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IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 29, NO. 1, JANUARY 2014 201

Maximum Power Transfer Tracking forUltralow-Power Electromagnetic Energy Harvesters

Gyorgy D. Szarka, Stephen G. Burrow, Plamen P. Proynov, and Bernard H. Stark

Abstract —This paper describes the design and operation of power conditioning system with maximum power transfer track-ing (MPTT) for low-power electromagnetic energy harvesters. Thesystem is fully autonomous, starts up from zero stored energy, andactively rectifies and boosts the harvester voltage. The power con-ditioning system is able to operate the harvester at the maximumpower point against varying excitation and load conditions, re-sulting in significantly increased power generation when the loadcurrent waveform has a high peak-to-mean ratio. First, the papersets out the argument for MPTT, alongside the discussion on thedynamic effects of varying electrical damping on the mechanicalstructure. With sources featuring stored energy, such as a resonantharvester, maximum power point control can become unstable in

certain conditions, and thus, a method to determine the maximumrate of change of electrical damping is presented. The completepower conditioning circuit is tested with an electromagnetic en-ergy harvester that generates 600 mVrm s ac output at 870 µW un-der optimum load conditions, at 3.75 m·s−2 excitation. The digitalMPTT control circuit is shown to successfully track the optimumoperating conditions, responding to changes in both excitation andthe load conditions. At 2 Vdc output, the total current consumptionof the combined ancillary and control circuits is just 22 µA. Thepower conditioning system is capable of transferring up to 70% of the potentially extractable power to the energy storage.

Index Terms —AC–DC converter, energy harvesting, low power,maximum power tracking, rectification.

I. INTRODUCTION

THE output of small electromagnetic energy harvesters typ-

ically requires rectification and boosting in order to pro-

duce an output voltage that falls within the allowable operating

range of the load electronics. In some applications, there is also

a need to buffer energy in high capacity storage elements, such

as supercapacitors, in order to supply loads with a higher peak

demand than the harvester output [1]. Several circuit architec-

tures have been reported in published literature, which meet

these requirements, including single-stage ac–dc switch-mode

power converters [2]. Efficiencies up to 75%–80% at 500 µW

Manuscript received October 11, 2012; revised December 21, 2012 andJanuary 23, 2013; accepted February 19, 2013. Date of current version July18, 2013. Recommended for publication by Associate Editor S. Y. (Ron) Hui.

G. D. Szarka, P. P. Proynov, and B. H. Stark are with the Depart-ment of Electrical and Electronic Engineering, University of Bristol, Bristol,BS2 8BB, U.K. (e-mail: [email protected]; [email protected];[email protected]).

S. G. Burrow is with the Department of Aerospace Engineering, Universityof Bristol, Bristol, BS2 8BB, U.K. (e-mail: [email protected]).

Color versions of one or more of the figures in this paper are available onlineat http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/TPEL.2013.2251427

level have been reported [3]. However, in order to achieve the

maximum potential power of an energy harvester, it is important

that the power conditioning system provides the optimum load

for the generator for the particular input and output conditions.

Vibration harvesters have a “peak-power”-type response:

power variation with changing load damping is not monotonic,

displaying a peak at a damping level determined by harvester pa-

rameters [4]. Negative-feedback voltage regulation for switch-

ing converters cannot provide a stable operation at the peak

power point as the operating conditions required violate Middle-

brook’s stability criterion [5]. The optimum damping level of an

ideal harvester driven at resonance is independent of excitationamplitude; hence, one solution is to employ a converter emulat-

ing a fixed impedance to the harvester, as reported in [5] and [6].

However, fixed input impedance places restrictions on converter

design (principally requiring discontinuous conduction), and

this is difficult to maintain over the full range of input and out-

put conditions. The challenge for the power converter is then

to provide the basic functionality of rectification and voltage-

level shifting, while loading the harvester with the optimum

impedance, independently of its input and output conditions. In

this paper, the electromagnetic energy harvester is assumed to

be operating at its mechanical resonance frequency, making its

effective output impedance dominantly resistive [7], and con-stant over time. By contrast, the apparent input impedance of

the power converter depends on the input and output voltage

conditions. As these vary over time, dynamic control is required

to maintain the desired converter input impedance.

Maximum power point tracking (MPPT) schemes employ an

algorithm, such as gradient descent, to locate a peak power point

for the prevailing operating conditions. They are commonly used

to maintain temperature-dependent photovoltaic cells at their

peak power point [8], [9], and offer the ability to optimally load

an energy harvester, compensating for both variations in opti-

mal load and variations in converter output conditions. However,

when used with systems with significant stored energy (like the

kinetic energy harvesters investigated here) extra care must be

taken to ensure correct operation. The literature on maximum

power point tracking solutions for energy harvesting is relatively

sparse. Elmes et al. [10] reported a maximum energy harvesting

control scheme for an energy harvesting backpack generating

tens of watts of power. In [11], a microcontroller-based power

point tracker is reported for a rotational generator producing dc

output up to 10 mW; the circuit employs a resistance matching

strategy, similar to the approach adapted in [12] for submilliwatt

RF energy harvesting. One of the first authors to publish on peak

power control in the energy harvesting literature was Ottman;

the presented power converter architecture differed from the

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202 IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 29, NO. 1, JANUARY 2014

work here as the rectifier of the two-stage topology fed into a

stiff dc link, which itself was controlled to provide the power

tracking capability. Additionally, the paper focused on piezo-

electric transducers. Low-power solutions offering regulation

of the buffered output voltage of the rectification stage for max-

imum power point operation have been demonstrated in the lit-

erature: for piezoelectric harvesters using an off-the-shelf buck

converter operated intermittently [14], or for electromagnetic

generators using a low-power integrated boost converter [15].

