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Ultra Low Power
Bioelectronics
Fundamentals, Biomedical
Applications, and Bio-inspired
Systems
RAHUL SARPESHKAR
Massachusetts Institute of Technology
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26 Energy harvesting and the
future of energy
Nature uses only the longest threads to weave her patterns, so that each small piece of
her fabric reveals the organization of the entire tapestry.
Richard P. Feynman
Ener gy surrounds us, is within us, an d i s creat ed by us. In this chapter , w e shall
discus s how syst ems can harvest energy in their environm ents and thus function
withou t n e eding to constant ly c arry their own energy source. The potenti al ben
efits of an energy- harvesting strategy are that the lifeti me of the low-pow er syst
em is then not limited by the finite lifeti me of its energy sou rce, and that the weigh
t and volume of the system can be reduc ed if the size of the energy- harvest er is
its elf small. The challen ges of an energy- harvesting strategy are that many
energy sources are intermit tent, can be ha rd to effici ently harvest, and pro vide
relative ly low power pe r unit area. Thus , energy- harvesting syst ems are usually
practi cal onl y i f the syste m that they power ope rates with relat ively low power
con sumption.
We shall begin by discus sing energy- harvest ing stra tegies that have been
explore d for low-pow er biomed ical and portabl e applications . First, we discus s
the use of stra tegies that functio n b y con verting mechan ical body motio ns into
elect ricity. A circuit model develop ed for describing energy transfer in inductive
links in Chapter 16 is extremely simila r t o a circui t model that accurat ely
character izes how such mechani cal energy harvesters fun ction. Thus , tradeof fs
on maxi mizing energy effici ency or en ergy transfer are a lso sim ilar. Ener gy
harvest ing with RF energy is discus sed extens ively in Chapt ers 16 and 17, so
we shall not discus s i t i n this ch apter. Then, we discus s the use of therm oelect
ric strategi es that functi on by co nverting body heat into electricity. A fundame ntal
thermod ynamic princi ple limits the energy effici ency of a ‘heat engine’ , wheth er
in an inter nal combu stion engine in a car, in a refriger ator, or in a therm oelectric
device power ed by body heat. The limiting effici ency is called the Car not efficie
ncy . The Carn ot effici ency an d models of heat flow from the body will help us
unde rstand the limit s of operatio n o f therm oelectric energy harvesting.
W to 10 2This book has largely discus sed ultr a-low- power systems at relative ly small spati al scales in
biomedi cal and in bio-insp ired systems, most ly in the 10 12W range. In this final chap ter, we shall see
that princi ples of low-pow er design a r e also relev ant to syst ems at large spatial scale s with gigantic
power
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823Ener
gy harvesting and the future of energy
consu mption, e.g. , a 40 kW ga soline-pow ered car moving at 30 mph, whi ch if
operate d for 1 hour each day leads to an average power consump tion of 1.67 kW
.
1The average human be ing on Earth consumes 2.5 kW of power such that our
planet ’s current aggrega te power consump tion is roughly 15 TW. The average
power co nsumpt ion of people in richer cou ntries is high er than that in poor er
coun tries. For exampl e, the average person in the United State s consu mes 10.4
kW [1].We have be en able to susta in such power consump tion thus far large ly
because the 46,400 J/g energy density of gasolin e, the 53,600 J/g energy densit y
o f natural gas, and the 32,500 J/g energy de nsity of coal, and their relat ive abun
dance, hav e enabled us to burn en ergy at a profligat e rate. In compari son, a
well- optimized lithium- ion batte ry for portabl e applic ations ope rates at 6 5 0 J/g.
Gasol ine is currently cheaper per liter than bottl ed water in the United State s.
For every kW h o f oil, natural gas, or co al that is co nsumed, 250 g, 190 g, and
300 g, respect ively , o f C Ois dumped into our atmos phere [2]. Thi s means that
5.5 tons of CO22is generat ed on average per person per year, increasing CO 2level
s by 2.5 ppm (part s per million) pe r year today [3]. The accu mulation of CO 22ha
s increa sed the atmos pheric concentra tion from 280 ppm in pre-in dustrial times
to 390 ppm today [4]. The pace of COemissions is exp ected to increa se signi
ficantl y a s India, Chin a, and other developi ng nations outpu t more CO. For
every ppm increa se in CO22, the a verage Earth temperatur e appears to rise due
to a greenhou se effe ct [3]. Many climatol ogists belie ve that there wi ll be serious
and irreve rsible consequen ces to world clim ate, partly due to pos itive-feedb ack
loops, if the CO2concentra tions increa se significa ntly beyon d 5 5 0 ppm. The
profligat e burn ing of fossi l fuels will lead to their inevi table exti nction,
which is not only catastroph ic for energy and climate reason s, but also becau se
they are quite useful for making severa l mate rials like plastics cheap ly. Due to
the need for minimiz ing fossil- fuel CO2emissions that impac t clim ate change an
d due to the exh austion of these fossi l-fuel energy so urces, our planet will need
to functi on increa singly on renew able energy sources . These sources include
solar power , wind power , hydroelec tric power , wave power , tidal power ,
geother mal power , a n d bio fuels. Sin ce the areal power densit ies of these
sources are relative ly small, it is imper ative that our power co nsumpt ion be
reduced. M ost of our power consu mption arises from trans portat ion, heati ng,
elect ricity usage, and material synthes is costs .
We discus s how electric cars, power ed by ba tteries driving motor s, enable improvem ents i n t
ransport ener gy efficie nc y, i.e., energ y consume d pe r p ers on-km , over those of gasoli ne-pow
ered cars. We shall discus s a n e q uivalen t circuit for a car, which wi ll allow us to draw on principles
of low-po wer design in elect ronics to underst and how power consumpt ion in cars can and is being
reduced. We shall compare the energy efficienc y o f advance d e lectric cars versus ch eetahs, the
fastest land an imals on earth. Eve n thou gh legged locomot ion is signi ficantl y less
1
Interestingly, the average national per-capita income of a person in K$ divided by 4 i s a good
predictor of that nation’s average per-person power consumption in kW.
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Heat
Energy
storage
(battery,
824 Energy harvesting and the future of energy
effici ent than wheel s o n flat terr ains, we shall see that an imals have impressi
vely goo d trans port en ergy effici ency when comp ared with even highly
energy- effici ent elect ric cars.
We wi ll focus on two renewab le so urces that are likely to be very impor tant
in our futur e, na mely, solar photovo ltaics and biofuel s. The basic principles of
photo transdu ction descri bed in Chapter 11 will be useful for underst anding
how solar phot ovolta ic cell s functi on. W e sh all delve de eper into photo
transdu ction in this cha pter to unde rstand the lim its of solar-cel l effici ency.
Solar photovolt aic sources are impor tant at small scale s, e.g., for solar phot
ovoltaic cells that power portabl e a n d biomed ical ap plications , and also at
large scale s, e.g., for 300 MW elect ric gene rators. Solar energy is widely
viewed as the most impor tant renew able energy source because of its relat
ively high power density and ubi quitous presence [5]. We sh all discus s some
ch allenges in making solar electrici ty g eneration cost effe ctive. W e conclud e
b y discus sing biofuels, whi ch a r e create d b y plants storin g the energy of
sunlig ht in chemi cal bonds through the process of phot osynthesi s. Biofuel s
repres ent an energy-d ense method for the stora ge and dist ribution of solar
energy. Suc h biofuel s c ould be useful in cars and in impl antabl e biomedic al
syst ems in the future.
26.1 Sources of energy
Figure 26.1 shows six common sources of e nergy that we can harvest. We
have discus sed RF energy harvesting in near-fie ld syst ems in Chapt er 16 for
biomedi cal impl ants and in far-fi eld systems for cardia c mon itoring in Chapt
ers 17 an d 20. In general , ambien t R F e n ergy from cell phones and wireless
devices in the environment may be harvest ed. Implan table biomedi cal
systems can poten tially ha rness the energy of blood flow or the energy of
airflow during respi ration to functio n; work in this area is just beginni ng. Ultralow-pow er outdoo r monitoring app lications can ex ploit poten tial differences
between two poin ts on a tree trunk, whi ch can v ary by a few hundre ds of mV,
to ope rate [6]. In this chapter , we shall primaril y focus on inertial -motion, heat,
and solar energy harvest ing.
Air
flow
Energy
sources
Solar
RF
Inertial
motion
Energy
harvesting
ultra capacitor,
flywheel)
Figure 26.1. A typical energy-harvesting architecture.
L
i
q
u
i
d
f
l
o
w
impedance
matching
Load
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82526.2
Electrical circuit models of mechanical systems
At first, we shall only focus on harvesting at small scale s for low -power biomedi
cal applic ations.
Noninva sive and implan ted biomedi cal systems can harvest the energy in the
inertial motion s o f the bodily limb s o r the head to whi ch they are attached to
functi on. Small ultra-l ow-po wer implanted systems that are attached to the heart
or to the lungs can harness the mechani cal e nergy of heart or lung moti ons to
operate . The body is maintained at ne arly 37C while the environm ent is usually
below this tempe rature. Ther efore, the flow of heat en ergy from the body toward
s its surround can be harness ed in a thermoelect ric device to operate elect ronics
attach ed to the body . For exa mple, the micr opower EKG or PPG amplifi ers
discus sed in Chapte r 2 0 can be power ed in such a fashi on. Solar cells atta ched
to the body can power noninva sive electronics atta ched near them as they now
power wat ches. In gen eral, severa l energy sources are intermittent , e.g., solar
energy is only avail able during the day, mechan ical en ergy is only av ailable dur
ing motio ns of the body , and RF energy may only be available when there is a
wirele ss device in the environm ent. The intermittenc y o f the en ergy impl ies that
there is need for stora ge of the harvest ed en ergy, e.g., in a battery or in a large
capacit or as shown in Figure 26.1. The energy- stora ge syst em serves to smoot
h energy fluc tuations such that power is always reli ably availab le to the load. To
pr event resid ual power -suppl y fluctuat ions output by the energy- storag e
system from affe cting the electro nics that it power s, and to ensu re that there is
good impeda nc e matching for maximum or energy- efficien t trans fer of power to
the load, a regu lation and impeda nce-m atchi ng stage is usu ally necessa ry. For
exampl e, the load may need high vo ltage an d low current while the en ergy
harvest er inherent ly provides low volta ge and high c urrent. Thus , a dc-to-dc
up-convert er from the output of the energy- stora ge elemen t t o the load may be
necessa ry. In the RF antenna- based energy- harvest ing syst em that we discus
sed in Chapt er 17, the energy harveste r is an antenna, and the e nergy-stor age
and impeda nce-m atching fun ctions are combined in the c harge pump an d i n
the capacito rs of the pum p. In general , to red uce the variab ility in avail able en
ergy and to g ather more en ergy, severa l energy sources can be simulta neously
harvested an d store d.
Before we be gin wi th our discussion of inert ial-motion mech anical-ener gy
harvest ing, we shall digress briefly to exp lain how elect rical circui t m o dels of
mechani cal systems a r e con structed.
26.2 Electrical circuit models of mechanica l system s
The electrica l equival ents of Newton’s three law s o f motio n i n mechan ical syst
ems are as foll ows:
1. Newton’s first law: Every body cont inues in a state of rest or in its state of mot ion unle ss it is acted
on by a force.
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826 Energy harvesting and the future of energy
Electrical equivalen t: Every capaci tor holds its charge unle ss it is charge d o r
discharge d b y a n elect rical current.
2 . New ton’s second law : F ¼ mdv=dt ð 26 : 1 Þ
F is the force, m is the mass , and v is the veloci ty of the moving or stationa ry
mass. Electrical equivalen t:
I ¼ CdV=dt ð 26 : 2 Þ I is the current , C is the cap
acitance, and V is the voltage on the capacit or.
3 . New ton’s thir d law : For every action, ther e i s a n equal and opposi te
reaction. Electrical equivalen t: In any two-termina l electrica l element, whe ther a
ctive or passive, depend ent or independe nt, linear or nonlinea r, the curre nt flo
wing into one ter minal on the element is equal to the curre nt flow ing out of the
other terminal of the element.
In the form ulatio n above , c urrent is a nalogous to a force, c apacitance is
analogo us to a mass, a n d v o ltage is an alogous to a veloci ty. The electrica l
equ ivalent of Newton ’s third law is such that it is au tomatica lly satisfied and
repres ented in an y circui t. Mutual interacti ons be tween two bodies are represen
ted as a floating current betwe en two nodes su ch that one of the current s through
the two -termin al elem ent creat es a sink current on the node that it is atta ched to
whi le its paired current c reates a source current on the node that it is atta ched to.
