IEEE Circuits and Systems Magazine - Q3 2018 - 31
Owing to different environmental conditions or application fields,
the power conversion efficiency alone is often not sufficient when
comparing the performance of different harvesting systems.
According to [55], the mechanical part of the impedance can be expressed as:
Z mec = b + j c m~ - k m
~
(1)
The electromechanical impedance Z m considering
both the electrical and mechanical domain can be evaluated as:
Zm = c
b~ + jm~ 2 - jk
~
2
mc 1 m // 1
-n
j~C p
2
b~ + j~ m - jk
=
~ ^ - C p ~ 2 m + C p k + n 2 h + j~ 2 C p b
R opt =
(2)
where real R m and imaginary X m components are given
by the two following expressions:
Rm =
Xm =
n2 b
^- ~ C p m + C p k + n 2 h2 + (~C p b) 2
2
2
- C p ^~ 2 m - k h + ~ 2 ^mn 2 - C p b 2 h - kn 2
2
~ ^^ - ~ 2 C p m + C p k + n 2 h + ^ ~C p b h2 h
(3)
(4)
Therefore, the ideal load impedance expression,
which maximizes the harvested energy, is obtained with
conjugate matching and is given by [56]:
Z *m =
~ 2 m - k + j ~b
~ C p b + j~ ^ - ~ 2 C p m + C p k + n 2 h
2
(5)
B. Conversion Efficiency
Conversion efficiency metrics are typically employed to
measure the performance of electronic interfaces. The
power conversion efficiency, defined as the average output and input power ratio when the converter runs in
steady-state conditions, is a common parameter used to
measure the efficiency of the harvesting system. In this
paper the power conversion efficiency is also referred to
as conversion efficiency.
Owing to different environmental conditions or application fields, the power conversion efficiency alone
is often not sufficient when comparing the performance
of different harvesting systems. The k 2 Q M product is a
parameter used to compare different piezoelectric
harvesting systems, where k 2 is the squared coupling
coefficient, which reflects the available energy that
can be converted into electricity, and Q M is the quality
THIRD quaRTeR 2018
factor of the electromechanical structure, which indicates the mechanical energy available in the physical
structure. The k 2 Q M product is used to indicate how
much piezoelectric material is needed to obtain a given performance.
To compare different piezoelectric harvesting systems under different load conditions, the output load
is usually normalized with respect to the piezoelectric
resistive matching impedance1 [57]:
r
2C p ~ n
(6)
Another alternative way of comparing piezoelectric harvesting rectifiers, conceptually similar to the normalized output load, consists of normalizing the rectified
voltage with the sinusoidal voltage amplitude generated
by the piezoelectric transducer. Using the first normalization, relative to the matching resistance, the vibrational frequency is assumed to be constant, while, using the second normalization, relative to the transducer
open circuit voltage, the amplitude of the oscillations is
assumed to be constant.
The power achieved by different rectification approaches is also usually normalized when comparing different piezoelectric harvesting systems. One common option is to normalize the output power with the maximum
output power attainable by using the Standard Energy
Transfer (SET) technique, discussed in Section II-C. Unless otherwise stated, in this paper the normalized output
power is referred to according to this definition. Another
popular metric used to express the harvesting efficiency
(proposed in [58]) is the power extraction efficiency h,
Eq. (7), defined as the power ratio attained by considering
the extracted power using a specific converter with the
maximum output power, Eq. (9), achieved with the theoretical conjugate matching of the piezoelectric impedance
Eq. (5). The normalized output power using the first definition, relative to the SET rectifier, can be greater than 1
while, using the power extraction efficiency, the normalized power is always lower or equal to 1.
h=
Pconverter
Pmatched
(7)
1
The formulated expression must be derived considering a full bridge
rectifier in the harvesting system, the normalization has to be evaluated according to the specific resistive matching value.