Recently, an integrated maximum power point tracking circuit

has been presented in [16] that operates down to sub-100 µWlevels, using an approach referred to as power-optimal point of

charging for the control of a dc–dc charge-pump.

These solutions are designed to maximize the power gener-

ated by the harvester without considering the losses of power

conversion or the quiescent power overheads of any control and

ancillary circuits. Derivatives of the MPPT technique, referred

to as maximum power transfer tracking (MPTT) [8], are de-

signed to maximize the power transferred to the load and the

energy storage element. Dayal and Parsa [17] proposed a low-power implementation for an MPTT scheme, but only simulated

results are presented for the control circuit. In the reported pa-

per, the output voltage is maximized by varying the duty ratio

of the pulse width modulation (PWM) driving signal of a split-

capacitor ac–dc converter. This technique assumes that the load

is near constant and purely resistive; otherwise, maximizing

the voltage would not yield maximum output power conditions.

Also, it requires the energy storage element to be small in order

to be able to monitor the effect of varying duty ratio. These

assumptions pose impractical limitations on small-scale energy

harvesting that is typically characterized by very low generated

power levels, large energy storage elements, and load circuitswith highly dynamic power consumption.

The effects of the stored energy within the mechanical os-

cillator of the harvester on MPPT are alluded to in [10] and

[11], by stating that the control loop has to be slow in or-

der to avoid instability. However, the behavior of the har-

vester under varying damping and the implications regarding

the design of the control circuit has not been discussed in the

literature.

In this paper, the maximum response rate of the MPTT

algorithm resulting in stable operation is investigated and a

complete MPTT harvesting system is presented. Section II de-

scribes an electromagnetic energy harvester with the governing

equations of motion, investigating the harvester’s response todynamic electrical damping experimentally. Next, an analysis

of the harvester’s response to a step change in the damping is

described, which enables the derivation of the minimum settling

time required between perturbations of the control parameter.

Section III provides a description of the power conditioning

circuit. Section IV presents the operating principles for the

perturb-and-observe algorithm and describes the control circuit.

Section V presents experimental results that show the steady-

state performance of the MPTT and the behavior under transient

load and excitation conditions. Finally, Section VI summarizes

the key findings and concludes with suggestions for future

work.

Fig. 1. Small-scale electromagnetic energy harvester with a 3.4 g NdFeBmagnetactingas themovingmass withina coil woundusing600 turnsof 100 µmdiameter copper wire. The resonant frequency is 43.8 Hz. A piezoelectric thinfilm is bonded to the top of the cantilever for displacement monitoring.

II. ENERGY HARVESTER: STEADY-STATE AND

TRANSIENT CHARACTERISTICS

A. Electromagnetic Energy Harvester

A cantilever-type vibration harvester is used in this paper,

shown in Fig. 1. It features a BeCu beam with a 3.4 g Nd-

FeB magnet acting as the tip mass. Energy from the motionis transferred to the electrical domain via the electromagnetic

coupling between the moving magnet and a wound coil. The tip

mass is large compared to the beam; hence, the generator can

be modeled as a base excited, second-order, velocity-damped

mass–spring system, where the response to external forcing is

described by

mz̈ + cż + kz = mω2 Y sin ωt. (1)

The base displacement has an amplitude Y at an angularfrequency of ω . The equivalent mass at the tip is given as m,while c denotes theviscous damping within the system that is thecombination of the mechanical and the electrical damping. The

spring constant of the compliant beam is k , and z refers to themotion of the moving mass relative to the frame. The schematic

illustrations of the electromagnetic energy harvester and the

lumped element model of the spring-mass-damper system are

presented in Fig. 2.

The steady-state solution, referring to the condition where the

amplitude of the periodic motion is constant, is given as [4]

z(t) = Z sin(ωt − ϕ) (2)where the amplitude is given by

Z = mω2 Y

(k − ω2 m)2 + c2 ω2(3)

and the phase angle between the base and tip displacement is

given by

ϕ = tan−1 c ω

k − ω2 m . (4)

At the natural resonance frequency, which is described by

ω = ωn

= km

(5)

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SZARKA et al.: MAXIMUM POWER TRANSFER TRACKING FOR ULTRALOW-POWER ELECTROMAGNETIC ENERGY HARVESTERS 203

Fig. 2. (a) Schematic illustration of the electromagnetic energy harvestershown in Fig. 1, and (b) illustration of the lumped elements of the spring–mass–damper system.

