Stresa, Italy, 2527 April 2007
STEPUP CONVERTER FOR ELECTROMAGNETIC VIBRATIONAL ENERGY
SCAVENGER.
Chitta Saha
1
, Terence O?Donnell
1
, Jeffrey Godse11
1
, Louis Carlioz
1
, Ningning Wang
1
, Paul
McCloskey
1
, Steve Beeby
2
, John Tudor
2
and Russel Torah
2
1
Tyndall National Institute, Cork, Ireland.
2
University of Southampton, School of Electronics and Computer Science, Southampton, UK.
ABSTRACT
This paper introduces a voltage multiplier (VM) circuit
which can step up a minimum voltage of 150 mV (peak).
The operation and characteristics of this converter circuit
are described. The voltage multiplier circuit is also tested
with micro and macro scale electromagnetic vibrational
generators and the effect of the VM on the optimum load
conditions of the electromagnetic generator is presented.
The measured results show that 85% efficiency can be
achieved from this VM circuit at a power level of 18 ?W.
1. INTRODUCTION
A significant amount of research has already been done
on vibrational power generators using electromagnetic [1
6], piezoelectric [3] [79], and electrostatic principles [3]
[8]. These generators require the use of a converter circuit
to convert the acgenerated voltage to a usable dc level.
In particular an electromagnetic generator generally
requires a voltage stepup circuit. A suitable voltage
stepup circuit for a low voltage energy scavenger has not
been previously established and the optimum load
conditions of an EM generator with such a converter have
not been investigated. There are different topologies
which can be used to perform the acdc conversion
required to convert the low voltage AC generated by an
electromagnetic vibrational generator, to a useable DC
voltage level. Possible approaches include a transformer
followed by a rectifier, a rectifier followed by a DCDC
converter, or a voltage multiplier. For example, Wen J.
Li [1] demonstrated a laser micromachined vibration
based power generator with diode based voltage
multiplier (VM) circuits which could produce 2V DC,
however the optimum conditions for the generator with
the multiplier circuit and the efficiency of the circuit were
not analyzed. E.P. James [2] developed the prototype EM
generator with stepup transformer combined with VM
circuits and discussed the circuit efficiency. A. Kasyap
[7] presented the piezoceramic composite beam coupled
with a flyback converter circuit and also derived the
equivalent circuits and verified the optimization theory. S.
Roundy [8] described the theoretical analysis of a
piezoelectric generator and verified the optimum
condition with a resistive load and also demonstrated the
generator with a capacitive load rectifier circuit. E.
Lefeuvre [9] demonstrated the detailed analysis and
optimum conditions of piezoelectric generator with acdc
converter circuit using synchronized switch damping
techniques
Most previous works suggest [4] [5] that micro scale
electromagnetic generators typically generate a maximum
of 200500 mV (peak) at 100 Hz frequency, so that step
up conversion id required. Size and efficiency are
important factors in determining the choice of technique
used for the conversion. A relatively large transformer
would be required because of the generally low
frequencies. The simple full wave direct rectification
using diodes, or a voltage multiplier using diodes could
not be used because of the minimum diode forward
voltage drop of 0.3 V. If the diode in the voltage
multiplier circuit is replaced by an active switch (e.g.
mosfet or analogue switch) then the voltage multiplier
circuit can be used to step up very low generated
voltages. However such switches require an additional
power supply and hence consume power which affects
efficiency.
In this paper we introduce the prototype of a four stage
VM circuit, using active switches, which has been built
and characterized using as input source a signal generator
and the EM vibration harvesting device. The measured
and calculated results of the VM circuits for the both
inputs are discussed and analyzed.
2. VIBRATIONAL GENERATOR.
Two EM generators have been built and tested with the
VM circuits. Figure 1 shows the prototype of a micro
generator. The macro generator is simply a larger version
of this. The detailed structure of the micro generator and
the macro generator was explained in the paper [4] and
[6] respectively. Table I summarises the main generator
parameters.
?EDA Publishing/DTIP 2007
ISBN: 9782355000003
Chitta Saha
1
, Terence O?Donnell
1
, Geffrey Godse11
1
, Louis Carlioz
1
, Ningning Wang
1
, Paul
McCloskey
1
, Steve Beeby
2
, John Tudor
2
and Russell Torah
2
Stepup converter for electromagnetic vibrational energy scavenger.
Figure 1 : Prototype of the EM micro generator.
