1
A Passive Impedance Matching Interface
Using a PC Permalloy Coil for Practically
Enhanced Piezoelectric Energy Harvester
Performance at Low Frequency
A. Giuliano and M. Zhu (IEEE Member)

Abstract—This paper presents an analytical and experimental
study of a passive impedance matching interface based on a large
inductive reactance but with a centimeter-scaled size for
practically enhanced piezoelectric energy harvester performance
at low frequency. Low frequency vibration normally leads to a
large capacitive reactance value for small-sized piezoelectric
energy harvesters and it is impractical to achieve the maximum
power transferring condition by use of a conventional inductor as
its volume would be a few cubic meters. In this paper, a PC
permalloy material was used to implement a passive impedance
matching interface to reduce the size of the inductor to a few cubic
centimeters as it has a very high initial magnetic permeability of
6×104 H/m, and is able to practically perform the complex
conjugate load matching of a Macro-Fiber Composite energy
harvester at a frequency below 10 Hz. The effects of the interface
on the voltage, current and power transferred to resistive loads
were examined through comparisons of the results between
configurations with and without the interface for applied strain
levels of between 480–1170 µε peak-to-peak and frequencies in the
range of 2.5–10 Hz, respectively. Around 94.6% of an increment
of the power was obtained under an excitation of 480 µε at 10 Hz
associated with an optimal resistive load reduced by over 70%.
Compared with the state-of-art active impedance matching
techniques, which use power sources to control a signal generated
by piezoelectric energy harvesters, the developed interface is
passive, without need for an additional power source, has the
advantages of being easier to be implemented, and can be
potentially used for the enhancement of vibrational EH
performance.
Index Terms—passive impedance matching, maximum power
transfer, inductor circuit, low frequency strain energy harvesting.
I. INTRODUCTION
There is a significant demand of self-powered systems
using energy harvesting (EH) technology in fields of such as
aeronautics, automotive, transports, civil engineering,
biomedical engineering, etc. due to the truly energy
autonomous manner, without the need for power supplies and
batteries [1]. Therefore, EH technology is becoming
increasingly important as a promising solution for powering the
growing number of electrical and electronic devices requested
The authors gratefully acknowledge the financial support from the
Engineering and Physics Science of Research Council (EPSRC) in the UK to
the projects EP/K020331/1 and EP/K017950/1.
by both industrial and personal applications.
Comprehensive studies on different transduction
mechanisms have been carried out over the recent years on
converting mechanical energy into electrical energy for
supplying power to electronic systems (e.g., wireless sensors)
[1], [3]–[5]. Mechanical vibrations are almost ubiquitous in the
environment around us and piezoelectric transducers, in
particular, are characterized by high energy densities and
integration potential for applications [6]–[9]. However, power
harvested by small-scale piezoelectric transducers is still
limited in the range of a few milliwatts or a few ten milliwatts
due to the low electromechanical transduction factor of the
piezoelectric transducers. Different approaches have been
reported in order to address this issue, such as introducing
nonlinearities either in the mechanical domain (to increase the
mechanical energy transferred from the host structure by use of
permanent magnets [10]–[12] or a bistable structure [13]) or in
the electrical domain (to increase the transduction capability of
the piezoelectric harvester by use of an inductor, electrically
connected to it through a synchronized switching technique
[14]). Modeling of simple piezoelectric EH systems (e.g.,
harvester connected to a resistive load [15]–[16]) and of
complex systems (e.g., harvester connected to an electrical load
through a nonlinear power conditioning interface [17]–[18])
have showed that the circuit connected to the piezoelectric
harvester influences its vibration response and, in turn, its
power output. In [19], Renno et al. demonstrated that adding an
inductor to a piezoelectric EH circuit can substantially enhance
the harvested power and allow tuning the piezoelectric device
for achieving a broader range of operational frequencies.
Because of the dielectric behavior of the piezoelectric
transducer, for an operational frequency below its resonance, an
inductive load needs to be added in order to implement the
complex conjugate matching of the transducer’s impedance and