Fig. 3. Load resistance profiles with various gradients, resulting in linear loadresistance sweeps between 1000 Ω and 100 Ω in 0.5, 1 s, 2, 4, and 8 s. Both(left) decreasing and (right) increasing resistance profiles are considered.

(2) simplifies to

z (t) = mωY

c sin

ωt − π

2. (6)

Depending on the application, both of the excitation fre-quency ω and amplitude Y can vary over time. Furthermore,damping arising from the interfacing electronics affects the to-

tal damping given by [4]

c = cm + θ2

Rcoil + Rload(7)

where cm represents the mechanical damping, θ the electromag-netic coupling coefficient, and Rcoil is the parasitic resistanceof the coil. Rload is the load resistance, which is synthesized bythe input impedance of the power converter in a practical sys-

tem. In typical small-scale electromagnetic energy harvesters,

the impedance of the parasitic coil inductance at the excitationfrequency is several orders of magnitude lower than the com-

bined equivalent mechanical resistive output impedance and ac

coil resistance. Therefore, it is assumed that close to the theoret-

ical, maximum power can be extracted using a purely resistive

load at resonance.

B. Illustration of Response to Dynamic Damping

The transient response of the mechanical system is related

to the energy stored in the oscillator and the total damping of

the system. To illustrate this experimentally, the load applied to

the harvester of Fig. 1 is swept from 100 to 1000 Ω at differing

rates (see Fig. 3), while the excitation is kept constant. Prior to

Fig. 4. Generated output power versus time corresponding to the 0.5, 1, 2, 4,and 8 s load resistance sweep profiles of Fig. 3. Excitation amplitude is activelyheld at 3.75 m·s−2 and the frequency is 43.8 Hz.

Fig. 5. Measured generated power profiles of Fig. 4 mapped onto correspond-ing load resistance sweeps and compared against steady-state measurements.

each sweep, the harvester is in steady state. The instantaneous

generated power is measured and averaged over one cycle. The

resulting output power–time profiles are presented in Fig. 4.

The output power mapped onto the corresponding load re-

sistance is shown in Fig. 5, resulting in hysteretic trajectories

of output power as the load is swept up and down at a particu-

lar rate. The cycle-averaged power recorded under steady-state

conditions is also shown for comparison. This reveals that the

maximum power that can be sustained by the energy harvesterat the optimum resistance of 400 Ω is around 870 µW; how-ever, during a sweep, much higher powers are available if the

damping is rapidly increased and much lower powers while the

damping is being reduced.

This behavior can be understood by considering the energy

stored in the mechanical components of the harvester. Most

harvesters feature significant amplification of source vibrations,

analogous to the quality factor or “Q” of electrical resonant cir-cuits. Q also defines the ratio of energy stored in an oscillator tothat dissipated each cycle. Thus, for high-Q systems, a change inthe operating point requires significant energy to be either added

or dissipated. At high load resistance, corresponding to low

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Fig. 6. (a) Generated rms current and voltage waveforms during the 4 s sweeptransients, and (b) current and voltage excursions mapped to the correspondingload resistance.

damping, significant energy is stored in the system. Increasing

the damping reduces the displacement of the mass, thereby re-

ducing the stored energy, which is seen as transient additional

output power. Conversely, reducing the damping leads to an

increase in stored energy, which although is supplied by the

vibration source, limits the rate at which the new steady state

is approached. As the rate of change of the electrical damp-ing is reduced, the measured output power levels converge to

the steady-state solution. The generated rms current and volt-

age transients are illustrated in Fig. 6 for the 4-s sweep case.

The curves show that during the increase of the damping, the

corresponding transient voltage and current travels are higher

than during decreasing damping, as some of the initial kinetic

energy of the energy harvester is dissipated. The behavior illus-

trated here is of great importance when implementing a power

tracking scheme. If the controller does not take into account the

transient component of the output power by allowing sufficient

settling time of the harvester, the system can become unstable.

C. Response to Step Change in Damping

In this section, a step change in the damping is considered,

as might be the case when a digital system steps a control refer-

ence signal. The harvester is modeled as a highly underdamped,

single-degree-of-freedom mass–spring–damper system, excited

at its natural frequency with constant acceleration amplitude.

Also, prior to the change, the mechanical structure is assumed

to be in steady state. The damping as a function of time can be

described as

c(t) = co , t ≤ 0cs , t > 0

. (8)

In the steady-state solution of (6), the amplitude of the tip

displacement before the step change is

Z o = mωY

co(9)

and after the step change, the oscillation should settle to the new

steady-state solution with a tip displacement amplitude of

Z s = mωY

cs. (10)

The initial conditions for the nonhomogeneous second-order

differential equation of (1) are obtained by finding the steady-

state displacement and velocity at time t = 0. Hence, the initialdisplacement is z (0) = −Z o , and velocity is ż (0) = 0. Thesolution of the differential equation is

z (t) = (Z s −Z o ) e−(cs /2m )t cos (ωβt)

+ (Z s −Z o ) cs

2mωβ e−(cs /2m )t sin(ωβt) − Z s cos (ωt) (11)

where β is given as

1 − ζ 2 , and the damping ratio ζ is

ζ = c

2√

mk. (12)

In a highly underdamped system (ζ < 0.1), such as typicalsmall-scale electromagnetic energy harvesters, β is assumed tobe 1. This simplifies the solution to

−z (t) =

Z s + (Z o − Z s ) e−(cs /2m )t

cos(ωt)

+ (Z o −Z s ) cs

2mω e−(cs /2m )t sin(ωt) . (13)

This equation shows that the underlying sinusoidal oscillationwith initial amplitude of Z o decays exponentially to a sinusoidaloscillation with amplitude of Z s , with a rate that is determinedby the total damping and the moving mass.

