IEEE Circuits and Systems Magazine - Q3 2018 - 33

A numerical evaluation of the power extraction efficiency is shown in Fig. 5(b). All of the parameters used
in the estimation are summarized in Table II, while the
values of the variables, estimated at the resonant frequency point, are shown in Table III.
Figure 5 gives a visual demonstration of the importance of a complete matching of the piezoelectric impedance. The peak value of the power extraction efficiency
occurs at the natural frequency point, where the phase
of the piezoelectric impedance is close to zero. Just
close to the resonance frequency point, a harvesting interface, with an impedance equivalent to the modulus of
the transducer impedance, can be a valid rectification
solution, because the value of the reactive component
X m is close to zero. On the other hand, if the complete
matching of the piezoelectric impedance is achieved,
the maximum harvested power is almost constant over
a wide frequency range.
C. Rectification Approaches
The Direct Energy Transfer (DET) or Standard Energy
Transfer (SET) approach, depicted in Fig. 6, was the first
attempt to implement a self-powered energy harvester.
In this paper the SET or DET interface is also referred to
as the standard technique.
The DET approach consists of a direct connection between the piezoelectric element to a bridge rectifier followed by a storage capacitor. The rectification stage is
usually connected to a DC-DC converter to scale the rectified voltage according to the application requirements.
The DET rectifier cannot ensure that the energy
always flows from the power source to the storage element. When the transducer instantaneous power is
negative, the energy stored in the capacitor C p contrasts with the mechanical vibration flowing back to the
piezoelectric element. This effect is referred to in the
literature as the energy return phenomenon [60], [61].
It is very difficult to match both the internal parasitic
components of the piezoelectric element (the internal
resistance R p and capacitance C p ) using the DET rectifier, because it would require a value of the matching inductance on the order of hundreds of H (one estimation
example can be found in the implementation described
in [43], where a 285 H inductor is required to match the
parasitic capacitance).
One technique used to provide a matching load to the
piezoelectric impedance is depicted in Fig. 7 [62].
The primary coil resonance frequency is chosen to
be equal to the resonance frequency in the secondary
coil, ~ 1 = 1/ C p L 1 = ~ 2 = 1/ C 2 L 2 . The main drawback
with this technique is the high inductance value needed
to properly match the impedance of the piezoelectric element, . 9171 H for a vibrational frequency of 32 Hz as
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Table II.
List of the electromechanical parameters used
for the power extraction efficiency estimation.
Parameter

Value

Units

Equivalent mass m

Spring constant k

3437

N/m

Dumping coefficient b

0.496

N # s/m

Piezoelectric coupling n

13.9

mm/s

Parasitic capacitance C p

11.4

Force Magnitude F in

2.8

Table III.
List of variables estimated at the resonant
frequency point.
Function

Value

Units

Natural frequency ~ n = k m

58.63

Resistive component R m

217

µΩ

Reactive component X m

-0.03

pΩ

Modulus Z m

-6.629

dB Ω

- 1.45 # 10

Phase Z m

-10

rad

Ppartial and Pcomplete

6.54

dBm

Power extraction efficiency h

Vpiezo
Cp

Ipiezo

Vdc
Cstore

Vdc
Ipiezo Vpiezo
t
Negative
Power

Positive
Power

Figure 6. circuit schematic of the direct energy transfer rectifier and typical voltage Vpiezo, current I piezo and rectified voltage VDC waveforms.

l1
Ip

C2
L1

Figure 7. Traditional interface used to match the piezoelectric output impedance.

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