IEEE Solid-States Circuits Magazine - Fall 2021 - 100

[31] into an equivalent circuit model
shown in Figure 1(b), where
R /,S
VF /.S
= H Figure 1(b) also shows the
electromechanical interface as the
line
= h H2
AA .l
The transducer structure
exhibits two resonant frequencies,
namely, the open-circuit resonant frequency
//()LC CC C
1 PP11
1
and short-circuit resonant frequency
/.
~SC =1 LC
11
As shown in Figure 1(b), a power
processing circuit transfers the extracted
power to the supplied system
after proper conditioning, including ac-
dc conversion, energy storage, and, in
many cases, voltage regulation. In addition,
the power processing circuit also
sets the loading seen by the transducer.
In fact, if the power processing circuit
and its parallel combination with Cp
can be modeled as a linear impedance
ZR ,jXLL L
=+ according to the maximum
power transfer (MPT) theorem,
the power that flows into the electrical
domain reaches the maximum when
the impedances at two sides of the electromechanical
interface ()
AACK1
2
=
H /, LM /
1 = H2 and
VR F88S /( )/(), which depends
2
S =
2
h
only on the force and mechanical
damping coefficient but not on the
piezoelectric coefficient. However, in
practice, the electrical behavior and
actual extracted power depend significantly
on the interface operations.
~OC=+ Basic Interface Circuits
Full-Bridge Rectifiers
As a piezoelectric transducer generates
ac current during vibrations,
a rectifier is required to supply a dc
voltage to the application circuits. Figure
2(a) shows an FBR that has been
used extensively due to its simplicity.
A large capacitor CRECT
at the rectifier's output so that VRECT
is constant during the quasi-steady
state. Figure 2(c) shows the waveforms
of the interface current IS
positive half cycle and discharges CP
to VOC
-
2V .OC
during the negative half cycle,
therefore creating a peak-to-peak
open-circuit voltage of
On the
other hand, when a rectifier is used,
the diodes D1
on when VCP
and D4
to C .RECT
will be turned
is charged up to VRECT
(assuming a zero diode voltage drop),
directing IS
Similarly, during
the current's negative half cycle,
D2
and D3
will be turned on once VCP
is discharged to -V ,RECT again directIn
other words, only
ing IS to C .RECT
part of the charges are delivered to
the load, while some are wasted in
charging and discharging
C .P
is placed
and
voltage V ,CP with and without the rectifier.
From the equivalent model in
Figure 1(b), the interface current IS
depends on the operating frequency
as well as the equivalent load
Z .L
l are complex
conjugate to each other. In other
words, the MPT can be achieved with
ZR jX ZR jX
LL LS SS
=+ == +
whereXL ).C /(1
S 11
~~
() ()),
)
(3)
=- At the MPT,
the extracted power ideally equals the
theoretical available power PAVL
IS
D1
D2
CRECT RLOAD
VCP
PET
CP
D4
(a)
IS
D1
VCP
PET
CP
D2
VRECT
CRECT
RLOAD
+VRECT
(b)
(c)
FIGURE 2: The schematics of the (a) FBR and (b) HBR as well as the (c) interface current and voltage waveforms. PET: piezoelectric transducer.
100
FALL 2021
IEEE SOLID-STATE CIRCUITS MAGAZINE
Time
+VRECT
-VRECT
HBR VCP
D3
VRECT
+VOC
-VOC
FBR VCP
Time
VCP, OC
Time
In
many application scenarios, the extracted
power is so small compared to
PAVL
can
or, equivalently, the real part of
ZL is so small that the current IS
of
be considered constant, independent
of the extracted power [9].
Without any loading, the transducer
sees an open-circuit load. In this
case, IS
charges CP
IS
QS
Time
to VOC+ during the
=- -cm (4)
which peaks when
per half cycle is
2
Ehalf
CVOC
2
P
P
2CVRECT
VOC
2
2
,
VV /,2
RECT = OC
and the maximum extracted power is
CV .f·
2
P
OC
The simplicity of using the FBR
facilitates its wide adoption, and its
passive operation further allows
autonomous systems. This renders
it as a benchmark for other interface
circuits. However, it has several drawbacks:
1) it needs an MPPT circuit so
as to set VRECT
at V /2OC
and V ,OC
and 2) its
maximum output power depends on
CP
which, in turn, depends
on the operating frequency. For a
typical piezoelectric transducer, CP
It can be
shown that the energy harvested on
CRECT
IEEE Solid-States Circuits Magazine - Fall 2021

Table of Contents for the Digital Edition of IEEE Solid-States Circuits Magazine - Fall 2021
