California Eastern Laboratories APPLICATION NOTE AN1030 Microwave Power GaAs Device Thermal Resistance Basics 1-INTRODUCTION 2-DEFINITION OF THERMAL IMPEDANCE (RTH) The operating temperature of GaAs power devices affects their reliability and RF performance. Since the majority of GaAs power microwave device failures occur in the channel (FETs) or junction ( HBTs) area, all life-test data is referenced to the channel or junction temperature. In the following the term channel will be used for simplicity. The importance of accurately determining the channel temperature of each device cannot be overstressed. With a knowledge of the case or flange temperature, DC bias conditions, and RF power levels (PIN and POUT), the channel temperature may be calculated using the thermal resistance of the device. The thermal resistance (RTH) may be used to compute the channel temperature of a device under a given set of operating conditions, i.e., case or flange temperature (TF), DC bias, and RF input and output power levels. The problem for power amplifier designers who use GaAs devices is that the data sheet, in general, gives the device thermal resistance with the measurement conditions for only one set of conditions (case temperature and power dissipated or channel temperature). It doesn't give any information on calculating the device thermal resistance versus flange and channel temperature or power dissipated. A common error is to assume that the thermal resistance for GaAs devices is a constant and use that value for different device operating conditions. The thermal conductivity of GaAs material is a fairly strong function of temperature, which means that the channel and case or flange temperatures should be considered in order to calculate the thermal resistance of GaAs devices. The purpose of this application note is to give the power amplifier designers a simple methodology to accurately calculate the device thermal resistances versus their operating temperatures from the data sheet information. Channel Temperature Thermal resistance, illustrated in Figure 1, defined as: RD = (TCH-TF)/PD where: RD is the channel-to-flange device thermal resistance (K/W or °C/W) TCH is the channel temperature (K or °C) TF is the case or flange temperature (K or °C) PD is the power dissipated by the device, which is equal to the DC input power plus RF input power minus RF output power (PD = VDS x IDS + PIN - POUT) (W) 3-THERMAL CIRCUIT Heat flow can be analyzed with a thermal circuit in the same way that current flow can be analyzed with an electrical circuit. In Fig. 2 the dissipated power (PD) is analogous to a current-source driver, temperatures are analogous to voltages, and each element in the thermal path has a thermal resistance (RTH) associated with it. The first element in the heat flow path is the channel-to-chip-bottom RTH (RC). The second element not shown in fig. 2 is the back side gold metalization (Au plated heat sink) of the chip Rth (RAu). The third element is the solder (interface chip-to-case) RTH (RS). The fourth FET Chip Au Plating Solder Channel-to-Flange RTH Package Flange Flange Temperature (Eq. 2-1) Flange-to-Heatsink Interface Heatsink Figure 1. Power FET Channel-to-Flange Thermal Resistance. AN1030 element is the case or flange RTH (RF) . The next element is the Rth associated with mounting the device on the heat sink (RI). The last element in the circuit shown is the heat sink-toambient RTH (RH). where: RD is the channel-to-flange device thermal resistance given in the data sheet. 