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Energy Harvesting for
Wireless Sensor Module
ECE 191 FALL 2008
Sponsor: Spirit AeroSystems, UCSD/CEAM
Mentor: Jon Isaacs
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Table of Contents
I. List of Figures 3
II. Executive Summary 4
III. Introduction 5
IV. Approach 5
a. Inductive Charging 6
i. Results and Discussion 7
b. Piezoelectric Energy Harvesting 12
i. Results and Discussion 13
c. Thermal Energy Harvesting 19
i. Results and Discussion 20
V. Conclusion 25
VI. Acknowledgement 26
VII. References 26
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I. List of Figures
Figure 1: Schematic of Inductive Charging Circuit
Figure 2: Inductive Charging Circuit Setup
Figure 3: Transmitted Power (mW) vs. Distance (cm)
Figure 4: Receiving Voltage vs. Distance
Figure 5: Piezoelectric Effect
Figure 6: Theoretical Setup of Piezoelectric Energy Harvesting circuit
Figure 7: Piezoelectric Energy Harvesting Circuit Setup
Figure 8: Model of Piezoelectric Circuit
Figure 9: Total Voltage measured at Capacitor C89 Output
Figure 10: Energy Transfer Flow Chart
Figure 11: Thermal Energy Harvester
Figure 12: Performance Spec Sheet
Figure 13: Experimental Setup, no thermistors
Figure 14: Experimental Setup with thermistors
Figure 15: Power vs. R-T Coefficient
Figure 16: Temp vs. R-T Coefficient
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II. Executive Summary
Wireless sensor modules are often embedded in airplane wings for structural analysis.
Often times, powering these modules can be a hassle. These sensor modules are more
convenient and efficient when powered wirelessly or self-powered. Three methods of
energy harvesting were tested: inductive charging, piezoelectric energy harvesting,
and thermal energy harvesting.
Inductive charging is an age old technology. The most used inductive charging is the
transformers. However, who to transfer large amount of power in between two coils
from far away has never been considered until recently (MIT “Wielectricity”
research). In order to test the inductive charging method, two inductive loops were
made with magnet wires (Gauge 16, copper wire coated with insulting Polyurethane).
A Matlab model is also plotted in comparison with the experimental data.
The piezoelectric energy harvesting method was tested by acquiring a piezoelectric
element (PCFB W-14 obtained from AmbioSystems LLC). Since the voltage
generated by the element is in AC domain, a full-wave bridge rectifier was built to
convert the signal to DC power that can be transferred to the battery.
The thermal energy harvesting method is a lucrative method because it is a fully self-
sustainable form of DC power. The harvester was tested in the lab to determine the
practicality of implementing such a unit into a working prototype. A temperature
differential was applied across the energy harvester and the power output was
After research and experiments were conducted for these three types of energy
harvesting methods, we conclude that the piezoelectric harvesting method is the most
appropriate method to power the wireless sensor modules. It is completely self-
contained (no manual recharge necessary) and can generate enough power to support
both the sensor module and the MCU.
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Wireless sensor module using acoustic sensors are embedded in enclosed
compartments of airplanes to monitor the structural integrity. To make these modules
self-contained, DC power needs to be provided to the modules by energy harvesting.
The objective of this project is to investigate various methods of energy
harvesting need to be explored and evaluated to determine the most appropriate to
implement in the lab. In addition, a functioning energy storage circuit needs to be
designed to properly store the harvested energy.
The three types of energy harvesting methods that were tested are inductive
charging power transfer, piezoelectric energy harvesting, and thermal energy
harvesting. These three methods of energy harvesting need to be explored and
evaluated to determine which is the most appropriate to implement given that the
sensor modules are in enclosed compartments.
