REMOTE RF BATTERY CHARGING
CH
Hubregt J. Visser1*, V. Pop1, B. Op het Veld2, R.J.M.
J.M. Vullers1
1
imec/Holst
Holst Centre,
Centre Eindhoven, The Netherlands
2
Philips Research,
Research Eindhoven, The Netherlands
Huib.visser@imec-nl.nl
Abstract: The design of a remote RF battery charger is discussed through the analysis and design of the
subsystems of a rectenna
enna (rectifying antenna):
antenna): antenna, rectifying circuit and loaded DC-to-DC
DC
voltage (buckboost) converter. Optimum
m system power generation performance is obtained by adopting a system-level
system
integration strategy. Our approach differs from the state of the art, i.e. interconnecting optimized subsystems which
would lead to a sub-optimum system.
Keywords: battery, antenna,, rectenna, RF, charging, remote, maximum power point, buck-boost,
buck
converter
INTRODUCTION
A general Microwave Power Transmission (MPT)
(
system is shown in Fig.1. In the far-field
field of a transmit
antenna, a receive antenna picks up part of the
propagating radio waves. This antenna is connected –
through an impedance matching network – to a
rectifying circuit, where the Radio Frequency (RF)
signal is converted into a DC signal. This DC signal
sig
is
used to power an application or charge a battery.
battery The
combination of the rectifying
ifying circuit and antenna
ant
is
commonly denoted as rectenna.
2.5GHz,, the load may be considered to be a short
circuit.
Fig. 2: Packaged diode with source and load.
Fig. 1: General
eneral MPT system.
system
For charging batteries at a large distance we need to
maximize the rectenna’s output voltage. Thereto we
may employ passive voltage multiplication techniques
in the rectifier circuit and/or use (RF) voltage boosting.
For the short-circuit
circuit load, the input impedance is
obtained in a very time-efficient
efficient way applying the RK.
Fig. 3 shows the real and imaginary part of the input
impedance as a function of the available input power
for the AVAGO HSMS-2850 Schottky diode at
2.45GHz thus obtained.
RECTIFIER ANALYSIS
The rectifying circuit will consist of a single
Schottky diode or a cascade of Schottky diodes.
A. Single Schottky Diode
In Fig. 2 we show the equivalent circuit for a
packaged diode. Herein, d denotes an ideal diode, Cj is
the junction capacitance, Rs is the
th bulk series
resistance and Lp and Cp are the packaging parasitic
inductance and capacitance, respectively. The values
may be found in the diode’s datasheet.
This packaged diode will be terminated with a load,
consisting of a parallel circuit of a load resistor
re
and a
load capacitance and will be excited by a voltage
source Vg with internal resistance Rg, see Fig. 2. Vg
and Rg represent the antenna in our rectenna, see Fig. 1.
A thorough Runge-Kutta (RK) analysis revealed that
for CL ≥ 0.1µF, for most commercially available
Schottky diodes in the frequency range from 0.1 to
Fig. 3:: Time domain analysis results for HSMSHSMS
2850 diode at 2.45GHz.
2.45GHz
When the RLCL time is orders of magnitude larger
than the microwave voltage period, the time-domain
time
circuit equations tend to become stiff and the RK
analysis becomess extremely time-inefficient.
time
Therefore, for the DC modelling, we employ the
Ritz-Galérkin
Galérkin averaging method described in [2]. For
the unbiased diode, the relation between output voltage
Vo and available antenna power Pinc is given by
Ι0
(
q
nkT
) (
)
 1+ Rg + Rs  q V

o
RL 
 nkT
8 Rg Pinc = 1 + RVLoI s e
,
(1)
where I0 is the zero-order modified Bessel function of
the first kind, q is the electron charge, n is the diode’s
ideality factor, k is Boltzmann’s constant, T is the
temperature in Kelvin and Is is the diode’s saturation
current. Again through a RK analysis we found that
the frequency-independence of equation (1) is justified
and the outcome of the equation is good compared to a
RK analysis for load resistors RL ≥ 1kΩ and fair for RL
< 1kΩ in the frequency range 0.1 - 2.5GHz. This is
demonstrated in Fig. 4 that shows the output voltage as
a function of available input power for the AVAGO
HSMS-2850 Schottky diode [3], as calculated with
equation (1) and as obtained with a RK4 method. The
region of interest for energy harvesting is Pinc≤ 0dBm.
Fig. 4: RK and approximate V0 for several RL at
2.45GHz.
In the next section, we will apply the analysis
method for voltage multiplyers.
B. Voltage Multiplication
The most basic voltage multiplier is the voltage
doubler, see Fig. 5(a).
Fig. 5: Voltage doubler. (a) Circuit. (b) RFequivalent circuit. (c) DC-equivalent circuit.
