Online proceedings - EDA Publishing Association

q h
T h
7-9 October 2009, Leuven, Belgium
Heat Source
Heat
Spreader
TEG
P
N
Heat
Sink
q c
T c
I
Fig. 2. Thermoelectric energy scavenging module.
R L
Fig. 1. Schematic of a thermocouple in generation mode.
This section shows a proposed thermoelectric (TE) energy
scavenging module to recover the wasted energy from PA
transistors. This section also presents a fully-coupled TE model
developed to explore the performance and parametric behaviors
of the energy scavenging module.
A. Energy Scavenging Module
An energy scavenging module contains a Cu heat spreader, a
Bi 2 Te 3 based thermoelectric generator (TEG), and a heat sink
as illustrated in Fig. 2. A Cu heat spreader is used to minimize
the thermal resistance between the transistor and the
thermoelectric generator (TEG). Forced-air convection is
utilized for the reliability of high power PAs, e.g. PAs for
macro-cell base stations. Hence, the module contains a heat
sink that enhances the heat transfer from the TEG to the
ambient.
B. Fully-Coupled TE Model
A fully-coupled TE model was developed to explore the
power generation performance as well as the thermal
performance of the energy scavenging module. The TE model
integrates the TE theory with heat transfer theory by
embedding a power generation cycle in a thermal network; as
per Fig. 3. q tot is the total heat flow from the source (the
transistor), q h is the heat flow to the TEG hot side, h, P L is the
generated power by the TEG, and q c is the heat flow out of the
TEG at the TEG cold side, c. j and a denote the junction and
the ambient. θ jh and θ ca are thermal resistances between j and h
and between c and a. Fig. 3 shows basic physics of the TE
model, i.e., heat flow from the source conducts to the TEG, a
fraction of the heat is converted into the useful power, and the
remainder is dissipated to the ambient.
q h and q c can be expressed by the following equations.
q
( ) /
2 tot
= qh
= NIα Th
+ Th
−Tc
θTEG
− NI R / 2 (1)
q = NIα T + ( T −T
) / θ NI
2 R / 2 (2)
c c h c TEG +
where N is the number of thermocouples, I is the generated
current, α is the Seebeck coefficient, T h and T c are temperatures
of hot and cold sides of the TEG, respectively, θ TEG is the TEG
thermal resistance, R is the electrical resistance of a
thermocouple. Equation (1) shows that q tot is equal to q h . It is
based on the assumption that the heat loss from the source to
the ambient is negligible compared with the heat flow
conducting through the heat spreader to the TEG hot side.
In (1) and (2), the first terms, NIαT h and NIαT c are the energy
terms due to Peltier effect, the 2nd term, (T h -T c )/θ TEG is the heat
conduction purely due to the temperature difference across
pellets, the 3rd term, NI 2 R/2 is the Joule heating effect. The
further information including the derivation of q h and q c in the
form of three terms can be found in the literature [14].
q h and q c can be expressed in the form of heat flows between
j and h and heat flow between c and a as
q
q
h
c
( T j −Th
)/
θ jh
= (3)
( Tc
−Ta
)/
θca
= (4)
where T j is the junction temperature and T a is the ambient
temperature.
I is defined as
( T −T
)
N h c
I = α (5)
NR + R
where the numerator is the generated voltage across the TEG,
the denominator is the total electrical resistance of the
generation system evaluated by adding the net electrical
resistance of the TEG, NR to R L .
R is defined as
p
L
H
R = 2 ρ + Rc
(6)
A
where ρ is the electrical resistivity of the pellet, H is the height
of the pellet, A p is the pellet cross sectional area, R c is the
electrical contact resistance of a thermocouple.
R c is defined as
R
c
Rc−ρ
= 4 (7)
A
where R c-ρ is the electrical contact resistivity of a thermocouple.
θ TEG can be defined as
P
θ H
TEG
= 2 N⋅kA
(8)
where k is the thermal conductivity of the pellet.
The generated power, P L , associated with R L is defined as
2
L
R L
p
P = I
(9)
Considering the energy balance in a TEG, one can see that the
©EDA Publishing/THERMINIC 2009 76
ISBN: 978-2-35500-010-2