IEEE Solid-States Circuits Magazine - Fall 2021 - 99

The basic standard full-bridge rectifiers
(FBRs) have the advantages of
simple structure and operation. However,
the extracted power tends to be
low [8], [9]. Nonlinear switching techniques,
such as synchronous electric
charge extraction (SECE) and parallel
synchronized switch harvesting
on an inductor (P-SSHI), have shown
to successfully boost the extracted
power with synchronous switching
when vibration displacement reaches
its peak [4], [5], [10]-[30]. Delays are
introduced into the switching timing
[18], [31]-[35], allowing complex impedance
matching and performance
improvement at off-resonance. Furthermore,
interfaces that employ multiple
transducers are developed to
boost the extracted power [36]-[38].
Regardless of the architecture, the
operation of an individual interface
needs to be optimized through proper
parameter settings. For example,
the extracted power often varies with
the effective loading that the transducer
sees. Many works incorporate
a switching power converter after the
rectifier, and the effective loading can
be adjusted by changing the converter's
switching timing [39]. Start-up or
runtime calibrations are required to
maintain optimal performance when
the operating condition varies. Different
implementations with maximum
power point tracking (MPPT) algorithms,
such as perturb and observe
(P&O) and fractional
V ,OC
are proposed,
exhibiting tradeoffs in circuit complexity,
tracking accuracy, convergence
time, and power consumptions [40]-
[43]. This article introduces the stateof-the-art
interface designs and MPPT
methods for piezoelectric energy harvesting
while emphasizing the circuit
implementation considerations.
Equivalent Circuit Model
Piezoelectric materials produce
electrical charges when mechanical
strain is applied [3]. While piezoelectric
transducers can be of various
shapes and sizes [44], a common
structure is a cantilever beam with
a mounting mass, as shown in Figure
1(b). In the presence of a shock or
Vibration
CP
ZS = RS + jXS A
IS
RS C1 L1
VS
CP
ZL = RL + jXL A′
Piezoelectric Transducer
(Equivalent Circuit Model)
Power Processing
Circuit
(b)
FIGURE 1: The (a) power density versus voltage for various energy sources and (b) piezoelectric
energy-harvesting system and equivalent circuit model.
IEEE SOLID-STATE CIRCUITS MAGAZINE
FALL 2021
99
IL
+
VCP
-
Power Interface
Circuit
Energy
Energy
Harvest Control
Circuit
Control
Signal
vibrations, the dangling mass moves
up and down, causing strain onto the
piezoelectric material. With conductive
wires connecting the piezoelectric
cantilever electrodes to a load, the generated
charges flow through the current
loop, and power can be delivered
to the supplied system. Supposing the
structure has widely separated model
density and is vibrating at around its
resonant frequency, it can be modeled
as a mass + spring + damper + piezoelectric
system [8], and the governing
equations can be described as
Mu tu tKut Vt Ft() ()
po
() () ()++ H+=
h
CP
-+H o () PL
ut CV tI t
.
CP()=- (),
(1)
(2)
Power Density (W/cm3)
1,000
10,000
Fuel Cell
100
10
0.01
0.1
1
Electromagnetic
Piezoelectric
Thermoelectric
Solar Cell
where M, ,h K, Θ, and CP
are the mass,
mechanical damping coefficient, effective
stiffness, piezoelectric coefficient,
and capacitance between the
electrodes, respectively. In addition,
F(t) is the forcing function applied to
the system. In cases of constant vibrations,
F(t) is assumed to be a singletone
sinusoid with an amplitude of ,F0
and, in cases of shock excitation, F(t)
can be modeled as an impulse function.
In addition, u(t) is the displacement
of the mass,
Vt
ItL
CP () is the voltage
across the piezoelectric electrodes,
and ()
the piezoelectric electrodes.
With (1) and (2), the piezoelectric
transducer can be further transformed
is the current flowing out of
0.01
Mass
0.1
1
Voltage (V)
(a)
10
100
Energy Storage
Supplied System
IEEE Solid-States Circuits Magazine - Fall 2021

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