This time-domain solution is validated (see Fig. 7) using

measured output power for several step changes in the load

resistance. The measurement results show a good correlation

with the calculated waveforms.

The second exponential term of (13) can be considered negli-

gible in a highly underdamped system, where the damping coef-

ficient is very small, as the denominator of multiplying fraction

is typically greater than 1, and the product of (Z o −Z s ) cs issmall, in the order of 10−

5

. Hence, the amplitude of the sinu-soidal oscillation is dominated by

|z| ∼= Z s + (Z o −Z s ) e−(cs /2m )t (14)an exponential decay to the new tip displacement amplitude.

Differentiating this solution yields the approximate solution for

the velocity

v (t) = Z s ω sin(ωt) + (Z o − Z s ) cs2m

e−(cs /2m )t cos(ωt)

+ (Z o − Z s ) ωe−(cs /2m )t sin(ωt) . (15)Considering that the velocity amplitude in the steady-state

solution is given as V̂ = Z ω and that ω c/2m, the velocity

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Fig. 7. Calculated, based on (13), and measured average output power duringthe transient response of the system that occurred after a step change in theload resistance. Initial load resistances are shown on the right; after the stepchange, the resistance is constant at 400 Ω. Excitation is a constant 3.75 m

·s−2

acceleration at 43.8 Hz.

amplitude during the transient response can be approximated

with great fidelity in a highly underdamped systems as

|v| = V̂ s +

V̂ o − V̂ s

e−(cs /2m )t . (16)

D. Minimum Settling Time Selection

The assumption is made that in order to avoid instability from

any system condition, a digital control system should initiate a

step change in damping c only once the system has settled. Thesettling time in this paper is defined as the time required for the

output power to reach within 1% of its final value. In a typi-cal MPPT system, adjusting of the control parameter varies the

apparent input resistance of the interfacing power electronics,

resulting in discrete step perturbation of the generator damp-

ing. Considering these steps, a harvester settling time can be

defined and used as the lower limit on the time period between

adjustments.

The counterelectromotive force induced in the coil is propor-

tional to the velocity of the moving magnet according to

U (t) = Blv(t) = θv(t) (17)

where B is themagneticfield strength and l is the effective length

of the conductor within the magnetic field. Thus, the amplitudeof the induced sinusoidal voltage is the coupling coefficient

θ times the velocity amplitude given in (16). The steady-stateinstantaneous current is dependent on the total load resistance

of the circuit and is equal to

i(t) = U (t)

Rcoil + Rload2(18)

where Rload2 denotes the load resistance after the step change,and during the settling time. During the settling time, the ampli-

tude of the generated current will decay exponentially toward

the steady-state value

I (t) = I s + (I o − I s ) e−(cs /2m )t

(19)

where I s and I o are given according to

I = θmω2 Y

c (Rcoil + Rload2 ) (20)

with c=cs and c=co , respectively. The instantaneous generatedpower dissipated in the load resistance is given as

P (t) = i2 (t) ·Rload2 . (21)Defining a common factor as

A = θ2 m2 ω4 Y 2

(Rcoil + Rload2 )2 Rload2 (22)

allows us to write the current and power amplitudes as

|I | =

A

Rload2

1

cs+

1

co− 1

cs

e−(cs /2m )t

(23)

and

|P | = A 1

c2s +

2

cs 1

co − 1

cs

e−(cs /2m )t

+

1

co− 1

cs

2e−(cs /m )t

. (24)

According to the definition of the settling time, at t = t s theamplitude of the power for increasing damping should be

|P | = P s (1 + ε) (25)where P s = A/c

2s , and the error ε is 0.01. Substituting (25) into

(24), then dividing both sides by A and rearranging to one sideyields

− ε 1c2s

+ 2cs

1co− 1

cs

e−(cs /2m )ts

+

1

co− 1

cs

2e−(cs /m )ts = 0 (26)

Multiplying both sides by ec sm ts c

2s co / (cs − co ) gives a

quadratic equation in the form of

ε co

cs − co x2 − 2x − cs − co

co= 0 (27)

where x = exp[(cs /m)ts ]. Only the positive root of thequadratic equation yields a real solution

e(cs /2m )ts = 1 + √ 1 + εεco /(cs − c0 ) (28)

Isolating the settling time ts gives

ts = 2m

csln

1 +√

1 + ε

εco|cs − co | . (29)

Equation (29) gives a conservative estimate that typically falls

within 0.5% of the exact solution derived numerically from (13).