Table 1 : Generator parameters
Parameters Macro generator Micro generator
Magnet size (mm) 15 x 15 x 5 2.5x 2 x 1.5
Coil outer diameter
(mm)
19 2.4
Coil inner diameter
(mm)
1 0.6
Coil thickness (mm) 6.5 0.5
Magnet and coil
gap (mm)
13 0.25
Coil turns 1100 2300
Coil resistance
(ohm)
46 1613
Acceleration (m/s
2
) 0.405 0.647
Moving mass (kg) 0.05 0.0066
Resonant frequency 14.1 53
The equation of motion of the linear vibrational generator
consisting of a mass, m, fixed to a spring with constant k,
which is free to move in the x direction is given by [5];
tFkx
dt
dx
DD
dt
xd
m
ep
?sin)(
2
2
=+++ (1)
where D
p
, D
e
are parasitic and electromagnetic (EM)
damping, and F is the driving force. The displacement at
resonance (?=?
n
) can be defined as;
])[(
cos
?
?
ep
DD
tF
x
+
= (2)
The EM damping can be expressed as;
lc
e
RLjR
dx
d
N
D
++
=
?
?
2
)(
(3)
Copper coil
NdFeB magnet
Keeper
Beam
Tungsten
mass
where d?/dx, N, R
c
and L are the coil flux linkage,
number of turns, resistance and inductance respectively
and R
l
is the load resistance. The maximum electrical
power is generated when the EM and parasitic damping
are matched, and this can be expressed as;
pp
D
ma
D
F
P
8
)(
8
22
max
== (4)
However this condition is valid only when the parasitic
damping and the resonance frequency are independent of
the displacement and consequently the load.
Under these condition the optimum load resistance for the
maximum power condition can be defined by;
c
p
lopt
R
D
dx
d
N
R ?=
2
)(
?
(5)
Initially the macro generator and the micro generator
were tested by the force control EM shaker with resistive
load and then with the VM circuit in order to compare the
generated voltage and the maximum power conditions.
2.1 Generator Characteristics
Figure 2 and figure 3 show the measured no load peak
voltage for the macro and micro generator respectively.
The macrogenerator shows linear behavior and the
microgenerator shows nonlinear behavior for this
acceleration. This nonlinear behavior is caused by a non
linear dependence of the spring constant on the
displacement, which can give rise to the discontinuous
response as shown. Due to this nonlinear effect it was
not possible to verify the results from the microgenerator
with the linear modeling approach. In order to analyze
the nonlinear behavior of the mass, damper and spring
system, it is necessary to know the maximum linear
displacement and the nonlinear spring constant [1213],
which is beyond the scope of this work. However the
measured results of the macro generator were verified
with the linear theoretical model. The graph in figure 4
shows that the maximum power of the macro generator is
delivered to the load when the parasitic damping is equal
to EM damping which agrees with equation (4) and the
maximum power is transferred at 100 ohm load which
also agrees with equation (5).
?EDA Publishing/DTIP 2007
ISBN: 9782355000003
Chitta Saha
1
, Terence O?Donnell
1
, Geffrey Godse11
1
, Louis Carlioz
1
, Ningning Wang
1
, Paul
McCloskey
1
, Steve Beeby
2
, John Tudor
2
and Russell Torah
2
Stepup converter for electromagnetic vibrational energy scavenger.
180
255
330
405
480
13.8 13.95 14.1 14.25 14.4
Acceleration frequency (Hz)
M
eas
u
r
ed
p
eak vo
l
t
a
g
e (
m
V
)
Figure 2: Noload voltage vs. frequency of macro
generator.
0
160
320
480
640
52.2 52.45 52.7 52.95 53.2
Acceleration frequency (Hz)
M
eas
u
r
ed p
e
a
k
vol
t
age (
m
V
)
Figure 3: Noload voltage vs. frequency for micro
generator.
0
70
140
210
280
0 300 600 900 1200
Load resistance (ohm)
Lo
a
d p
ow
e
r
(
u
W
)
0
0.06
0.12
0.18
0.24
D
a
m
pi
ng f
a
c
t
or
(
N
.
s
/
m
)
Measured load power
Parasitic damping
EM damping
Figure 4: Measured load power and the calculated
damping factor of macro generator.
