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I - Energy
LUCA GAMMAITONI NiPS Laboratory – Università di Perugia, Italy
www.nipslab.org
Luca Gammaitoni - NiPS Summer school - 1-8 Aug 2010
What is Energy Harvesting ? Why are we spending time with the subject of
Energy Harvesting ?
Luca Gammaitoni - NiPS Summer school - 1-8 Aug 2010 2
- Usually people harvest corn so why not harvesting energy?
Why are we spending time with the subject of Energy Harvesting ?
Luca Gammaitoni - NiPS Summer school - 1-8 Aug 2010
Wireless sensor networks
Present (cubic centimeter)
Future (cubic sub-millimeter sub-micrometer)
Luca Gammaitoni - NiPS Summer school - 1-8 Aug 2010
This challenge clearly address the problem of energy conversion in nano-scale IT devices and systems.
Luca Gammaitoni - NiPS Summer school - 1-8 Aug 2010
Self-powered means energetically autonomous devices capable of harvesting energy from the environment.
Different approaches:
1) Energy produced in one central place: battery-like 2) Energy produced when and where available (and locally stored)
Energy harvesting deals with the approach 2)
Luca Gammaitoni - NiPS Summer school - 1-8 Aug 2010
Impact The impact is hardly overestimated
Basic science:
Advances in nano-scale energy-conversion mechanisms.
Advances in nonlinear stochastic dynamics: the usual vibration-to-electricity conversion mechanisms are based on linear oscillators tuned to the frequency of vibration sources. New approaches could take advantage of nonlinear dynamics to improve the efficiency of the conversion mechanism.
Luca Gammaitoni - NiPS Summer school - 1-8 Aug 2010
Impact The impact is hardly overestimated
Technology
The availability of onboard power generators will open up the possibility of building nano-scale devices (from sensors/ actuators to computing/communicating) with application in a vast number of fields. ICT technology can be seriously affected by such possibility.
Luca Gammaitoni - NiPS Summer school - 1-8 Aug 2010
Impact The impact is hardly overestimated
Economy:
The impact on the economy of ICT can be very relevant. A new class of devices, up to now only dreamt of, could be made available for practical applications.
Estimated growth of the energy harvesting devices in the next ten years, in million USD. Source: IDTechEx, “Energy Harvesting and Storage 2009-2019”, Cambridge 2009.
Impact The impact is hardly overestimated
Society:
The impact on society can be extremely relevant for a number of fields.
Among these: - wireless communications and social behaviours, - human health remote monitoring and control, - remote sensing, - environmental control, - privacy and security, - …
Luca Gammaitoni - NiPS Summer school - 1-8 Aug 2010
Communities It is clearly a multidisciplinary area, where physics, chemistry, electronic engineering, signal analysis and mathematics play each their own role, under the more general umbrella of ICT.
The topic is of interest for different research communities:
- the nanotechnology comm. interested in new information oriented devices.
- computer science community (wireless sensor networks) - nonlinear stochastic dynamics community - the electronic eng. devoted to powering solutions design - …
For further info see: www.nipslab.org
I – Energy II – Harvesting vibrations
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I – Energy - Basic ideas on energy - Basic ideas on energy harvesting - The random character of kinetic energy
Energy… is conserved
R. Feynman ideas about energy…
Energy… what is it?
Let’s start from the very beginning…
Energy appears to be a fascinating subject …usefully introduced to large use during the industrial revolution…
Although not completely well understood (in my opinion)
Luca Gammaitoni - NiPS Summer school - 1-8 Aug 2010
A text-book definition: Energy is the capability to do some work..
Energy… what is it?
… in the meantime energy is transformed from one kind to another… es: from chemical energy to kinetic energy to thermal energy…
1 J = energy that takes to rise 1 m an apple on Earth.
Even if we do not have a very satisfying definition we know how to measure energy: in Joule (J)
If we do this work in 1 s than we have used 1 W of power
Examples: - A portable computer needs approx 50-100 W - A electric oven uses approx 500-1000 W - A human brain uses approx 20 W
Luca Gammaitoni - NiPS Summer school - 1-8 Aug 2010
. Source: IDTechEx, “Energy Harvesting and Storage 2009-2019”, Cambridge 2009. EH: Energy Harvesting; WSN: Wireless Sensors Network
Unlimited source of free energy, readily available for multiple uses…
Luca Gammaitoni - NiPS Summer school - 1-8 Aug 2010
Reality is slightly more complex…
Energy res.
Transduction sys.
Available energy
Dissipated energy
Different kinds of energies… can be ranked by “quality”
1° Electrical energy…
… … …
Thermal energy… The last
Lukily Thermodynamics helps out with the problem…
Luca Gammaitoni - NiPS Summer school - 1-8 Aug 2010
Energy is a property of a physical system but it is not the only one that matters
Entropy
rules the capability of transforming one kind of energy into another…
…second principle… increase in Entropy for spontaneous transformations…
Luca Gammaitoni - NiPS Summer school - 1-8 Aug 2010
Kinetic energy
Focus on vibrations of solid bodies….