increase the efficiency of the energy harvester based on the
condition of the maximum power transferring theorem. In [21],
Brufau-Penella and Puig-Vidal experimentally validated this
concept on a commercial piezoelectric transducer (i.e., QP40w
from Mide Technology) by showing 20% increment of the
A Giuliano is with the Manufacturing and Materials Department, Cranfield
University, Cranfield, MK43 0AL, UK. M. Zhu is with the College of
Engineering, Mathematics and Physical Sciences, University of Exeter, Exeter,
EX4 4QF, UK (e-mail: m.zhu@exeter.ac.uk).
2
generated power when an inductive element was directly
connected between the transducer and a resistive load.
However, this implementation was suitable for a high
operational frequency only (i.e., at 935 Hz, the fourth resonant
mode of the piezoelectric harvester), but not practical for low
frequencies because of the very-large value of inductive
reactance needed to make the complex conjugate impedance
match work. Synthetic [22] or virtual [23]–[24] impedance
circuits such as gyrators, op-amp integrators in conjunction
with voltage-to-current converters and differentiators in
conjunction with current-to-voltage converters [25], etc. have
been used in piezoelectric shunt circuits for vibration damping
so as to simulate large inductance values (thousands of
Henries). However, virtual inductor implementations are
generally a poor representation of an ideal inductor as they are
difficult to tune, very sensitive to component variations, and
require an external power supply. Therefore, they don’t suit for
practical implementations of small-scaled piezoelectric EH
systems. In order to obtain an equivalent resistive-reactive load
to achieve the maximum power output from a piezoelectric
harvester, a bidirectional DC-to-DC converter tuned by a twodimensional Maximum Power Point Tracker (MPPT) via a
microcontroller was used in [26]. Autonomous methods able to
maximize the power output from the piezoelectric harvester, by
providing it with a constant optimal electrical load, have also
been presented. Ottman et al., for instance, achieved automated
power optimization by using an adaptive DC-to-DC converter
[27], and then introduced an optimized method to regulate the
power flow from the piezoelectric element to the connected
electrical load by defining the optimal duty cycle for a stepdown converter operating in discontinuous conduction mode
[28]. Similarly, Lefeuvre et al. [29] proposed the use of a
sensor-less buck-boost converter running in discontinuous
conduction mode to track the optimal working points of a
piezoelectric generator. Lallart and Inman [30] reported an
architecture capable of enhancing energy harvesting when the
piezoelectric voltage reaches the optimal voltage, based on
sensing zero-crossing detections of the harvester’s
displacement. In [31], a power conditioning circuit consisting
of an AC/DC converter followed by a DC-to-DC converter with
adaptive duty cycle was implemented by Kong et al. for the
resistive matching of a given piezoelectric harvester’s
impedance. Also in [32], the nonlinear interface circuit
presented by Kim et al. was taken as an equivalent resistance in
order to increase the electrical power transfer from a multilayered piezoelectric transducer. Although more power has
been extracted using the methods, they become impractical due
to their high power consumption in a few milliwatts, which are
not suitable for the low-power piezoelectric transducers at the
current state of the EH technology development.
The work presented here aims to meet the condition for the
maximum power transferring theorem by using a passive
impedance matching interface based on a large inductive
reactance but with a centimeter-scaled size for practically
enhanced piezoelectric energy harvester performance at low
frequency. In order to reach a large inductance (i.e., kiloHenries) in a small size (i.e., centimeter-scale) at low
frequency, the interface is implemented as a toroidal PC
permalloy core coil, which has a very large initial magnetic
permeability of 6×104 H/m and thus a small size of the inductor.
Being a passive element, the implemented interface does not
need an additional power source, on the contrary of most of the
state-of-art active impedance matching techniques for
piezoelectric energy harvesters, which use the power to control
the system. The novelty of this work is the implementation of
a passive impedance matching interface requiring a large
inductive reactance but with a centimeter-scaled size for
practically enhanced piezoelectric energy harvester
performance at low frequency to improve the power output in a
very low frequency range (≤10 Hz). The work presented here
confirms the improvement of passive inductive impedance