The macrogenerator has a load voltage of approximately
230 mV (peak) and generates a load power of 260 ?W for
a 0.4 m/s
2
acceleration at 14 Hz frequency. The micro
generator generates a load voltage of 350 mV (peak), a
load power of 17.5 ?W for a 0.65 m/s
2
acceleration at 53
Hz frequency.
3. ANALYSIS OF THE VM CIRCUIT
It is important to know the fundamental equations of the
VM circuits in order to characterize the prototype and
analyze the measured results. Figure 5 shows the simple
diode capacitor voltage multiplier circuit and its
equivalent dc circuit. The output voltage of the capacitor
diode VM is given by [10];
mi
IRnVV ?=
0
(6)
where n is the number of stages, V
i
is the ac peak
generated input voltage, I is the load current and R
m
is the
resistance of the VM circuit which can be defined for
odd and even stages respectively as;
Cf
nn
R
m
12
)1(
2
?
= (7)
Cf
nn
R
m
12
)2(
2
+
= (8)
where C is the stage capacitor and f is the frequency of
the supply voltage.
The voltage transformation factor can be defined by;
i
o
V
V
=? (9)
Ideally this transformation factor, at noload, should be
equal to the number of stage of the VM circuit. However
in a real circuit it is always somewhat less than the
number of stages. In this case the efficiency of the circuit
is defined by;
i
nV
V
0
=? (10)
Vi
D1
C1
C2
D2
Dn
Cn
0
R
0
nVi
Rm
R
0
Figure 5: Equivalent dc circuit of the VM
The next section gives a brief overview of the prototype
of the four stages VM which is built and tested with the
signal generator and real vibrational energy harvesting
device.
?EDA Publishing/DTIP 2007
ISBN: 9782355000003
Chitta Saha
1
, Terence O?Donnell
1
, Geffrey Godse11
1
, Louis Carlioz
1
, Ningning Wang
1
, Paul
McCloskey
1
, Steve Beeby
2
, John Tudor
2
and Russell Torah
2
Stepup converter for electromagnetic vibrational energy scavenger.
3. PROTOTYPE OF THE VM CIRCUIT
Figure 6 below shows the topology of the four stage VM
circuit which is used, where the diodes are replaced by
active switches, which are switched on and off using a
comparator. Figure 7 shows the prototype of the VM
circuit which has been built and characterized. The VM
circuit is constructed using Intersil ISL43L120 switches,
Seiko S89530A comparators and Vishay Sprague
CTS13107X9010C 100 ?F capacitors. The next section
describes the measured and calculated results of the VM
circuits using a signal generator as input.
Vi
+

C1
+

C1
+

C1
+

C1
R
0
0
S1 S4 S3
S2
Figure 6: Topology of four stage VM circuit.
Figure 7: Prototype of the VM circuit.
4. CHARACTERISTICS OF THE VM
The input and output voltage of the VM circuit are
measured using the signal generator as a source in order
to characterize the circuit. Figure 8 shows the measured
and calculated voltage and the measured and calculated
voltage transformation factor for 580 mV (peak) source
voltage at 50 Hz frequency. The input voltage and the
ratio of the outputinput voltage were calculated
according to equation (6) and (9) respectively. The
measured results agree well with the calculated results.
The graph shows that the VM achieves a stepup close to
4 under light loads.
Figure 9 shows the measured load power and efficiency
of the VM circuit. This measured results show that 95 %
efficiency can be achieved from this VM circuit at
maximum load power condition. However these results
do not include the power consumption of the switches
and the comparators.
In order to determine the power consumption of the
switches and comparators the supply current were
measured for different loads and for different fixed
supply voltages.
0
450
900
1350
1800
100 1000 10000 100000
Load resistance (ohm)
Peak vo
l
t
ag
e (
m
V
)
0
1
2
3
4
Vo
l
t
ag
e t
r
an
sf
o
r
m
at
i
on
r
at
i
o
Measured input voltage
Calculated input voltage
Measured load voltage
Measured voltage ratio
Calculated voltage ratio
Figure 8: Measured and calculated voltage and
measured and calculated voltage transformation
factor.
0
25
50
75
100
100 1000 10000 100000
Load resistance (ohm)
M
ea
su
r
ed
l
o
ad
p
o
w
e
r
(
u
W
)
0
0.25
0.5
0.75
1
M
ea
su
r
e
d
ef
f
i
ci
en
cy
Measured load power
Measured efficiency
Figure 9: Measured power and efficiency.