Therefore, this formula provides a convenient means of esti-

mating the minimum interval between perturbations in digital

maximum power tracking control systems. It also shows the

dependence on harvester parameters and tolerances.

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Fig. 8. System-level block diagram showing the main power electronics blocks and the power definitions within the main power flow of the system.

III. POWER CONVERTER AND ANCILLARY CIRCUITRY

The power conditioning system architecture is shown in

Fig. 8. It builds on the low-power system reported by Szarka

et al. [6], with the addition of low-power measurement and con-

trol circuits for the MPTT control, and a modified low-power

gate drive circuit design.

The output voltage across the supercapacitor varies, therebyallowing the stored energy to be maximized; at the same time it

is kept within the allowable dc supply voltage range of the load

electronics, which avoids the losses of additional voltage reg-

ulation. Zero-energy start-up is provided by a passive voltage

multiplier circuit that is automatically disconnected when the

active power converter circuit becomes operational. The main

power converter is a nonsynchronous full-wave boost rectifier,

as shown in Fig. 9, which provides rectification and voltage

boosting in a single stage. The parasitic coil impedance, al-

though considered to be negligible at the mechanical resonance

frequency, is significant at the switching frequency of the power

converter and can be used to eliminate the need for an additionalboost inductor. The MPTT control circuit adjusts the duty ratio

δ of the PWM gate drive signals. This controls the apparentinput impedance of the converter, preserving maximum output

power Pstore. Consequently, near-optimum damping conditions

for the energy harvester are maintained independently of vari-

ations in the output voltage, the conduction mode, and the ex-

citation magnitude; all of which are time-varying factors that

influence the apparent input impedance of the power converter.

The particular converter topology selected here does not support

bidirectional power flow, thus restricting the control to resistive

impedance matching only. This approach may be suboptimal

when the generator is excited off resonance; however, it offers

Fig. 9. Circuit schematic of a nonsynchronous, full-wave boost rectifier thatuses the parasitic coil inductance as the boost inductor. The semiconductordevices used are M1/M2—PMF-280UN and D1/D2— 1PS79SB30.

high utilization when the source excitation is at the mechanical

resonance frequency [3]. An example of typical input current

and voltage waveforms are shown in Fig. 10.

The gate drive circuit generates two-variable duty ratio PWM

signals for the twolow-side transistors. Theswitching frequency

is constant 32.768 kHz, determined by the output of the low-

power oscillator chip (OV-7604), as shown in Fig. 11. Polarity

of the input voltage is sensed by a thin-film piezoelectric sensorbonded to the cantilever beam.

A saw-tooth signal is created using a one-shot circuit and a

modified RC filter that provides a slow discharge of the 15 pF

capacitor. The duty ratio is determined by the “Reference”

input, which is the common interface to the control circuits.

The logic output stage, which directly drives the gates of the

MOSFETS, receives polarity information from the detection

circuit. At any moment in time, only one of the outputs is tog-

gled at the switching frequency, while the other PWM signal is

kept high. The only exception to this is during a blanking period

around the zero-crossing of the generator’s output voltage, when

both outputs are low.

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Fig. 10. Measured typical input current I in and voltage V in waveforms. A period of 100 µs at 5 ms point is shown on the right for increased resolution. The dutyratio of the converter is 67% and the output voltage is 3.2 V. The energy harvester is excited with 43.8 Hz, 3 m·s−2 acceleration, producing a little over 450 µW.

The printed circuit board implementation of the power condi-

tioning system is shown in Fig. 12, corresponding to the block

diagram presented in Fig. 12.

IV. CURRENT-SHUNT-BASED MAXIMUM POWER

TRANSFER TRACKING

A. Operating Principles and Measurement

A typical low-power energy harvesting system requires large

capacity storage in order to be able to supply the high peak-to-mean ratio power demand required by load electronics such as

wireless sensor nodes. The combination of low output power

and large storage capacitance results in slow charge up of the

supercapacitor. This enables the MPTT control to rely solely on

output current measurement. The reference signal that sets the

duty ratio of the boost rectifier is perturbed, and the effect of

this on the power transferred to the supercapacitor is observed

by measuring the output current while the output voltage is as-

sumed to be near constant. This implementation requires the rate

of change of the output voltage to remain low enough to ensure

a near-constant voltage between successive measurements. In

the presented system, this limits the minimum capacitor size to

20 mF, when the worst-case voltage increase between measure-ments is 5 mV.

The measurement circuit is an operational amplifier based

circuit (see Fig. 13) that is designed to measure the voltage

drop across a 150 Ω precision shunt resistor. The current ripple,both at the switching and at the excitation frequency, must be

minimized to ensure correct measurement.

This is achieved by a combination of parallel capacitance

introduced before the shunt resistor in the circuit, and an ac-

tive low-pass Sallen–Key [18] architecture employed in the de-

sign of the amplifier circuit. The 30 µF capacitor smoothes theswitching frequency current ripple without adding any signif-

icant delay to the response of the system to the perturbation.