matching to the impedance of a piezoelectric energy harvester
at low frequency.
II. DESCRIPTION OF THE DEVELOPED SYSTEM
A. Description of the interface
Fig. 1(a) shows the circuital configuration of the developed
passive impedance matching interface, where there is a
specifically added inductive element of Ladd to be used to
practically enhance the performance of a piezoelectric harvester
in power output. When the frequency f of the input vibration
is low, the impedance of small-sized piezoelectric harvesters
features a large capacitive reactance X s  1 /(ωCs ) with
ω  2πf , and it is not practical for the use of conventional
inductors to match the large capacitive impedance in order to
satisfy the condition in (1) for the maximum power transferring
as Ladd would be in a few thousand of Henries.
Ladd 
1
2
ω Cs
(1)
Where Cs is the inherent harvester’s capacitance?
Indeed, a few meters in diameter of the physical size would
be required if standard manufactured ferrite or powdered-iron
solenoid inductors were used to achieve the right Ladd value for
the complex conjugate impedance match of typical
piezoelectric harvesters working at low frequency. In order to
reduce the size, a PC permalloy material is introduced to
implement the passive complex conjugate impedance matching
interface because it has a high initial magnetic permeability
property and permits to have a few thousand of Henries with
a centimeter-scaled inductor at low frequency.
B. Implemented interface
Fig. 2 shows the physical coil sourced from Shin Core
Technology (HK) Ltd and used to implement the inductance
Ladd of the passive impedance matching interface. The coil has
a toroidal shape and is made of 1J85 PC permalloy (~78–80%
Ni-Fe, 4.2–5.2% Mo) core. The PC permalloy material has a
high magnetic permeability property from 6×104 H/m ( μ r_init. )
to a maximum of around 45×104 H/m ( μ r_max. ), which enables
to achieve a large inductance value with a very small physical
3
size of a few centimeters in diameter, rather than a few meters
required in a low-frequency range to satisfy the complex
conjugate impedance matching condition in (1). As Ladd is
μ μ N 2h b
(8)
Ladd  0 r
ln
2π
a
where a , b , h and N are the inner diameter, the outer
diameter, the height of the coil, and the number of turns of the
copper wire , respectively.
For the implemented interface, a  15mm, b  35mm,
h  20mm, and N  2800, the total volume and weight of
the toroidal coil were respectively around 15 cm3 and 75g to
perform the impedance match with the connected piezoelectric
harvester and it can achieve the required inductance of
Ladd ≈1.6 kH at 10 Hz (under the applied AC voltage of 1 V
amplitude) for satisfaction of (1). It should be noted that other
physical parameters and electromagnetic material properties of
the toroidal coil used are listed in Table I.
C EXPERIMENTAL SETUP
Fig. 3 shows the experimental setup used for the
characterization of the EH performance achieved by connecting
the implemented passive impedance match interface in series
between the energy harvester and its resistive load. The setup is
similar to the one reported in [36]–[37] but with the added
interface. A 250 kN tensile testing machine (Instron, High
Wycombe – Bucks, UK) was used for testing and, for
comparison reasons, the same mechanical loads used in [36]–
[37] were applied to the piezoelectric energy harvester. The
strain range of between 480 and 1170 με peak-to-peak was
used to produce the peak-to-peak amplitude through an applied
force from 1 to 51 kN at the frequencies ( f ) of 2.5, 5.0, 7.5,
and 10 Hz.
The piezoelectric energy harvester used for this study is also
same as the one in [36]–[37], which is a Macro-Fiber
Composite (MFC) piezoelectric transducer (Smart Material
GmbH, Dresden, Germany) bonded to the center of an
aluminum alloy (Al 2024) substrate.
III Theoretical analyses
In order to understand how the added inductive element of
inductance Ladd effects the power output from a piezoelectric
harvester, theoretical analyses are made in this section.
Fig. 1(b) shows the analytical circuit model of the
piezoelectric harvester with the added inductive element Ladd ,
the resistance Radd to take into account the internal losses of
the inductive element, and the resistive load RL . The analytical
circuit model of the piezoelectric harvester is assumed to be a
voltage source ( Vs ) in series with its inherent capacitance ( Cs )
and resistance ( Rs ) [34]. The dielectric behavior of the
piezoelectric harvester leads to a predominantly capacitive
impedance of the circuit at low frequencies and affects the total
electric charge generated by the piezoelectric transducer under
an externally applied stress. This can be analyzed by the linear
constitutive equation of piezoelectricity [35].