Whit an RF signal applied to the doubler the
capacitors will act as short-circuits and the input
impedance will halve with respect to that of a single
diode, see Fig. 5(b). For DC, the capacitors will act as
open circuits and the diodes will become voltage
sources in series connection, see Fig. 5(c). Since, for
the doubler, RK analysis is prevented by stiff
equations and an implicit equation using the RitzGalérkin averaging method does not exist, we apply
the following approximation. We may analyse the
doubler as a single diode if, in equation (1) we double
Rg (to obtain the same current flowing into the circuit)
and halve RL (to obtain the same current flowing out of
the circuit). We do not double the output voltage as
mentioned in [4]. We may extend the circuit in Fig. 5(a)
to a n-times voltage multiplier, employing n diodes.
We now use equation (1) wherein we multiply Rg by n
and divide RL by n.
Fig. 6 shows the measured and calculated output
voltage as a function of Pinc for a voltage doubler. A
fair agreement between model and measurement
results – good enough for design purposes - is shown.
For n ≥ 4, measurement and calculation results start to
differ substantially, the resistance of the capacitors is
believed to be the main reason for this difference.
Fig. 6: Modelled and measured output voltage of a
doubler circuit.
A recently claimed way of increasing the output
voltage is by increasing the RF voltage at the input of
the rectifier.
RF VOLTAGE BOOST CIRCUIT
The RF voltage boost principle is best explained by
virtue of the lossless, LC-circuit shown in Fig.7.
Fig. 7 Example RF voltage boost circuit.
The voltage gain GV of this circuit may be
calculated as
GV =
Vout
1
,
=
Vin 1 − ω 2 LC
(2)
where ω=2πf is the angular frequency. At resonance
(ω2LC=1) the voltage gain becomes infinite. To boost
the RF voltage at the input of the rectifier circuit, we
place a reactive L-network
network between the antenna and
rectifier of Fig.3 [5], see Fig.8
ANTENNA
The antenna needs to have sufficient geometrical
parameters to tune for realizing the desired (complex)
input impedance. Moreover, we need a model for
analysis and design of the antenna. For rectennas on
objects we employ a rectangular microstrip antenna [1,
[
6], see Fig. 9(a).. For free standing applications we
employ folded dipole array antennas [1,
[ 7], see Fig.
9(b).
Fig. 8: Rectenna with RF
F voltage boost circuit.
circuit
Since the RF voltage boost circuit is assumed to be
lossless, the output power must equal the input power:
2
1 2
1
1
Pout = Vout
Re{YL } = Pin =
Vav2 Re{Yin }. (3)
2
2 1 + RgYin
For a maximum power transfer the electronics
circuit is matched to the antenna, so that
R g = Re{Z in } ∧ Im{Z in } = Im{Yin } = 0
.(4)
With equations (3) and (4) the voltage gain is
calculated as
GV =
 B + BL 
Vout 1 Re{Yin } 1

=
=
1 + 
Vav 2 Re{YL } 2
 GL 
2
.
(5)
For a compact design, we incorporate Z=jX into the
antenna [1]. The antenna impedance ZAnt then becomes
Z Ant = Rg + jX =
GL
B + BL
+j 2
2
2
GL2 + (B + BL )
GL + (B + BL )
. (6)
Equation (5) leaves the impression that for a load
admittance YL=GL+jBL the output voltage level may be
controlled by circuit component Y=jB. It is true that
the voltage gain GV may be controlled by jB, but this
is not true for the parameter that really matters, i.e. the
output voltage Vout.
The available antenna voltage Va is given by
Vav = 8Rg Pinc ,
(7)
where Pinc is the available power incident on the
receive antenna. Substitution of equation (6) in
equation (7) and using equation (5) leads to
Vout = GV Vav =
2 Pinc .
GL
Fig. 9: Rectenna using a microstrip patch antenna
(a) and a folded dipole antenna (b).
DC-TO-DC
DC CONVERTER
The voltage of a single rectenna element (Vo) will be
too low to charge most batteries directly.
directly Fluctuations
on the incidental power (P
Pinc) will further hinder the
battery charging. Both imply that a DC-to-DC
converter is needed to adapt the rectified voltage to the
voltage of a battery or super-capacitor.
super
Furthermore,
the input resistance of the converter should be
designed to sett the rectenna circuit at its maximum
power point (MPP). The rectenna’s
rectenna output power
(Pdc=Vo2/RL) can be derived from Vo(RL,Pinc) see
equation (1) . Figure 10 shows Pdc vs. Vo for several
values of Pinc. The red dots reveal the maximum power
point (Pmpp) locations and the related voltages
voltage (Vmpp).