Thus , New ton’s third law is nothing more or less than stat ing that a floa ting
current source betw een two node s may alw ays be rep resented as a groun ded
sink current at one node and a grounded source current at the other node. The
automa tic and natural represen tation of Newton’s thir d law by a circuit makes
elect rical representat ions of mechani cal syste ms power ful because one is
relieved from the burden of having to co nstantly keep track of symm etric pushing
and pulli ng between bodies. Fur thermore, force balanci ng is also automa tic.
Since the volta ge on a capacit or stops chan ging when all the current s flowi ng
tow ards (or away from ) it sum to zero, Kir chhoff’s current law is the law of force
balance. Vector forces requir e 3 D electrica l circui ts because the electrica l a n
alogies of mechani cal syst ems hold separat ely for ea ch of the x , y ,and z
componen ts of force and veloci ty. For exampl e, Figure 17.1 shows how circui t
descrip tions of Maxw ell’s equ ations con ceptually repres ent vector s.
In the form ulation ab ove, capa citance is a mass . I f
F ¼ k ð vdt
I ¼ 1 Vdt; ð 26 : 3 Þ
Lð
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82726.3
Energy harvesting of body motion
then the recipr ocal of an indu ctance represe nts a s p ring sti ffness, or equival ently inducta nce
represen ts a complian ce. Mechanica l damping is repres ented by a cond uctance:
F¼
ð 26 :
vI¼
4Þ
GV
Thus , a resonan t mechani cal mass -spring-da mper syst em acted on by a force is repres
ented by a p a rallel LCR resonat or sourced by a c u rrent.
Frequen tly, a dua l versio n o f Equat ions (26. 1), (26.2), (26. 3), and (26. 4) is used to
repres ent mechan ical syst ems by an electrica l equival ent: force is repres ented by a volta
ge, velocity is represen ted by a current , mass is repres ented by an inducta nce, damping is
repres ented by a resistance , and co mpliance is rep resented by a capacit ance. In this
analogy, a resonant mechani cal-spri ng-dam per system acted on by a force is repres ented
by a series LCR resonato r sourced by a volta ge. Both forms are mathe matical ly equival
ent. How ever, one form is often more intuiti ve than the other and one sho uld always work wi
th a form that is the most intuiti ve. For exampl e, in pur ely mech anical syst ems composed
of intera cting solid s, if the equ ivalence describ ed by Equat ions (26. 1), (26. 2), (26. 3), and
(26. 4) is used, a parallel mechani cal geomet ry maps to a parallel elect rical topology , and a
seri es mech anical geo metry maps to a serie s elect rical topology ; the dua l ana logy flips
pa rallel mechan ical geometries to series electrica l topologi es an d vice versa and is less
intuiti ve. In co ntrast, in mech anical systems invo lving fluids, if we repres ent pressur e b y
volta ge an d volume velocity by current , parall el fluid geo metries map to parallel electrica l
c ircuits an d series fluid geomet ries map to seri es electrica l circuits; thus, the dual analogy
is more intui tive for fluids. In piezoel ectric electromec han ical de vices, forces cause charge
displace ments and v oltages cause mechani cal displacement s. Thus , for reasons of
symmetry , i n piezoel ectric devices , i t i s more na tural to repres ent force by a volta ge and
veloci ty by a current .
26.3 Energy harvesting of body motion
Mech anical energy harvest ing ha s been perfor med with three kinds of devices , namel y, elect
romagne tic, elect rostatic , a n d piezoele ctric. An elect romagne tic device co nverts flux ch anges
induced by mechani cal motion into an electrica l volta ge as in hydroelec tric gen erators. If the
voltage acro ss a sen sing cap acitance is fixed, an elect rostatic device, e.g. , like the MEM S c a
pacitance discus sed in Chapt er 8, convert s capacitan ce changes due to mechani cal displ acement
s into charge changes. Elec trostatic devices also convert capa citance changes into voltage chan ges
if the charge on the sensi ng capacit ance is fix ed. A force impos ed on a piezoel ectric dev ice cau
ses mech anical de formati on and charge changes within it. The ch arge ch anges man ifest as a
voltage across the piezo electric de vice’s electrica l capacit ance. An e xhaustive review of energy
harvest ing wi th all three kinds of
C
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p
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82
8
En
er
gy
ha
rv
es
tin
g
an
d
th
e
fut
ur
e
of
en
er
gy
Mechanical
e(s
Electrical
V
)
(a)
(s)
Frc
m
+
Vel
(s
)
m
(s) Gin(s) +
sdV e(s) sdFrc (s)
C
C
e
–
m
(
b
)
V m
e (s
l )
1
m
ins +(s)
–
G
l
eff
Vs 1 –sdmG(s)+Ce(s)
manifest as
a voltage
across their
elect rical
capacitance.
Figure 26.2. A circuit description of a piezoelectret in (a) and a feedback block diagram Appli ed
that represents this circuit in (b).
volta ge indu
ces mechani
cal displ
acement
devices may be found in [7]. Wo rk in [8] has shown that models for elect
romechanical en ergy harvest ers are mathe matical ly identical across all threechanges,
classes of devices . Ther efore, for reasons of brevit y, we shall focus primaril ywhi ch man
ifest as a
o n piezoe lectric energy harvest ers.
‘back force’
In all su ch passi ve devices , the presen ce of mechani cal-to-e lectrical
transd uction impl ies that there is also corres pondin gly elect rical-to-me chanacro ss their
mechan ical
ical transdu ction in the reverse direction. The presen ce of trans duction in both
complian ce.
direct ions, each of whi ch affe cts the other, leads to a feedba ck loop in the dev
Figure 26.2
ice. For example, elect rical generat ors or elect romagne tic ene rgy ha rvesters
don’t just convert mechanical moti on to an electric vo ltage. Thei r operati on (a) reveal s
causes a ‘back torque’ in add ition to the mecha nical torque drivin g the gen a tw oport e
lectromecha
erator becau se the elect ric volta ge that is generat ed also causes the generato
r t o beh ave like a m o tor. In elect rostatic de vices, mechani cal displacementnical
s circui t
that
repres
lead to v oltage or charge chan ges and also changes in the attr active electrost
ents
the
atic force between the capacit or plate s. Piezoele ctric devices are no excepti
functi
oning
on. Appli ed force induces charge mo tions within the piezoel ectric, which
of a a Piezoelectret
piez tion
oel s Frc
m
ectrican
c be
devi don
ce. e in
Figuterm
re s
26.2
(b)
reve
al s
the
feed
bac
k
loop
that
repr
ese
n ts
this
two
por
t.
In
Figu
re
26.2
(a),
for
con
ven
ienc
e,
we
ope
rate
with
curr
ent ,
whic
h is
the
deri
va
tive
of
char
ge,
suc
h
that
all
devi
ce
char
act
eriz
+–
G (s)+C
sd
l
eff
e
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Energy harvesting of body motion
of voltag e a nd current rather than in term s o f volta ge and ch arge. The mechani cal compli ance of
the piezoel ectre t i s represen ted by C. The electrica l capacit ance is repres ented by Cem. The
mechani cal force is represen ted by the vo ltage Frc( s) and the elect rical volta ge by V em(s ). The
piezoe lectric forward- and-back coefficien ts from the mechani cal to the elect rical domain an d vice
versa are typicall y symm etric a n d repres ented by d . The inertial input to the piezoel ectric de vice
is represented by a Nort on velocity sou rce of value Ve l( s) i n parallel with an outp ut admit tance
Ginm( s ). The outp ut admittance is often due to an inert ial mass M wi th impeda nce Ms , i.e., Ginð s
Þ¼1 = ð Ms Þ . The output voltage of the piezo electric de vice drives an electrica l load with e
ffective admittance G eff l( s ). Some algebra maps the two-po rt of Figure 26.2 (a) to the feedb ack loop
of Figure 26.2 (b). For maximu m effici ency, or maxi mum power transfer, we should configu re G(s )
such that it is resonant with Cms , and arrange Geff lin( s ) such that it is resonant with Cs. The alert
reader will then immediat ely notice that Figure 26.2 (a) is exactly the dua l circui t of the reson ant
mutual-i mpedance link that we de scribed in Chapt er 16. The simila rity of Fi gure 26.2 (a) to its dual
c ircuit in Figure 16.2 an d the sim ilarity of Figu re 26.2 (b) to the feedback loop in Figure 16.3 are stri
king: in mapping Figure 16 .2 to its dual versi on in Figure 26.2 (a), we sim ply exchange voltage for
current , imped ance for co nductance, and a seri es tw o-port circui t for a parall el two-po rt circuit.
The piezoel ectric co efficien t d is analogou s t o the mutual inductance M , Cmis an alogous to L1,
Ceis analogo us to L2e, and we can defin e a cou pling coeffici ent k given by
C 2
ð 26 :
¼d
2
5Þ
C
m
e
k
identi cal to that defin ed in other treatment s [9]. Ther efore, we can exp loit the analys is discus sed in
Chapt er 16 to analyze piezoel ectrets since the mathe matic s is virtu ally iden tical. We can de fine a
reflect ed admittance Grefl( s ) analogo us to the reflect ed impeda nce of Chapt er 16 that is given by
ð s Þ¼ d Ce2s2s þ Geff lð s Þ ð 26 : 6 Þ
G
refl
This admittance is reflect ed from the electrica l dom ain to the mech anical domain and appears in
parall el with Gnin( s ). From Chapter 16, for maxi mal en ergy effici ency, the reson ance in the elect
rical and mech anical doma in must both occu r at the same optim al o ¼ o. For maximal energy effici
ency in the ‘pri mary’ mechani cal domain, the reflected cond uctance must be much great er than the
cond uctive portio n o f Gin( s ). For maximal energy effici ency in the ‘secondar y’ electrica l dom ain,
the con ductive porti on of Geff lsðÞ mu st be much great er than an effecti ve parasiti c
conductance, G e, that is in pa rallel wi th C, and whi ch repres ents electrica l losses. Note that G eeis
not shown in Figu re 26.2 (a) since it is a parasiti c. To determine the maxi mum overal l e n ergy effici
ency, we can define an effecti ve qua lity factor Q1for the resonat or in the mechani cal domain and an
unload ed quality factor Q2for the resonator in the ele ctric al doma in.
S
S
L
S
¼R
Q
opt L
The power dissip ated in the electrica l load P
¼ 1k4 k22QQ11QQ22þ
1
3
, accordi ng to Pe
P
ð 26 :
8Þ
m
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; maxi mum
the energy e
er 16, it can
830 Energy harvesting and the future of energy
The n, E qua tions (1 6.3 5) and (16. 36) in C hapter 1 6 apply ex ac tly to pi
ezoele ctric ener gy ha rvesters and describe their energy efficiency. From [8 ],
since the mathematic s o f t hroug h-a nd -ac ros s v aria bl e s is ve ry simila r f
or ele ctromag ne ti c and ele ctrostatic energy ha rvesters , we can analyze other
motion-energy ha rv este rs through the equations o f C hapter 16 as well.
Through va riable s a re analogous to ge ne raliz ed curr ent v aria bles while
across variable s are analog ous to g eneralized voltag e var iable s. Late r i n thi
s chapter, w e shall disc us s the op era tion o f elec tric m otor s, which ar e ele
ctroma gnetic energy generators (harvesters) that oper ate in rev erse. This
discussion will further illus trate the s imilar ity be twe en d iffer ent kinds of e lectr
ome ch a n i c al d e vi c e s.