After much deliberation, we decided to research 4 different methods of energy
harvesting. The first is inductive charging where a charge is induced wirelessly
through electromagnetic induction. The second method is piezoelectric energy
harvesting where mechanical vibrations induced an electric charge. The third method
is thermal energy harvesting where a charge is induced through an applied
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IV.a Inductive Charging
The inductive charging approach uses two air-core coils to transfer power
wirelessly. The type of technology used in the inductive charging is the same as in
transformers, which has existed for many decades. Although it is an old technology
which has been developed and matured for a very long time, it could not transmit
power efficiently over a long distance until recently.
A group of researchers in MIT published a paper title “Wi-tricity” (wireless
electricity). Their concept is simple: to use the resonance phenomena to wirelessly
transmit power. The only trick here is to add a capacitor in parallel with the inductive
When the impedance of the inductor is the same as the reactance of the
capacitor, the two elements will resonate when connected in parallel. If the two
inductive coil circuits have the same resonant frequency, power can be transmitted
from one coil to the other efficiently and in long distances.
The primary coil (left) of the resonance circuit is coupled to receive power from a
source oscillating at natural resonant frequency. The secondary coil (right) is
coupled to the power supply so that power induced in the secondary coil charges
the power supply.
Below is an analysis of how magnetic induction generates power (Watts).
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The power is transferred in form of EM wave, where:
H xI , wherex
2 r2 z2
U c0 H , whereE cB
H: Magnetic field intensity; B: Magnetic flux; U: Energy; E: Electric field.
Fig. 1 Schematic of Inductive Charging Circuit
250mV Vac C1 L2
0Vdc C2 R1
Vin is set at the resonant frequency 31.8 kHz and the supply voltage is set at 250mV.
We set the resistor value to be R = 10Ω to calculate power. However, the load
resistance in final design will depend on the input resistance of the receiving circuit.
See Fig. 2 for the actual setup.
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Fig. 2 Inductive Charging Circuit Setup
Equipments: Properties of Magnet wire
- Breadboard and leads -Gauge: 16
- Function Generator and Oscilloscope -Outer Diameter: 0.048in
- 1 Resistor, 2 Capacitors -Insulation Thermal
- 2 coils of Magnet wire Class: 105oC
-Length of each wire: 1.58m -Copper wire coated with
-Radius of coil: 3.1cm Polyurethane as insulator
-8 loops per inductor
To find the value of the inductors, let C = 10uF (for calculation simplicity). The gain
of Fig. 1 can be modeled by:
At f = 44 kHz, Vo/Vin = ½. The equation above gives L=75.9uH.
To minimize power loss during voltage transfer, C=0.33uF was chosen.
Inductive Charging Experimental Results
The results of the circuit can be seen in Table 1 and Fig. 3 below.
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Table 1 Amount of Power Transferred
Distance Vpeak Power at
(cm) (mV) Load (mW)
1 86.5 187.05
2 50.0 62.5
3 33.5 28.06
4 20.0 10.0
5 14.5 5.26
6 9.00 2.03
Fig. 3 Transmitted Power (mW) vs. Distance (cm)
Transmission Power vs. Distance (supply voltage = 250mW peak)
Power received (mW)
y = 404.86*e
1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6
Distance between two coils (cm)
The impedance of this circuit is . At resonant frequency,
which means Zs goes to infinity. As a result, the only power consumed is in the
parasitic impedances, which is very little and can be negligible.
An inductive power transfer model was built to compare the theoretical values
with the values obtained from the experiment. See Fig 4 for the comparison.
The magnetic field from a loop is given by which yields H K I r 2 2 r 2 z 2 2 e z
where I receivez 2rreceive H z ,
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and γ is the loss in the medium, where 1.112610 3.3310 j ,
17 2 9
where r = radius of the loop, Z = distance away from the loop, and K = coupling ratio
Shown below is the matlab code written to calculate and plot the model of the
inductive charging circuit.