Fig. 11. Gate drive circuit generating 32.768kHz output PWMsignals. “Pos,”“Neg,” and “Blank” are digital signals from the polarity detection circuit [6].“Reference” is an analogue signal from the control circuit to set the duty ratio.

Fig. 12. Printed circuit board implementation of the main power conditioningsystem blocks, corresponding to Fig. 12.

The second-order Butterworth filter has a cutoff frequency of

20 Hz, approximately half the excitation frequency, in order to

provide a close to dc current measurement at the output of the

amplifier. The micropower operational amplifier MCP6031 is

selected because of its low input offset voltage that is typically

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Fig. 13. Shunt-resistor-based current-sense amplifier using a low-passSallen–Key architecture [18].

Fig. 14. Digital MPTT circuit using a low-power MSP430 microcontrollerthat samples the output current using a 10-b ADC and controls the referencevoltage of the duty ratio by an 8-bit 0–450 mV output R–2R ladder. The samplereadings are synchronizedto the generator’s displacement cycle using the outputof the piezoelectric displacement sensor.

around 150 µV [19], its low current consumption, and rail-to-rail input/output signal support. The gain of 30 V/V is selected,

in order to maintain a sufficient signal-to-noise ratio.

B. Digital Implementation of MPTT

The well-known perturb-and-observe algorithm is imple-

mented on a MSP430F1132 microcontroller: the PWM dutyratio of the boost converter is altered and the consequent change

in the output power is measured when the mechanical struc-

ture has settled. Based on the measured outcome, the direction

of the subsequent alteration is determined and the process re-

peated. The controller’s CPU is clocked at 5 MHz frequency

in order to minimize the power hungry on-time. The 10-b on-

board analogue-to-digital converter (ADC) converts the current

amplifier’s output, and the reference voltage for the duty ratio is

set by an R–2R ladder, shown in Fig. 14. The top two bits of theladder are connected to ground, while the remaining eight bits

are controlled via a full output port of the controller. This pro-

vides a 1.75 mV resolution with a maximum output of 450 mV.

Fig. 15. Steady-state characterization of power conditioning system in open-loop configuration. Voltage reference is stepped using an external signal at>5 s intervals. Excitation is held at 3.75 m·s−2 and 43.8 Hz. Output voltage isregulated using a shunt regulator circuit as a load (LM4041).

The reference voltage is therefore changed in discrete steps of

1.75 mV, corresponding to a 0.6% change in the duty ratio.

The worst-case minimum time required between perturbations,

using (29), is approximately 350 ms, roughly 15 displacement

cycles. The output of a level-crossing detection circuit that mon-

itors the piezoelectric sensor output is used as a nonmaskable

interrupt (NMI) that wakes the microcontroller up from “sleep

mode.” This approach not only circumvents the need for a power

hungry timer circuit but also ensures that the sample readings are

synchronized to the displacement, which was shown to improve

the control circuit’s stability [10].

Under this configuration, the microcontroller is active for atotal of 90 µs, plus an additional 25 µs when only the internalADC is ON, in every 342.5 ms period. This results in an average

power consumption of approximately 750 nW.

V. EXPERIMENTAL RESULTS

A. Steady-State Performance

In order to evaluate the effectiveness of the MPTT circuitry,

the power P store as a function of the duty ratio is measured. Thisis the useful output power after subtracting lossesincurred dueto

nonideal loading of the generator, during the power conversion

process, and the quiescent power overheads of the ancillary and

control circuits. In this test, the output voltage is kept constantusing a micropower shunt regulator (LM4041) and the reference

voltage is stepped using an external source in 5 s intervals to

create quasi-steady-state measurements. During all of the tests

presented in this section, a 68 mF supercapacitor is used as the

main energy storage element. The combined current consump-

tion of the ancillary circuits and the leakage current drawn by

the start-up circuits is 19 µA at 2 V output voltage and increasesto 22 µA at 4.5 V output. The digital control circuit adds anadditional 3 µA, amounting to a total of 44 µW of minimumquiescent power loss.

Fig. 15 presents the results measured at 3.75 m·s−2 excitationmagnitude, corresponding to a maximum extractable power of

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Fig. 16. Measured duty ratio samples and their modal values compared withthe range of duty ratios (shaded region) that correspond to over 99% of themaximum useful output power based on the measurements of Fig. 15.

870 µW under optimum load conditions. The maximum trans-ferred power is 615 µW at 2 V at the optimum duty ratio. Thiscorresponds to a power conversion efficiency of 78.5%, and an

overall system efficiency of 70.7%, where 100% is the maxi-

mum extractable power from the energy harvester. As the output

voltage is increased, the optimum duty ratio is also increased.

The maximum useful power is, however, reduced due to the

increased power overheads of the power conditioning circuits.

It is worth noting that a small dip in the power level can be

observed in the 4.5 V line around 80% duty ratio, creating two

local maxima that could result in the failure of a perturb-and-observe MPTT algorithm. During normal operation however,

this situation would not arise, as the output voltage rises slowly

across the large capacity storage element, allowing the algorithm

to track the correct peak. Starting the tracking at high duty ratios

would also reduce the risk of finding the wrong local maximum.