5-CHIP BACK SIDE METALIZATION AND SOLDER THERMAL RESISTANCE The channel-to-flange RTH of the device alone (RD) which is given in the device data sheet consists of three practically constant RTH versus temperature, RAu, RS & RF , and the RTH of the GaAs chip, RC, which is a function of the temperature of the channel (TCH) and the temperature of the chip bottom (TCB): RD=RF+RS+RAu+RC(TCH,TCB) The thermal resistance of the chip back side metalization (RAu) is very low due to gold good thermal conductivity and the relative thin layer (2 to 30 um). This RTH can be disregarded for our purpose. When the chips are correctly mounted to the flange (no voids underneath the chips), the interface chip-to-flange thermal resistance (RS) is low in comparison with the flange and chip RTH and can be ignored. It is about 2 to 3 % of the global device thermal resistance (RD). (Eq. 3-1) 4-CASE OR FLANGE THERMAL RESISTANCE For the case of power GaAs devices, the chips are long and narrow and the thermal resistance of the flange can be approximated with the following formula: RF= [LN (16 t/π W)]/(π σF N L) If needed it can be approximated by assuming uniform heat flow through the interface chip-to-flange: (Eq. 4-1) RS=t / (σs N L W) where: LN is the natural logarithm (or loge) RF is the case or flange thermal resistance (K/W) L is the length of the chip (cm) σF is the thermal conductivity of the flange material (W/cm.K) t is the flange thickness (cm) W is the width of the chip (cm) N is the number of chips used in the device where: t is the solder thickness (cm) σs is the solder thermal conductivity (W/cm.K) N is the number of chips L is the chip length (cm) W is the chip width in (cm) If these parameters cannot be obtained by the amplifier designer from the device supplier, the following assumption for power devices can be made: If these parameters cannot be obtained by the amplifier designer from the device supplier, the following assumption for power devices can be made: RF=0.3 RD RS=0.025 RD (Eq. 5-2) The value of these parameters (RAu and RS) will be assumed to be negligible for the rest of this application note. (Eq. 4-2) Device Thermal Resistance Power Dissipated TChannel Chip RTH Die Attach RTH Flange RTH RC RS TChip TFlange Top (Eq. 5-1) RF TFlange Bottom Heatsink-toFlange-toHeatsink RTH Ambient RTH RI THeatsink Bottom Figure 2. Thermal Circuit. RH TAmbient AN1030 6-CHIP THERMAL RESISTANCE VERSUS TEMPERATURE 7-Methodology to Calculate Device Thermal Resistance versus Temperature from the Data Sheet Information (Fig. 3 shows the flow chart of this methodology) The thermal conductivity of the GaAs material can be expressed1,2 by: σGaAs=0.44 [(T+273.2)/300] -1.25 (Eq. 6-1) where: σGaAs is the GaAs substrate thermal conductivity at T (W/cm.K) T is the temperature of the GaAs substrate (°C) Step 1: Get from the data sheet: RD1, TF1, VDS & IDS1. Calculate PD1 = VDSXIDS1 Step 2: Define new conditions: IDS2, TF2, PIN & POUT. Calculate PD2 = VDS IDS2 + PIN - POUT From this Eq. 6-1 and the Kirchhoff’s transformation the following formula can be derived (see appendix A): Rc2=Rc1 A/B (Eq. 6-2) where: A=[(TCH1+273.2)-0.25-(TCB1+273.2) -0.25] / (TCH1-TCB1) B=[(TCH2+273.2)-0.25-(TCB2+273.2)-0.25] /(TCH2-TCB2) Step 3: Can you get the flange & chip information from the transistor supplier? Yes No Calculate the flange thermal resistance, RF, with Eq. 4-1 Assume RF = 0.3 RD1 RC1 is the chip thermal resistance for a chip bottom temperature TCB1 and a channel temperature TCH1 (°C/W or K/W) RC2 is the chip thermal resistance for a chip bottom temperature TCB2 and a channel temperature TCH2 (°C/W or K/W) Step 4: Calculate chip RTH RC1 = RD1-RF TCH1 and TCH2 are the channel temperatures (°C) TCB1 and TCB2 are the chip bottom temperatures (°C) From the known thermal resistance (RC1) of the chip for one set of temperatures (TCH1, TCB1), its thermal resistance (RC2) can be calculated for any set of temperatures (TCH2, TCB2). Step 5: Calculate chip bottom temperature: TCB1 & TCB2, with Eq. 7-3 & Eq. 7-4 Step 6: Solve iteratively Eq. 6-2 & Eq. 7-5 Step 7: Calculate the global new device