%% Magnetic field by a loop
V1 = 0.25; %I1, r1 -> loop 1 (source)
a = 1.291e-3/2; %radius of 16AWG wire
r1 = 0.031; %I2, r2 -> loop 2 (receiving)
r2 = 0.031; N1 = 8; N2 = 8;
L1 = 4*pi*1e-7*r1*(log(8*r1/a)-2)*N1;
L2 = 4*pi*1e-7*r2*(log(8*r2/a)-2)*N2;
w = 2*pi*31.8e3; %frequency
C1 = 1/(L1*w^2); %parallel capacitor values (at resonance)
C2 = 1/(L2*w^2);
K = 0.5; %coupling ratio
I1 = V1*w*C1;
gama = sqrt(-1.1126e-17*w^2 + j*3.33e-9*w); %transmission loss ratio
H(:,1) = K*I1*(r1^2./(2*(r1^2+z.^2).^1.5)).*exp(-1*gama*z); %mag. field at distance z on top of the loop
1 (lossy medium)
H(:,2) = K*I1*(r1^2./(2*(r1^2+z.^2).^1.5)); %mag. field at distance z on top of the loop 1
I2 = 2*r2.*H;
plot(z, abs(I2/(w*C2)), 'linewidth',3); %plot voltage at receiving circuit vs. distance
The graph of the model and the experimental results of the inductive charging
circuit are shown in Fig. 4 below. The actual data is taken with a full-wave rectifier
circuit. Some of the power transmitted to the load is consumed in the diodes. Thus, it
is expected to be lower than the model curve.
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Fig. 4 Receiving Voltage vs. Distance
Receiving Voltage vs. Distance (V1=0.25)
Peak Voltage (V)
0 0.01 0.02 0.03 0.04 0.05 0.06
distance from source loop (m)
Another concern with the inductive charging method is the orientation of the
coils. In order to transmit power from one coil to another, the two coils must be
parallel aligned with each other. If the two are aligned in an angle, the efficiency of
power transfer will be greatly reduced. When the two coils are perpendicular to each
other, no power will be transmitted between the two coils, due to the orientation of the
magnetic field. One of the solutions to this issue is to have multiple source coils
arranged in different angles. However, this method will waste more power in the
In conclusion, the transferred power in the experiment is lower than the model
prediction. This is caused by parasitic resistances in the coil and capacitors. The
maximum power transferred by two inductors of radius 3.1 cm with eight loops per
inductor is at 187.05 mW if the distance separating the inductors is 1 cm.
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IV.b Piezoelectric Energy Harvesting
The second approach in building a wireless energy harvester is by using the
piezoelectric effect. See Fig. 1 below.
Fig 5. Piezoelectric Effect
Piezoelectricity can be
generated by applying stress to
an element (notably crystals or
ceramic), which in turn creates
an electric potential.
*image taken from http://upload.wikimedia.org/wikipedia/commons/c/c4/SchemaPiezo.gif
Since piezoelectricity is generated by applying stress to a piezoelectric element,
Young’s constant measures the ratio between stress and strain of the element.
F = force (N)
A = area of element (m2)
L = length of element (m)
ΔL = change in length of element (m)
As the element vibrates, there will be an elastic potential, ue, present.
Lo = length of element (before compression)
Ao = area of element (m2)
The energy generated from a piezoelectric element (by applying stress) is modeled by:
E = (piezoelectric coefficient) ue
The unit conversion analysis of how a piezoelectric element can generate power (in
Watts) is shown below.
E = (piezoelectric coefficient) ue =>
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Energy has units of Joules = Nm
Power from piezoelectric element =>
This is exactly what is expected.
Piezoelectric Energy Harvesting Experimental Setup
Our experimental setup can be seen in Fig. 2 and 3 below.
Fig.6 Theoretical Setup of Piezoelectric Energy Harvesting circuit.