Figure 10 plots the measured power consumption for a
1.64 V, a 2 V and a 2.4 V supply voltage respectively vs.
the load resistance of the converter. We can see from
these plots that the power consumption has a dependence
on the load and that the power consumption for a 2.4 V
supply is considerably higher than for a 1.64 V and a 2V
supply. The four comparators were found to dissipate a
constant power of approximately 0.5 ?W under all load
conditions. This closely agrees with the value given in the
datasheet of the Seiko S89530A. Thus it appears that the
switches are responsible for the large increase in
consumption. If the measured power dissipation of the
switches and comparators is included in figure 4 then the
overall converter efficiency would be 88 % for 2 V
supply voltage.
?EDA Publishing/DTIP 2007
ISBN: 9782355000003
Chitta Saha
1
, Terence O?Donnell
1
, Geffrey Godse11
1
, Louis Carlioz
1
, Ningning Wang
1
, Paul
McCloskey
1
, Steve Beeby
2
, John Tudor
2
and Russell Torah
2
Stepup converter for electromagnetic vibrational energy scavenger.
0
5
10
15
20
25
30
100 1000 10000 100000
Load resistance (Ohms)
Po
w
e
r
(
u
W
)
Vsupply = 2.0 V Vsupply = 1.64 V
Vsupply = 2.4 V
Figure 10: Power dissipation of the switches and
comparators for different supply voltages.
The next section will examine the optimum conditions of
the generator with the VM circuits and the efficiency of
the VM circuit with real EM energy harvesting device.
6. CHARACTERISTIC OF THE VM WITH
VIBRATION GENERATOR.
0
300
600
900
1200
1000 10000 100000 1000000
Load resistance (ohm)
Vo
l
t
a
g
e
(
m
V
)
0
1
2
3
4
V
o
l
t
ag
e t
r
a
n
sf
o
r
m
at
i
o
n
f
act
o
rVM Output voltage
Measured generated voltage
Calculated generated voltage
Measured transformation factor
Calculated transformation factor
0
450
900
1350
1800
100 1000 10000 100000
Load value (ohm)
P
e
a
k
vo
l
t
ag
e (m
V
)
0
1
2
3
4
V
o
l
t
ag
e tr
an
s
f
o
r
m
a
ti
o
n
fa
cto
r
Measured generated voltage
Calculated generated voltage
VM output voltage
Measured transformation factor
Calculated transformation factor
Figure 11 and figure 12 shows the generated voltage, the
load voltage and the voltage transformation factor vs.
load resistance where the VM circuit is supplied by the
vibration generators. The vibration generators are excited
at their resonance frequency with the acceleration levels
given in table I. The coil resistance and the resistance of
the VM circuit according to equation (8) for macro
generator are 46 ohm and 4.3 k and for micro generator
are 1.6k and 1.2 k respectively. The generated voltage
and the voltage transformation factor are calculated from
the equation (6) and (9) respectively. The measured
results agree well with the calculated values. However for
less than 2 k load for the macro generator and for less
than 10 k load resistance for the micro generator, the
measured voltage and transformation factor did not match
with the calculated values due to very low transformation
factor. In this region most the generated voltage is
dropped across the coil resistance and the internal VM
circuit impedance. Figure 13 and figure 14 show the
comparison of the load power of the macro and the micro
generator with resistive load and with the VM circuits.
This measured results show that the 8085 % efficiency is
achieved of the VM circuit without considering switches
and comparators loss. It can be seen that the optimum
load resistance required to achieve maximum load power
changes significantly when the converter circuit is used.
We can see from the power graphs that for the macro and
micro generator, the maximum power is delivered at 5.5 k
? and 50 k? load when the VM is attached with a step
up ratio of 3.2 and 3.8 respectively. This compares with
optimum load resistances of 100 ? and 3 k? for the
generator attached directly to a load. Because the VM
circuit steps up the voltage, it also performs an impedance
transformation of ?
2
on the load impedance seen by the
generator. Thus with an ideal stepup ratio of 4, the
impedance seen by the generator is 1/16
th
the actual load
impedance. We can see from the results for the micro
generator that the optimum load with the VM attached is
approximately 16 times the optimum load without the
VM. However the same theory would imply that for the
macro generator the optimum load with the VM generator
should be approximately 1.6 k?. However as show in
figure 11 with a 1.6 k? load the transformation ratio of
the VM circuit is approximately 1.5, thus indicating that
the design of the VM does not match well the
characteristics of the macrogenerator. The micro
generator is a better match than the macro generator with
this VM circuit.
