Efficient, Compact, Wireless Battery Design Jeroen A.C. Theeuwes#1, Huib J. Visser#*^2, Martijn C. van Beurden*3, Gert J.N. Doodeman#4

#TNO Science & Industry P.O. Box 6235, 5600 HE Eindhoven, The Netherlands

Phone: +31 40 265 0891, Fax: +31 40 265 0305 1jeroen.theeuwes@tno.nl 2huib.j.visser@tno.nl 4gert.doodeman@tno.nl

*Faculty of Electrical Engineering, Eindhoven University of Technology Den Dolech 2, 5612 AZ Eindhoven, The Netherlands

Phone: +31 40 247 3462 2h.j.visser@tue.nl

3m.c.v.beurden@tue.nl

^Holst Centre P.O. Box 8550, 5605 KN Eindhoven, The Netherlands

2visser@ieee.org

Abstract Wireless batteries or rectennas rectifying antennas are conceived for converting wireless RF power into DC power. Although power conversion efficiencies exceeding 80% have been reported for high (20dBm) rectenna input power levels, wireless batteries will be most beneficial at large distances from sources that will radiate at power levels limited by national and international regulations. Therefore, the challenge is in maximizing the power conversion efficiency of wireless batteries for low input power levels, say 0dBm and below. By directly conjugate matching a rectifying circuit to a microstrip patch antenna, the need for a matching network between the two no longer exists. Thus the efficiency of the wireless battery will improve. Moreover, this matching technique automatically suppresses the reradiation of harmonics by the microstrip patch antenna since the harmonics will be mismatched. Thus, the impedance matching and filtering network encountered in traditional wireless battery designs has become obsolete. With the aid of analytical models developed for antenna and rectifier, single-layer, internally matched and filtered PCB rectennas have been designed for low input power levels. An efficiency of 52% for 0dBm input power has been realized at 2.45GHz for a wireless battery realized on FR4, showing an improvement next to the size and complexity reduction - of more than 10% over a traditional rectenna design. A series connection of these wireless batteries is shown to be able to power a standard household wall clock.

I. INTRODUCTION A wireless battery or rectenna is used to convert wireless

RF power into DC power. Therefore a rectifying circuit is connected to an antenna. The rectifying circuit in general consists of one or more diodes. A diode becomes a more efficient rectifier at higher input power levels. In [1], a rectenna power conversion efficiency is reported exceeding 80%, but for an input power level of 20dBm. Whenever a physical connection for feeding an application is not possible and distance is not critical, i.e. the radiating source will be

close to the rectenna, such a high-input-power solution is preferred. For feeding wireless applications on larger distances however, using ISM frequency bands that are restricted in allowed transmitting powers, the challenge is to maximize power conversion efficiency for low rectenna input power levels while at the same time minimizing dimensions of the wireless battery. In the remainder we will discuss how we have accomplished solutions for both parts of the challenge. In section II, we will discuss the traditional wireless battery design and means to improve this design. In section III, the analytical models developed for antenna and rectifier will be discussed, followed, in section IV, by the verification of the models. In section V, a 2.45GHz wireless battery design will be discussed as well as the application of eight of these batteries in series to power a household wall clock.

II. TRADITIONAL WIRELESS BATTERY DESIGN A traditional wireless battery or rectenna design consists of

a receiving antenna that is connected to a rectifier (diode) through a matching network that also acts as a filter. The filtering suppresses the reradiation of harmonics, generated by the diode. Fig. 1 shows the PCB lay-out of a rectenna in microstrip technology, [2].

Fig. 1 PCB lay-out of a planar microstrip rectenna. The antenna is probe-fed, the microstrip patch and the microstrip network share a common ground plane.

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Proceedings of the 10th European Conference on Wireless Technology

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A first improvement consists of employing a microstrip edge feed instead of a probe feed. Thus, the whole structure reduces to a single, grounded layer PCB. Next, the diode is directly conjugate matched to the microstrip patch antenna. This will make the impedance matching network redundant. Besides, the higher order harmonics, generated by the diode, will be mismatched to the small-band microstrip patch antenna and therefore will not be reradiated. Thus also the need for a filtering network has been eliminated.

Since the characteristics of the individual parts of a wireless battery are very critical with respect to the overall system performance, a need exists for accurate, yet easy to implement models for the wireless battery parts.

III. ANALYTICAL MODELS Analytical models have been developed both for the

antenna and for the packaged diode.