*taken from IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 17, NO. 5, SEPTEMBER 2002
Fig 7 Piezoelectric Energy Harvesting Circuit Setup
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Equipments used in the experiment:
1) Massager (3V) to generate vibration
2) Power supply
4) Piezoelectric Element (PCFB W-14 obtained from
5) Energy Storage Device
- 100uF capacitor
6) AC/DC Rectifier converter
7) Weights (as load on element)
- LR03 AAA Alkaline
- Weight: 11.3g/pc
A vibrating piezoelectric element generates an ac voltage but since batteries
need a dc voltage, an AC/DC rectifier (built with four zener diodes 1N4232) is
connected to the output of the piezoelectric device.
The energy storage capacitor is 100uF, and the vibration frequency of the
massager (measured from the oscilloscope) is approximately 109 Hz.
As can be seen from Fig 3, the resonant frequency of the piezoelectric element
was changed by adding a load at the end.
The results of how long it took for the massager to charge up the 100uF
capacitor can be seen in Table 1 below.
Results for Piezoelectric Element Power Output
Table 1. Time (s) for Piezoelectric Element to charge 100uF capacitor
Piezoelectric Element with Different Loads
No 1 weight 2 weights
Time (sec) to charge Capacitor
load 11.6g 22.6g
From 0V to 2V 19s 10s 20s
From 0V to 4V 28s 5s 11s
Shown below are outputs seen on the oscilloscope.
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0 to 2V in 19 sec
Power output = 10.5μW
22.6 g as load
0 to 4V in 11 sec
Power output = 73μW
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11.3 g as load
0 to 4V in 5 sec
Power output = 0.16mW
The optimal piezoelectric output power from the experiment was 0.16mW
(calculated using E=½CV2 and dividing the quantity by the amount of time it took to
charge the capacitor).
From testing the circuit, some observations were that the peak-peak voltage of
piezoelectric element depends on the weight (load) on the tip of the element, and the
size of the temporary capacitor CP and load capacitance Cf (see Fig 2 for reference.
The piezoelectric can be modeled as an AC current source with a resistive load.
THe model was tested in Pspice.
Fig. 8 Model of Piezoelectric Circuit
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Fig 9. Total Voltage measured at Capacitor C89 Output
To compare our results, we acquired datasheets from AmbioSystems give a
more exact power approximation. Shown below are the specs for two kinds of
piezoelectric elements, depending on the amount of power needed.
Property PFCB-W14 PFCB-W24
Dimensions [mm] 132 x 14 x 1.3 132 x 24 x 1.3
Resonance Frequency fr (Hz) 30 50
Bending Stiffness [N/m] 56 138
*acquired from AmbioSystems
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The power output from the piezoelectric element PFCB-14 can reach up
to 48 MW if it is at its resonant frequency (30Hz).
*acquired from AmbioSystem LLC
Power output from the piezoelectric element PFCB-14 can reach up to 48mW,
depending on its resonant frequency, vibration force, and resistive load. Our experimental
results were acquired with a resonant frequency of 100Hz since we cannot change the
vibration of the mini-massager.
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IV.c Thermoelectric Energy Harvesting
Consider the typical commercial airplane engine. Its engine temperature can vary
anywhere from a few 100 degrees Celsius to 1-2k degrees Celsius. A lot of this energy is lost
in the form of mechanical energy (i.e., combustion and thrust) but there is also a portion that
is just dissipated heat. Now imagine there exists a way to convert this wasted heat into
electric potential energy. A thermal energy harvester does just that; it captures ambient
thermal energy and converts it into DC power.
Fig.10 Energy Transfer Flow Chart
You apply a heat source which in this case can potentially be the heat exhaust from a jet
engine. The applied temperature is then related to the thermal voltage, Vt, by Boltzmann’s
constant which is then used thermodynamically within the thermal energy harvester. The
thermal energy harvester then outputs a DC voltage and current at its terminals which give
the desired power output.
Thermal Energy Harvester
*Fig. 11 Thermal Energy Harvester
Thermal energy harvesting is the conversion of ambient thermal energy into electrical
power. Fundamentally, a thermal energy harvester consists of two different conductive
materials, A and B, that when attached to a resistive load, L, causes an electric potential
difference. This effect is achieved by applying a temperature differential, T2 – T1, across the
two conductive materials which will then cause charge to flow, Je, through the resistive load.