In Chapt er 16, since we had a requ ired load power consumpt ion in the secon dary and we want ed
to ensure that the reflect ed power consumpt ion in the prim ary due to this load was minimal , w e
focu sed on opt imizing en ergy effici ency. In many energy- harvest ing situati ons, energy effici ency
may not be as important as maxi mizin g e n ergy transfer, i.e., getting as much absolut e energy out
of the harvest er as possibl e, even if it means that a large fract ion of en ergy is wasted. For exampl e,
in a resi stive-di vider circui t composed of a v oltage sou rce with a source impeda nce Rdrivin g a
load impeda nc e RL, energy effici ency is maxi mized when RL R
1þk QQ
ð 26 :
2
7Þ
e
2
m
¼
Q
2
1
at this optimal value is relat ed to the power dissipated at
the mechani cal inpu t with no reflect ed load ( d or k ¼ 0), P
Piezoele ctric ha rvesters for wirele ss senso r networks are descri bed in [10] and have
generat ed 180–335 m Win1cmof volume . They can be adap ted for use in the nonin vasive medica
l-monit oring systems de scribed in Chapt er 20. A piezoel ectric energy harvest er that scavenge s
energy from comp ression of the sh oe sole has been able to generat e 0.8 W o f elect rical power [11],
[12]. Atte mpts to gen erate large amoun ts of elect rical power from body motions, howeve r, create a
significa nt reflect ed elect rical load on the mechani cal side such that the metab olic effor t need ed to
gen erate electrica l power is conscious ly felt by the user. Since only 25% of the chemi cal oxidat ive
energy of glucose is output as useful mechani cal work by the body, even a highly effici ent energy
harvest er at 31% can lead to a meta bolic load to the body that is 12 tim es great er than the energy
being harveste d. One inn ovative effor t t o reduce such meta bolic loading on the body uses an
electromag netic en ergy harvest er placed on a knee brace sli ghtly above the kne e that harvests ene
rgy only during leg deceler ations . I t helps the leg to
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83126.4
Energy harvesting of body heat
ate by serving as an effe ctive en ergy-h arvester ‘brake’ to slow the leg at
the end of a leg-extens ion mo vement. The meta bolic load on the muscle is then
reduced on average co mpared with the con dition when an energy- harvesting
brake is not present [13] . I n the proof- of-conc ept design, the weight of the de
vice, howeve r, increased the mean meta bolic load of wal king by 20%. The device
success fully generat ed 5 W of power . A n electro static gen erator meant to ha
rness ventri cular wall motion s o f the heart generat ed 36 m W w i t h simulat ed
hea rt motio ns, suffici ent to power a cardiac pacemaker . However, it was too big
to impla nt an d test direct ly on the he art [14] . I n gen eral, devices less than 1 c
min volume are unlikel y t o generat e more than 1 m W o f power from body motio
ns [7], but for many low-pow er applic ations like we ha ve discus sed in Chapt er
20 100 m W i s more than ad equate. One chall enge in the field is that it is easy to
make small devices that ha ve high resonan t frequenci es but most of the power
spectru m of moti on energy is below 100 Hz. Fur thermo re, if the body motion is
far in excess of the maxi mal motions possible in a small device, resona nt amplifi
cation is not necessa rily an advan tage. Non-r esonant con version stra tegies are
being invest igated [15].
3deceler
26.4 Energy harvesting of body heat
When heat flows from a hot body at tempe ratur e Tto a cold body at tempe rature
Tlowhigh, some of the heat en ergy c a n b e harness ed to pe rform useful work. For
exampl e, the intern al combu stion engine in a car burns gasoli ne fuel in a con
trolled fashi on, which releases energy prim arily as he at. A fraction, i.e. 25%, of
this heat energy is exploited to perform useful mechan ical work. A large fract ion,
i.e., 75%, of it is wasted as heat from the radiat or to the surroun d. In the body ,
energy in glucose molec ules is first convert ed to energy in many smal ler e
nergycarryi ng molecules called ad enosine tri-phosphat e (ATP) a t nearly 50% e
fficiency within our cell s. The ATP mo lecules serve as univers al energy currency
throug hout the cell a n d power various activit ies in the cell that perfor m useful
work. For exampl e, ATP power s electrici ty generation across all cell membran es
in all cells of the body and also power s the contrac tions of muscl e cells. The effici
ency of energy conve rsion from ATP to useful work is nearly 50%. Thus , the
overal l effici ency from fuel to useful work in the body is also 50 % 50 % ¼ 25 %
as in a gasoline engine. Hence 75% of the energy in the foo d that we eat is co
nverted to he at energy. This heat energy is used to maintain the body at a n
internal 37C tempe ratur e significan tly higher than the exter nal tempe rature, at
say 22C, and compen sates for heat lost from the body to the environm ent. With
tempe rature analogou s t o volta ge, and heat flow analogous to current ,
a circuit for therm oelect ric generat ion is as shown in Figu re 26.3 [16]. Each resistance in Figure
26.3 is de scribed by an Ohm’ s law equ ation of the form
heatR
ð 26 :
T
x
9Þ
¼I
x
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832 Energy harvesting and the future of energy
I
heat
TbodyRthermoelecRair37ºC
Tenv
Vthermoelec+
–
Figure 26.3. A circuit model for body heat loss.
body
22ºC R
is the temperatur e drop a cross the resi stance
Rx
, i s m easure d in units of
W/m2
heat
2K/W.
, an d th us th e va lue of Ihe at
a
i
r
,
a
n
d
R
2
b
o
d
y
The Rth er m oel ec
bod
y
2
2
2m
air
2
orair
6
m
W
/c
m2
2
air
whe
n
the
am
bie
nt
tem
per
atur
eis
28
2
b
o
d
y
2
a
i
r
2
is
t
h
e
r
m
o
p
il
e
2
, and is measur ed in units o fC. The heat flow, I.wF rom E qua tion ( 26.9 ), the t he
her e D Txrm al res istance is then me asured in uni ts o f mel ement is built with a c ascade
of severa l BiTe See be ck-effe ct thermopiles that e ac h provide about 0 .2 m
V/C of outpu t voltag e. S uc h therm op iles a re bui lt by b ringing two dissimi lar
me tals toge the r at two junctions , on e at the hot side a nd on e at the c old side.
A se ries stac k of s everal of these thermopiles i s neces sary to deve lop voltages
of 1 V. F or exa mple, the rec en t de sign des cribed in [1 6] us ed 1 58 8 4 ¼
5056 of these d ev ice s in se ri es to dev elop n ea rl y 0.7 V. What dete rmines
the val ues o f R, Rthermoelec? Since 0.75 of the body’s rest ing power dissipati on
of 81 W i s dissi pated ov er
surface area, the net average he at flow out of the body may be expecte d
t o be 30 W/munder rest ing or sleepi ng co nditions. Und er normal conditio ns,
wher e the power dissipati on average s t o 125 W – 150 W, it has bee n measur
ed to be 60 W/mC [17] . A t steady stat e, the heat flow out of the body must be
match ed by the heat that it generat es to ensure that the body does not heat up
or coo l W/mor 10 mW/c m. The therm al resistance of the body, whi ch is 500 cmK/W,
down. Notis reduced in this region to 100 cmK/W. The therm opile resi stance , R, i s
surprisingldetermined by the heat-co nduction prop erties of the thermop ile mate rial, the
y, the value
cross-sect ional area of the legs that join toget her to creat e its junction s, an d
of the bodyits length. Lar ger cross-sect ional areas and smal ler lengths lead to low er resi
’s effe ctive
stances. The de penden ce of therm opile hea t resi stance on geo metry is sim
therm al ilar to that of electrica l resistance s excep t that the heat con ductivity k plays
resi stancethe
, role of the electrica l condu ctivity s . I n Figure 26.3, Rthermoelecmu st have its
R, i s
geomet ry de signed such that it is co mparabl e t o Rþ R. I t i s hard to make it
altered v i signi
a
ficantl y large r than this value withou t making de vices too long or
bloo
cross-sect ional areas too thin, since the value of R
dvessel is typica lly quite high. For exampl e, commer cially availab le thermop iles
dilation and
have Rthermopileat 50 cmK/W while Ris 1000 cmK/W. The v alue of R
constr iction
an d other
feedback
mechani
sms to
ensure that
the body ’s
temperatur
e i s maint
ained. Ther
e i s varia
nce in the
heat flow at
diff erent
posit ions in
the body .
For exampl
e, the relat
ively hot
blood in the
radial artery
on the
undersi de
of the forear
m, wher e
watches a r
e worn, is
only separat
ed from the
ambie nt air
by a 7 m m
layer of skin
witho ut any
heat-insul
ating muscl
e. Thus ,
the heat
flow in this
region of
the body is
arou nd 100
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83326.4 Energy harves
high
Hot reservoir T
high
low
ΔQ
Figure 26.4. A heat engine.
W
ΔQ
T
low
C
old reservoir
air determ
ined by radiat ive an d convecti ve losse s i n air. The presen ce of
wind low ers Rby promot ing heat exchange and increa sing heat flow. A value
of Rthermopile
air
þR
Q
2
high
low
low
h
i
g
h
low
high
low
will not thave much temperatur e dropp ed across it, and lead to a loss in sen
hat is signi ficantl y smal ler than Rbody tivity.
2The dev ice descri bed in [16] ach ieved 250 m W o f power extra ction wi
h e a t flow of 20 mW/c macross a 6 cmwristwat ch-sized device with an amb
nt air tempe ratur e o f 2 2C. The outp ut volta ge into a matc hed load was 0
V. Given that we have 120 mW of heat flowing into our device, why are we o
able to extra ct 2 5 0 m W? A fundame ntal limit known as the Car not effici e
limit s the amoun t o f power that ca n b e extra cted from a therm oelectric d
vice.
Figure 26.4 sho ws what is termed as a ‘heat engine’ , i.e., a syste m that
generat es useful work W as he at flows from a ‘hot reservoir’ at temperatur e
Tto a ‘cold reser voir’ at temperatur e T. A n a mount of he at, Q, flows out o
the hot reser voir, some of it generat es useful work W , a n d the rest, Q, fl
into the cold reserv oir. By energy conserva tion, it is necessa ry that
¼ Qþ W ð 26 :10Þ The reser voirs are assum ed to have so man y degre
of freedom in which to
absorb heat energy, i.e., a high heat capacit y, such that their tempe ratur e
barely chang es with the modest amoun t o f heat drawn out of or pour ed int
them. But what determ ines how much of Qhighend s u p a s useful work W,
rather than wasted heat Q? The fundame ntal second law of therm odynam
in physics states that the
amoun t o f disorde r i n the worl d, measured by ‘entr opy’, can only have a
e t increa se or remain the same. It is based on the fact that disorde red and
highly rando m system states wher e e nergy is dist ributed equall y amon gs
many de grees of freedom a r e statistica lly significan tly more likely than
ordered system state s wher e energy is concentra ted amon gst a few
degrees of freedom . I n fact ,
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834 Energy harvesting and the future of energy
tempe ratur e i s just a measur e o f the average random thermal energy per degree of freedom in a
system. A degree of freedom repres ents the volta ge on a capacit or, the current in an inductor , the
posit ion of a spring, or the veloci ty of a mass in a phy sical syst em. (Degrees of freedom are discussed
in Chapt er 7 i n the co ntext of the equipart ition theorem .) Heat flows from a hot high-te mperature body
to a c o l d low -temperat ure body becau se the rando m therm al energy tries to red istribute itself
equally amo ngst all de grees of freedom in both the hot body and the co ld body . Since the hot body has
more ave rage therm al en ergy per degree of freedom than the cold body , there is a net therm al ene
rgy flow from the hot body to the cold body as the ene rgy redistri bution oc curs. When a smal l amount
of heat Qlow
flows into a heat reservo ir of tempe ratur e T low, its en tropy is defined to increa se by Q= Tsince the
num ber of access ible states in the reser voir increa ses as more energy is poured into it, leadi ng to mo
re unc ertainty abou t its stat e, and mo re disorde r. When a smal l amou nt of hea t Qflows out of a h e
a t reser voir of tempe ratur e T, its entropy is defined to decreas e b y Qhighsince the numb er of a
ccessible states in the reser voir decreas es as energy leaves it, leading to less uncerta inty abou t its
state, an d less disorde r. Since the ne t entropy chang e must be nonz ero by the seco nd law
T
0 ð 26 : 11 Þ
þ Qlow
low
T
Qhigh
lo
w
high
low
hig high
h =T
high
Some algebr a o n Equations (26.10) and (26.11) then reveals that
W QhighT1 Tlow ð
2 6
:
1 2
Þ
high
high
Thus, the maxi mum effici ency of the heat engine, that is the fraction of heat Qthat is convert ed to
useful work W, i s lim ited to a maximu m value known as the Car not efficienc y, C,
TC ¼ 1
ð 26 :
Tlowhigh
13 Þ
highThe Car not efficie ncy sets limit s o n the efficien cies of steam en gines, plane engines , car engines
, and on our therm oelectric ha rvester as well. If the body is at T¼ 37C, and the ambie nt tempe ratur e i
s a t Tlow¼ 22C, the maxi mum possibl e efficiency for the therm oelect ric harvest er is given by
¼ 1 273 þ
ð 26 :
22273 þ 37 ¼
14 Þ
C
thrm hrv 0 : 0484
Thus, if 120 mW flows into a therm oelectric en ergy harvester, the be st we can hope to do is extra ct 5.8
mW of power. It is not atypica l for an experi menta l syst em to operate at 10% of the limit ing possibl e
Carn ot efficien cy, which is onl y achieva ble at infinit ely slow ope ration. The system de scribed in [16]
ach ieves nearly 4% of the Car not limit but it is one of the be st systems report ed thus
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83526.5
Power consumption of the world
far. Its de livered power densit y o f 0.2 W/m 2is in excess of what an average
10%-e fficie nt solar cell might de liver in ind oor environm en ts. An effici ent cha
rge pump for such thermal harvest ers is de scribed in [18].
