discrete far-field frequencies between 100 MHz and 5 GHz, from which the optimal far-field transmission frequency for a particular loop radius has been determined. Figs. 15 and 16 show this optimal frequency and the power transfer over a distance of 1 m for this optimal frequency. To a first approximation, the optimal frequency is inversely proportional to the coil size, and corresponds to a circumference to wavelength ratio of approximately 0.2, as shown in Fig. 17. The oscillations in this graph at larger radius values are due to the finite resolution of the numerical calculations. The relationship between optimal frequency and coil size can be understood by viewing the radiation efficiency and directivity graphs (Figs. 18 and 4) in conjunction with the Friis equation (10). From the Friis equation, it can be seen that the power received for a particular transmit power decreases with frequency squared (if all else remains constant). If the loop radius is held constant increasing frequency will improve the radiation efficiency as shown in Fig. 18. The directivity will alter little until Fig. 19. Low-power colpitts oscillator transmitter presented in [13]. the circumference to wavelength ratio becomes 0.5. The optimal frequency occurs at the point where any further increase in the radiation efficiency would not overcome the frequency squared term in the denominator. It should be noted that the optimal circumference to wavelength ratio is relevant only for a fixed antenna radius. If the constraint is instead fixed frequency then the antenna radius can be increased to give larger radiation efficiency and larger directivity as desired in order to improve the power transfer. V. OSCILLATOR TRANSMITTER Since current conventional transceivers do not achieve the low-power operation needed for ubiquitous computing, we have considered oscillator transmitters such as that presented in [13] and shown in Fig. 19. The device presented in [13] achieves a range of 3 feet, a data rate of 1 Mb/s while dissipating only 300. For any resonant oscillator, incresing the Q of the tank components will lower the power required to achieve oscillation. In the case of an oscillator transmitter, increasing the Q will also reduce bandwidth of the transmitted signal. This will reduce the

8 1412 IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS I: REGULAR PAPERS, VOL. 51, NO. 7, JULY 2004 Fig. 20. Q-factor of a single-turn loop antenna against electrical size. noise power within the signal band at the receiver, allowing improved receiver sensitivity. For these reasons, it is generally desirable to maximize the Q of the tank components, including the antenna. Fig. 20 shows the variation in Q-factor with electrical size for a single turn loop antenna. This was derived using the impedance calculated in Section III-A and hence does not take into account eddy-current losses in surrounding objects. Comparison of this figure with Fig. 17 clearly shows that the loop antenna can have both optimal far-field transmission characteristics and a high Q-factor. It can be seen that the optimal circumference to wavelength ratio for a loop antenna of radius 5 mm is about and this corresponds to a Q-factor of about 300. This is a very important result because it means that the requirements of efficient power transfer and high Q-factor can be achieved simultaneously. The designer of a wireless transceiver for ubiquitous computing will generally be able to choose between the ISM bands, which are at approximately 13, 40, 434, 900 MHz, and 2.4 and 5 GHz. The likelihood that the optimal frequency given by Fig. 15 will lie precisely in one of the ISM bands for a given maximum loop radius is minimal. Choosing a frequency above the optimal will lead to a poor Q-factor. Choosing one below will lead to a poor radiation efficiency. If the constraint is antenna size, the only option the designer has in order to achieve a high Q-factor is to choose the ISM band above the optimal frequency and decrease the antenna size. However, reducing the loop radius will decrease the power transfer because the radiation efficiency will decrease as shown in Fig. 18. The designer must evaluate whether the reduction in the signal-to-noise ratio (SNR) due to the degradation in power transfer is compensated by the increase in antenna Q-factor. This will depend on whether the total Q-factor of the oscillator is dominated by the antenna Q-factor. VI. DISCUSSION We have presented a method of determining the optimal transmission frequency in terms of maximum power transfer across a wireless link for different antenna dimensions. This is the first time a comparison between near-field and far-field transmission has been presented. This comparison has been facilitated by the derivation of a near-field power transfer formula equivalent to the far-field Friis equation. The analysis is important for ubiquitous computing where devices will be size constrained and power is crucial. The optimal/preferred frequencies have been illustrated for the particular case of peer-to-peer communications, where the transmitter and receiver antennas are assumed to be identical. The analysis presented is, however, not limited to this case and can be used to evaluate the optimal transmission frequency for the case where the transmitter and receiver have a different size limitation. We have shown that the optimal frequency for far-field transmission corresponds to an antenna circumference of about 0.2 wavelengths for peer-to-peer communication. It has also been demonstrated that a single-turn loop has a high Q-factor for this electrical size. We can therefore conclude that the requirements of efficient power transfer and minimum noise can be achieved simultaneously. The choice of transmission frequency will affect the power dissipated in the transceiver RF electronics. The analysis and results presented in this paper do not take this into account. 