thermal resistance: RD2 = RF + RC2 Figure 3. Thermal Resistance Calculation. AN1030 Step 1: get RC1, TF1 and PD1 from the data sheet TCH2=TCB2+RC2 PD2 (Eq. 7-5) Get the value of the device thermal resistance (RD1) for a defined set of conditions from the data sheet. The measurement conditions are in general without RF. The drain-tosource voltage (VDS) and the drain current (IDS1) or the power dissipated (PD1=VDS IDS1) are given. It can be solved by using an iterative method. The nth approximation of the chip thermal resistance, RC2/n, and the channel temperature, TCH2/n, are obtained respectively from Eq. 6-2 and Eq. 7-5 in the nth step by using the previous approximation of RC2/n-1 and TCH2/n-1 obtained in the n-1th step. Step 2: calculate PD2 from the new operating conditions The initial assumed values of RC2 and TCH2 for starting the first iteration, n=1, are respectively RC2/0=RC1 and TCH2/0=TCB2+RC1 PD2. The new conditions are defined by the application: IDS2, TF2, PIN & POUT. From the set of values, RC1, TCB1, TCH1, TCB2 and TCH2/n-1 and Eq. 6-2, calculate the nth approximation of RC2/n. Then calculate the nth approximation of TCH2/n from Eq. 7-5. The power dissipated is: (Eq. 7-1) If the following double inequality is satisfied, -0.01<(RC2/n-RC2/n-1)/RC2/n-1<0.01 stop the iteration process, RC2=RC2/n and TCH2=TCH2/n where: VDS is the drain voltage (V) IDS2 is the drain current (A) PIN is the input power (W) POUT is the output power (W) If this double inequality is not satisfied, then perform a n+1th iteration with the same process. Remark: VDS is assumed to be the same as the one defined in the data sheet because RD is a function of VDS. Step 3: calculate the flange thermal resistance (RF) From the device supplier or from measurement and literature get the flange thickness (t), and thermal conductivity (σF), the chip width (W) and length (L), the number of chips (N) used and use Eq. 4-1 to calculate the flange thermal resistance (RF). If these parameters cannot be obtained from the device supplier or measured use Eq. 4-2: Step 4: calculate the chip thermal resistance for TF1 and TCH1 RC1=RD1-RF (Eq. 7-2) Step 5: calculate the chip bottom temperatures TCB1=TF1+RFPD1 TCB2=TF2+RF PD2 (Eq. 7-3) (Eq. 7-4) Step 6: new chip thermal resistance (RC2) and channel temperature (TCH2) The following set of equations has to be solved: RC2=RC1 A/B A small program may be written to solve this system of equations iteratively (see Appendix B) or, because this sequence converges to the solution rapidly (two to three iterations), a simple calculator with an exponential function may be used. The graphical plot in Fig. 4 may also be used to calculate RC from Eq. 6-2. The plot represents the normalized chip thermal resistance, KC=RC/RCO, RCO being the chip thermal resistance for TCHO=140°C and TCBO=20°C, versus TCH and TCB. To determine RC2 from the graphical plot Fig. 4, proceed as follows: first get KC1=RC1/RCO for TCB1 and TCH1, then get KC2=RC2/RCO for TCB2 and TCH2. The new thermal resistance value at TCB2 and TCH2 is given by the equation RC2=RC1 KC2/KC1. 1.5 KC = RC (TCH, TCB)/RC (140°C, 20°C) PD2=VDS IDS2+PIN-POUT 240°C 220°C 200°C 180°C 160°C 140°C 1.4 1.3 1.2 120°C 1.1 100°C 80°C 1 TCH = 60°C 0.9 (Eq. 6-2) 0.8 where: A=[(TCH1+273.2)-0.25-(TCB1+273.2) -0.25] / (TCH1-TCB1) B=[(TCH2+273.2)-0.25-(TCB2+273.2)-0.25] / (TCH2-TCB2) and -20 0 20 40 60 80 100 120 140 Chip Bottom Temperature, TCB, in D.C. Figure 4. GaAS FET Chip RTH vs. Channel & Chip Bottom Temperature. AN1030 Step 7: Calculate RD2 Step 7: The new device Channel-to-flange thermal resistance at TCB2, TCH2 is: The new device thermal resistance is: RD2=1.111+0.312= 1.423 K/W and TCH2=168.7+1.111x60=235.4°C RD2=RF+RC2 (Eq. 7-6) Example 1 Step 1: The data sheet gives the following information: RD1=1.04 K/W at TF1=25°C, VDS=10.0 