D3  e33
E3  d 31 1
(2)

where D3 is the charge density present on the electrodes, e33
is the dielectric permittivity of the piezoelectric material under
a constant stress (  ) condition, E 3 is the electric field
developed in the 3-direction (the thickness direction of the
piezoelectric material), d 31 is the piezoelectric charge
coefficient, and  1 is the stress applied in the 1-direction ( the
length direction of the piezoelectric material).
Under the applied condition of D3 =0, the voltage source Vs
can be calculated as the open circuit voltage:
d tY
Vs   31 1
(3)
e33
where t is the thickness of the MFC patch, Y its Young’s
modulus, and  1 the strain induced on it by the mechanical
stress  1 . Assuming the piezoelectric harvester undergoes a
sinusoidal steady-state stress due to the external vibration and
given the applied strain level  1 , then the amount of AC current
I flowing through the circuit can be calculated as:
d31 tY 1
I 
.
(4)
2


1

e33
 Rs  Radd  RL 2   ωLadd 

ω
Cs 

It can be deduced that the Ladd yields an increment of the
maximum current I generated by the piezoelectric harvester
due to the cancellation of its capacitive reactance of the
piezoelectric materials ( Ladd 
1
 0 ) and, in turn, of
Cs
the maximum power PL dissipated by the load RL , which can
be calculated from (4) as:
2





 R
d31 tY 1
 L . (5)
PL  
2 2


1  

 e33
 Rs  Radd  RL 2   ωLadd 

ωCs  


Therefore, the developed passive impedance matching
interface can enhance the power output due to the cancellation.
From (4), the amplitude of the voltage V and VL , respectively
across the piezoelectric harvester and the resistive load RL , can
be also calculated as:
d tY 
V  31  1
e33

( Radd  RL )2  ω2 Ladd 2
2
 Ladd 2 2

2  R  R
 ω Ladd  1  Rs  Radd  RL     add L  ωRs Ladd 

 Cs
  ωCs

and
(6)
2
4
RL d31 tY 1
VL 

e33

 Rs  Radd  RL 2   ωLadd 
1 

ωCs 
2
.
(7)

It should be mentioned that in a practical application, such as
vibration powered wireless sensor nodes, an AC/DC rectifier
followed by a smoothing capacitor, rather than the resistive load
RL , is added to the energy harvesting circuit for conditioning
the generated signal and the load is then connected in parallel
to it. The smoothing capacitor typically acts as an energy
reservoir (on its own or in connection to a rechargeable battery),
which stores the generated electric charge for later activations
of the load under higher peaks of power; thereby, it features a
capacitance much higher than the inherent capacitance Cs of
usual small-scaled piezoelectric harvesters. During the charging
time of the energy storage, the load is typically disconnected
from the rest of the circuit or kept in a high-impedance state so
as to draw as less current as possible, thus limiting the power
consumption of the system. In such a case, connecting an
inductive element in series to the energy harvesting circuit
would work in a similar way to the circuit connected to a
resistive load to improve the performance of the system but the
required inductor in value would be a little small. For example,
considering the piezoelectric energy harvester to be connected
to a capacitive storage in the range of mF through a full-wave
bridge rectifier, then the inductive element Ladd would be
smaller than the circuit connected to a resistive load due to the
large capacitance but the increment of this current due to the
reactance cancellation in the considered electrical path is still
there, and would lead to a higher amount of energy
accumulating into the capacitive storage during a certain
interval of time compared to the circuit connected to a resistive
load.
IV RESULTS AND DISCUSSIONS
C. Characterization methods
The electrical impedances of the implemented MFC energy
harvester and the toroidal coil were individually measured by a
N4L PSM1700 impedance meter under the applied AC voltages
of 1, 5, and 10 V amplitude, and the swept frequency of up to
25 Hz. Different voltages were applied in order to observe the
effects on the material's electrical response under the different
mechanical strain levels.
The power dissipated by the connected resistive load RL was
used to characterize the MFC’s EH capability. For the
characterization, a number of resistors (up to 350 kΩ) were
individually connected to the MFC’s terminals, both directly
and through the series-connected inductive element Ladd . The
power was calculated based on the voltage VL developed across
the connected resistive load RL . The instantaneous voltage was
measured by an Agilent 34401A; hence, the current I through
the circuit was calculated from the Ohm’s law. Then, the
average value of the power transferred to the load ( PL ) was
calculated based on:
VL 2 I 2
(16)