A. Microstrip Patch Antenna Model The rectangular microstrip patch antenna employed in the

wireless battery is being analysed by employing a cavity model, [3], [4]. The fringe fields of the microstrip patch antenna are taken care of by virtue of employing an effective length and width. These effective dimensions are calculated first, using empirical relations found for an open-end transmission line, [3]. Next, by performing one iteration only with a full-wave electromagnetic analysis program, over a limited frequency range, these effective dimensions are corrected. The corrected effective dimensions result in an improved-accuracy cavity model over the frequency range of interest.

B. Packaged Diode Model The equivalent electric circuit for a packaged (Schottky)

diode is shown in Fig. 2, embedded in a circuit for determining the diode impedance. The diode will be employed in the wireless battery with a capacitance placed in parallel over the diode.

Fig. 2 Packaged diode model, consisting of a diode model d, with a conductance as described in (1), a junction capacitance Cj, a series resistance Rs and parasitic capacitance and inductance Cp and Lp, respectively.

The junction capacitance Cj is inversely proportional to the square root of the voltage Vd over diode d. Cp and Lp are, respectively, parasitic capacitance and inductance due to

packaging. The current flowing through the diode d is given by

( )[ ]1exp = dnkTqsd VII (1), where Is is the saturation current, q is the electron charge, n

is the diode ideality factor, k is Boltzmanns constant and T is the temperature.

The source voltage is

( )tVV gg cos= (2), where a single input frequency is being assumed. Rg is

the source internal resistance. The circuit of Fig. 2 is described by the following three

first-order differential equations

tI

tX

pptI

gptV

ptV

jV

sg

Vsst

Vjsggdt

Ipg

g

ggddnkTq

dnkTq

dg

X

LCRCCCeII

eIRCRIRVLV

=

++

=

++++=

1

1

(1) A fourth-order Runge-Kutta routine is being employed to

solve for the packaged diode voltage and the generator current, subject to the condition that at t=0, Ig(0)=0 and Vd(0)=0, [5].

Next, an FFT is used to transform these time-domain parameters to the frequency domain, where for each harmonic a (packaged) diode impedance is determined for a fixed frequency and incident power level.

IV. MODEL VERIFICATION The models developed for the microstrip patch antenna and

the packaged Schottky diode have been verified by comparison with full-wave analysis results and measurements.

A. Improved Cavity Model Verification In Fig. 3a and Fig. 3b, the real and imaginary part of the

input impedance of a rectangular microstrip patch antennas as function of frequency are shown as calculated by the improved cavity model and as calculated by Ansofts Ensemble. The width and length of the patch are, respectively 27.7mm and 30.8mm. The substrate is 1.6mm thick FR4, having a relative permittivity of 4.28 and a loss tangent of 0.016. The feed is positioned at 0.4mm from the corner on the short side.

Since measurement results are nearly identical to the full-wave calculation results, they are not shown in the figures.

Fig. 3a and Fig. 3b clearly show the validity of our improved cavity model, the difference with full-wave calculations being only a few percent which is good enough for a wireless battery design.

Indicated in the impedance curves are the real and imaginary part of the input impedance for a frequency of

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2.45GHz. The reason for this will become clear in the next section.

a

b

Fig. 3 Real (a) and imaginary(b) part of the simulated input impedance of an edge-fed rectangular microstrip patch antenna. Width: 27.7mm, length: 30.8mm, thickness 1.6mm, relative permittivity: 4.28, loss tangent: 0.016, feed position: 0.4mm from corner on short side.

B. Packaged Diode Model Verification Fig. 4a and Fig. 4b show the real and imaginary parts of the

simulated and measured packaged fundamental diode impedance as function of the frequency for a 0dBm input power level. The diode is an Agilent diode type HSMS-2852. Measurements have been performed taking only the fundamental frequency into account.

The HSMS-2852 package contains two diodes that share one pin. The floating pin of the second diode that has not been used in the measurements, gives rise to a capacitive coupling. The measurement data as presented in Fig. 4a and Fig. 4b has been corrected for this capacitive coupling that was estimated to have a value of 0.3pF.

The noise that is visible on the measurement data is the result of the fact that the network analyzer is not able to fully suppress the higher harmonics on its input. Nevertheless, we see that we are still able to predict the input impedance of the

packaged diode with accuracy within a few percent at the frequencies of interest. This accuracy is enough to be able to design a wireless battery.

a

b

Fig. 4 Real (a) and imaginary (b) part of the simulated and measured input impedance of a HSMS-2852 Schottky diode.

Simulations and measurements of the wireless battery subcircuits have shown that our analytical models are accurate within a few percent, which is sufficient for design purposes.