Fig. 16 shows duty ratio at discrete output voltages, held con-

stant by the adjustable shunt regulator circuit. As the duty ratio is

constantly changing, even in these steady-state conditions, 100

recordings of the duty ratio are plotted, as dots, for each voltage,

showing a range of around ±2.5%. The solid black line is fittedover the statistical modal value of each group of 100 samples,

representing the most frequent duty ratio. The shaded region

in Fig. 16 represents the duty ratio range over which in excessof 99% of the maximum transferred power is obtained. This

region widens toward the low output voltage levels, as can also

be seen in Fig. 15. The modes of the duty ratio measurements

fall within the 99% power region for most of the output voltage

points, which shows that the control circuit can effectively track

the optimum power point.

Duringthe measurementsof theduty ratio samples, theenergy

harvester’s generated power, the transferred power, and the qui-

escent power overhead of the power conditioning system were

also recorded. The 100 measurement points were averaged, to

take into account that the duty ratio ranges around an optimum

value. These values are plotted in Fig. 17 against output volt-

Fig. 17. Average power obtained from 100 measurements per output voltage.Output voltage is regulated by an adjustable shunt regulator. Constant frameacceleration of 3.75 m·s−2 at 43.8 Hz. P m ax is the maximum extractableharvester power under optimum load conditions.

age, along with the maximum extractable power from the energy

harvester under optimum load conditions for comparison.

The difference between the measured generated power and

the transferred power are due to a combination of three major

loss mechanisms: 1) a nonideal power conversion process; 2)

quiescent power overheads of the control and ancillary circuits;

and 3) the conduction loss in the shunt resistor used for the

monitoring of the output current.

The ratio between the generated power of the nonideally

loaded harvester and the maximum potentially extractable

power under optimum load conditions is referred to as the uti-lization factor. The utilization of the energy harvester peaks

above 89% at 1.8 V output, and remains over 86% over the en-

tireoutput voltage range. Less than 100% utilization is primarily

due to the increased conduction losses within the coil that result

from switching frequency current ripple. The power conversion

efficiency is calculated as the ratio of the useful output power

(P store ) of the converter to the generated power of the harvester,while the overall system effectiveness is defined as the useful

output power normalized to the maximum extractable power

from the energy harvester under optimum load conditions. The

conversion efficiency is at its maximum of 76.5% at low voltage

levels where the quiescent power overhead is at its minimum,

dropping down to 66% at 4.5 V. The peak overall effective-

ness reaches almost 70%, which when compared against the

maximum of 70.7% recorded under the steady-state characteri-

zation (see Fig. 15) shows a highly effective control.

B. Transient Response to Step Change in Excitation and

Output Voltage

The dynamic performance and stability is evaluated by

recording the transient behavior of the power conditioning cir-

cuit, monitored by the duty ratio of the converter, in response

to a step change in the frame excitation magnitude and in the

output voltage under the worst-case considerations.

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Fig. 18. Outputcurrentand duty ratioin response toa step change in excitationmagnitude from 3 to 4 m·s−2 at a constant 2.5 V output. The frequency isconstant at 43.8 Hz. The current is inferred from the output of the current-senseamplifier circuit.

First, a step change in the acceleration magnitude from 3

to 4 m·s−2 is considered (see Fig. 18) potentially providingtwice the generated power. The output voltage is maintained at

a constant 2.5 V for the test. The increase in excitation ampli-

tude results in increased generated power and voltage, which,

in turn, affects the emulated resistance of the power converter.

The control adjusts the duty ratio of the rectifier, and is seen to

reestablish optimum damping conditions within around 4.5 s.

At the instant of the step change in the frame acceleration mag-

nitude (just before the 2 s mark), the available generated power

and thus the useful output power increases at a rate that is dom-inated by the mechanical response of the energy harvester, i.e.,

the time required by the tip mass to build up its momentum.

The duty ratio of the power converter, as a means of moni-

toring the control trajectory of the algorithm, is also presented

in Fig. 18. The results show the clearly distinguishable duty

ratio steps that characterize the digital implementation of the

perturb-and-observe algorithm, and the tracking around a new

“optimum” point.

A worst-case step change in the load conditions is also con-

sidered in this study: a rapid discharge of the energy storage

element from its maximum rated output voltage of 4.5 to 2 V, as

shown in Fig. 19. This situation mimics the burst release of en-

ergy from the storage that may occur as a result of the executionof a power hungry task by the load electronics. Small dynamic

variations in the power consumption of the load do not affect

the output power performance of the power conditioning circuit

as the 68 mF supercapacitor provides a buffer between the load

and the power converter that smoothes these changes.

The output current waveform is also presented in Fig. 19.

During the discharge of the output capacitor, the output of the

current-sense amplifier is saturated, and then the current starts

to increase as a result of the changing duty ratio of the power

converter. The duty ratio drops from around 84% to below 70%

and converges to a new optimum condition in approximately

8.5 s after the start of the discharge.