26.5 Power consumption of the world
Mack ay estimat es the average power consumpt ion of an afflu ent British citizen
today in his book [1]. If we adap t his units of 1 k W h/day to simple kW units wi th
the conve rsion fact or 1 k W h/day ¼ 41.67 W , we find that this consump tion may
be broken down as shown in Tabl e 26.1.
The co sts of Table 26.1 are esti mated for an afflue nt Br itish citizen. An ave
rage British citizen actually consu mes 5.2 kW , a n average Europ ean citizen con
sumes 5.46 kW , whi le an average Ame rican citizen co nsumes nearly 10.4 kW.
The world average is 2.5 kW with great varia nce across nations . Since there are
Table 26.1 Power consumption of the world
Item Power consumption Comment
1. Car usage 1.67 kW 30 mph at 30 mpg for 1 hour at 10 kW h/ liter for gas with 3.8 liters ¼
1 gallon. Or equivalently, the cost of an average 42 kW car driven for 1 hour each day.2.
One transatlantic flight per year on a Boeing 7471.25 kW Such planes operate at 0.14 mpg
but amortize this cost over 400 passengers such that they effectively operate at 60 mpg
per person. The power consumption of a Boeing 747 is 150 MW.3. Heating 1.540 kW Not
important in some geographical areas. 4. Material synthesisenergy costs 2.08 kW It costs
energy to manufacture appliances.
5. Electric lighting 0.167 kW Estimated for an average home. 6. Electric gadgets 0.208 kW
Washers, dryers, cell phones, etc. 7. Material transport 0.500 kW Trucking and
transportation costs to move
materials. 8. Food 0.625 kW This energy cost
in food only tracks industrial
energy flows associated with food, not the
natural embedded energy in food. For
example, it costs energy to transport food, and
to maintain animals to be used later as food.
9. Defense 0.167 kW These national costs are amortized per person.
Total 8.207 kW Does not include the cost of imported goods, which bear their own energy costs, at 1.667 kW.
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EN
G
836 Energy harvesting and the future of energy
app roximatel y 6 billion pe ople on our planet today, the power consumpt ion of
the world is 15 TW. The elect ricity con sumption of the world is 2 TW. How
ever, since typic al ge nerating stations burn fossil fuels like coal to generate
elect ricity and are only 40% effici ent, the actual power co nsumpt ion due to
electricity use is 5 TW. We notice that a large fraction of the power consumpt ion
of the world revolv es around trans portation, heati ng, and elect ricity costs. This
book has alrea dy discus sed princi ples for low ering power in electrica l syst
ems. No w, we shall discus s some principles for the design of low -powe r trans
portation syst ems of the futur e.
26.6 A circuit model for car power consumption
ENGv
v
ENG
ENG
= Car velocity vCAR
E
N
G
Figure 26.5. Equivalent circuit of a car showing losses due to air drag, rolling friction, braking, and
chemical-to-mechanical energy conversion.
Figure 26.5 shows a circuit model of a car that is useful for unde rstand ing
power to be extra cted from the chem
fact ors that affect its power consumpt ion. We shall use current to represe nt pe riodic. The engine force is co nve
force and volta ge to repres ent veloci ty in accord with Equat ions (26.1),
wheels. The trans form er in Figure 2
(26.2), (26.3), and (26. 4). Thus , mass is repres ented by a capacitan ce,
trans mission) that perfor ms an imp
mechani cal damping by a con ductance, and mechan ical compli ance by an admittance of the secondary wheela
inducta nce. A c h emomec hanical dep endent force iENGdue to the burning of must be such that most of the power
fuel along wi th a Nort on-equiv alent mechani cal admittance Grepres ents
reflected admittance , not in G, whi c
the charact eristic s o f the engine power source. The fuel-to- mechani cal
tics of the impeda nce in the seco nd
work effici ency is typic ally 25% such that the iENGpower out put by the eng roa d con ditions, the gear rati os are
ine requ ires 4 i
preser ved.
A
DRAG
C ROLL
M
g
CAR
D
rr
Brake
iENGChemo-mechanical engine force Mechanical
ENG
G
Gears
2
v
i
=i
M
DRAG
ENG
CAR
force
CAR
i
v
12
M
RGN
B
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83726.6 A circuit model for car power consumption
charges the cap acitance MCAR
DRAGto
a v o ltage vCAR
,i
The mechani cal cu rrent iCAR
R OLL
CAR
BR
K
respectivel y that oppose
iCAR
C BRK
i
C
A
R
A
R
and iR OLL
v2
CAR CA
R
A
ð 26
:15Þ
must balance iDRAG
DRAG
DRA
G
2 C
D
CAR
CAR
2
as 3 m
¼1
CAR
ROLL
, which repres ents the
car’s veloci ty. When Mis charged, the car accelerates in accord with New ton’s second law . The car has
three force currents i, and iand attempt to deceler ate the car. Wh en no brake is applie d, iis 0. The
brake current is sho wn as a switche d resi stance in Figure 26.5. When the ca r i s moving at a steady
velocity and no brake is applied , isuch that there is no chargi ng or discharging current on t he capa ci
tor a nd the v el oc ity of t he car i s m ai nt ai ne d a t a constant value.
The dr ag force iis due to viscous air resistance caused by the fluid mo ving past the car. It can semi-em
piricall y b e repres ented by the current through a quad ratic condu ctance [19] :
The parame ter Ais the effecti ve cross- sectional area of the car, whi ch must be kept small to reduce
air drag. That is why most natural creatu res and artificial trans port mechani sms that move efficien
tly, e.g. , trains, are arch itected to be long and thin su ch that Ais small wi thin a given vo lume constr
aint. We can estimate Afor a 1.5 m high an d 2 m wide car. The parame ter CD3is called the coeffici ent
of drag and is typic ally near 0.3 in most cars and low er in stre amlined racing cars. The parame ter r
is the densit y o f air, whi ch is 1.3 kg/m. The mass of the car, M, i s typic ally one ton ne, i.e., 1000 kg.
The force iis the force due to ‘rol ling friction ’ i n the car. It is due to the fact that the tires sligh tly dist
ort and recove r shape when they move, and some of the energy in the tir es and tire bearing s i s dissi
pated. The force iROLLis semi empir ically represen ted by [19] , [20]
rr M
¼
C
CAR
i
RGN
ROL L
rr
rr
BRK
2
v
CAR
g ð 26 :16Þ with C¼ 0 : 013 for a relative ly smoot h road and average c a r tires. The parame ter Cis
relative ly invariant with speed. The braking force idissip ates the car’s kinetic en ergy as heat when
the brake is applied and the brak ing resistance is switche d t o ‘ground’ , i.e., to zero veloci ty as
shown in Figure 26.5. J ust as the dischar ge cu rrent in digit al CMO S d e sign dissip ates the ð1 = 2
ÞCV2 CARcapacit ive en ergy store d i n a vo ltage node as heat, the braking force dissipates the ð 1 =
2 Þ Mkinetic energy store d i n the mass of the car as heat. As in ad iabatic CMO S design, discussed
in Chapter 21, the switche d braking en ergy can be parti ally recover ed an d store d o n a n
ultra-capa citor , flywhee l, or batte ry and then used to provide energy bac k t o the car when it is time
to ac celerate. Hybrid cars recover 50% of the switchi ng ene rgy through such ‘rege nerative braking’
strategi es. Equat ion (21.50) in Chapt er 21 sho wed that, in a high-qua lity-f actor syst em, the switchi
ng energy can be reduced by as much as 2 p = Q wher e Q is the qua lity factor of the system. In Figu
re 26.5, we have repres ented the regen erative storage abstr actly by a mass Malthoug h any form of
storage may be used.
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838 Energy harvesting and the future of energy
Lots of br aking corres ponds to a high activit y fact or or lots of switchi ng in elect ronic systems. A high
maximum velocity of the car corres ponds to a large V DD
and iROLL
clk
TOT
a
v
av
avt
v
v
¼P ¼P
,
trv
trv
TOT
d
¼E
ð 26 :
17 Þ
TOT
I
av
av
t
r
v
mtrc
n electronic systems. The iDRAG
tforces
i co rrespond to stat ic ‘leak age’ current s i n electron ic syst ems. One
leak current increa ses quadrati cally with volta ge (the drag cu rrent) and on
leak cu rrent is a constant vo ltage-i ndepend ent current like sub thresh old
leakage c urrent in digital systems (the roll current ). We can therefo re draw
upon princip les learne d i n low-pow er digit al design to reduce static energ
and dy namic switchi ng energy for a given distance of trans port. But what i
o o d metric for energy- effici ent trans portat ion?
As we discus sed in Chapt er 21, the energy pe r cycle of operatio n, E¼
PTOTð 1 = fclkÞ , i s used to charact erize the energy efficienc y o f digit al
systems. Tran sport is rarely pe riodic such that ‘a cycle of ope ration ’ doe s
not make sense in trans portation syst ems. How ever, the analogy to speed
of operatio n, f, i s the average veloci ty of travel, v. Thus , the average powe
consumpt ion divide d b y the average veloci ty of trave l might be a g o o d
metr ic. If the total time of trave l i s den oted by t
Thus , our metr ic inspi red from elect ronics is mathe matical ly equ ivalent to the metr ic that is actual ly us
ed to characteriz e energy effici ency by trans portation engineer s: the energy co nsumed, ETOT, divided by
the total distan ce trave led, dTOT. It is pleasi ng that metrics used in complet ely differen t fields are intuiti
vely sim ilar.
Suppos e the average distance be tween braking stops is dstpand that we can recover a fraction argnof the
kineti c energy wasted during braking. Also suppo se that the tim e spen t t o accele rate to cruis ing
veloci ty VMXor to brake to 0 i s negli gible compared with the time spent traveling at this cruis ing veloci
ty, i.e., we have a square- wave-lik e profile in our veloci ty. Then, from Equation s (26.15), (26. 16),
(26.17), an d Figure 26.5, the metr ic for trans port ene rgy effici ency is given by
2C A V
2 rr M
ð 26 :
CAR
18 Þ
In Equat ion (26.18),
M
Imtrc
X
þ1
þC
D
CA
R
CA
R
an d argn
s
t
p
CAR,
and the drag coeffici ent, CD
MX
I
t
r
c
¼ð1
g
argnÞM2is a current , which impl ies that we are energy effici ent for a given distance of trave l i f w
m
dstpCARVaverage
2
force or ‘thrust’ requir ed dur
ing this travel. Equation (26.18) also reveal s that, t
MX
ent, dshou ld be high such that we do not brake often and that we recove r most of the en
respect ively; that Mshou ld be low to mini mize roll ing frictio n and en ergy dissipated du
the front al area of the car, A, should be minimiz ed by ha ving the car c reated in a tear d
Vshould be low to minimiz e dra g and braking forces. If the car wer e a n elect rical syst
that, for low -power operati on, the acti vity factor should be smal l and recycl ing efficien
such that switchi ng en ergy is mini mized ; that capac itances shou ld
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83926.6
A circuit model for car power consumption
3
10
stp
d = 150 d = 5000
stp
2
10
1
10
0
10
-12
3 4 5 6 7 8 9 10 20 30 40 50 60 70 10
Car speed (mph)
Figure 26.6. Power consumption of a car versus its speed.
