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•θ jh
•θ ca
j h c a
q tot TEG
q h
q c
P L
Fig. 3. Schematic of fully-coupled thermoelectric model.
power can be also obtained by subtracting q c from q h .
The power generation efficiency, η, is defined as the ratio of P L
to q tot as follows.
P
=
q
L
η (10)
Solving (1) to (10) simultaneously, thermal and power
generating performances and generation efficiencies are
determined.
IV. THERMOELECTRIC ANALYSIS
This section shows optimized pellet geometries to obtain the
maximum performance and the maximum efficiency of the
energy scavenging module under various q tot , θ ca and R L.
Predicted power generations and efficiencies corresponding to
the optimized pellet geometries are also shown here.
A. Parameters and Conditions
The optimized pellet geometries; pellet height, H, number of
thermocouples, N, pellet cross sectional area, A P ; were
predicted by solving the TE model; see (1) to (10). The
solutions were obtained for N ranging from 25 to 2500 and H
ranging from 0.01mm to 10 mm under q tot ranging from 20W
to 100W, θ ca of 0.1K/W and 1K/W and R L of 5Ω and 100Ω.
Consequently, the TE model determined maximum power
generations, P max , and generation efficiencies, η max associated
with the optimized pellet geometries. . The junction
temperatures, T j , of PA transistors operating at nominal
conditions of wireless access network equipments range from
150˚C to 200˚C. In this study the arithmetic mean value; i.e.
175˚C was used for all the cases.
The material properties of Bi 2 Te 3 were used. The used
properties are Seebeck coefficient of 4×10 -4 V/K, electrical
resistivity of 1×10 -5 Ω-m, thermal conductivity of 1.5 W/m-K,
and electrical contact resistivity of 1 × 10 -9 Ω-m 2 . Thermal
resistance between the junction and the TEG hot side, i.e., θ jh
was estimated considering interfacial resistances as well as the
resistance through the heat spreader, and the estimated value
was 0.3K/W. A typical air temperature in the enclosures of
the electronic equipments is 35ºC , and thus the ambient
temperature was assumed to be 35ºC. The used parameters for
the analysis are summarized in Table 1.
B. Results with θ ca of 0.1K/W
The results associated with θ ca of 0.1K/W are presented in
Figs. 4a to 4c. Figs. 4a and 4b show optimized pellet
geometries (N opt , H opt , and A Popt ) for q tot ranging from 20W to
100W associated with R L of 5Ω and 100Ω. Fig. 4c shows P max
and η max corresponding to N opt , H opt , A Popt for various q tot . H opt
was determined to be 10mm for all q tot and R L . It is useful to
note again that the used H for the calculation range from 0.01
to 10 mm. This interesting result is mainly due to the fact
tot
7-9 October 2009, Leuven, Belgium
TABLE 1
PARAMETER VALUES FOR ANALYSIS
Parameter Symbol Value
Seebeck coefficient α 4 × 10 -4 V/K
Electrical resistivity ρ 1 × 10 -5 Ω-m
Thermal conductivity k 1.5 W/m-K
Electrical contact resistivity R c-ρ 1 × 10 -9 Ω-m 2
Thermal resistance between
junction and TEG hot side
that maximum temperature difference across pellets occurs at
the maximum height in the parametric range. The effect of the
temperature difference across pellets is seen to be a dominant
effect to the power generation.
The results associated with both R L show that both N opt and
A Popt increase with the increase of the q tot ; N opt increases from
95 to 250 with R L of 5Ω and 435 to 1125 with R L of 100Ω and
A Popt increases from 4.6 to 11.5mm 2 with R L of 5Ω and from 1
to 2.6mm 2 with R L of 100Ω as q tot increases from 20 to 100W.
To maintain T j consistently, i.e., 175ºC against the increase of
q tot , the thermal resistance across the TEG, θ TEG , should be
reduced. The product of N and A P determines the effective
pellet area of the TEG, A e and the increase of A e reduces θ TEG .
Hence, both N opt and A Popt increase with the increase of q tot .
η max was found to decrease with the increase of q tot ; e.g.,
7.4% at 20W and 5.7% at 100W; see Fig. 4c. It is mainly due
to the reduction of the temperature difference across the TEG
induced by the decrease of θ TEG to consistently maintain the T j
against the increase of q tot . η max strongly depends on the product
of N opt and A Popt . N opt with R L of 100Ω is found to be about 4.5
times greater than that with R L of 5Ω whereas A Popt with 100Ω
is about 4.5 times smaller than that with 5Ω. The result
suggests that the value of the product of N opt and A Popt for each
R L is very similar to each other. Consequently, the similar
product values may explain the similar efficiencies despite 20
times difference between two R L .
C. Results with θ ca of 1K/W
Optimized pellet geometries, maximum power generations
and generation efficiencies were further explored associated
with θ ca of 1 K/W. Figs. 5a and 5b show N opt , H opt , A Popt for
various q tot ranging from 20W to 100W associated with R L of
5Ω and 100Ω. Fig. 5c shows P max and η max corresponding to
N opt , H opt , A Popt for various q tot . Similar to the previous result
with 0.1K/W, H opt was found to be 10mm and the result
supports again that a dominant parameter affecting η max and
P max is T h -T c .
Similar to previous cases, N opt and A Popt increase with the
increase of q tot to consistently maintain the junction
temperature; N opt increases from 105 to 765 with R L of 5Ω and
465 to 2500 with R L of 100Ω and A Popt increases from 4.7 to
37.2 mm 2 with R L of 5Ω and from 1.1 to 12.1mm 2 with R L of
100Ω as q tot increases from 20 to 100W. T h -T c should be
reduced to consistently maintain the junction temperature
against the increase of q tot . Consequently, η max was found to
decrease with the increase of q tot ; e.g. 6.4% at 20W and 0.5% at
100W.
θ jh
0.3 K/W
Ambient temperature T a 35 ºC
©EDA Publishing/THERMINIC 2009 77
ISBN: 978-2-35500-010-2