Fig. 19. Rapid discharge of the 68 mF supercapacitor from its maximumrated voltage of 4.5 to 2 V via an adjustable shunt regulator (LM4041), thusmimicking a burst release of the stored energy for the load application.

Fig. 20. Charging of a 68-mF supercapacitor over 500 s, showing zero-energystart-up and active MPTT. The overall system efficiency is normalized to themaximum extractable power of 870 µW. Measurements were taken at constantframe acceleration of 3.75 m·s−2 at 43.8 Hz.

This reaction time represents the worst-case scenario as it

corresponds to the largest optimum duty ratio difference that

can occur under normal operation conditions and is a function

of the maximum rate of change of the duty ratio of the control

circuit and, thus, of the calculated settling time. An energy

harvesting system with smaller tip mass, for example, would

have a smaller settling time and the control could be set to react

more quickly to rapid changes in the environmental conditions

or in the power drawn by the load electronics.

C. Overall System

The last test is aimed to present the capability of the power

conditioning system to start-up from zero-energy conditions

and then track the maximum power transfer point actively while

charging a 68 mF supercapacitor.

At a constant excitation of 3.75 m·s−2 , the charging of thesupercapacitor is recorded over 500 s (see Fig. 20) along with

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Fig. 21. Comparison of charge up times of a 68 mF supercapacitor using: 1)passive voltage quadrupler circuit; 2) full-wave boost rectifier in an open-loopwith constant duty ratio of δ = 0.67; and 3) full-wave boost rectifier with MPTTcontrol. Excitation is regulated to be 3.75 m·s−2 at 43.8 Hz.

the duty ratio (inferred from the reference voltage of the control

circuit). The measured output voltage and useful output current

of the power converter are used to calculate the transferred

power. Theratio of this to the maximum extractable power under

optimum load conditions provides the overall system efficiency

ηover (see Fig. 20).The passive quadrupler circuit provides zero-energy start-

up, charging the supercapacitor to 1.85 V at which point the

active boost rectifier circuit starts to operate. The duty ratio,

starting from a high initial value, quickly finds and tracks the

optimum power transfer point over the charging of the capacitor.

The overall efficiency is highest at low output voltages with anaverage value of close to 70%, as presented in Section V-A.

The recorded instantaneous efficiency may exceed this due to

the inertial effects of the mechanical structure resulting in short

burst of power when the damping is increased.

Fig. 21 presents the transient accumulation of energy in the

68 mF supercapacitor when charged by differing power condi-

tioning solutions: 1) passive voltage quadrupler; 2) the full-wave

nonsynchronous boost rectifier in open loop with a constant duty

ratio of δ = 0.67; and 3) full-wave boost rectifier with MPTTcontrol. The start-up phase is common for all approaches, pro-

vided by the passive voltage multiplier circuit, during which the

capacitor is charged from 0 to 1.85 V.

The results illustrate that the overall output power gain of the

system when MPTT control is employed: The total charge-up

time, corresponding to 0.5 J of energy stored, is reduced by

26.5% and by 8.6% as compared to the passive circuit and the

open-loop systems, respectively. A summary of the key system

metrics is presented in Table I.

VI. CONCLUSION

The work presented in this paper aimed to address the chal-

lenges that arise from implementing MPTT for low-power, ki-

netic electromagnetic energy harvesters. The transient response

of the single-degree-of-freedom mechanical system is presented

TABLE IKEY SYSTEM METRICS

and discussed using experimental results and analytical deriva-

tions. A method that aids the design of perturb-and-observe

algorithm-based control with discrete perturbations of the con-

trol parameter is presented: the minimum time required between

perturbations in order to allow the mechanical structure to set-

tle is calculated for highly underdamped mass–spring–damper

systems under the assumption of a constant, sinusoidal, nondi-

rect excitation that occurs at the natural resonance frequency of

the mechanical structure.A complete power conditioning circuit for a low voltage, sub-

milliwatt electromagnetic energy harvester has been presented

that requires no external power and is capable of self-starting

from zero-energy conditions. In contrast with previous work,

the transferred power is maximized instead of the generated

power, thus accounting for the losses suffered during the power

conversion process and the due to the quiescent power over-

heads. Good peak power tracking effectiveness is demonstrated

despite of the lack of accurate regulation of the apparent input

impedance of the boost rectifier, thus allowing the use of a slow

feedback control, and consequently, a reduced quiescent power

implementation. The total power consumption of the power con-

ditioning system is 44 µW at 2 V output.Steady-state and transient measurements show that the system

is stable and capable of tracking the maximum power transfer

point by optimizing the duty ratio of the PWM signals of the

boost converter over the entire output voltage range. A harvester

utilization of up to 89% is achieved. Overall system effective-

ness up to 70% is recorded, corresponding to approximately

600 µW of useful output power. The transient responses showthat the calculated settling time provides a reasonable choice for

the minimum time between perturbations. The power converter

topology used in this study can only synthesize resistive load

conditions, limiting the maximum achievable utilization when

the harvester is not in resonance as the optimum load required

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can have a significant reactive component. A natural extension

of the work would be to apply MPPT control to converters

capable of synthesizing complex load impedances.

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