RL .
2RL
2
It is worthwhile to mention that, in all calculations, the
internal resistance of the multimeter was kept into account to
deduce the real electrical load connected to the MFC energy
harvester. In order to test the effects of the developed interface
on the MFC’s EH performance, a comparison between the rootmean-square value of the measured voltage VL , the current I
PL 
and the power PL transferred to the connected resistive load
was performed for different frequencies and applied strain
levels.
D. Impedance of the MFC energy harvester
Fig. 4 shows the measured electrical impedance of the
implemented MFC energy harvester. From Fig. 4, it can be
observed that there is a dominant capacitive behavior of the
piezoelectric harvester under low-frequency (below resonance)
excitation as the amplitude varies with an inverse relationship
on the applied frequency and the phase is approximately
constant and near -90 deg, which means that the resistive part
of the MFC’s impedance is much smaller than its capacitive
part within the tested low-frequency range; and (2) the
measured capacitance of the MFC is around 175 nF under the
tested applied voltages and frequencies, which is very close to
the value of 172 nF provided by the manufacturer [38].
E. Impedance of the implemented interface
Fig. 5 shows the measured electrical impedance of the
toroidal coil used to implement the impedance matching
interface to enhance the performance of the connected
piezoelectric harvester. From Fig. 5, it can be observed that (1)
the measured coil’s impedance amplitude is linearly dependent
on the applied frequency, which is typical of an inductor; (2)
the higher the amplitude of the applied voltage the higher the
amplitude of the coil’s impedance, (3) there is a strong inverse
dependence of the impedance phase on the applied voltage,
which means a decrease of the quality factor Q of the coil with
the increase of the amplitude of the applied voltage, and also
means that the resistance of the coil increases with the increase
of the applied voltage, where the measured Q values are 59.5,
13.0, and 1.9 at 10 Hz for the applied voltages of 1, 5, and 10 V
amplitude, respectively, (4) the measured Q values are
approximately constant for different excitation frequencies
within the measured frequency range of up to 25 Hz as the
phase curves are almost flat lines; however, it should be
expected that there is an increment of the parasitic resistance
at frequencies higher than the tested range due to the skin effect
in the winding wires and the losses in the core material, thus
causing a decrement of Q; (5) the measured inductance of the
coil was around 1.6 kH and 2.4 kH when 1 V and 10 V
amplitudes of voltage were respectively applied to the coil at
10 Hz of frequency; and (6) higher values of inductance were
5
obtained at lower frequencies.
F. Effects of the interface on the energy harvester performance
Fig. 6 and 7 respectively show comparisons of the rootmean-square current I rms and the average power PL transferred
to the connected resistive load between the configurations with
and without the interface (with L and stnd) for different applied
peak-to-peak strain levels of 480, 710, 940, and 1170 με and
excitation frequencies, where the scattered points represent the
measured data, and the fitted curves respectively represent the
results from the circuits without and with the interface.
From Fig. 6–7, it can be observed that (1) for the case of the
applied strain of 1170 με peak-to-peak at 10 Hz, around 20 mW
of power was transferred to a 40 kΩ resistive load for the circuit
with the interface whilst 12.16 mW was the highest average
power developed across 66 kΩ for the circuit without the
interface. The corresponding root-mean-square currents are
702 μA and 430 μA, respectively; and (2) I rms of the current I
and PL transferred to the connected resistive load RL increase