Pmpp and Vmpp can be translated to a load resistance
(Rmpp). The input resistance of the DC-to-DC converter
should be identical. The dependence of Rmpp on Pinc is
shown in Figure 11. The curve is considered ‘flat’
enough to be represented by a constant resistance in
the antenna incident power range of -10 to 0 dBm.
An unregulated buck-boost
boost converter operating in
the discontinuous conduction mode (DCM) is used to
achieve a constant input resistance Rdc see Figure 12.
(8)
So, none of the RF voltage boost circuit components
can actually be used to increase the output
o
voltage.
We may even leave out the admittance Y=jB. To
increase the voltage Vout, we need to realize a
rectifying circuit with a minimum GL-value.
value. In case of
using a single Schottky diode, we need to select one
with a very low GL-value,
value, when RF short-circuited.
short
The converter’s input resistance RL=Rdc is given by
2 Lc
,
(9)
Rdc =
f s t s2
where Lc is the inductance of coil Lc, fs is the
switching frequency of the oscillator and ts is the ontime of switch Sc. This means that Rdc is constant only
if the term f s t s2 is constant because Lc has a fixed
value.
inefficient conversion. A battery over-voltage lockout
is used to protect the battery from overcharging.
-4
5
x 10
P INC
-10 dBm
-9 dBm
-8 dBm
-7 dBm
-6 dBm
-5 dBm
-4 dBm
-3 dBm
-2 dBm
-1 dBm
0 dBm
Pdc (W)
4
3
2
Figure 13 shows the measured output voltage (Vbat)
and power efficiency as a function of the input voltage
(Vin=Vdc) for three values of the circuit feeding voltage
(Vscr). The inset shows the circuit.
1
0
0
0.2
0.4
0.6
0.8
1
Vdc (V)
Rmpp (Ω)
Fig. 10: Rectified power (Pdc) and voltage (Vo) for
several Pinc. The red dots indicate the maximum power.
600
400
Fig. 13: Measured output voltage and power
efficiency as a function of input voltage.
200
WIRELESS BATTERY CHARGING
0
-10
-8
-6
-4
Pinc (dBm)
-2
0
Fig. 11: Optimal load resistance (Rmpp) vs. Pinc.
A system consisting of a rectenna with voltage
doubler, a DC-to-DC converter and a Li-Ion
rechargeable battery for a 3-4.2V voltage range has
been realized and subjected to an incident RF signal
(EIRP≈1.2W). In comparison with a non-optimized
system, using the same rectenna, battery and incident
RF signal, an increase in working distance of 164%
was achieved, going from 25 to 66cm.
CONCLUSIONS
Fig. 12: DC-to-DC discrete buck-boost converter.
Both fs and ts are set by the oscillator which is based
on a positive feed-back (3 times Rhys) and a delayed
negative feed-back (Rl, Rh, D and Cosc). Assuming that
the diode forward voltage drop of D is negligible, both
feed-back paths scale with the oscillator’s supply
voltage (Vsup=Vdc+Vbat) which makes timing
independent of Vsup. Equations (10) give the
expressions for ts and fs.
t s = αRh Cosc , f s =
 2 Vsup − Vd
1
, α = ln 13
 V −V
α (Rl + Rh )Cosc
d
 3 sup
 . (10)



The converter may charge a battery within a voltage
range of 2.1 to 4.5V assuming a rectenna voltage range
Vo of 0.21 to 1V (DC). An input under-voltage lockout
of 210mV is used to prevent battery discharging due to
The subsystems of a wireless RF battery charger are
analyzed and designed for obtaining a maximum
battery voltage. It is shown that including resonant
circuits in the rectenna does not increase the voltage
level.
Using a voltage doubling rectifyer and
designing a DC-to-DC converter matched to both the
rectenna and the battery does lead to voltage
maximization.
REFERENCES
[1] H.J. Visser, Approximate Antenna Analysis for
CAD, John Wiley & Sons, Chichester, UK, 2009.
[2] R.G. Harrison and X. Le Polozec, “Nonsquarelaw
Behavior of Diode Detectors Analyzed by the Ritz
Galérkin Method”, IEEE Trans. Microw. Theory
Techn., Vol.42, No.5, pp.840-846, May 1994.
[3] -, “HSMS-285x Series”, Datasheet, Avago
Tech., 2009.
[4] -, “Designing the Virtual Battery”, Application
Note 1088, Agilent Technologies, 1999.
[5] A. Shameli, et al., ‘Power Harvester Design for
Passive UHF RFID Tag Using a Voltage Boosting
Technique’, IEEE Trans.Microw. Theory Techn.,
Vol. 55, No. 6, pp. 1089-1097, 2007.