DESIGN ISSUES OF A VARIABLE THERMAL RESISTANCE. Székely V., Mezősi G

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1 Nice, Côte d Azur, France, 7-9 September 6 DESIGN ISSUES OF A VAIABLE THEMAL ESISTANCE Székely V., Mezősi G Budapest University of Technology & Economics Department of Electron Devices szekely mezosi@eet.bme.hu ABSTACT A flat mounting unit wi electronically variable ermal resistance has been constructed. The design is based on a Peltier cell and e appropriate control electronics and software. The device is devoted especially to e ermal characterization of packages, e.g. in dual cold plate arrangements. The paper is dealing mainly wi e dynamic behavior of e device and wi e problems arising from e incertitude in Peltier model parameters. Finally experimental results are presented. Keywords: variable ermal resistance, Peltier model, DCP measurements. INTODUCTION Creation of boundary condition independent ermal package models is nowadays in e focus of e activity of many ermal engineers. This activity requires e measurement of packages under different boundary conditions. These boundary conditions appear as ermal resistance sets between e top/bottom/side of e package and e ambience. Usually a number of ese resistance sets is fixed. These sets have to be applied during e measurements. Changing e ermal boundary conditions requires e dismounting and mounting again e measurement setup, which is a tedious work. This fact raises e idea of a new tool: e mount wi variable ermal resistance (VT). By using such tools at e boundaries of e package, measurement for a number of different boundary conditions become possible in a single setup. A few attempts to realize VT structures can be found in e literature, but for very different applications. One solution is to apply ermally conductive fluid between two metal plates wi interleaving fins. Change in e fluid quantity causes e change in e ermal resistance between e metal plates []. Anoer approach realizes ambient temperature dependent ermal resistance, using an array of bimorph cantilevers in a MEMS structure. The cantilevers deflect if e temperature raises. Since ey have different leng, ey make contact wi e opposite layer at different temperatures. This way e ermal resistance between e array and e opposite layer changes wi e temperature []. Some years ago we have proposed a ermal mount wi electronically variable ermal resistance, using Peltier cell [3]. In is earlier work e feasibility of such a structure has been demonstrated. Now we intend to realize is mount in a maturated form, suitable to e everyday use in e practice of package ermal qualification and modeling. The design of such a device raises a number of new questions and problems. The present paper is dealing wi ese problems and e possible solutions.. OPEATING PINCIPLE Let us briefly summarize e operating principle of e electronically variable ermal resistance. This mount is a sandwich structure, consisting of a Peltier cell, wi a heat spreading plate in bo sides (Fig.). Temperature sensors are placed in bo sides of e structure; e temperature data are forwarded to e control unit. This unit provides e driving current for e Peltier cell. The Peltier current is controlled by e two temperatures T and T in such a way at e virtual ermal resistance "seen" on e top of e structure has to be e prescribed value. Due to e nonlinear behavior of e Peltier cell, is control is described by a nonlinear function, in order to achieve linear virtual ermal resistance. The proper operation requires constant backside T temperature. This is why mounting on a good cold plate is recommended.

2 Fig.. The mount providing variable 3. MODELING OF THE PELTIE CELL The eoretical investigation of e structure requires an appropriate model of e Peltier cell. In connection wi our research work concerning e electroermal simulation algorims we have developed a circuit model for e Peltier cell [3], [4]. This model is shown in Fig.. The model has e following ree model parameters: is e electrical resistance in ohms, is e ermal resistance in K/W, α is e Peltier conversion constant in V/K. In Fig. I denotes e electrical current, while T and T are e temperatures in e two sides of e cell, in Kelvin. Fig.3). The upper side has satisfy e equation at describes e linear virtual ermal resistance : T T = () P Fig.3. Circuit model of e sandwich mount The following equation can be written to e T node of e Fig.3: Fig.. Peltier cell model As an example, let us recall e parameters of a 4 4 mm surface, I max = 4A Peltier cell: = K/W, α=.54 V/K, =3.6Ω. 4. BASIC EQUATION OF THE OPEATION The model of Fig. has to be completed wi e effect of e cold plate. That means T =constant (see I T T TαI + T T = () This is an equation of e second degree for e current I. earranging is equation leads to Tα ± T α ( T T )(/ / ) I = (3) This equation has to be used for e control of e current of e Peltier cell, in order to achieve a variable, linear virtual ermal resistance. Preliminary experiments