be small; that leakage current s sho uld be optimized to be smal l; and that the
power -suppl y v o ltage, VDD, o f the syst em shou ld be smal l. Equation (26.18)
reflect s the en ergy effici ency of the secondary wheel side. If we
reflect this back to the prim ary side, the actual energy efficien cy of trans port, which is related to the
fuel c onsumed, is given by
rr
ð M2 þ DA
V
MX
1 dstp 1
a CAR 2 CAR
þC
2
ENG
rg V2
C
MX
n
MX
MX
Þ
M
; ð 26 :19Þ
CAR
mtrc
MX
þ
1
mtrc
DA
MX
rr M
CAR
D
MX
gV
MX
¼0:
013,
V
2
2 C
þC
,C
CAR
r
g
n
3
M
X
rr
¼
g
wher e the fact or of 4 arises from the 25% fuel- ato-mechan ical-work effici ency, and the e ð VÞ
the
4 that the effici ency of the engine change s with speed V. I t i s usuall y maximum at an o
c fact
t
Vdue
to the charact eristic s o f Ga n d the nature of the fuel-to- mechani cal-energy trans fer. T
ion
m of1a car on the secon dary side is just V MXtimes Isince Irepres ents the force thrust of the ca
t
power
econsump tion back to the seco ndary side, and assum ing that e ð VÞ is 1, for simplicity,
r
the
c power con sumption of the car to be
ð
I
V
M
X
Þ
P
C
A
R
¼4ð1
ð
2
6
argnÞ M2
:
2
0
Þ
dstpCARV3 Figure 26.6 plots the power c onsumpt ion, PCAR, versus its veloci ty Vfor a¼ 0, MCAR3¼
MX
C¼ 0 :3, ACAR¼ 3 m
stp
3 MX
MX
the parame ters used in Figure 26.6
at d
stp
MX
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9780521857277c26.3d
power con su
/or brak ing f
Equat ion (26
1, a n d i t ign
approxim ate
small. For ex
840 Energy harvesting and the future of energy
rameters tha
curve with a
higher speed
car power co
between curv
port energy e
tsp¼ 150 m a
force. The ca
car burns 40
is usua lly op
Equation
large . The tr
and g ¼ 9 : 8m= s 2for tw o that observed
differen t values of dstp¼ 1 5 0 m (city drivi ng) and d¼ 5000 m (highway drivi ng). The transitio n o f a Part of the st
car from a linea r V
has to trans p
weigh t o f its
in the car imp
four. Trains t
making them
ent pe r pers
brak e and h
18) is nearly
set it to 0. Se
(see Chapt e
small value:
ency per per
2 rr pr snN
þC
A
TRN
NV
M
X
I
perprsn
mtrc
I
¼ 12
CD
g
þ NMM
TRN
¼
prsn
ð
2
6
:
2
1
MN
Þ
g
1
2
Hence, theCfuller a train is, the lower its drag and rolling-friction terms per person, and the more
efficient
it Dbecomes. Third, their long and lean design with relatively low frontal area reduces drag.
p
Fourth,
the coefficient of rolling friction, Crr, for steel on steel is 0.002 rather than 0.013 for a car.
e
r they can run at an optimal speed where their engine has optimal efficiency. Sixth, they can
Fifth,
p
be run
on electricity and
r
s
n
m
t
r
c
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84126.7
Electric cars versus gasoline cars
thus have engine efficiencies o f over 80%. The overall result is that t rains can
operate at high speeds with a transport energy efficiency of 58 N per person, about
50 time s l ess t ha n t hat o f a c ar. In prac ti ce, tr ai ns ar e ra rely f ull i n de ve
loped countrie s. Never theless, in Japan, rail trans port ope rates at 216 N-per
-pers on efficiency, i.e., it has a 1 4 times bette r trans port efficien cy than that of an
average car today.
26.7 Electric car s versus gasoline car s
Give n the high energy efficiency of elect ric en gines in train s, c a n w e build pur
ely electric cars that are more efficien t than gasoline cars? Pur ely electric cars
function by using a battery to power a motor, which , afte r geari ng, provides
torque to turn the wheels of the car. The battery takes the place of the fuel as the
en ergy source, and the motor takes the place of the car engine. The pr imary side
of Fig ure 26.5 in a purely elect rical car is different from that in a gasoline car. The
secon dary side of Figure 26.5 is identi cal in a purely elect rical car to that in a
gasoline car. From now on, for brevit y, we shall refer to purely electrica l cars as
electric cars. Befo re we compare the effici ency of electric cars versus gasoline
cars, it is useful to unde rstand how a motor works .
( s) and a ‘back emf’ , K Omin(s ). The motor has an electrica l impeda nc e Z( s) repres ents the inpu t v
o ltage sou rce to the motor with source impeda nce ZinFigure 26.7 (a) reveal s the eq uivalent
electromec ha nical circuit of a motor and Figure 26.7 (b) reveal s the feedback loo p that de scribes
Figure 26.7 (a). In Figure 26.7 (a), Vð s Þ , which is prop ortional to its angular velocity O með s Þ . The
back emf aris es, becau se, just as in a piezoel ectre t, mechan ical-to-elec trical trans duction occurs
simultaneously with elec trical-to-mec ha nical transduction. Equivalentl y, all motor s generat e a ba ck
emf because they are also electrica l gen erators. The net c urrent in the motor, Iin(s), generates a t
orque, ð s Þ , w hi ch drives the mechanical admittance of the motor , G m( s ), and the effecti ve
mechani cal admittance of the load, Geff lmð s Þ ,to creat e the motor ’s angular veloci ty, O ð s Þ .
The admittance of the motor, G(s ), is typic ally inertial /capaci tive with a little loss. To find Geff lm( s),
the effe ctive load on the motor , w e need to mod el an electric car. We ca n use the model shown in
Figure 26.5 to model an electric car. The load G eff l(s ) i s the reflect ed load of the secondary side of
Figure 26.5, whi ch ap pears, after geari ng, as a load to the motor on the prima ry side. If the torque
and angular veloci ty of the motor are represen ted by t and o , respect ively, and if the trans form er,
whi ch repres ents the gears, is lossless,
m
m
t o
CAR
CA
v
R
CAR
Ci
¼
A
R
¼
v
ð 26 :22Þ As an aside, note that,
if R is the wheel radius on the secondary side of
Figure 26.5, we can also choose to pa rametri ze the mechani cal output varia bles of the car by the
torqu e o n the wheel an d the angu lar veloci ty of the wheel , i.e.,
CAR = R ð 26 :23Þ
¼
i
t CAR
Ro
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Electrical Mechanical
842 Energy harvesting and the future of energy
(a)
(s)
(s)G (s) O
m
I
in
Z (s) Z
in
(s
)
e
in (s)
+(s) +V(s)eG(s)Gm
(s) V
KI
in
–– +
l
eff
(s)KO
m
–
Motor
in
in(s)+Z(s)
1
K
V
G (s)(s) IinK O(
1
s
G(s)+Gm
(s) +
Z
e
Figure 26.7. Equivalent circuit of an electric motor in (a) and a feedback
equivalent in (b).
m
+
(
b
)
–
(s)
l eff
ENG
m
eff l(s
) replac ed by the gears an d secondary side of Figure 26.5.
Hence, there are tw o 2-port circui ts in an elect ric car, whi ch a r
e cascaded wi th one another: The first occurs due to the
electromec ha nical motor tw o-port circuit of Figure 26.7 (a) and
the second occu rs due to the sim ple gearing trans former of
Figure 26.5.
The m ec ha ni c al l oa d of t he motor i s r efl ecte d to the ele ct
ri cal side i n F igure 26 .7 ( a ) as an equivalent electrical im pe
da nce of v alue
Gð s Þ¼ K eff l2ð s Þþ G mð s Þ ð 26 : 24 Þ
Z
mtr
refl
)
In Fi gure 26.7 (a), KIinð s Þ is analogous to I(s ) i n Figure 26.5 and simila rly (s ). Thus , the ov erall circui t o f a n
G(s) is analogo us to GENG
circuit of Figure 26.7 (a) replac e the
CARwhi ch ap pears in series wi th Zin( s ) and Ze(s ) i n Figure
26.7 (a), i.e., the reflec ted impeda nce Zmtr refl( s) replac es the K
Oð s Þ de pendent generat or in Figure 26.7 (a). A phy sical
inter pretation of Equat ion (26. 24) leads to the realizat ion that
admit tance on the second ary side in Figure 26.5 sim ply trans
forms to a scale d identi cal elect rical admittance Gmtr
refls ð Þ ¼ 1 = Z mmtr reflðs Þ that is an exact mim ic of the
mechani cal admit tance. If g is the gear ratio, great er than 1,
that repres ents the up-con version of force from the primary to
the secon dary side in Figure 26.5, and Gð s Þ ¼ I CARð s Þ =
VCARð s Þ is the c a r admittance , then, from Equat ions (26. 24)
and Figu res 26.5 and 26.7(a), we get
ðsÞ 2
K2 G ð
s
Þ
ð
2
6
:
CAR 2
K
5
Þ
G
þ 1g
m
t
ð rs Þ¼
G m2
r
e
f
l
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84326.7
Electric cars versus gasoline cars
CAR!
vCARNote that Equation (26. 25) is only a smal l-signal frequency -domai n c h
aracterizatio n o f the refl ected impeda nce of the car. Ho wever, the feedback loop
of Figure 26.7 (b), suggest s that even if the ! O or equival ently i 2trans formati on
is nonl inear due to the nonlinear load charact eristic s o f the car (quadrat ic drag
con ductance and fixed roll ing-resi stance current source in Figure 26.5) , w e can
still repres ent this relat ionship a s a nonlinear block in an equival ent time-dom ain
feedback loop versi on of Figure 26.7 (b). We can then reflect this nonl inear blo ck
into the electrica l dom ain of the mo tor by replacing the ba ck emf by a nonlinear
I–V block that charact erizes the car. That is, in Equat ion (26.25), we sim ply use
the scaling c onstants 1 = Kan d 1 = ð g2K2Þ on the I–V curves that charact erize
the motor admittance gmor the c a r admit tance gCARin the tim e domain respectivel
y, and reflect these summ ed-and- scaled I–V curves into the elect rical domain as
a nonlinear I–V elemen t. A small-signal frequen cy analys is abou t each large
-signal ope rating poi nt as in trans istor circui ts, howeve r, is still useful for providi
ng intuiti on.
eThe factors that affe ct the efficien cy of elect ric cars are the same ones that affe
ct the efficie ncy of mutual-i nductance links that we discus sed in Chapt er 16.
Most of the torque cu rrent of the motor in Figure 26.7 (a) shou ld flow through Geff
l( s ) rather than throu gh G m(s ) t o preser ve go od effici ency in the mechani cal
outpu t domain. The motor mass is significan tly below the car’s mass and the mo
tor damping losses are usu ally significantl y less than the drag and other car losse
s. Thus , g o o d effici ency in the mechani cal domain can be achieve d w i t h
modest ge ar ratios in Equation (26. 25). Most of the vo ltage drop of the motor ’s
input voltage should be dr opped across the refle cted impeda nce Zmtr refl( s )
rather than across Z( s ) or Z(s ) t o preser ve good efficien cy in the electrica l
input domain, that is Ginmtr refl( s ) should be su fficiently small. Thi ck wiring in the
mo tor win dings reduces electrica l losse s Re, large ba tteries ha ve low outp ut
source impeda nce, and typic ally the motor ’s electrica l indu ctance Lis such that
the elect rical time constant of the motor , Le/Ree, i s much less than the mechani
cal tim e constant caused by the reflect ed impeda nce. Hence, if K, which is
primarily determ ined by the amou nt of flux in the motor, is suffici ently large , Gmtr
refl( s ) can be made small enough in Equat ion (26.2 5) such that effici ency in the
elect rical domain is excell ent. The overal l effici ency of the motor is the pro duct
of the efficien cy in the electrica l domain times the effici ency in the mechani cal
dom ain. Mo tors can ope rate with excell ent energy efficie ncy. Indeed, the Tesla
Roadst er electric car has achieve d effici encies that average 92%, whic h are
significan tly higher than the 25% effici ency of a gasoli ne c a r engine [21].
The Tesla Roadster electric car is a n impr essiv e engineer ing feat since it achieve s the specifica
tions of a high-pe rform ance sports car wi th exce llent transp ort energy effici ency and zero
emissions . Its source of power is a 450 kg lithium- ion battery with 53 kW h cap acity (424 J/g)
capable of 2 0 0 k W outp ut. The car its elf weigh s 1222 kg , h a s a peak mech anical power output
of 189 kW, accele rates from 0 t o 60 mp h i n 3.9 seconds, has a top speed of 125 mph, and can go
244 miles on a single batte ry charge. Its battery lifetime is limit ed to about 500 c harge-recha rge
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844 Energy harvesting and the future of energy
cycles ( 100,00 0 miles) , and it takes 3.5 hours for a full batte ry recharg e
althoug h a full recharg e may rarely be necessa ry. It implemen ts regener ativ e
braking. The lithium- ion batte ry has severa l short-cir cuit protect ion features
includi ng in-bui lt fuses that disconnect it in sit uations of high temperatur e a n d
pressur e. The batte ry is archit ected to be safe ev en dur ing co llisions.