with the increase of the applied strain and frequency; under the
same excitation frequency and applied strain level, however, for
the circuit with the interface, there is a clear increment of I rms
and PL associated with lower values of the connected resistive
load RL . This is due to the fact that the inductive reactance of
the interface diminishes the internal impedance of the energy
harvester by matching, wholly or in part, its capacitive
reactance. Such a reactance cancellation causes upward and
leftward shifts of the current vs. load curves, and power vs. load
curves for the circuit configuration with the added interface. It
can be also observed that there is a decrease of the optimal
resistive loads ( RL_MPP ) at the Maximum Power Points
(MPPs). Ideally, when the electrical resonance is perfectly
achieved by mean of the added inductance, RL_MPP is equal to
the real part ( Rs ) of the harvester’s impedance.
In order to compare effects of the implemented interface on
the energy harvesting performance, Table II lists the results,
obtained at the MPPs under tested strain levels and frequencies,
of the root-mean-square voltage VL_MPP and the current I MPP ,
the optimal average power PL_MPP , and corresponding resistive
load RL_MPP
for the configuration with and without the
interface (with L and stnd). It further confirm lower values of
RL_MPP , and higher values of I MPP and PL_MPP when the
developed interface is added into the circuit. The theoretical
values of VL_MPP , I MPP , and PL_MPP , respectively calculated
based on (7), (4), and (5) for the circuit with the added interface,
have also been listed in Table II. For the calculation of the
theoretical values, the medium value of 5 kΩ was used for Rs
and Radd regardless of the strain and frequency effects on the
harvester’s impedance reported in Fig. 4 whilst the medium
values of 4.7 kH, 2.5 kH, 2.05 kH, and 2.0 kH were used for
Ladd for taking into account the frequency effect on the coil’s
impedance described in Fig. 5. From Table II, it can be observed
that (1) the experimental results for the circuit with the interface
reasonably agree with the theoretical results; (2) there is a
higher enhancement in the absolute value of the energy
harvester performance under the excitation frequency of 10 Hz
for all the tested strain levels; (3) there is a major dependence
of the resistive loads at the MPPs on the excitation frequency
and a minor dependence on the applied strain level for the same
applied vibration frequency. The strong dependence between
RL_MPP and the frequency is a direct consequence of the
impedance matching theory; thereby, there is an inverse
relationship between them as the MFC harvester has
predominantly capacitive impedance at the low frequencies
investigated here. The minor dependence between RL_MPP and
the strain is the nature of optimal resistive load of the system as
it is determined by the system itself, rather than the applied
load. In theory, RL_MPP should be kept the same for all the
applied strains for a liner system. But the system we
implemented, there is a minor non-linearity in term of the
impedance of the MFC and the interface.
Furthermore, the effects of the energy harvester performance
in current and voltage experimentally obtained by adding the
developed impedance matching interface are listed in Table III
in terms of the increased or decreased percentage on the VL_MPP
, I MPP , PL_MPP and the corresponding RL_MPP . From Table III,
it can be seen that there is more enhancement of the energy
harvester performance for a lower applied strain level at the
same excitation frequency. This is possibly caused by the Q of
the implemented interface at the low applied strain discussed in
the previous section. The maximum percentage in I MPP and
PL_MPP were 158.4% and 94.6%, for the case that
the
excitation of 480 με peak-to-peak at 10 Hz.
III. CONCLUSIONS
This paper has presented a passive impedance matching
