Antenna Impedance Matching for Maximum Power Transfer in Wireless Sensor Networks Trevor S. Bird, Nicholas Rypkema, and Ken W. Smart CSIRO ICT Centre Epping, Sydney NSW 1710, Australia
[email protected] Abstract— The conditions for maximum power transfer from a source antenna to a receiving antenna are examined when the two antennas are in close proximity. As an example, computed and measured results are described for the power transfer efficiency for two-element Yagi antennas. These results can be used to design matching networks between the antenna and a load such as a voltage multiplier for power transfer in a wireless sensor network. It is concluded that maximum PTE could be obtained by continuously tuning the antenna and matching network as the antenna separation and load conditions change.
I.
INTRODUCTION
The wireless devices currently being designed and built to be used as nodes in sensor networks typically run on batteries, which results in a limited lifespan or operating time for these devices. As the number of nodes in a wireless sensor network increase, the cost in time and money to replace depleted batteries escalates. A variety of methods exist for recharging the sensor nodes [1]. Solar and wind energy are the most common methods. However, there are circumstances where such methods are not feasible, for example in closed environments or under tree canopy.
Power Power Source Source
Antennas Antennas
Matching Matching Network Network
Rectifier/ Rectifier/ Voltage Voltage Multiplier Multiplier
Power Power ManageManagement ment
Load Load
Figure 1: Model of wireless power transfer system.
A schematic of a typical wireless power transfer system is shown in Fig. 1. It is assumed here that RF power is available at the transmitting antenna and the main problem to be solved is at the nodes i.e. the receivers. The antennas transfer RF power from the transmitter to a receiving antenna, where the signal is rectified by the rectifier/voltage multiplier circuit to provide power to the load. A matching network may be required to reduce any loss of power due to impedance
978-1-4244-5335-1/09/$26.00 ©2009 IEEE
mismatch between the receiving antenna and the rest of the system. The power management circuit determines how power is best applied to the load; this will depend on the requirements of the entire system as well as characteristics of the load. The implementation of a wireless power transfer system depicted in Fig. 1 depends on the application. For instance, the differences between a system for RFID and sensors are the power source, frequency, range, scale and channel usage. Some power transmission systems for sensor networks are described in [1]-[4]. This paper focuses mainly on the antennas, and to a lesser extent on the rectifier/voltage multiplier and impedance matching circuit to maximize the power transfer for a sensor network. Other aspects of Fig. 1 are considered including tunable RF components, the voltage multiplier and the power source. Some possible approaches are suggested. II.
THEORY
In recent power transfer system design for applications such as RFID [5]-[6], various forms of the Friis transmission equation are used to calculate the power transfer efficiency (PTE) (the ratio of the power received by the receiving antenna to the power input into the transmitting antenna) of the antenna system. However, the Friis equation is valid only for antennas in the far field [7]. In applications requiring storage recharging, it is advantageous to be in the near field. The system shown in Fig. 1 can be represented by a cascade of two-port networks. The transmitting and receiving antennas can be approximated by the Z-parameters of the two input ports, which will consist of contributions from any parasitic elements. Neglecting the rest of the system in Fig. 1 and concentrating only on the antenna block, the PTE is given by
PTE =
Pout Re{Z load } Z 21 = Pin Re{Z in } Z 22 + Z load
2
(1)
where Z 21 is the mutual impedance, Z 22 is the input impedance of antenna 2 when antenna 1 is open circuited and
916
IEEE SENSORS 2009 Conference
Z load is the load impedance at antenna 2 and Z in is the input impedance of antenna 1 (the transmitting antenna at port 1) and is given by
Z in = Z 11 −
(1)
Z 12 Z 21 ( Z 22 + Z load )
.