This thermodynamic effect is known as the Seebeck Effect.
The Seebeck Effect is the underlying thermodynamic phenomenon that converts
thermal heat to electric power. The main equation to take into consideration is
*Fig.11 = Fig. 51-3, G.N. Hatsopoulos, J.H. Keenan, “ Principles of General Thermodynamics,” Wiley & Sons
Inc, p.681, June 1965.
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Єb – Єa = Єabo – JeRAB . *(51.46)
This equation describes the electric potential difference, measured in units of volts (V),
across a resistive load L. Je is the induced current flowing through the resistive load and is
measured in units of amperes (A). RAB is the total resistance of the isothermal loop and is
measured in units of ohms (Ω). RAB is a function of resistivity of materials A and B and is
integrated over the entire length of the temperature gradient due to its dependence on
Єabo is the open-circuit voltage and is the most important quantity of the equation as is
relates applied temperature to voltage.
Єab0 = πAB (1/ T) dT. *(51.47)
The open-circuit voltage is a function of the Peltier coefficient, πAB, and is unique for the
given materials A and B. By inspection, the unit for the Peltier coefficient is joules per
coulomb-Kelvin, J/(C*K). The open-circuit voltage is integrated over the entire temperature
gradient to give units of voltage (V).
Based off of the design requirements discussed previously and the specification sheets
of various thermal energy harvesters, we decided to purchase the Z-Max G1-1.4-219-1.14
thermal energy harvester by Tellurex Corp.
Fig.12 Performance Spec Sheet
*Equations 51.46 and 51.47, G.N. Hatsopoulos, J.H. Keenan, “ Principles of General Thermodynamics,” Wiley & Sons Inc,
p.682, June 1965.
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The experiments conducted were based off of the data sheet provided by Tellurex’s
website. The experiments were designed to test the performance of the energy harvester that
we purchased. The results would help gauge how much power the energy harvester can
potentially output in the lab.
The purpose of this test was to see if the unit functioned properly. A temperature
differential was simply applied to the unit in the form of a hair dryer for the hot side and a
bag of ice for the cold side. At the time of the experiment, a proper method of measuring
temperature was not developed so we were restricted to deductive reasoning. The results were
purely tabular but gave us a somewhat intuitive understanding of how the energy harvester
Fig. 13 Experimental Setup, no thermistors
As specified in the documentations that came with the energy harvester, a heat sink
was fabricated in the ME department workshop. The purpose of the heat sink is to dissipate
direct heat along each side of the energy harvester as to not damage the delicate conductive
materials contained inside the unit.
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Voltage(V) Current(mA) Power(mW)
0.239 60 14.34
0.24 60 14.4
0.236 60 14.16
0.234 60 14.04
0.228 60 13.68
0.222 60 13.32
0.215 60 12.9
0.183 50 9.15
0.182 50 9.1
0.18 50 9
0.179 50 8.95
0.156 50 7.8
0.155 50 7.75
0.151 50 7.55
0.148 40 5.92
0.147 40 5.88
0.139 40 5.56
0.095 30 2.85
0.093 30 2.79
0.077 20 1.54 Tcold
0.02 10 0.2
The measurements were taken with a DMM and measured the voltage and current output of
the thermal energy harvester as steady heat was applied by the hair dryer. This was a very crude test
because there were no other forms of data collected other than voltage and current. Another parameter
that would have been of relevance is temperature. The test was performed with the idea that, with time,
we would eventually reach a point where the hair dryer would output a maximum temperature on the
hot side of the heat sink and thus would achieve a maximum heat differential across the harvester.
After about 15-20 minutes of heat application there was a noticeable cap to the power output.