Luca Gammaitoni - NiPS Summer school - 1-8 Aug 2010
Basic Scheme
Vibrating body
transducer
+ -
contact
Luca Gammaitoni - NiPS Summer school - 1-8 Aug 2010
Energy budget
Energy res.
Energy in the transd.
Coupling/dynamic properties
Available
Dissipative properties
Transduction properties
Heat sink
Luca Gammaitoni - NiPS Summer school - 1-8 Aug 2010
Dynamical model
Vibrating body z
+ -
x
Energy stored
Energy dissipated
Energy transd.
m
γ
k
c
Luca Gammaitoni - NiPS Summer school - 1-8 Aug 2010
Dynamical model
€
m˙ ̇ x = − dU(x)dx
− γ˙ x − c(x,V ) + ζ z
Where:
€
U(x) Represents the Energy stored
€
γ˙ x Accounts for the Energy dissipated
€
c(x,V ) Accounts for the Energy transduced
€
ζ z Accounts for the input Energy
Luca Gammaitoni - NiPS Summer school - 1-8 Aug 2010
Dynamical model
€
m˙ ̇ x = − dU(x)dx
− γ˙ x − c(x,V ) + ζ z
€
˙ V = F( ˙ x ,V )
Equations that link the vibration-induced displacement with the Voltage
Luca Gammaitoni - NiPS Summer school - 1-8 Aug 2010
Dynamical model
€
m˙ ̇ x = − dU(x)dx
− γ˙ x − c(x,V ) + ζ z
€
˙ V = F( ˙ x ,V )Details depend on the physics…
Three main transduction mechanisms…
Luca Gammaitoni - NiPS Summer school - 1-8 Aug 2010
€
ζz Represents the vibration (force)
Luca Gammaitoni - NiPS Summer school - 1-8 Aug 2010
What does it look like?
Random vibrations / noise
Thermal noise Acoustic noise Seismic noise Ambient noise (wind, pressure fluctuations, …) Man made vibrations (human motion, machine vibrations,…)
All different for intensity, spectrum, statistics
For further info see: www.nipslab.org
“Precision is the ability of an instrument to produce the same value or result, given the same input”
Example: the measurement of the pendulum position
Where does this noise comes from?
Motion equation
The almost “simple” pendulum
Small oscilation approximation, with damping
What if we wait long enough ?
The very small oscillation limit. Let the pendulm swing freely…
Example: the real measurement of a free swinging pendulum
Mass m= 1 Kg Length l = 1 m rms motion = 2 10-11 m
Mass m= 1 g Length l = 1 m rms motion = 6 10-10 m
Mass m= 10-6 g Length l = 1 m rms motion approx 1 mircon
10-15
For further info see: www.nipslab.org
Where all these fluctuations come from?
1828 R. Brown 1905 A. Einstein
Luca Gammaitoni - NiPS Summer school - 1-8 Aug 2010
Luca Gammaitoni - NiPS Summer school - 1-8 Aug 2010
Luca Gammaitoni - NiPS Summer school - 1-8 Aug 2010
To describe such a dynamics it is necessary to introduce a statistical approach
a) Fokker-Plank equation b) Langevin Equation
Luca Gammaitoni - NiPS Summer school - 1-8 Aug 2010
−6π η a x
ζ ( )t
m x a x t ( )= − +6π η ζ
Luca Gammaitoni - NiPS Summer school - 1-8 Aug 2010
Generalization: The viscous drag expression can be generalized in order to describe a wider class of damping functions
− −−∞∫m t x dt
γ τ τ( )
m x m t x d tt
( ) ( )= − − +−∞∫ γ τ τ ζ
Is the stochastic force with known statistical properties:
Probability density function, moments, correlations, ... ζ ( )t
For the pendulum we get:
( ) ( )x x t x d tmp
t
= − − − +−∞∫ω γ τ τ
ζ2
ζ ζ γ( ) ( ) ( )t k T m t0 =
In the spectral domain, for a linear system, is always possible to write its response to an external force like:
X H F( ) ( ) ( )ω ω ω=
The F-D Theorem can be written here as:
S k T Hx ( )( )
ωω
ω=−
ʹ′ʹ′4
H H i H H ei( ) ( ) ( ) ( ) ( )ω ω ω ω φ ω= ʹ′ + ʹ′ʹ′ =
Where H is the system transfer function.
See SUBTLE: SUB KT Transistors and Sensors, FPVI FET http://subtle.fisica.unipg.it/
Luca Gammaitoni - NiPS Summer school - 1-8 Aug 2010
First paper in 1981 by Benzi, Parisi, Sutera, Vulpiani.
Since then more than 4000 papers (to date)…
For further info see: www.stochastic-resonance.org
For further info see: www.nipslab.org