Most impor tantly, the Tesla Roadst er’s transp ort energy effici ency is 50 0 N ,
abo ut 6 tim es better than that of an average car. The transp ort efficien cies of
severa l light er, low er-range, and low -speed electric cars are not significan tly
different from that of the Roadst er and some are much wors e [1]. To be fair to the
average gasoli ne car, though, the Tes la Roadst er uses high-g rade elect ric
energy, while the average car need s t o extract its energy from fossil fuel. M ost
elect ricity generat ing fossi l-fuel plants are 30%–40% effici ent such that one cou
ld argue that the real impr ovement of a Roadster is a factor of 2 to 2.4 . Never
theless , the Tesla Roadst er doe s ill ustrate that direct conversi on between high
-grade form s o f energy, e.g. , e lectrical to mechani cal rather than from chemi
cal-to-he atto-m echanical as in a gasoli ne car, is effici ent. In the futur e, if
electricity is generat ed in solar plants, such a car could indeed have a zero-emis
sion footpr int, especi ally if it is manu factured in plants using solar electricity as
well. Even though the en ergy densit y o f the lithium- ion batte ry that was used is
1 1 times less than that of gasoli ne, the weight of the car is managea ble because
the heavy gasoline engine is replac ed with an electric motor.
26.8 Cars versus animals
2Anothe
r impr essive exampl e i n trans portat ion eng ineering is the cheetah ( Acino nyx jubat us), the
fastest land anima l. Its top sp rint speed ha s been measur ed to be 30 m/s, i.e., 68 mph [22]. It can
accelerate to 68 mph in 3 secon ds, fast er than a Tesla Roadst er, which gets to 60 mph in 3.9 seconds,
a n d fast er than most high-pe rform ance cars [23] , [24]. Sin ce the average cheetah weigh s nearly 50
kg, we can estimat e that its mechan ical power output during this accele ratio n i s ð 1 = 2 Þ 50 ð 30Þ =
3 ¼ 7 :5 kW. Its rudder- like tail enables it to make incredi bly quick turns dur ing its chase of a prey
animal. The cheetah uses its spring -like ba ckbon e to partly store and regen erate energy in each stri de
and is airbor ne for mo re than half its stride. Its trans portation effici ency for aerobic speeds, which can
typic ally be maint ained for long distances only if they are less than half the top spee d [25] , has be en
measur ed to be eq uivalen t t o 0.14 ml of oxyge n consumpt ion pe r g.km [26] . Fro m the energet ics of
a glucose or carb ohydrate react ion, and from the weigh t o f an average ch eetah, these numb ers work
out to an en ergy e fficiency of 132 N. The cheetah’ s trans port en ergy effici ency is 4 times better than
that of a highly energyeffici ent elect ric car. What is more impressi ve is that this trans port energy
efficiency is achieve d even though the cheetah ha s t o make do with a 25% effici ent engine (fuel-t
o-mec hanical-w ork) an d that it runs with legs, not as opt imal as wheel s o n flat terr ain. For exampl e,
the en ergy efficien cy of humans wal king at
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84526.8
Cars versus animals
22.5
mph can be calculated from measur ement s i n [27] to be close to that of a
cheetah, 130 N, but human s ridi ng average unopt imized bicycl es with wheels
can achieve 81 N even tho ugh the dr ag coeffici ent of such bicycles is extre mely
poor (0.9 vs. 0.3 in a car).Gazelles and goats have a trans port energy effici ency
simila r to that of a chee tah at ae robic spe ed s [ 2 6]. Th us , m a ny anima ls
including the chee tah a chieve a 4 time s improve ment in tr ansport efficiency over
a highl y e ne rgyefficie nt ele ctric ca r, while opera ting w ith at l eas t a ð 0 :94= 0
:25Þ ð13 0 = 81 Þ¼6 time s disadvanta ge compared to it (inefficient e ng ine, no
wheels). Pronghorn ante lopes, the prey of chee tahs, h ave top speeds t hat ar e
near ly as fa st as cheeta hs sinc e they nee d to outrun the c he eta h to live [ 29 ].
Howev er, unlike s printing c he eta hs, the y can m aintai n a 4 5 m ph spee d ( 2 0
m/s) for l ong sus tained periods of t ime with an ener gy efficie nc y c om par able to
chee tahs, to whic h they are simila r i n w eig ht. The p owe r consum ption o f an a
nte lop e running at 30 mph is 1 .9 kW ( 130 N 13 m/s ), about 20 times less tha n
a n avera ge gasoline car at the same speed.
Airplanes an d birds both operate ne ar the funda mental lim its set by the laws of
aerodyn amics an d fl y a t a n optim al speed needed to supp ort their wei ght and
minimiz e air drag [30] . A ba r-tailed godwi t bird fly ing nons top from Ala ska to
New Zealand (7,008 miles) at 36 mph on its store d-fat fuel [31] ha s nearly the
same range as the maxi mal range of a Boei ng 747–300 (7,4 40 miles) flying at
555 mph on its store d jet fuel. The bar-t ailed god wit takes 8.1 da ys for its flight
ov er the centra l Pacific Ocean and maintains a 9 times increa se in its basal meta
bolic rate. Som ehow, it endures sleep dep rivation and potenti al deh ydration to
complet e its he roic journey [31] . Ther e i s signi ficantl y more room for impr
ovement in land-tran sport energy effici ency than in air-tra nsport energy effici
ency [1]. How ever, new designs for micr o-air veh icles are exp loring the use of fla
pping and flexibl e wing s that are aerodyn amically impor tant in small birds but
less impor tant for large airplan es and in big birds that glide [32].
Could anima l transpo rt inspi re the de sign of cars? It is pos sible that it will, but it wi ll requir e deep a
n d insigh tful knowl edge of both anima l trans port and ca r engineer ing to pluck this high-ha nging
fruit. Clea rly, many of the con straints and goals of hum an transp ort are different from those of anima
l trans port and we can’t incorpora te our energy for high-s peed transpo rt wi thin our own bodi es like
fast anima ls do. Therefor e, it is likely that insi ghts and princi ples will be useful , not details, just as
has oc curred in bird- versus -airplane design since the days of the Wright brother s. How ever,
paradoxi call y, to get these insi ghts, one will need to unde rstand a lot of details in both fields. This
principle is true in all of bio-in spired design. For exampl e, in the RF -cochlea sectio n i n Chapt er 23,
we described how the architectur e o f a bio logical cochlea inspired the design of an efficient RF
2
In contrast, on recumbent bicycles where the supine rider is enclosed in a
carbon-fiber-Kevlarcomposite shell, the drag coefficient of the overall highly streamlined bicycle
c eed > 82 mph on such a bicycle and an energy efficiency near 41 N [28]. P. Grogan. Sam
a Whittingham tops 80 mph – o n a push-bike. The Sunday Times. September 20, 2009.
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846 Energy harvesting and the future of energy
spectr um analyze r for ad vanced radio applic ations. This exampl e requir ed a
good knowl edge of both co chlear mod els and of tradi tional RF de sign, failing
which the algori thmic insight of a coch lear model woul d h a v e been mis sed
or the experi menta l p e rformance of the RF design woul d h a v e b e e n poor.
26.9 Principles of low-power design in transportat ion
Wh y d o a n imals ha ve excell ent trans portat ion e fficiency? One key is that
they are light , the analog of having smal l capacitan ce to reduce power in elect
ronic design. A car weighs 1000 kg but transp orts a 6 5 k g human. If four peo
ple use a car, the car’s pe r-person trans port energy effici ency impro ves by a
fact or of almost 4. So, we are obs erving the classic fle xibility-ef ficiency tradeof
f o f low -power design. If the c a r i s t o b e flexibl e enough to ha ndle situati
ons involv ing transpo rt of up to 4 p e rsons, its effici ency for trans portin g a
singl e p e rson is degraded. Degre es of freedom ne eded to maintain flexibi lity
hur t energy effici ency as in electro nic syst ems. In fact, an imals pay a price
for flexibi lity as wel l. In order to have a univers al energy cu rrency molec ule,
ATP, availa ble to power various acti vities flexibl y, they have to suffer the
inefficiency of two energy- conversi on steps , one from food to ATP , and
another from ATP to useful work, rather than one direct step that co nverts from
fuel to electrici ty, as some bacter ia acco mplish. All energyeffici ent trans port
vehicles from trai ns to cheetahs have encod ed in the shape of their bodies a
long-a nd-lea n structure that mini mizes drag. Tra ins exploi t parall elism to
achieve better trans port effici ency than cheetahs when full (see Equat ion (26.
21)). Anim als recycl e spring energy in their tendon s t o improve their trans port
effici ency just as cars with regener ative braking or adiabat ic digital circui ts do
[29]. The car is also subject to a robustne ss-effici ency tradeof f a s i n other
low-pow er syst ems: heavier cars do better in acciden ts but are highly en ergy
ineffic ient. So, there are clear conn ections be tween the princi ples of low -pow
er trans portation and the princi ples of low -power electronic design which we
discussed in Chapt ers 21 an d 22. But what is the con nectio n betw een infor
mation and energy in transpo rtation, a con nection that led to severa l power
-saving princi ples in prior cha pters?
The physica l varia bles that change stat e when we mo ve are our posit ion
and veloci ty. Transpo rtation may be descri bed as an informat ion-pr ocessi ng
pr oblem wher e our stat e n e eds to chan ge from x 0, our init ial position, to x,
. And, as is true for all systems, it costs energy to maintain state (mai ntain veloci ty in spit e o f d r a g
and rolling frictio n) and to trans form state (the costs of increa sing car kin etic en ergy). W e exploi t
the techn ology of trans port, whi ch can be designe d i n various topo logies (gasoline cars, electric
cars, train s), to solve this task. Higher average spee ds at whi ch the task is solved lead to higher
power con sumption. The feedback loop implemen ted by the visual sensing system of
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Principles of low-power design in transportation
3the
driver and his con trol strategy of the actuat ing system, i.e., the car, en sures
that the car stops and starts at needed pos itions along the way, with what is usuall
y adequate precis ion. Thus , the task, technol ogy, topology , speed, and precis
ion costs of a low-po wer syst em illustr ated in the low-pow er ha nd of Figure 1.1
also ap ply to cars. The car alread y implement s one good princip le of low -power
de sign through its use of a feedb ack loop, i.e., it separat es the costs of speed
and precision by having an accurat e sensor (the driver ’s eyes) an d control
system (the driver ’s br ain) determ ine the precis ion of transp ort whi le the
actuato r determ ines its speed . The mutual infor mation that is of relevan ce in a
trans portation task is that betw een a desir ed smooth , relative ly fast trans port
traj ectory in the head of the driver and the actual trans port trajector y that is ac
hieved. In the futur e, a trajector y that weighs the costs of carbon emissions will
also be impor tant.
2> R2One principle of low-pow er design that cars can exploi t i n the future lies in
impr oving the balance be tween c omputation costs and communi cati on co sts.
Car s can wi relessly communi cate with traffi c lights and with each other such that
the trans portation of severa l driver s i s more optim al, theref ore saving energy.
For exampl e, traf fic lights could automa tically ad apt their timing within a reasona
ble range su ch that the direct ions and locations of high flux have low er waiti ng tim
es than the direct ions and locat ions of lower flux . Traffic lights c a n b e coord
inated and synchron ized like inter acting phase-lo cked loops that recei ve
correction inputs based on traffic flux counts. Traffic lights could also adap t t o patte
rns that are au tomatica lly recogni zed as being due to a n accident scen ario. The
power costs of wirele ss transmis sion for relative ly short ran ges is extremely
cheap, especi ally when compared wi th the phe nomenal power costs of trans
portation (1 to 10 W versus tens of kW ). Furtherm ore, energy ha rvesting from
LEDs in traffic light s o r R F transmis sions from incomi ng cars can provide con
stant recharging boos ts to such systems such that they can be self -powered (see
Chapt er 17 for a discus sion of far-field wirele ss recharg ing syst ems). Car-to-ca r
hoppi ng can be used for longe r-range communi catio n, whi ch is significan tly
more power efficie nt per unit dist ance than a non-hop ping strategy (N ð R = N
Þfor N > 1in an N-hop ne twork). Needl ess to say, the be nefits of such
sensor- network schemes will have to be weighed aga inst their costs and
ease of impl ement ation within an existing infr astructure. Adapt ive tr af fic
lights and car-t o-car communi cation a r e being resear ched [33].