Based on the data collected, we were able to achieve some sort of temperature differential
across the thermal energy harvester as exemplified by the maximum power output of 14.4mW. In
theory, this is more than enough DC power to sustain our system of interest.
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The next test performed was much like the first except this time temperature was
recorded on both sides of the energy harvester. What was recorded was the relationship
between the energy output and temperature applied to the hot side of the heat sink.
Fig. 14 Experimental setup with thermistors
In addition to the previous setup, 2 thermistors were used to record the varying
temperatures on both sides of the harvester. A thermistor’s resistance depends on temperature;
the resistance of the thermistor at room temperature over the new resistance at a varying
temperature gives you the R-T curve coefficient. This coefficient can be used with the data
sheet provided by the manufacturer to extrapolate a rather accurate measure of temperature
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Power vs. R-T Coefficient
0.86 0.88 0.9 0.92 0.94 0.96 0.98 1 1.02
Fig. 15 Power vs. R-T Coefficient
Temp vs. R-T Coefficient
0.86 0.88 0.9 0.92 0.94 0.96 0.98 1 1.02
Fig. 16 Temp vs. R-T Coefficient
The maximum power output recorded was roughly 13mW of power. This is consistent with
the previous test which is a good indication that the thermal energy harvester is working properly. It
should also be noted that the temperature recorded on the cold side was fairly constant throughout the
test; Tcold was roughly 25-26.5 degrees Celsius. This means that as temperature on the hot side
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increases so does the temperature differential across the energy harvester. So at the highest recorded
temperature we get the largest temperature differential at around 4 degrees Celsius.
4 degrees Celsius is not a huge temperature differential which might explain the drastic
discrepancy between the manufacturer’s data sheet claim of 5.7 W and the measured 13mW of power.
The manufacturer claims this power output at a temperature differential of 100 degrees Celsius. This
type of differential was just not feasible in the lab and slightly impractical in the field without any sort
of active cooling system maintaining the cold side cold while allowing the hot side to stay hot. This
type of system, unless already naturally occurring within the airplane, would require a substantial
power source to function properly.
Achieving and maintaining a constant temperature differential is the single biggest design
flaw behind the thermal energy harvesting method. For this reason, it would be impractical to
implement this method into a working prototype unless otherwise overcoming the inherent
temperature issues. Perhaps the engine, itself, contains cooling compartments where temperature
differentials are naturally sustained for fueling purposes.
A list of comparisons to all three types of energy harvesting methods is listed below:
Inductive Fast charging, allows for large Need to be manually charged
Piezoelectric Doesn’t need to be manually Each element has to be manually tuned
charged. Plane provides to the plane's vibration frequency
sufficient vibrational force.
Thermal Continually supply sufficient Temp differential impractical in an
DC power enclosed compartment
The piezoelectric energy harvesting method is most practical for wireless sensor modules in
an enclosed compartment.
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The work described in this paper was sponsored by Spirit AeroSystems and University of
California, San Diego.
Special thanks to:
1. Marin Soljacic at el, Efficient wireless non-radiative mid-range energy transfer. (2007)
2. M.J. Guan, W.H. Liao, On Efficiencies of Piezoelectric Energy Harvesting Circuits
toward Energy Storage Devices. (2005)
3. AmbioSystems Advanced Cerametrics Incorportated, Piezoelectric Fiber Composite
Bimorph (PFCB) Datasheet. (2008)
5. G.N. Hatsopoulos, J.H. Keenan, “Principles of General Thermodynamics,” Wiley &
Sons Inc, p.682, June 1965.
6. Thermistor model sheet:
7. Thermistor R-T conversion table:
8. Thermal Energy Harvester datasheet: http://www.tellurex.com/pdf/G1-1.4-219-
9. J.A. Hagerty, T. Zhao, R. Zane, Z. Popovic, “Efficient Broadband RF Energy
Harvesting for Wireless Sensors,” Department of Electrical and Computer
Engineering, University of Colorado at Boulder