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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
7-9 October 2009, Leuven, Belgium Nopt Nopt 300 250 200 150 100 1200 1000 800 600 400 200 Pmax(W), ηmax(%) 50 0 0 8 7 6 5 4 3 2 1 0 N opt A Popt H opt 0 20 40 60 80 100 120 N opt A Popt H opt q tot (W) 0 20 40 60 80 100 120 q tot (W) η max P max 5Ω 100Ω 5Ω (a) (b) (c) 100Ω 20 15 10 5 0 0 20 40 60 80 100 120 q tot (W) 20 15 10 Fig. 4. (a) and (b) are optimized number of thermocouples (N opt), pellet cross sectional area (A Popt), pellet height (H opt) versus various heat flows from the source (q tot) associated with R L of 5Ω (a) and with R L of 100Ω (b). (c) is maximum power generations (P max) and generation efficiencies (η max) versus various heat flows from the source (q tot) associated with both R L of 5 and 100Ω. θ ca is 0.1K/W for all the cases. Fig. 5c shows that η max associated with two R L is very similar to each other despite 20 times difference between two R L . The similar η max can be explained by the fact that the value of the product of N opt and A Popt for each R L is very similar to each other. The calculated results show that η max considerably decreases, 7.4% to 6.4% at q tot of 20W and 5.7% to 0.6% at q tot of 100W, as θ ca increases from 0.1 to 1K/W. The deteriorated η max can be explained by the decrease of T h -T c induced by the increase of the net thermal resistance of the module. 5 0 APopt(mm 2 ), Hopt(mm) APopt(mm 2 ), Hopt(mm) Nopt Nopt 800 600 400 200 0 3000 2500 2000 1500 1000 500 Pmax(W), ηmax(%) 0 8 7 6 5 4 3 2 1 0 N opt A Popt H opt 0 20 40 60 80 100 120 q tot (W) N opt A Popt H opt 0 20 40 60 80 100 120 q tot (W) η max P max 5Ω (a) (b) 100Ω 5Ω 100Ω (c) 0 20 40 60 80 100 120 q tot (W) 50 40 30 20 10 0 50 40 30 20 10 Fig. 5. (a) and (b) are optimized number of thermocouples (N opt), pellet cross sectional area (A Popt), pellet height (H opt) versus various heat flows from the source (q tot) associated with R L of 5Ω (a) and with R L of 100Ω (b). (c) is maximum power generations (P max) and generation efficiencies (η max) versus various heat flows from the source (q tot) associated with both R L of 5 and 100Ω. θ ca is 1K/W for all the cases. V. CONCLUSION A thermoelectric (TE) energy scavenging module was proposed to generate the electricity from the waste heat of PA transistors. A fully-coupled TE model was developed combining TE physics and heat transfer physics. The TE model optimized pellet geometries such as pellet height, number of thermocouples, pellet cross sectional area to maximize power generations and efficiencies under various thermal and electrical conditions; heat dissipations of a PA transistor, heat 0 APopt(mm 2 ), Hopt(mm) APopt(mm 2 ), Hopt(mm) ©EDA Publishing/THERMINIC 2009 78 ISBN: 978-2-35500-010-2
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International Workshop on THERMal I
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Poster session: Introduction* 7-9 O
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x −1 V(x) = , f(y) = x + 1 y + 1
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of 75 o C for fair comparison. Only
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profile describes the temperature v
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[5] P. Lee and S. Garimella, “Hot
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