IEEE Circuits and Systems Magazine - Q3 2018 - 30

input power is approximately 10-100 µW, this
could prove insufficient to power up complex electronic control schemes.
4) Adaptivity: Environmental changes affect the harvested energy so, to maximize the efficiency, the
harvesting algorithm should monitor and adapt to
the environment. The two main parameters that
might change with time are the excitation frequency and the amplitude of the transducer oscillation. Some rectifiers are designed and successfully
tested considering random excitation signals in the
harvesting process; one such implementation example can be found in [42].
5) Micro-scale compatibility: This criterion illustrates how easily the energy harvester can be integrated. Above all, in systems relying on passive
magnetic components where the operational frequency is relatively low (approximately 20-50 Hz),
the need for a high quality factor might lead the
design toward implementations in which bulky external components are needed.
Two other criteria that can be adopted to evaluate
the performance of piezoelectric harvesting interfaces not mentioned in [41] are start-up operation
and the minimum operating voltage of the conditioning circuit.

Vin 1/k

-n : 1

Fin

Cp
Mechanical Domain

Vout

Electrical Domain

Figure 3. circuit diagram representation of the electromechanical model [51]-[54].

Table I.
Electromechanical model parameters.

Symbol

Model Parameters

Spring constant

Parasitic capacitance

F in

External exciting force on the piezoelectric
material

Vin

Exciting velocity

Piezoelectric coupling coefficient

Equivalent mass

Parasitic resistance

Dumping coefficient

Ieee cIRcuITs anD sysTems magazIne

6) Start-up operation: Power conditioning algorithms
implemented in the harvesting interfaces partially
dissipate the available energy from the piezoelectric
transducer. The power required to guarantee a correct operation might not be present in the harvesting
interface when the system is first started. A simple
solution employed to address this problem comprises in the use of small pre-charged batteries used to
start the harvesting process [43]-[45]. This solution
can lead to a system failure when the battery is completely discharged. Some implementations overcome
this problem by proposing the use of power management units with cold startup capability.
To implement the start-up block Kong et al. in [46]
proposed an oscillator and a micro-controller unit
in conjunction with two level detectors, which are
used to determine the control mechanism by sensing the voltage levels. Initially, the circuit starts
the harvesting process by employing the oscillator; then, when enough charge is accumulated in
the storage capacitor, the micro-controller begins
the harvesting algorithm by disconnecting the oscillator. Conversely, in [47], [48] cross coupled rectifiers are employed in conjunctions with parallel
active diodes. The active diodes are idle when the
system is first started. Analogously to [46], the active diodes are operative when enough charge is
accumulated in the storage capacitor.
7) Minimum operating voltage: Discrete components
(transistors and diodes) used in the power conditioning circuit limit the scavenged energy. This is
because the voltage produced by the piezoelectric
element is often below the working operational
threshold voltage of the electronic interface. This
criterion is more relevant in systems in which the
available input AC voltage generated by the piezoelectric transducer is relatively low. Two designs
optimized considering this criterion can be found
in [49] and [50].
A. Electromechanical Model
To maximize the harvested energy, the electronic interface must properly match the output reactance of the
piezoelectric element. The electromechanical model,
consisting of a mechanical part and a coupled electrical
interface, is shown in Fig. 3.
All of the model parameters are summarized in Table I. From Fig. 3, it is important to note the capacitive
nature of the impedance in the electrical domain. The
parasitic resistance R p is not considered in the following derivations because the value of the resistance is
relatively high, R p & 1/ (~C p), where ~ is the vibrational frequency.
THIRD quaRTeR 2018

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