V. WIRELESS BATTERY DESIGN In the final wireless battery design we will not use a single

diode, but a pair in a voltage doubler configuration, see Fig. 5, [6].

Fig. 5 Voltage doubler diode rectifier.

In the above figure, ZL is the load impedance of the wireless battery. We see that at microwave frequencies, the capacitor C is a short-circuit and that the input impedance of the rectifier is that of an (anti-) parallel pair of diodes. Thus, by halving the input impedance as calculated for the circuit of Fig. 2, we obtain the input impedance of the voltage doubler rectifying circuit. For DC, the diodes act as sources that are connected in

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series and therefore the output voltage is doubled in comparison to a single-diode rectifying circuit.

So, the design of the virtual battery starts with calculating the input impedance of a packaged diode at the fundamental frequency for a fixed input power level. Fig. 4a and Fig. 4b show the results of this exercise for a HSMS-2852 diode having a 0dBm input power level.

Next, the impedance values are halved to obtain the input impedances for the voltage doubler rectifying configuration of Fig. 5. From Fig. 4a and Fig. 4b, we find at a frequency of 2.45GHz, that this impedance is equal to (80-j90).

Then, we design a microstrip patch antenna with an edge feed, having an input impedance at 2.45GHz that is equal to the complex conjugate of the input impedance of the voltage doubler rectifying circuit, i.e. (40+j45) . The crosses in Fig. 3a and Fig. 3b indicate that for this particular patch antenna the dimensions are such that this requirement has been fulfilled.

To suppress the presence of the fundamental frequency and to a lesser extent the presence of higher harmonics in the output signal, it is common practice to add a stub after the rectifying circuit, see for example Fig. 1. Measurements have shown however, that this stub may be omitted without significantly decreasing the performance of the system. This, finally, results into a wireless battery that is hardly larger than the microstrip patch antenna, see Fig. 6.

Fig. 6 Single-layer, grounded PCB rectenna consisting of a microstrip patch antenna with a diode voltage doubler and SMD capacitor connected immediately to the edge of the patch.

The optimum load resistance for this wireless battery, operating at 2.45GHz, turned out to be 900. For this optimum load resistance, the power conversion efficiency, for a 0dBm power level received by the antenna, turned out to be 52%. This efficiency is a more than 10% improvement over a traditionally designed wireless battery operating at the same frequency, having the same input power level, [2].

The rectenna as shown in Fig. 6 has been employed in a

series circuit of eight elements to power a common household electric wall clock, see Fig. 7a and Fig. 7b.

a

b

Fig. 7 Front view (a) and back view (b) of a common household electric wall clock powered by eight 2.45GHz wireless batteries in series. The additional circuit in b is a voltage protection circuit.

Using a 20dBm transmitter and a 5dB gain horn antenna in the focal point of a 51cm diameter parabolic dish, resulted in getting the clock to operate up to 6m from the antenna.

VI. CONCLUSIONS A cavity model for rectangular microstrip patch antennas

has been improved using a single full-wave simulator iteration. Solving the differential equations that describe diode current and voltage has led to the determination of a diode input impedance. Both models have been successfully employed to design a compact, integrated, efficient, low-cost wireless battery in a very time-efficient way.

REFERENCES [1] Y.-H. Suh and K. Chang, A High-Efficiency Dual-Frequency

Rectenna for 2.45- and 5.8-Ghz Wireless Power Transmission, IEEE Transactions on Microwave Theory and Techniques., Vol. 50, No. 7, pp. 17841789, July 2002.

[2] J.A.G. Akkermans, M.C. van Beurden, G.J.N. Doodeman, and H.J. Visser, Analytical Models for Low-Power Rectenna Design, Antennas and Wireless Propagation Letters, Vol. 4, 2005, pp. 187-190.

[3] K.R. Carver and J.W. Mink, Microstrip Antenna Technology, IEEE Transactions on Antennas and Propagation, Vol. AP-29, January 1981, pp. 2-24.

[4] W.F. Richards, Y.T. Lo, and D.D. Harrison, An Improved Theory for Microstrip Antennas and Applications, IEEE Transactions on Antennas and Propagation, Vol. AP-29, January 1981, pp. 38-46.

[5] D.A. Fleri and L.D. Cohen, Nonlinear Analysis of the Scottky-Barrier Mixer Diode, IEEE Transactions on Microwave Theory and Techniques, Vol. MTT-21, No. 1, January 1973, pp. 39-43.

[6] Agilent Technologies, Designing The Virtual Battery, Application Note 1088, 1999.

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