V and IDSQ1=6.0 A The power dissipated is: PD1=10.0x6.0=60.0 W If the original value, RD1, were used it would introduce an error of -23.0°C for the channel temperature. Example 2 Step1: The data sheet gives the following information: RD= 0.66 K/W at TF1=65°C, VDS=10.0 V and IDS1=12.0 A. The power dissipated is: PD1=10.0x12.0=120.0 W Step 2: Step 2: This device is used for a reliability test at TF2=150°C with a power dissipated PD2= 60 W. Its thermal resistance needs to be known for these new operating conditions to calculate the device channel temperature. This device is used at TF2=20°C and with PIN=3.0 W, POUT=60.0 W, IDS2=15 A, VDS=10.0 V. The power dissipated is: PD2=15.0x10.0+3.0-60.0=93.0 W Step 3: Step 3: The flange and chip parameters are unknown, we assumed in this case that: RF=0.3 RD1=0.3x1.04=0.312 K/W Step 4: The flange is 0.178 cm thick and made of Cu/W-15 material with a thermal conductivity of 1.90 W/cm.K. Four chips are used and each chip is 0.42 cm long and 0.10 cm wide. From Eq.4-1, the flange thermal resistance can be calculated: RF=0.220 K/W The chip thermal resistance is: RC1=1.04-0.312=0.728 K/W Step 4: Step 5: The chip thermal resistance is: RC1=0.660-0.220=0.440 K/W The chip bottom temperatures are: TCB1=25+0.312x60= 43.7°C TCB2=150+0.312x60=168.7°C Step 5: Step 6: First iteration From Eq. 6-2 and R C1 =0.728 K/W, T CB1 =43.7°C, TCH1=25+1.04x60=87.4 ° C,T CB2=168.7° C, T CH2/0 =168.7+0.728x60=212.4°C, calculate R C2/1 : RC2/1=1.08 K/W, which corresponds to a difference of 48 % from the initial assumed value. A second iteration is necessary. Second iteration Perform a second iteration with TCH2/1=168.7+1.08x60= 233.5 °C, which gives: RC2/2=1.109 K/W which corresponds to a difference of 2.7 % from the assumed value RC2/1. A third iteration is necessary. Third iteration Perform a third iteration with TCH2/2=168.7+1.11x60= 235.2 °C, which gives: RC2/3=1.111 K/W which corresponds to a difference of 0.2 % from the assumed value RC2/2. A forth iteration is not needed. The chip bottom temperatures are: TCB1=65+0.220x120=91.4°C TCB2=20+0.220x93=40.5°C Step 6: First iteration From Eq. 6-2 and R C1 =0.440 K/W, T CB1 =91.4°C, TCH1=91.4+0.440x120=144.2° C,TCB2=40.5°C, TCH2/0=40.5+0.440x93=81.4°C, calculate RC2/1 : RC2/1= 0.362 K/W, which corresponds to a difference of -18 % from the previous assumed value. A second iteration is needed. Second iteration Perform a second iteration with TCH2/1=40.5+0.362x93= 74.2 °C, which gives: RC2/2=0.357 K/W which corresponds to a difference of -1.4 %. A third iteration is needed. Third iteration Perform a third iteration with TCH2/2=40.5+0.357x93= 73.7 °C, which gives: RC2/3=0.357 K/W which corresponds to a difference of 0.1 %. A new iteration is not needed. AN1030 Step 7: The new device thermal resistance is: RD2=0.357+0.220= 0.577 K/W If the original value, RD1, were used it would introduce an error of 7.5°C for the channel temperature. perature rise or thermal resistance of an uniform heat sink of any shape with no further approximations and negligible further effort. At each point x of the conductor a fictitious linearized temperature α(x) is associated with the actual temperature T(x) with the formula3: α(x)=TO+σO-1 Remarks: ∫ T σ(T) dT (Eq. A-2) TO Sometimes the following formula is used to calculate device RTH versus channel temperature where σO=σ(TO) is the thermal conductivity at T=TO. RD2=RD1 (TCH2/TCH1)-1.25 Chip Thermal Resistance Versus Temperature where: TCH2 and TCH1 are the channel temperature in K Substituting the expression of σ from Eq. A-1 into Eq. A-2 and solving for the linearized channel temperature corresponding to chip bottom temperature TCB1 and channel temperature TCH1: This is correct only if the TCB1=TCH1 and TCB2=TCH2, in other terms if PD1=PD2=0 W, which is rarely the case. This