IEEE Circuits and Systems Magazine - Q3 2018 - 34

M
Ip

Vdc
Cstore

Vc 2

S
Vdc
Vc 2

VS
t

Figure 8. schematic of the frequency up-conversion rectifier
and relative simplified waveforms.

Vpiezo

Vpiezo
S
Cp

u
L

VS
t

Figure 9. Typical voltage Vpiezo, displacement u, and switching Vs waveforms due to the resonant effect when no load is
connected [69].

estimated in [63]. To overcome this limitation, due to the
low operational frequency of conventional piezoelectric
transducers, Li et al. [63] proposed a frequency up-conversion technique to shift the working operational frequency to higher values (from 32 to 3.2 kHz); see Fig. 8.
An alternative rectification approach, which uses
switched magnetic components to reduce the size of
inductors and transformers, employs resonant PEH rectifiers to efficiently scavenge vibrational energy. There
is a clear distinction between the resonant rectification
techniques and the frequency up-conversion techniques
because, the operational frequency of the electronic interface in the first case is shifted to higher frequencies
while, in the second case, the electronic interface works
synchronously with the vibrational frequency. The resonant rectification technique relies on switched magnetic
components (inductors and transformers) to achieve a
resonant effect with the parasitic reactance of the piezoelectric transducer. All of the rectification schemes require strict timing control to guarantee correct operation. Resonant rectifiers usually allow an efficient energy
harvesting from a wide range of vibrational frequencies
since autonomous switch techniques are employed to
constantly monitor the environmental conditions, see
34

Ieee cIRcuITs anD sysTems magazIne

Section III-I. Furthermore, some of the proposed rectification schemes have been successfully employed to
scavenge energy from multi-mode vibrations [64] or
from random vibrations [65].
Another popular technique employs MPPT algorithms
to monitor and regulate the load seen by the piezoelectric
element. MPPT-based PEH rectifiers can be further categorized in two approaches [66], one taking into consideration the vibration sweep of the open circuit voltage VOC
and the current I p generated by the piezoelectric transducer to determine the optimum operational voltage V MPP
(12) [67], [68]2. The other approach tries to achieve resistive matching of the piezoelectric impedance Eq. (6).
The second approach is based on the assumptions that
the impedance nature of the piezoelectric transducer is
mainly resistive close to the natural frequency (as estimated in Table III) and that the vibrational frequency is
constant over time. To determine the optimum operational voltage using the first approach, the rectifier must be
temporarily disconnected from the piezoelectric transducer to measure VOC and, once V MPP is determined, the
optimum operational voltage cannot be changed before
the next sampling period. Using the second approach,
the rectifier continuously harvests energy because, the
optimum resistance only depends on two constants: the
natural frequency and the parasitic capacitance.
V MPP =

Ip
V
= OC
2~ n C p
2

(12)

In a real scenario, the mechanical behavior of the
piezoelectric mechanical structure will be affected
by the energy extraction process, since the mechanical and electrical domain are coupled together. This
unwanted effect causes a mechanical attenuation, reducing the harvested energy. This attenuation is even
more significant when the harvesting process makes
the output voltage of the piezoelectric element (Vout in
Fig. 3) no longer in phase with the piezoelectric mechanical displacement.
III. Resonant PEH Rectifiers
Different harvesting interfaces have been proposed to
maximize the energy extraction derived from mechanical vibrations. The first category of rectifiers discussed
and analyzed in this paper exploits a resonance effect to
efficiently rectify the piezoelectric voltage.
The piezoelectric transducer is intermittently connected to the resonant electronic interface for very short
time intervals. The resonant effect, depicted in Fig. 9, is

The formulated expression has been derived considering a full bridge
rectifier in the harvesting system; for further clarifications, MPPT algorithms are presented in Section IV.
THIRD quaRTeR 2018

Table of Contents for the Digital Edition of IEEE Circuits and Systems Magazine - Q3 2018