(2)
For a given antenna configuration, the maximum value of is given when ∂ PTE / ∂ Re{Z load } = 0 and
∂ PTE / ∂ Im{Z load } = 0 , from which the optimum load impedance can be shown to be +
2
2
D ≈ − X 12 X 21 / R11 R 22 and A ≈
PTE max ≈ 1 . This corresponds to the situation described by Kurs et al. [8] for power transfer in the 1 to 50MHz range. At ranges between the near and far zones, the maximum PTE is given by (5). This equation suggests the possibility that to maintain maximum PTE the matching of the receiving antenna should be tuned as the antenna separation changes. This could be achieved by tuning the antenna and the matching network.
2
(3)
d1
where Z in = Rin + jX in and R12 = Re{Z 12 } etc. The elements of the Z-matrix depend on the antenna separation distance. At large separations (here denoted by s as shown in Fig. 2), (3) simplifies to
source
[
2
R11 R22 (1 + A) + C
2
]
A B
load reflector
reflector #3
The maximum PTE is found by substituting (3) into (1). The result is
PTE max =
x s
the usual condition for conjugate matching.
2
d2
~
(4)
Z 21
Antenna 2
z
X load = − X 22 + ( R12 X 21 + R21 X 12 ) / 2 R11
Z load ≈
l3
Antenna 1
Rload = R22 − R22 ( R12 R21 − X 12 X 21 ) R11 − ( R12 X 21 + R21 X 12 ) ( 4 R11 )
* Z 22
D ≈ B , resulting in
(5)
#1
#2
#4
Element No.
3
1
2
4
Element length
L3
L1
L2
L4
Figure 2: Parallel two-element Yagi antennas.
where
A = 1− D − C2
1.0
2
B =1 +
(2C − AD) (1 + A) 2 + C 2
[
]
0.9
( R X + R21 X 12 ) C = 12 21 2 R11 R22
2
4 R11 R22
Zload=87-40j (4nec2) Zload=73 (4nec2) Zload=10 (4nec2)
0.5 0.4
Clearly, as the distance between the antennas increases, C , D → 0 so that A, B → 1 . This reduces to the Friis result at large separations
Z 21
Zload=10(EMF)
0.6
( R12 R21 − X 12 X 21 ) R11 R22
PTE max →
Zload=73 (EMF)
0.7
PTE
D=
Zload=87-40j (EMF)
0.8
0.3 0.2 0.1 0.0 0.00
(6)
0.10
0.20
0.30
0.40
0.50
0.60
0.70
Separation (s) λ
Of considerable interest is when the antennas are close or moderately so. At small spacing, the maximum PTE depends on the antenna coupling characteristics. One possible case is if X 12 , X 21 >> R12 , R21 , corresponding to capacitive or inductive near-field coupling. Under these conditions,
917
Figure 3: PTE for two 0.5λ 2-element Yagi antennas, with 0.25λ reflector spacings for various load impedances. Comparison between induced EMF and 4nec2 models.
III.
RESULTS
To illustrate (1), we considered a pair of two-element Yagi antennas as shown in Fig. 2. Two identical single dipoles give a maximum PTE of 50%. By including the reflecting elements, the Yagi antennas are more directive and the input impedance of the receiver can be tuned by modifying the spacing d2. The same tuning effect could be obtained by fixing the element spacing and centre-loading the reflecting element with a variable reactance. The antennas can be modeled as a two-port network using standard electromagnetic codes. In this work, the Z-matrix was evaluated using two methods; the simple induced EMF method [7] and also with the 4nec2 code [9]. The former method is quite accurate for element lengths close to half wavelength.
load impedance on the load is approximately 73-40iΩ. We see that there is good agreement between theory and experiment. IV.
DISCUSSION
The antennas considered in Sec. III were of a very simple type. More compact and efficient varieties are possible. Also, tunable antennas are of interest. For example, tunable microstrip [10]-[11] or printed Yagi [12] antennas would provide compact solutions for applications requiring this feature. However, the PTE versus separation curves is similar to Fig. 5. The roll-off with antenna separation could be reduced with an asymmetrical configuration employing a large-source antenna.