formula doesn’t take into account that the flange RTH which is constant versus temperature and has first to be subtracted from RD1 before applying any temperature correction. ∫ TCH1 A Tn dT TCB1 =TCB1+TCB1-n [Tn+1/(n+1)] TCH1 TCB1 α1=TCB1+[(n+1)TCB1n]-1(TCH1n+1-Tcb1n+1) (Eq. A-3) Using the definition of the thermal resistance given in Eq. 1-1 to solve for the linearized channel temperature we get: APPENDIX A GaAs Chip Thermal Resistance versus Temperature GaAs Material Thermal Conductivity versus Temperature The thermal conductivity of GaAs material is a function of the temperature and can be expressed by the following formula1,2: σGaAs=A Tn α1=α(TCB1,TCH1)=TCB1+(A TCB1n)-1 (Eq. A-1) where: σGaAs is the GaAs material thermal conductivity at the temperature T (W/cm.K) T is the GaAs material temperature (K) n=-1.25 The dependence of σGaAs on the doping density is neglected because the regions where the material is doped are negligibly thick compared to the dimensions over which the heat is spread. Kirchhoff’s Transformation The temperature dependence of the thermal conductivity of the GaAs chip can be taken into account by using the Kirchhoff's transformation. The method consists of solving the heat-flow equation, analytically, numerically, or empirically under the boundary conditions of usual interest. Then Kirchhoff’s transformation immediately yields the nonlinear steady-state tem- α1=TCB1+ R (α1) PD1 (Eq. A-4) where R(α1) is the linearized thermal resistance corresponding to the linearized channel temperature α1. This is the value which the thermal resistance would have if the thermal conductivity of the GaAs material did not vary with temperature and was σ(T)=σ(TCB1). We may express R(α1) as: R (α1)=G/σ(TCB1)=G TCB1-n/ A (Eq. A-5) where σ(TCB1) is equal to the thermal conductivity of the material at a temperature of TCB1 [σ(TCB1)=ATCB1 n], and G is a factor depending on the device geometry. Substituting R(α1) from Eq. A-5 into Eq. A-4: α1=TCB1+ PD1 G TCB1-n/A solving for PD1 PD1=(α1-TCB1)A TCB1n/G (Eq. A-6) We want to find the channel-to-chip-bottom thermal resistance at TCB1 and TCH1 defined as: RC1=(TCH1-TCB1)/PD1 (Eq. A-7) Substituting Pd1 from Eq. A-6 into Eq. A-7: RC1=G(TCH1-TCB1)/[ A TCB1n(α1-TCB1)] (Eq. A-8) AN1030 Substituting the expression of α1 from Eq. A-3 into Eq. A-8, we obtain after simplification: RC1=[G/A)] (n+1)(TCH1-TCB1)/( TCB1n+1-TCB1n+1) (Eq. A-9) Similarly, for TCH=TCH2 and TCB=TCB2, RC2 can be calculated: RC2=[G/A] (n+1)(TCH2-TCB2)/( TCH2n+1-TCB2n+1) (Eq. A-10) Dividing Eq. A-10 by Eq. A-9 and solving for RC2 we obtain: RC2=RC1[(TCH1n+1-TCB1n+1)/(TCH1-TCB1)]/[(TCH2n+1-TCB2n+1)/ (TCH2-TCB2)] (Eq. A-11) where: RC2: chip channel-to-chip bottom thermal resistance at chip bottom temperature TCB2 and at channel temperature TCH2 (K/W) RC1: chip channel-to-chip bottom thermal resistance at chip bottom temperature TCB1 and at channel temperature TCH1 (K/W) TCB1 and TCB2: are the chip bottom temperatures (K) TCH1 and TCH2: are the channel temperatures (K) T in K=T in °C+273.2 n=-1.25 APPENDIX B HP48X or GX Calculator Program to Calculate GaAs Device Thermal Resistances versus Temperature Here is an example of a program for a HP48X or GX calculator to calculate the thermal resistance of GaAs devices versus temperature when this parameter is already known for one operating point. Begin by creating a directory for RTH, then get into that directory. 