interface that is able to practically enhance a piezoelectric
energy harvester performance at low frequency. The interface
was based on a large inductive reactance but with a centimeterscaled size so as to be able to match the capacitive reactance of
a given piezoelectric harvester when the frequency of the input
vibration is as low as a few hertz, and thus satisfy the conditions
for the maximum power transferring. The interface used for this
study consisted of a single passive PC permalloy toroidal coil
with a high initial magnetic permeability of 6×10 4 H/m, which
permits to achieve a large inductance of around 1.6 kH at 10 Hz
with a small volume of around 15 cm3. A comparison with the
results from standard MFC characterization showed that, by
adding the developed interface, there is a significant increment
in the levels of current and power transferred to a connected
resistive load, and a decrement of the MPP corresponding to the
optimal resistive load. 96.4% and 158.4% of the improvement
in current and power are obtained from the developed interface
6
in the case that the tested strain of 480 με peak-to-peak was
applied at 10 Hz to the MFC energy harvester.
The interface presented in this paper can be potentially useful
for the enhancement of vibrational EH performance where the
size and the weight of the implemented coil is not a significant
constraint in the design of the EH system (e.g., for energyautonomous wireless monitoring applications of heavy
machinery in industrial plants).
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7
A. Giuliano was born in Messina, Italy, in
1986. He received the B.S. degree in
electronic engineering from the University
of Messina, Messina, Italy, and the M.S.
degree in biomedical engineering from the
University of Rome “La Sapienza,” Rome,
Italy, in 2007 and 2010, respectively. He
was a Visiting Research Student at the
University of Utah, Salt Lake City, UT, in 2010 and he is
currently pursuing the Ph.D. degree in energy harvesting at
Cranfield University, Bedfordshire, UK.
His research interests include the design and development of
low-power management electronic circuits for energy
harvesting applications, and the fabrication and characterization
of macro/micro devices for wireless sensing and medical
monitoring systems.
M. Zhu gained her BEng degree in 1989,
MEng in 1992, and PhD in 1995 at
Southeast University, Nanjing, China. She
currently holds the Professor and the Chair
in Mechanical Engineering and Head of
Energy Harvesting Research Group in the
University of Exeter in the UK. Prior to
joining the University of Exeter, She
worked in a number of Universities: Cranfield University
(2002-13), the University of Leeds (2001-2); Stuttgart
Universität (1999-2001); the Hong Kong University of Science
and Technology (1998-9); and the Institute of Vibration
Engineering Research, in the Nanjing University of
Aeronautics & Astronautics (1994-98).
Her areas of expertise are design and prototype, modeling
(analytical and numerical) and dynamic analytical technology,
and characterization of macro/micro-devices. Her current
research is concentrated on piezoelectric energy harvesting
powered wireless communication and sensor nodes.
8
TABLE I
PHYSICAL PARAMETERS AND ELECTROMAGNETIC MATERIAL PROPERTIES OF THE TOROIDAL COIL USED TO IMPLEMENT THE PASSIVE IMPEDANCE
MATCHING INTERFACE
Parameter
Value
Core material
1J85 PC permalloy
Core’s case material
Nylon 66
Wire material
Copper (Cu)
Radius ( r )
25 mm
Inner diameter ( a )
15 mm
Outer diameter ( b )
35 mm
Height ( h )
20 mm
Wire diameter
0.14 mm
No. of turns ( N )
2800
Occupation coefficient
90%
Core weight
44.74 g
Coil weight
75.06 g
Initial magnetic permeability ( μ r_init. )
6×104 (H/m)
Maximum magnetic permeability ( μ r_max. )
45×104 (H/m)
Saturation magnetostrictive coefficient
< 2×10-6
Coercive force
< 2.3 (A/m)
Saturation flux density
0.75 (T)
Quality factor ( Q ) ( for 1 V applied at 10 Hz)]