We shall now shift gears from discus sing how to minimiz e power consu mption to discussing how to
gen erate power . W e shall be gin wi th what is likely to be the most impor tant source of the power in
our futur e, solar elect ricity.
3
A of different drivers, the imprecision and/or slow reaction times of a drunk-driver’s control
c algorithm, or the disobedience of traffic rules. Thus, driving precision is strongly determined by
c feedback loops. The power costs of precision are largely borne by the driver and are relatively
i small. From [27], D. J. Morton and D. D. Fuller. Human Locomotion and Body Form (New York,
d NY: Waverly Press, Inc., 1952), they are estimated to be an additional 83 W over the basal 81
e W metabolic rate of the driver.
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848 Energy harvesting and the future of energy
26.10 Solar elect ricity generation
per da y b y 100 0/24 yield s the average daily insol ation in units of
W/m2per da y. M ultipli cation of the num ber quoted in kW h/m 2of power to the
Earth when its rays are ortho gonal to a locat ion on it [34] . How ever, 30% of this
radiat ion is reflect ed back into space, partl y b y clouds, and about 19% is
absorbed directly by the atmos phere [35] . Attenu ation fact ors that vary as the a
ngle of the incide nt radiation varie s throu ghout the day, the varia tion in latitude of
various places on Ear th, the varia tion in cloud cover in diff erent regions, the
complete absence of the sun at night, and the varia tion in sun shine with seasons
cause the power density of the sun to fluc tuate over spatial locat ion and ov er
time. The power densit y o f the sun at a parti cular region on Earth, term ed its
insolatio n, is often integ rated over the span of a day and express ed in units of kW
h/m2The sun trans mits 1366 W/m 2Davi d Goodst ein and others have pointed out
that the only renewab le en ergy source cap able of solel y power ing our planet a t
its exp ected and futur e power con sumption without a n incredi ble use of land
area is the sun [5].4. The average an nual insolati on can rang e from 100 W/m 22in
Hels inki, Finland, to 320 W/min Inyokern, California, US A. Not surpri singly, there
is more varia bility across seasons at extre me latitudes than at equatori al latitudes
. To find the insolati on at any latitude an d longit ude on earth, or at the location
wher e you live, visit [36] . Insolation for va rious major US cities is availab le a t
[37] .
So la r photovoltaic cells or photovoltaics that convert s ol ar energy to electricity
have efficienc y l im it s t ha t a re determined by laws of physics that g ov er n t he
interaction o f l ig ht with matter. W e s ha ll di sc us s s om e of t he se laws.
Losses due to shadow ing, du e t o r eflection at the c el l s ur fa ce , due to a l os s
i n l ig ht coll ec ti on area (a loss in ‘fill factor ’ a s i n t he imagers d es cr ib ed in
Chapter 1 9) can f ur ther reduce efficienc y. Lo w- ef fic ie nc y c el ls are t ypically
cheap t o m an uf ac ture while highefficiency c el ls are t yp ic al ly expens iv e t o
m an uf ac ture. The efficiency o f s ol ar cells can r an ge from 2% to 40%. Most
commercial systems t ha t c an be mass manufactured a re in the 1 0% –2 0% rang
e t oday. W e s ha ll fir st discus s h ow solar photovoltaics func ti on and t he n d is
cuss fundamental l im it s o n t he ir energy efficiency.
In Chapter 11, we discus sed how light creat es elect rons in pn junctio ns, an d
how we co uld e xploit such phototr ansducti on to create a photorecept or. In
Chapt er 19, we discus sed how to bui ld low -power imag ers using pn juncti ons.
The basic princi ples of phot otransd uction discus sed for these applic ations also
apply to solar cells. Solar radiat ion is largely compo sed of energy in the visi ble
light and near-i nfrared regions . Figure 1 1.2 (a) reveal s a pn jun ction form ed by
abutting a semico nductor of n-type mate rial with a semi cond uctor of p-type
material. Figure 11 .2 (b) reveal s the energy diagra m that describ es such juncti
ons with EC
Vand Erepresen ting the minimal and maxi mal en ergy of the cond uction band and valence band respect
ively. The depletion region created by the equilibrat ion of
4
Nuclear energy from fission sources will eventually also be non-renewable and there has not yet
been a breakthrough in nuclear fusion, which could potentially be renewable.
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0 Solar electricity generation
drift and diffusion current s a t the bor der be tween the n-type and p-type regions
causes the be nding of the band ene rgies. The electric fie ld in the depletion region
is such that positive dep letion charge in the n-type region, creat ed when electron
s diffuse away from the n-type region, rais es the potenti al of the region or e
quivalently lowers the electron energy in the n-type region. Simi larly, ne gative
depletion charge in the p-type region, creat ed when holes diffu se away from the
p-type region, low ers the poten tial of the region or equival ently raises the elect
ron ene rgy in the p-type region. In a juncti on with zero vo ltage across it, at
therma l equilib rium , the Fermi level EFis the same at all spatial locat ions such
that the average energy of an elect ron is the same at all spati al locat ions. If a
photon with energy hv great er than the band -gap energy EG¼ EC EVis absorbed
by the juncti on, the energy can be used to pro mote an electron from a low-energ y
state in the valence band to a higher energy state in the condu ction ban d. The
absorpt ion of energy creat es a hole in the valence ba nd in the en ergy state that
the elect ron has come from and an electron in the co nduction ba nd in the energy
state that the electron has gone to.
Th e c r e a t e d e l e c t r o n s t r a v e l ‘h om e ’ to th e i r n a t i v e m a j or it y - c a r r i e r n- ty pe r
e g i o n a n d t h e c r e a te d h o l e s t r a v e l ho m e t o th e i r n a t i v e m a j o r i t y - ca r r ie r p t y p e r e g i o n be ca us e t he s e r e gi on s r e p r e se nt a t tr a c ti v e r e gi on s o f l ow en er g y
. Fi g u r e 1 1 . 2 ( b) s h o w s t ha t e l e c t r o n s c r ea t e d i n a n n - t y p e r e g io n d o n o t tr a
v e l s i n c e th e y a r e a l r ea dy i n a r e g io n o f l o w e n e r g y . Si m i l a rl y , ho l e s c r e a t e
d i n a p - t y p e r e g io n do no t t r a ve l s i n c e th e y a r e a l r e a dy in a r eg i o n o f l ow e n e r
g y . I n a ny c a s e , t h e a b s o r p t i on of t h e p h o t o n r es ul ts i n th e n e t a r r i v a l o f a n e l
e c t r o n i n t h e n- ty pe r e g i o n a n d t he ne t a r r iv a l of a h o l e i n t he p- ty pe r e g i on . T h
e a r ri v a l of e l e c t r o n s i n th e n - t y p e r e g io n a nd t h e a rr i v al of h o l e s i n t he p- t y pe
r e g i on e f f e c t i v e l y r e su l t s i n a flo at i n g c ur r e n t so ur c e ac r o s s t h e j un c t i o n . Fi
g u r e 1 1 . 2 ( c ) i n Ch ap te r 1 1 s ho ws th a t li g h t e f f e c ti v e ly s h i f t s t h e I–V c u r v e o f
t he ju nc t i o n du e t o t h e p r e se nc e o f t he flo a t i n g c ur r e nt w i t h i n it . I f t he ju nc t i o n i
s i n a s ho r t c i r c ui t c o n fig ur a t io n , t h e c ur re nt w i l l ap p e a r a s a n e n h a nc e d r e v e
r s e - bi a s c u r r e n t . If t h e j u n c t i o n i s i n a n o p e n - c i rc ui t m o d e, t h e fl o a t i n g c u r
r e n t forward-biases the j un ctio n to a voltage such that the forwa rd- bias cur re nt ba l a n c e s t h
e l i g ht - d e p e n d e nt re v e r s e - b i a s cu r r e nt . C on se qu en tl y , t h e o p e n- c i r c u i t v o
l t a g e is a t a s t e a d y - s t a t e v a l u e . I n F ig ur e 1 1 . 2 ( c ) , t he s h o r t - c i rc ui t c ur r e nt
c o r r e s po nd s t o t he v a l u e a t V ¼ 0 w h i le th e o p e n- c i r c ui t v ol ta g e c o r r e s p o n d
s to the valu e at I ¼ 0.Suppos e the junction can be charact erized by the usual equ ation for a p n
juncti on,
S
I¼I
voltag
e. The
p ar am et er IS
qV =kT
ðe
1 Þð26 :26Þ where I is th e f or wa rd -b
ia s c ur re nt through t he junc tion and V is the f or wa rd -bias
is determined by minor ity-carrier c on ce nt ra ti on s, the a re a of cros s- se ct ion, and c ar ri er diffus
ion l engths within the j un ct ion [38]. Su pp os e initially t ha t a ll photon s a re of freque nc y v and
have a n e ne rg y hv. Th en, i f t he pr obability t ha t a ph ot on of energy, hv, c re at es an electron
ho le pair is a ð v Þ and
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850 Energy harvesting and the future of energy
there a re Ilphoton s p er second arriving ov er the c ol le ct io n a re a of t he junction , the c ur re nt in
the j unction i nc lu di ng the r ev er se -b ia s photocurrent i s g iv en by
qV = kT 1 Þ a ð v
ð 26 :
ðe
ÞqI
l
29 Þ
S
I¼I
I
l
sc
oc
q ln
V
l
I
S
oc
ð 26 : 27 Þ The short-cir cuit cu
rrent is obtaine d b y setting V ¼ 0 i n Equat ion (26. 27). Thus ,
¼a ð v Þ qIð 26 : 28 Þ The open-ci rcuit volta ge, V, o f the junction is given by setting I ¼ 0in
Equat ion (26. 27). W e find that
¼
a ð v ÞqIþ
1
kT
The incomin g radiation has a power of hvIlwhile the power of the solar cell cann ot be great er than VocIsc.
Ther efore, the ratio ð VocIscÞ = ð hvIlÞ establ ishes a crude upper bound on the solar -cell effici ency. From
Figure 11.2 (c), since Isc
Socand Vcan not simulta neously be maximal, the actual power outp ut of the solar cell IV is maximize d
when I < Iscand V < Voc. For a given Ilset by solar insol ation, it is clear that the effici ency of the solar cell s i
s maxi mized when a ð v Þ is maxi mum, whi ch impro ves bot h the open-ci rcuit volta ge and short- circuit
current , and when Iis minimum, whi ch impr oves the ope n-circu it vo ltage. What de termines a ð v Þ ,
what is the distribut ion of photons of a given frequency v in solar radiation, and what is the exact bound on
the limit of solar -cell efficien cy?
G
Shock ley an d Queisser provided insig ht into the limits of solar -cell efficiency in a landma rk paper [39] .
The analys is in their pap er ind icates that the limit s o f solar -cell effici ency in a singl e-bandgap pn
junction recei ving 1 sun’s wort h o f radiat ion is 31%. We sh all summ arize the ke y ideas in an intuiti ve
fashion here. Reader s interest ed in furt her details should consult [40] . Figure 26.8 (a) shows that, when a
photo n with energy hv > Ecreates an electron -hole pair, energy in excess of EGGis quickly lost as heat
such that only an energy equal to Eis avail able as elect ricity. Thus , while high-e nergy photo ns have a
high pro bability of creat ing an elect ron hole pair since many possibl e stat es are avail able for their creat
ion, a goo d fraction of their energy is lost as heat. Lowe r-energy photo ns wi th an en ergy hv just great er
than EGGha ve bette r efficienc ies of en ergy extra ction. Shoc kley and Quie sser assumed that any photo
n with en ergy hv > Ethat created an elect ronhole pair woul d d o s o with effective energy EGGand that any
photo n w i t h ene rgy hv < Ewoul d create no elect ron-hol e p a ir. Figure 26.8 (b) sho ws the known 6000
K black -body spectr um of solar radiation, i.e., the solar photon probabil ity dist ribution for photons of various frequenci es v . The shad ed
area to the right of the minimal hvg¼ Efrequency yiel ds the net fract ion of photon s i n solar radiation
that c ontribu te to elect ric energy generat ion. Each of the high-en ergy photon s that are repres ented in
this region con tributes an en ergy of EGGto electric gene ration an d wastes hv EGas heat energy. From
the entire probab ility distribut ion of Figure 26.8 (b), and the en ergy hv of single photon s, we can
compute the total incoming energy in solar radiat ion.