Various passive element spacings were tried with different fixed impedances. Figure 3 compares the PTE resulting from the induced EMF method and 4nec2 code for Yagi antennas with 0.25λ reflector spacing and various load impedances. It can be seen that the two sets of results are very similar especially as the separation (s) increases above about 0.1λ. Also, a low resistive load gives higher efficiencies for close separation, while the 87-40iΩ load is a better match to the receiving antenna at large antenna separations. We found that the best compromise for PTE was obtained with a reflector spacing of about 0.15λ and length of antenna elements of about 0.5λ when loaded with a fixed load given by (4). The results are shown in Fig. 4 and compared with the same situation for a reflector spacing of 0.25λ. The figure shows that an efficiency in excess of 25% could be achieved at separations up 0.5λ.
1.0 0.9 0.8 Experiment (0.149w 'length)
0.7
Induced EMF (0.149w 'length)
0.6
PTE
4nec2 (0.15w 'length)
0.5 0.4 0.3 0.2 0.1 0.0
1
0.0
0.9
0.1
0.2
0.3
0.4
0.5
0.6
0.7
Separation (s) λ
0.8 0.7 0.6
PTE
Figure 5: Power transfer efficiency versus antenna separation for a pair of 2-element Yagi antennas. Key: experiment (d=0.149λ), induced EMF method (d=0.149λ) and 4nec2 code (d=0.15λ).
d=0.15λ Zload=41.3-j72.5
0.5 0.4 0.3 d=0.25λ Zload=78-j71.2
0.2 0.1 0 0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Separation (s) λ
Figure 4: Power transfer efficiency for two 0.5λ 2-element Yagi antennas, with various spacing, and matching impedances. Key: solid line - induced EMF method; symbol - 4nec2 code.
To test the models, a pair of antennas was constructed and the PTE measured. The Yagi feed elements were fitted with baluns to match the instrumentation and balance coaxial cables. To provide a good input match the driven elements were trimmed to 0.48λ. The measured and computed results with a reflector spacing of 0.149λ are shown in Fig. 5. The
In a typical wireless power transfer system (Fig. 1), the receiving antenna is connected via a matching network to a voltage multiplier, typically of the Dickson type. The input impedance of this multiplier varies with input power, as well as output load impedance, due to the non-linear nature of the diodes in the multiplier circuit. The multiplier input impedance decreases as the number of stages increases (i.e. doubling the number of stages results in a halving of the input impedance), since the diodes appear anti-parallel to the input source. Clearly from (5), it would be advantageous to maintain maximum power transfer by varying the matching impedance and/or receiving antenna impedance. If the impedance matching circuit is not properly designed, the resulting impedance mismatch between the multiplier circuit and the receiving antenna would cause a loss of overall efficiency. In addition, to ensure high efficiency, it is important to have a matching circuit with higher Q than the antenna and also it should not store energy in the same form as the antenna i.e. capacitive or inductive [13]. A tunable matching circuit such
918
as the approach described in [13] or [14] could be employed to match most impedance mismatches. Another practical problem with multiplier circuits is the dissipation of power by the diodes. As a consequence there will be a trade-off between the number of multiplier stages (and the output voltage) and the conversion efficiency. For example, with standard diodes the efficiency of a four-stage Dickson multiplier can be about half the predicted efficiency [15]. Finally, there is a trade-off between the voltage required to recharge the storage device (‘load’ in Fig. 1), the frequency and the transmitted power. In conventional energy harvesting, the power levels are relatively modest and possibly at insufficient level for sensor networks, especially in remote locations. A power transmitter can be supplied in the absence of sufficient power. This raises questions of maximum power level and safety. The transmitted power level is frequently constrained by the radiation exposure limits for safety of humans. However, sensor networks in remote locations operate virtually independently of humans. Therefore, it should be possible to raise the transmitted power levels above the usual safe-working limits by autonomously providing the power to sensor nodes. The power could then be broadcast if the radius of the network is within about one wavelength. Alternatively, a robotic vehicle could traverse the network to provide power to a sensor node when it comes within range. V.