1-Get subprograms These following subprograms prompt the user to input a value for each of the following parameters: RTH1 (device thermal resistance @ TF1 & TCH1 in K/W), TF1 (flange temperature in °C), TCH1 (channel temperature in °C), TF2 (flange temperature in °C), PD2 (power dissipated at TF2 & TCH2 in W), RF (flange thermal resistance in K/W) and n (n=-1.25). <<“Key in RTH1 in K/W” “ ” INPUT OBJ—>‘RTH1’STO >> ENTER ‘GetRTH1’ STO to put GetRTH in the stack and store the program GetRTH1. <<“Key in TF1 in D.C.” “ ” INPUT OBJ—>‘ TF1’ STO >> ENTER ‘GetTF1’ STO to put GetTF1 in the stack and store the program GetTF1. <<“Key in TCH1 in D.C.” “ ” INPUT OBJ—>‘ TCH1’STO >> ENTER ‘GetTCH1’ STO to put GetTCH1 in the stack and store the program GetTCH1. <<“Key in TF2 in D.C.” “ ” INPUT OBJ—>‘ TF2’STO >> ENTER ‘GetTF2’ STO to put GetRTF2 in the stack and store the program GetTF2. <<“Key in PD2 in W” “ ” INPUT OBJ—> ‘ PD2’ STO >> ENTER ‘GetPD2’ STO to put GetPD2 in the stack and store the program GetPD2 . <<“Key in n” “ ” INPUT OBJ—> ‘ Expo’ STO >> ENTER ‘Getn’ STO to put Getn in the stack and store the program Getn. 2-Compute subprograms The compute subprograms handle the computational chores in the program. <<‘RTH1’ RCL ‘RF’ RCL - ‘RC1’ STO ‘RC1’ RCL ‘RC2’ STO>> ENTER ‘CompRC1’ STO to put CompRC1 in the stack and store it. <<‘TCH1’ RCL ‘TF1’ RCL - ‘RTH1’ RCL / ‘PD1’ STO >> ENTER ‘CompPD1’ STO to put CompPD1 in the stack and store it. <<‘RF’ RCL ‘PD1’ RCL x ‘TF1’ RCL + ‘TCB1’ STO >> ENTER ‘CompTCB1’ STO to put CompTBC1 in the stack and store it. <<‘RF’ RCL ‘PD2’ RCL x ‘TF2’ RCL + ‘TCB2’ STO >> ENTER ‘CompTCB2’ STO to put CompTCB2 in the stack and store it. <<‘TCB2’ RCL ‘PD2’ RCL ‘RC2’ RCL x + ‘TCH2’ STO >> ENTER ‘CompTCH2’ STO to put CompTCH2 in the stack and store it. << ‘Expo’ RCL —> a b c << ‘(((a+273.2)^(c+1))((b+273.2)^(c+1))) / (a-b)’ EVAL —> NUM>> >> ENTER ‘CompAorB’ STO to put CompAorB in the stack and store it. << ‘TCH1’ RCL ‘TCB1’ RCL CompAorB ‘TCH2’ RCL ‘TCB2’ RCL CompAorB ‘RC1’ RCL —> a b c <<‘axc/b’ EVAL —> NUM >> ‘RC2’ STO >> ENTER ‘CompRC2’ STO to put CompRC2 in the stack and store it. 3-Label program The final subprogram which adds a tag to the calculated RC2 value. << “RTH2 in K/W=“ —> TAG>> ENTER ‘Label’ STO to put Label in the stack and store it 4-Main program (five iterations are performed to calculate RC2) << GetRTH1 GetTF1 GetTCH1 GetTF2 GetPD2 GetPD2 GetRF Getn CompPD1 CompRC1 CompTCB1 AN1030 CompTCB2 1 5 START CompTCH2 CompRC2 NEXT ‘RC2’ RCL ‘RF’ RCL + Label >> ENTER ‘RCAL’ STO to put Label in the stack and store it. 5-Running RCAL program Run the RCAL program to find the Thermal Resistance of a device, RTH2, at TF2= 150°C and PD2= 60 W when its thermal resistance, RTH1, is known and is 1.04 K/W at TF1=25°C, and TCH1=87.4°C and knowing that its flange thermal resistance, RF, is 0.312 K/W. Press RCAL Program Prompt or Display Key in RTH1 (K/W) Key in TF1 (D.C.) Key in TCH1 (D.C.) Key in TF2 (D.C.) Key in PD2 (D.C.) Key in RF (K/W) Key in n RTH2 in K/W= 1.423 Your Action 1.04 ENTER 25 ENTER 87.4 ENTER 150 ENTER 60 ENTER 0.312 ENTER -1.25 ENTER References 1. Robert Anholt, “Electrical and Thermal Characterization of MESFETs, HEMTs, and HBTs” Artech House, Boston.London, chapter 4, page 62. 2. P.D. Maycock, “Thermal Conductivity of Silicon, Germanium, III-V Compounds and Alloys”, Solid-State Eletronics, Pergamon Press 1967. Vol. 10, pp. 161-168. Printed in Great Britain. 3. W.B. Joyce, “Thermal Resistance of Heat Sinks with Temperature-Dependent Conductivity”, Solid-State Electronics, 1975, Vol. 18, pp. 321-322. Pergamon Press. Printed in Great Britain. California Eastern Laboratories Exclusive Agents for NEC RF, Microwave and Optoelectronic semiconductor products in the U.S. and Canada 4590 Patrick Henry Drive, Santa Clara, CA 95054-1817 Telephone 408-988-3500 • FAX 408-988-0279 •Telex 34/6393 Internet: http:/WWW.CEL.COM Information and data presented here is subject to change without notice. California Eastern Laboratories assumes no responsibility for the use of any circuits described herein and makes no representations or warranties, expressed or implied, that such circuits are free from patent infingement. © California Eastern Laboratories 02/20/2003