59.5
8
9
TABLE II
COMPARISONS OF THE OPTIMAL RESISTIVE LOAD, AVERAGE POWER, ROOT-MEAN-SQUARE VOLTAGE AND CURRENT ACROSS THE LOAD AT THE
MPP between the configurations with and without the interface (with L and stnd) FOR DIFFERENT APPLIED PEAK-TO-PEAK STRAIN LEVELS AND
EXCITATION FREQUENCIES
 1 (με)
480
710
940
1170
I MPP (μA)
RL_MPP (kΩ)
VL_MPP (V)
stnd
with L
stnd
exp.
theor.
exp.
theor.
exp.
theor.
2.5
304
216
12.5
11.9
11.0
41
55
51
0.51
0.65
0.56
5
155
88
12.1
11.9
11.6
78
135
131
0.95
1.61
1.52
7.5
105
47
12.8
11.4
10.9
122
241
233
1.56
2.75
2.54
10
79
23
12.7
09.6
9.4
161
416
408
2.05
3.99
3.82
2.5
284
226
17.9
18.0
16.8
63
80
74
1.13
1.44
1.25
5
144
98
17.4
18.1
19.0
121
185
193
2.11
3.35
3.67
7.5
98
52
18.3
17.0
17.1
187
328
330
3.43
5.58
5.65
10
74
35
18.3
16.7
17.7
247
479
504
4.52
8.00
8.91
2.5
268
219
23.0
23.5
21.8
86
108
99
1.97
2.54
2.17
5
136
97
22.4
23.6
23.9
164
245
247
3.68
5.78
5.91
7.5
93
56
23.5
22.8
23.6
253
407
422
5.96
9.28
9.97
10
70
39
23.5
22.8
24.6
336
584
631
7.92
13.31
15.52
2.5
253
207
27.7
28.4
26.1
109
137
126
3.02
3.89
3.30
5
128
96
26.1
28.5
29.6
205
294
309
5.35
8.38
9.14
7.5
86
57
28.1
28.2
29.7
325
494
521
9.11
13.93
15.45
10
66
40
28.2
28.1
31.0
430
702
774
12.16
19.73
23.98
f (Hz)
with L
9
stnd
PL_MPP (mW)
with L
stnd
with L
10
TABLE III
EFFECTS IN PERCENTAGE (%) OF THE INTERFACE ON THE OPTIMAL RESISTIVE LOAD, AVERAGE POWER, ROOT-MEAN-SQUARE VOLTAGE AND
CURRENT ACROSS THE LOAD AT THE MPP FOR DIFFERENT APPLIED PEAK-TO-PEAK STRAIN LEVELS AND EXCITATION FREQUENCIES BASED ON THE
EXPERIMENTAL RESULTS COMPARED TO THE CONFIGURATION WITHOUT THE INTERFACE
 1 (με)
480
710
940
1170
f (Hz)
Effect (%)
RL_MPP
VL_MPP
I MPP
PL_MPP
2.5
-28.9
-4.8
+34.1
+27.5
5
-43.2
-1.7
+73.1
+69.5
7.5
-55.2
-10.9
+97.5
+76.3
10
-70.9
-24.4
+158.4
+94.6
2.5
-20.4
+0.6
+27.0
+27.4
5
-31.9
+4.0
+52.9
+58.8
7.5
-46.9
-7.1
+75.4
+62.7
10
-52.7
-8.7
+93.9
+77.0
2.5
-18.3
+2.2
+25.6
+28.9
5
-28.7
+5.4
+49.4
+57.1
7.5
-39.8
-3.0
+60.9
+55.7
10
-44.3
-3.0
+73.8
+68.1
2.5
-18.2
+2.5
+25.7
+28.8
5
-25.0
+9.2
+43.4
+56.6
7.5
-33.7
+0.4
+52.0
+52.9
10
-39.4
-0.4
+63.3
+62.3
In Table IV, the “+” sign represents the increased percentage and the “-” sign represents the decreased percentage.
10
11
(a)
(b)
Fig. 1. Circuital configuration of the passive impedance matching interface with an added inductive element to enhance the EH performance of a
piezoelectric harvester connected to a resistive load: (a) a schematic of the circuit and (b) an analytical circuit model of the piezoelectric harvester
and the interface.
11
12
Fig. 2. Toroidal coil used to implement the passive impedance matching interface.
12
13
Fig. 3. Experimental setup used for the characterization of the implemented passive impedance matching interface.
13
14
(a)
(b)
(c)
Fig. 4. Measured (a) impedance amplitude, (b) impedance phase, and (c) capacitance of the implemented energy harvester as a function of
frequency, where the applied AC voltage is 1, 5 and 10 V, respectively.
14
15
(a)
(b)
(c)
Fig. 5. Measured (a) impedance amplitude, (b) impedance phase, and (c) inductance of the toroidal coil used to implement the passive impedance
matching interface as a function of frequency, where the applied AC voltage is 1, 5 and 10 V, respectively.
15
16
(a)
(b)
(c)
(d)
Fig. 6. Comparisons of the root-mean-square currents between the configurations with and without the interface (with L and stnd) for different
applied peak-to-peak strain levels of 480, 710, 940, and 1170 µε and excitation frequencies: (a) for 2.5 Hz, (b) for 5 Hz, (c) for 7.5 Hz, and
(d) for 10 Hz.
16
17
(a)
(b)
(c)
(d)
Fig. 7. Comparisons of the average powers transferred to the resistive load between the configurations with and without the interface (with L
and stnd) for different applied peak-to-peak strain levels of 480, 710, 940, and 1170 µε and excitation frequencies: (a) for 2.5 Hz, (b) for 5 Hz,
(c) for 7.5 Hz, and (d) for 10 Hz.
17