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Solar electricity generation
Electron (a) (b) (c)
Solar
photon
E
E
Photon
E
C
high
probability
distribution
C
Photon EG high
E
G lo
w
G
hu
E
Frequency u
E
V high
V
hu
Hole
From the shaded area in Figure 26.8 (b), we can compu te the electric energy
generat ed by the high-en ergy phot ons. The ratio of the elect ric energy to the
total incomi ng radiation energy then yield s a n ultimat e limit for the solar -cell
efficien cy.
=E
G
g
Figure 26.8. Generation of an electron-h
only photons that can generate such e
than the bandgap energy such that on
spectrum at 6000 K can be converted
that attempt to improve energy efficien
shown in (c) to increase their photon c
S
G
S.
Hence, the ope n-circu it vo ltage given in Equat ion (26.29) is redu ced. The use of pure semic
onductors is thus impor tant for a chieving high effici ency, but making pure mate rials is expen sive. The
solar cell must be thick enough such that the probabil ity of ab sorbing a photon is high. Figure 11.6 (a)
and Figure 11.6 (b) in Chapter 11 show that bluer photons are ab sorbed at shallo wer depths whi le
redder photon s are absorbed at dee per depths. The solar cell shou ld not be too thick since the chanc e
for e lectron-hol e recombi nation is then increa sed. Hence, there is an optimal thickne ss in solar cell s
that maximize s efficiency . How ever, maxi mum power trans fer is not attained at this opt imum. Topol
ogies are now be ing explore d i n which electron -hole pa irs are creat ed by photons along one spati al
dimens ion while elect rons and holes travel a short dist ance in an ortho gonal direction to cr eate an el
ectr ical voltage ; t hus, the ele ct ron-hole p airs are giv en little opportunity to recombi ne [41] .
Figure 26.8 (c) illu strates an idea for increa sing the fraction of photo ns that contri bute to electrica l
energy in a solar cell . I f w e have multiple pn junction s made of materials with progres sively smaller
band gaps, we ca n first extrac t the
Shock ley and Quiesser sho wed that their ultimat e limit cou ld be attained if= q , o f the semico nductor. Any othe
the only method for electron -hole pa ir destr uction at 300 K i s radiative , i.e., impurities in the semic onductor, de c
incoming therm al en ergy at 300 K from the environm ent creates electro n-hole
conseq uently decreas e the minor ity
pa irs, which then reco mbine to generat e outgo ing 300 K black body radiationI
that ba lances such generation . I n this limit, the value of Iis as low as it can
possibly be, and the open-ci rcuit volta ge of the juncti on asympt otes to the
band gap voltage , VG
¼E
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852 Energy harvesting and the future of energy
Sun
Solar cell
Reflector
Figure 26.9. A solar concentrator to improve solar-cell efficiency.
energy in the highest -energ y photons efficien tly, then in those with mo derate
energy, then in those with the low est energy, and so on. Suc h a n hierar chical
spectr al-energy extra ction sch eme is very much like that in a biologi cal co chlea
or in an RF co chlea (see Chapt er 23), i.e. , i t i s like a ‘cochl ear solar c ell’. The
overal l scheme extracts incomi ng solar photon energy in all spectr al bands such
that the area of the shaded region in Figure 26.8 is maximize d. It also extracts this
en ergy in a fashion such that little of it is wasted as heat. In theory, such schemes
have been sho wn to be capable of nearly 70% efficiency [41] .
Figure 26.9 illu strates an idea for impro ving solar -cell effici ency in a ‘sol ar con
centrator’ . W e gather radiation ov er a large area and focu s i t into a small area
such that the effec tive intensit y o f the sun per uni t area is increa sed from ‘1 sun
’ to, say, ‘400 suns’. The Il= ISrati o i n Equation (26. 29) then increa ses, impr oving
ope ncircui t volta ge and thus effici ency. One ad vantage of the con centrator is
that smal ler acti ve areas of pur e mate rial are ne eded for the same power, whi
ch can mini mize cost. How ever, such schemes have to track the sun to ensure
that its radiat ion does not move off the focal point wher e the solar cell is locat ed.
Sol ar con centrators have inde ed impro ved effici encies ov er simple flat-pa nel
solar cells.
The ultimate limit on solar-cel l efficien cy occurs when a graded -bandgap or mult iple-junct ion material
like that in Figure 26.8 (b) is combined wi th a con centrato r like that in Figure 26.9 to create a structure
where it app ears that the solar cell is ‘surr ounde d’ by 6000 K black- body radiat ion from the sun , o n
all sides . I t absorbs all of this radiation, an d then reradiates a small fract ion of it as blackbody radiat ion
at 300 K. In this lim it, the solar cell is just a ‘heat e ngine’ as shown in Figure 26.4: it absorbs heat from
the 6000 K ‘hot reservo ir’ of the sun, convert s most of it to useful elect rical work, and loses some of it
as radiated heat to the
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surround ing 300 K ‘cold reservo ir’. Thus , from the Car not efficien cy limit of Equat ion (26. 13), the
best possibl e efficiency of a solar cell is given by
¼ 1 3006000 ¼ 95 % ð 26 :30Þ
C
slr
The best so lar cell s that have been built today operate very near 40%, with every small pe rcent impr
ovement that is eked out requ iring ingenui ty and relatively e xpensiv e fabricati on. The key bottlenec k t
o solar -electri city gen eration on a large scale in the world toda y i s the implement ation of cost-eff
ective stra tegies that are also effici ent.
If S is the solar insolati on in wat ts per squ are meter, e is the e fficiency of the solar cell expressed as
a fraction, C( e ) i s the cost in dollar s p e r squ are mete r o f install ation of a solar plant, N is the
desir ed num ber of years to recou p the install ation investmen t, and i is the average rate of inflati on
over N years exp ressed as a percent age, then Scost, the cost in cents per kW h o f solar electrici ty,
can be shown to be
¼ 11 :4 Cð e Þe S N
ð 26
1
0
0
1 þ iN
:31Þ
S
cost
Hence, if e ¼ 0 : 1, C (0.1) ¼ $600/m2, S ¼ 190 W/m2, N ¼ 30 years, and i ¼ 3 % , then Scost¼ 29 cents
per kW h. Hence, compet ing with the cost of generat ing fossilfuel electrici ty at 4 cents per kW h i s
difficul t. However, with increasing resear ch and wi th increa sing econo mies of scale, C( e ) has been
constant ly reducing. An impor tant wi n-win situati on can occ ur if we low er power co nsumpt ion such
that the net change to the user is cost neutral or onl y results in a modest increa se in cost: the elect
ricity costs more but we use less of it such that our overal l cost is relative ly unc hanged .
The inter mittency of solar en ergy impl ies that we mu st draw on store s when it is not availab le, e.g.,
at night, and repleni sh these store s during the da y. Variou s stora ge opt ions are being explore d
includi ng compres sed air, flywhee ls, and batteries. One promising option may be the use of e
lectrochemi cal capacit ors, sometimes called ultra-capa citor s o r super- capacitors, whi ch are capable
of many cycles of rapid ch arge and dischar ge and that have relative ly high power densities [42] . Such
capacito rs are essent ially high-s urface -area doubl e-layer cap acitors, i.e., the Helm holtz capacit ors
de scribed in Chapt er 25.
Ultra- capacito rs are co mplementar y t o batte ries that have few er c ycles of charge an d dischar ge
but relative ly high energy de nsity. They have alrea dy been used for regener ativ e brak ing app
lications in electric cars and hybrid cars. Ultracapacit ors implement sho rt-term storage of energy, and
ba tteries implement medium -term stora ge of en ergy. The ulti mate in long-term stora ge of en ergy
is to convert so lar energy to a highly energy- dense chemi cal fuel. Biology has accompl ished such
stora ge via the pro cess of photo synthes is in plants for hundreds of millions of years. W e shall now
briefly discus s biofuel s a n d their impor tance.
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854 Energy harvesting and the future
of energy
26.11 Biofuels
Figure 26.10 illustrates
an e ssential feedback
loo p between plants and
an imals. Plants harvest
the ene rgy in sunli ght to
spli t wat er into hyd
rogen and oxygen as
part of the pr ocess of
photosyn thesis. The
hydrogen is bound with
COto creat e energyrich molec ules suc h a s
glucose (C6H12O62) whi
ch in turn is often bound
up in pol ymers like
starch and cellulose. Pla
nts also generat e the
oxygen that we breathe .
Anim als eat plant food s
(or eat oth er animals
that eat plant foods) and
oxidiz e C6H12O6molec
ules to water (H2O) an d
carb on dioxide (CO2).
The en ergy derive d
from the pro cess of ox
idation generat es ATP ,
which is used to power
various energy- consumi
ng process es in anima
ls. Thus , plan ts are the
solar cell s and fuel
generato rs for animals.
Anim als provide raw
mate rials useful to
plants.
Resea rch is unde r
way to creat e biofuels
that can power cars in
the future by con verting
grass es and non-edibl e
plants that contai n cell
ulose to biofuel s, i.e., to
creat e ‘gras soline ’ [43].
Suc h fast-gr owing
plants can grow in land
areas where normal food
crops can not, use
relative ly littl e water,
and do not encroa ch on
valuabl e farm land.
Since plan ts absorb
CO2in the atmos phere,
which is then retur ned to
the atmos phere when
the fuel is burned, biofuel
s are net carbon neu tral.
The pro cess of co
nverting cellu lose in
plants to fuel in an e
conomica l fashi on is
techni cally very ch
allenging and is an activ
e area of resear ch.
Scientist s are attemptin
g t o take inspi ration
from bacter ia and fungi
in the guts of cows and
in termit es respectivel y
t o unde rsta nd how to
digest these recalcitr ant
plan ts and thus create
econ omical biofuel s
[44] , [45].
If electric cars operate with sufficien tly low
power consumpt ion in the futur e, biofuel s
could potenti ally power fuel-cell -based
batteries in these cars, i.e, direct ly con vert the
chemic al energy in a fuel to electricity, rather
than burning it via a heat engine as in a con
vention al gasoline-pow ered car. Chapt er 25
co ntains a discus sion of how fuel cells
operate . The high en ergy density of biofuel s
implies that car batte ries can then be lighter,
and the use of an electric motor rather than a
heavy engine can furth er lighten the car. It is
worth not ing that biofuel-bas ed fuel cells hav
e been exp lored for implantabl e applic ations
for a long time [46] . A micro fluidic fuel cell
suitab le for impl antable applications has
recent ly been descri bed [47]. One challenge
in the operatio n o f such biofuel cells has been
that
Sunlight
HO6 + 6 O
2
C
6
12
Animals Plants
2O+6CO
2
6H
Figure 26.10. Photochemical energy flows in nature.
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the enzymes that a r e used to ox idize the fuel lose their efficacy after some tim e,
making them unattr active in long-t erm implants or in car app lications that may
need years of ba ttery ope ration . Cells solve these pro blems by co nstantly de
grading an d regener ating en zymes needed for various biological process es such
that they always maintain their efficacy .
26.12 Energy use and energy generation
Low-pow er syst ems can enab le sources of ene rgy that woul d normal ly be impr
actical for power ing an applic ation to beco me pr actical. In inducti ve links (Chap
ter 16), in piezoel ectric harvest ers, in elect ric motor s, an d i n elect ric cars, we
have seen that a low-po wer syst em can impr ove the energy effici ency of an
overal l syst em by altering the e ffective reflect ed load seen by the energy source.
A syst em is most ene rgy effici ent when there is mini mal power trans fer but only
achieve s 50% effici ency at maxi mal power trans fer. In the chapter on ba tteries
(Chap ter 25), we saw that a low -power syst em does not increa se ba ttery
lifetime merel y beca use of a low-pow er draw but also because it enables higher
energy densit y, higher efficien cy, and low er fade capacit y i n the battery. In elect
ric cars, the use of a relative ly light and efficient electric motor rather than a heavy
en gine enabled a n energy source wi th significan tly lower en ergy density, i.e., a
batte ry, to beco me practical for power ing a c a r . The cost effe ctiveness of solar
elect ricity is impr oved if electricity con sumption can be redu ced, thus enablin g
green electrici ty rather than ‘red’ electrici ty. The principles of adiabat ic design in
Chapt er 21, the Shann on limit on the minimum energy needed to compute in
Chapt er 22, and the Ragone-cu rve tradeoff betw een energy den sity and power
de nsity in Chapt er 2 5 all reveal that if you ca n pull en ergy out of a source
slowly, you can waste less of it an d creat e a higher capacit y t o store it. The
centra l take- home lesso n from these numerous exa mples is that energy use an
d energy gen eration are deeply linked. We must try to optim ize them joint ly rather
than treat them as two separat e p r oblems.
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