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9 YATES et al.: OPTIMAL TRANSMISSION FREQUENCY FOR ULTRALOW-POWER SHORT-RANGE RADIO LINKS 1413 [14] P. Favre, N. Joehl, A. Vouilloz, P. Deval, C. Dehollain, and M. Declercq, A 2 V 600 A 1 GHz BiCMOS super-regenerative receiver for ISM applications, IEEE J. Solid-State Circuits, vol. 33, pp , Dec [15] D. C. Galbraith, M. Soma, and R. L. White, A wide-band efficient inductive transdermal power and data link with coupling insensitive gain, IEEE Trans. Biomed. Eng., vol. BME-34, pp , Apr [16] K. Finkenzeller, RFID Handbook. Chichester, U.K.: Wiley, Apr [17] M. Suster, D. J. Young, and W. H. Ko, Micro-power wireless transmitter for high-temperature MEMS sensing and communication applications, in Proc. IEEE 15th Int. Conf. Microelectromechanical Systems, 2002, pp [18] R. C. Johnson, Antenna Engineering Handbook, 3rd ed. New York: McGraw-Hill, [19] S. Ramo, J. R. Whinnery, and T. Van Duzer, Fields and Waves in Communication Electronics, 3rd ed. New York: Wiley, [20] G. S. Smith, Radiation efficiency of electrically small loop antennas, IEEE Trans. Antennas Propagat., vol. AP-20, pp , Sept [21] F. E. Terman, Radio Engineers Handbook. New York: McGraw-Hill, [22] G. S. Smith, Proximity effect in systems of parallel conductors, J. Appl. Phys., vol. 43, no. 5, pp , [23] C. A. Balanis, Antenna Theory, Analysis and Design, 2nd ed. New York: Wiley, [24] J. E. Lindsay Jr., A circular loop antenna with nonuniform current distributions, IRE Trans. Antennas Propogat., vol. AP-8, pp , July [25] A. Richscheid, Calculation of the radiation resistance of loop antennas with sinusoidal current distribution, IEEE Trans. Antennas Propogat., vol. AP-24, pp , Nov [26] S. A. Adekola, On the excitation of a circular loop antenna by travelling- and standing-wave current distributions, Int. J. Electron., vol. 54, no. 6, pp , [27] V. L. Takelar and K. R. Soni, Radiation characteristics of a travelling-wave multi-turn circular loop antenna in compressible electron plasma, Int. J. Electron., vol. 36, no. 5, pp , [28] S. Adachi, T. Kasahara, and Y. Mushiake, A loop antenna in a compressible plasma, IEEE Trans. Antennas Propagat., vol. AP-17, pp , May [29] K.-M. Chen and R. W. P. King, A loop antenna coupled to a four-wire line, Proc. Inst. Elect. Eng., C, vol. 109, pp , [30] R. W. P. King and G. S. Smith, Antennas in Matter: Fundamentals, Theory and Applications. Cambridge, MA: MIT Press, [31] D. H. Werner, An exact integration procedure for vector potentials of thin circular loop antennas, IEEE Trans. Antennas Propagat., vol. 44, pp , Feb [32] J. E. Storer, Impedance of thin-wire loop antennas, Trans. AIEE, vol. 75, pp , [33] G. Lancaster, Introduction to Fields and Circuits. New York: Oxford Univ. Press, [34] G. Vandevoorde and R. Puers, Wireless energy transfer for stand-alone systems: a comparison between low and high power applicability, Sensors Actuators, vol. A92, pp , David C. Yates (S 02) received the M.Eng. degree in electrical and electronic engineering from Imperial College London, London, U.K., in He is currently pursuing the Ph.D. degree in circuits and systems at the same institution. His research topic is ultralow-power short-range wireless links. Andrew S. Holmes (M 02) received the B.A. degree in natural sciences from Cambridge University, Cambridge, U.K. in 1987, and the Ph.D. degree in electrical engineering from Imperial College London, London, U.K. in He is currently a Senior Lecturer in the Optical and Semiconductor Devices Group, Department of Electrical and Electronic Engineering, Imperial College London. His current research interests lie mainly in the areas of micropower generation and conversion, and laser-based processes for fabrication and assembly of microelectromechanical systems (MEMS). Alison J. Burdett (S 90 M 95 SM 00) received the B.Eng. degree and the Ph.D. degree from Imperial College of Science, Technology, and Medicine, London, U.K., in 1989 and 1992, respectively. From 1992 to 1994, she was a Design Engineer for GEC-Plessey Semiconductors, Swindon, U.K. In 1994, she joined the Department of Electrical and Electronic Engineering, Imperial College London, London, U.K., as a Senior Lecturer in Analogue Circuit Design. In 2001, she joined the start-up Toumaz Technology Ltd, Oxfordshire, U.K., a spin-out company from Imperial College involved in low-power and RF integrated circuit design, where she is currently a Director of Technology. Dr. Burdett is a Chartered Engineer, a member of the Institute of Electrical Engineers (IEE). She has served on the Technical Review Committee for IEEE International Symposium on Circuits and Systems (ISCAS) from 1999 to 2002, and was Technical Co-Chair for ISCAS She served as Corresponding Editor of the IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS II: EXPRESS BRIEFS from 1999 to 2001, and is a member of the IEEE Circuits and Systems Society Analog Signal Processing Technical Committee (for which she was Chairman ).