3 show at e range of e realizable virtual ermal resistance extends to about two orders of magnitude, e.g.. K/W. 5. DYNAMIC BEHAVIO The circuit model of Fig. 3 has to be completed wi two heat capacitances as it is shown in Fig.4. Since T =const e capacitance C has no effect. Unfortunately e heat capacitance C is slowing down e operation of e module, especially if we intend to realize relatively large virtual heat resistance. Under real circumstances C =- Ws/K. If e virtual ermal resistance is K/W, e time constant of e transient is - s and e settling time is much more high. (At e same time in case of =. K/W e settling is only a few seconds.) four times faster. Approaching wi e value of m, however, holds e danger of oscillations in e control loop. In order to use Eq. (4), of course, we have to measure (or calculate) e time derivative of e T vs. time function. 6. AIM FO THE ACCUATE MODEL PAAMETES The virtual ermal resistance is realized by e control based on e equation (3). The resulting value is as accurate as is equation correct. Certainly, we know e Peltier model parameters wi some incertitude. The same is true for e temperatures T and T. An important question: in what extent is incertitude influences e value? Only one result of e detailed analysis is presented here. This is e effect of e incertitude in e value of e Peltier cell. The relative error of can be approximately expressed as (6) Fig. 4. Dynamic model network In order to reduce e settling time e base equation of e control loop has to be completed wi a dynamic part: This means at realizing K/W virtual ermal resistance wi e Peltier cell having = K/W we have to known wi % accuracy to achieve 5 % accuracy in e value of virtual resistance. T T T T dt = I TαI + mc (4) dt where m is a constant between and. Using is equation, e dynamic behavior of e module is described by e following differential equation dt T T = P dt ( m) C (Derivation of is equation is omitted here.) It is clearly visible at e solution of is equation is exponential but e time-constant of e transient is (-m) C instead of C. If we choose e.g. m=.75, e settling will be (5) 7. MEASUE THE POWE FLUX As an advantageous side effect e power flux streaming rough e VT module can be continuously displayed. The node equation for e node T gives us: P I T T + TαI + dt dt = + C (7) If we measure T, T and dt /dt we can calculate continuously e power flux across e module.

4 8. EXPEIMENTAL ESULTS We have built e first version of e controllable ermal resistance unit. This unit consists of a 4 4 mm Peltier cell [5] and 8 8 mm Cu heat spreading plates. The total ickness of e unit is mm. The two temperature sensors are forward biased pn junctions. The upper and e lower Cu plates are ermally insulated by using Teflon spacers. The photograph of e unit is shown in Fig. 5. T-T [Celsius] P=8W el=.8 K/W P=8W el=. K/W.4 a.). T-T [Celsius] Fig. 5. The variable ermal resistance (VT) mount The control of e VT unit is realized by software. The T and T temperature data are converted to digital ones and read in into e control program at runs on a PC. The program controls e current of e Peltier cell via an AD converter and a power voltage/current converter. Let us see e results of a sequence of experiments! Three results are plotted in Figs. 6a,b and c. The Peltier current was controlled in order to achieve a.).8 K/W, b.). K/W and c.) K/W ermal resistance. After e stabilization of e system a power pulse of 8 W has been forced by a transistor mounted on e unit (as shown in Fig. ). The temperature rise divided by e 8W dissipation gives us e value of e realized virtual ermal resistance. The obtained resistance values are.6 K/W,.5 K/W and.65 K/W, respectively. We can conclude at (i) e ermal resistance can be really controlled by using appropriate software control, (ii) e measured ermal resistance values differ from e expected ones wi about -5 %, (iii) e settling time rises wi increasing virtual ermal resistance. The error in e realized ermal resistance can be partly explained by e fact at some amount of e 8 W dissipation has been spread upwards instead of flowing across e VT unit. Second possible source of e error is at e used Peltier parameters were probably not accurate enough. T-T [Celsius] P=8W el= K/W Fig. 6 a,b,c. Temperature difference between e two sides of e unit if a power pulse of 8 W is applied Equation (7) provides us a meod to measure e heat flux flowing across e VT unit. The experiments show at is measurement of e power flux works quickly. Fig.7 shows e measured flux when 8 W dissipation is switched on/off in e device mounted on e unit (as shown in Fig. ). The measured heat flux is about 7 W (according to e former assumption at not all of e 8 W dissipation has been crossed e VT unit). b.) c.)

5 Dissipation [W] [3] V.Székely, A.Nagy, S.Török, G.Hajas, M.encz: ealization of an electronically controlled ermal resistance, Microelectronics Journal, Vol.3, pp.8-84 () [4] V. Székely: "Modeling of electro-ermal phenomena in integrated circuits", dissertation, Hungarian Academy of Sciences, 977 (in Hungarian) [5] Fig.7. Power flux streaming across e variable ermal resistance unit, measured using T, T and dt /dt. 9. CONCLUSIONS The design of a variable ermal resistance (VT) unit has been made. According to e former experiments, e measurements on e unit prove e feasibility of such a device. The experiments show at e ermal resistance can be varied between about.5 and 5 K/W for e actual design. The settling time is undesirably high above K/W. In order to overcome is, during e design of an improved version e C ermal capacitance has to be reduced considerably. Important progress has been achieved in e way to develop e practically applicable VT device. The experiments help us to furer improve e design. Furer efforts are needed to extract more accurate parameters of e Peltier cells. Finally, e applications have to be tested/demonstrated during e subsequent research work.. ACKNOWLEDGMENTS This work is supported by e "Gabor Baross" research and development innovation project of e Hungarian Government, KM-CSEKK The contribution of e Maxpert Ltd. in e realization of e experimental setup is very appreciated. Special anks are expressed to S. Török for his effort in e design of control electronics.. EFEENCES [] Ake_Apr_4.htlm [] "Feasibility study for a novel temperature regulator wi variable ermal resistance", ref.doc