Figure 11: Generated voltage and load voltage and the
voltage ratio of macro generator with VM.
Figure 12: Generated voltage and load voltage and the
voltage ratio of micro generator with VM.
?EDA Publishing/DTIP 2007
ISBN: 9782355000003
Chitta Saha
1
, Terence O?Donnell
1
, Geffrey Godse11
1
, Louis Carlioz
1
, Ningning Wang
1
, Paul
McCloskey
1
, Steve Beeby
2
, John Tudor
2
and Russell Torah
2
Stepup converter for electromagnetic vibrational energy scavenger.
0
70
140
210
280
10 100 1000 10000 100000
Load value (ohm)
M
e
as
u
r
ed l
o
ad po
w
e
r
(
u
W
)
Load power with VM
Load power without VM
Figure 13: Measured load power with and without
voltage VM of macro generator.
0
4.5
9
13.5
18
100 1000 10000 100000 1000000
Load resistance (ohm)
Load
pow
er
(
u
W
)
Load power without VM
Load power with VM
Figure 14: Measured load power with and without
VM of micro generator.
7. CONCLUSIONS
A suitable voltage multiplier circuit for low voltage
energy scavenger is introduced and characterized by
signal generator and the real EM energy harvesting
devices. The measured results showed 80% efficiency can
be achieved at resonance frequency and the optimum load
resistance with VM changes significantly at maximum
power condition compare to resistive load.
7. ACKNOWLEDGEMENTS
The authors wish to acknowledge funding for this work
under the European Union Framework 6 STREP project
VIBES, project reference 507911 and the Higher
Education Authority of Ireland fund for Digital Research.
8. References
[1] Wen J. Li, Terry C.H. Ho, Gordon M.H. Chan, Philip H.
W. Leong and H. Y. Wong ?Infrared Signal Transmission by
a LaserMicromachined VibrationInduced Power
Generator? 43rd IEEE Symposium on Circuits and Systems,
August 2000, Michigan, USA
[2] P. GlynneJones, M.J. Tudor, S.P. Beeby and N.M. White
?An electromagnetic, vibrationpowered generator for
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[3] P.D. Mitcheson, T.C. Green, E.M. Yeatman and A.S.
Holmes ?Architectures for VibrationDriven Micropower
Generators?, Journal of MEMS, Vol. 13, No. 3, June 2004.
[4] S. P. Beeby, M. J. Tudor, R. N. Torah, E. Koukharenko, S.
Roberts, T. O?Donnell and S. Roy ?Macro and micro scale
electromagnetic kinetic energy harvesting generator?,
Journal of Microsystem technology, November, 2006 .
[5] T. O?Donnell, C. Saha, S. Beeby and J. Tudor ?Scaling
effects for electromagnetic vibrational power generator?,
Journal of Microsystem technology, November, 2006.
[6] C. Saha, T. O?Donnell, H. Loder, S. Beeby and J. Tudor
?Optimization of an electromagnetic energy harvesting
device?, IEEE Transaction on magnetic, Volume 42, No. 10,
October 2006.
[7] A. Kasyap, J. S. Lim, D. Johnson, S. Horowitz, T. Nishida,
K. Ngo, M. Sheplak and L. Cattafesta, ?Energy reclamation
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international congress on sound and vibration, ICSV9.
[8] S Roundy and P K Wright ?A Piezoelectric vibration based
generator for wireless electronics?, Smart Materials and
Structures, 13(2004), 11311142.
[9] E. Lefeuvre, A. Badel, C. Richard, L. Petit, D. Guyomar,
?A comparison between several vibrationpowered
piezoelectric generators for standalone systems?, Sensors and
Actuators, A. 126, 405416, 2006.
[10] J. S. Brugler, ?Theoretical Performance of Voltage
multiplier circuits?, IEEE journal of solid state circuits, June
1971.
[11] M. Shepard and R. C. Williamson, ?Very lowvoltage
power conversion?, IEEE International Symposium on
Circuits and Systems, pp 289292, 2001.
[12] Andrew D. Dimarogonas, Sam Haddad, Vibration for
engineering, PrenticeHall International editions, chapter 12,
page 605.
[13] Ali H. Nayfeh, Dean T. Mook, Nonlinear Oscillation, A
Wileyinterscience publication.
?EDA Publishing/DTIP 2007
ISBN: 9782355000003