Ieee cIRcuITs anD sysTems magazIne
31
Table of Contents for the Digital Edition of IEEE Circuits and Systems Magazine - Q3 2018
Contents
IEEE Circuits and Systems Magazine - Q3 2018 - Cover1
IEEE Circuits and Systems Magazine - Q3 2018 - Cover2
IEEE Circuits and Systems Magazine - Q3 2018 - Contents
IEEE Circuits and Systems Magazine - Q3 2018 - 2
IEEE Circuits and Systems Magazine - Q3 2018 - 3
IEEE Circuits and Systems Magazine - Q3 2018 - 4
IEEE Circuits and Systems Magazine - Q3 2018 - 5
IEEE Circuits and Systems Magazine - Q3 2018 - 6
IEEE Circuits and Systems Magazine - Q3 2018 - 7
IEEE Circuits and Systems Magazine - Q3 2018 - 8
IEEE Circuits and Systems Magazine - Q3 2018 - 9
IEEE Circuits and Systems Magazine - Q3 2018 - 10
IEEE Circuits and Systems Magazine - Q3 2018 - 11
IEEE Circuits and Systems Magazine - Q3 2018 - 12
IEEE Circuits and Systems Magazine - Q3 2018 - 13
IEEE Circuits and Systems Magazine - Q3 2018 - 14
IEEE Circuits and Systems Magazine - Q3 2018 - 15
IEEE Circuits and Systems Magazine - Q3 2018 - 16
IEEE Circuits and Systems Magazine - Q3 2018 - 17
IEEE Circuits and Systems Magazine - Q3 2018 - 18
IEEE Circuits and Systems Magazine - Q3 2018 - 19
IEEE Circuits and Systems Magazine - Q3 2018 - 20
IEEE Circuits and Systems Magazine - Q3 2018 - 21
IEEE Circuits and Systems Magazine - Q3 2018 - 22
IEEE Circuits and Systems Magazine - Q3 2018 - 23
IEEE Circuits and Systems Magazine - Q3 2018 - 24
IEEE Circuits and Systems Magazine - Q3 2018 - 25
IEEE Circuits and Systems Magazine - Q3 2018 - 26
IEEE Circuits and Systems Magazine - Q3 2018 - 27
IEEE Circuits and Systems Magazine - Q3 2018 - 28
IEEE Circuits and Systems Magazine - Q3 2018 - 29
IEEE Circuits and Systems Magazine - Q3 2018 - 30
IEEE Circuits and Systems Magazine - Q3 2018 - 31
IEEE Circuits and Systems Magazine - Q3 2018 - 32
IEEE Circuits and Systems Magazine - Q3 2018 - 33
IEEE Circuits and Systems Magazine - Q3 2018 - 34
IEEE Circuits and Systems Magazine - Q3 2018 - 35
IEEE Circuits and Systems Magazine - Q3 2018 - 36
IEEE Circuits and Systems Magazine - Q3 2018 - 37
IEEE Circuits and Systems Magazine - Q3 2018 - 38
IEEE Circuits and Systems Magazine - Q3 2018 - 39
IEEE Circuits and Systems Magazine - Q3 2018 - 40
IEEE Circuits and Systems Magazine - Q3 2018 - 41
IEEE Circuits and Systems Magazine - Q3 2018 - 42
IEEE Circuits and Systems Magazine - Q3 2018 - 43
IEEE Circuits and Systems Magazine - Q3 2018 - 44
IEEE Circuits and Systems Magazine - Q3 2018 - 45
IEEE Circuits and Systems Magazine - Q3 2018 - 46
IEEE Circuits and Systems Magazine - Q3 2018 - 47
IEEE Circuits and Systems Magazine - Q3 2018 - 48
IEEE Circuits and Systems Magazine - Q3 2018 - Cover3
IEEE Circuits and Systems Magazine - Q3 2018 - Cover4
https://www.nxtbook.com/nxtbooks/ieee/circuitsandsystems_2023Q3
https://www.nxtbook.com/nxtbooks/ieee/circuitsandsystems_2023Q2
https://www.nxtbook.com/nxtbooks/ieee/circuitsandsystems_2023Q1
https://www.nxtbook.com/nxtbooks/ieee/circuitsandsystems_2022Q4
https://www.nxtbook.com/nxtbooks/ieee/circuitsandsystems_2022Q3
https://www.nxtbook.com/nxtbooks/ieee/circuitsandsystems_2022Q2
https://www.nxtbook.com/nxtbooks/ieee/circuitsandsystems_2022Q1
https://www.nxtbook.com/nxtbooks/ieee/circuitsandsystems_2021Q4
https://www.nxtbook.com/nxtbooks/ieee/circuitsandsystems_2021q3
https://www.nxtbook.com/nxtbooks/ieee/circuitsandsystems_2021q2
https://www.nxtbook.com/nxtbooks/ieee/circuitsandsystems_2021q1
https://www.nxtbook.com/nxtbooks/ieee/circuitsandsystems_2020q4
https://www.nxtbook.com/nxtbooks/ieee/circuitsandsystems_2020q3
https://www.nxtbook.com/nxtbooks/ieee/circuitsandsystems_2020q2
https://www.nxtbook.com/nxtbooks/ieee/circuitsandsystems_2020q1
https://www.nxtbook.com/nxtbooks/ieee/circuitsandsystems_2019q4
https://www.nxtbook.com/nxtbooks/ieee/circuitsandsystems_2019q3
https://www.nxtbook.com/nxtbooks/ieee/circuitsandsystems_2019q2
https://www.nxtbook.com/nxtbooks/ieee/circuitsandsystems_2019q1
https://www.nxtbook.com/nxtbooks/ieee/circuitsandsystems_2018q4
https://www.nxtbook.com/nxtbooks/ieee/circuitsandsystems_2018q3
https://www.nxtbook.com/nxtbooks/ieee/circuitsandsystems_2018q2
https://www.nxtbook.com/nxtbooks/ieee/circuitsandsystems_2018q1
https://www.nxtbookmedia.com