REFERENCES [1]
[2]
[3]
[4]
[5]
[6]
[7] [8]
[9] [10]
[11]
CONCLUSION
We have presented a model of a wireless power transmission system and presented conditions for maximum power transfer efficiency for antennas in close proximity. These reduce to the expected results at the extremes for antennas very close and far away to each other. An example was described for which theory and experiment are in agreement thereby verifying the model. We identified ways of ensuring maximum power transfer could be achieved by adaptively tuning the receiver circuit for maximum power transfer when the range between source and receiver varies. Finally, some issues relating to practical wireless power transmission in sensor networks were discussed.
[12]
[13]
[14]
[15]
ACKNOWLEDGMENT We are grateful to Steven Percy for comments and suggestions on Sec. IV.
919
S. Roundy, P. K. Wright, and J. M. Rabaey, “Energy scavenging for wireless sensor networks: with special focus on vibrations,” Kluwer Academic Publishers, 2003. J. Thomas, M. Qidwai, and J. Kellogg, "Energy scavenging for smallscale unmanned systems,” Journal of Power Sources, vol. 159, pp. 1494-1509, 2006. G. Park, C. Farrar, M. Todd, W. Hodgkiss and T. Rosing, “Energy Harvesting for Structural Health Monitoring Sensor Networks,” Los Alamos National Laboratory, 2007. K-Y. Lin, T. Tsang, M. Sawan, and M. El_Gamal, “Radio-Triggered Solar and RF Power Scavenging and Management for Ultra Low Power Wireless Medical Applications,” IEEE ISCAS, pp. 5728-5731, 2006. U. Karthaus and M. Fischer “Fully integrated passive UHF RFID transponder IC with 16.7-μW minimum RF input power,” IEEE J. Solid State Circuits, vol. 38, pp. 1602-1608, 2003. G. De Vita and G. Iannaccone, “Design Criteria for the RF Section of UHF and microwave passive RFID transponders,” IEEE Trans Microw. Theory Tech., vol. 53, pp. 2978-2990, Sept. 2005. C. A. Balanis, “Antenna Theory: Analysis and Design,” 3rd Ed, WileyInterScience, 2005. A. Kurs, A. Karalis, R. Moffatt J. D. Joannopoulos, P. Fisher and M. Soljačić, “Wireless power transfer via strongly coupled magnetic resonances,” Science Express, 10.1126/science.1143254, 7 June 2007. A. Voors, “4nec2: NEC Based Antenna Modeler and Optimizer,” Program, available from: http://home.ict.nl/~arivoors/, 2009. R.B. Waterhouse and N.V. Shuley., “Full characterisation of varactorloaded, probe-fed, rectangular,microstrip patch antennas”, Microwaves, Antennas and Propagation, IEE Proc.,vol. 141, pp. 367-373, Oct. 1994. G. Yang, M. Ali and R. Dougal, “A multi-functional stacked patch antenna for wireless power beaming and data telemetry,” IEEE Antennas and Propagation Society International Symposium, 3-8 July 2005, vol. 2A, pp. 359 – 362. B-S. Ke, Y. Qian and T. Itoh, “A Two-Element Yagi-Uda Array Using Tunable Slot Antenna”, Asia Pacific Microwave Conference, Hong Kong, China, 2-5 Dec., 1997, pp. 437-440. G.S. Smith, “Efficiency of electrically small antennas combined with matching networks,” IEEE Trans. Antenna Propagat., vol. 25, pp. 369373, May 1977. C. Hoarau, N. Corrao, J.-D. Arnould, P. Ferrari and P. Xavier, “Complete design and measurement methodology for a tunable RF impedance-matching network,” IEEE Trans Microw. Theory Tech., vol. 56, pp. 2620-2627, Nov. 2008. S. Percy, private communication.
