ATS WHITE PAPER Device Thermal Coupling on a PCB THERMAL MINUTES Device Thermal Coupling on a PCB 1 to 5 mm Gap Insulation to Board or Insulation to Package Junction Temperature Board Temperature Thermocouple Soldered to Middle Lead Figure 1. Cross Section Illustration of a Ring Style Cold Plate RΘJB [2]. Insulate with tape if necessary Insulation Water Channel 5 mm Minimum The objective of any thermal solution is to ensure that a device’s operating temperature does not exceed the safe limits defined by its manufacturer. In the electronics industry, this operating temperature is referred to as the device’s “junction temperature.” In a processor, for example, this term literally refers to the semiconductor junction where electrical power is converted to heat. heat path is from junction to board only. To measure ΘJB, the top of the device is insulated and a cold plate is attached to the board edge (Figure 1). This is the true thermal resistance, which is the characteristic of the device. The only problem is that, in a real application one does not know how much power is being transmitted from different paths. To maintain operation, the heat must flow out of the semiconductor at such a rate as to ensure acceptable junction temperatures. This heat flow encounters resistance as it moves from the junction throughout the device package, much like electrons face resistance when flowing through a wire. In thermodynamic terms, this resistance is known as conduction resistance and consists of several parts. From the junction, heat can flow toward the case of the component, where a heat sink may be located. This is referred to as ΘJC, or junction to case thermal resistance. Heat can also flow away from the top surface of the component and into the board. This is known as junction to board resistance, or ΘJB. ΨJB is a measure of the temperature differential when multiple heat transfer paths are used, such as the sides and top of the component as well as the board. These multiple paths are inherent in an actual system and measurements must be used with caution. Due to the multiple heat transfer paths within a component, a single resistance cannot be used to accurately calculate the junction temperature. The thermal resistance from junction to ambient must be broken down further into a network of resistances to improve the accuracy of junction temperature prediction. A simplified resistor network is shown in Figure 2. ΘJB is defined as the temperature difference between the junction and the board divided by the power when the © Advanced Thermal Solutions, inc. 2007 | 89-27 Access Road Norwood, MA 02062 | T: 781.769.2800 www.qats.com Page THERMAL MINUTES Figure 2. Junction to Ambient Resistor Network [1]. Prior work done by Joiner et al. correlates ΘJMA to board temperature (see Equation 1). The ΘJMA is the overall thermal resistance from the junction to the ambient when all heat transfer paths are evaluated. In this case, ΘCA is represented by the heat sink thermal resistance, as well as the interfacial resistance between device and sink. Table 1 lists JEDEC parameters for a typical BGA component. These are used in the following example calculation. Correlation Reynolds Number (110 ± 8) = ΘJMA = junction to moving air thermal fresistance ΘJB = Junction to board thermal resistance Re ΘJC = Junction to case thermal resistance f = 0.165(3.48 − log Re) 0.24 + (.081 ± 0.007 ) ΘCA = Case to ambient thermal resistance TBA = Board temperature rise (0.195 ± 0.017) f= θJMA 0.11 (θJC + θCA ) × θJB (θJC + θCA ) T Re = + × BA (1) 0.4 (θJC + θCA ) + θJB (θJC + θCA )Nu + θ= P JB 0.00222Pr Re1.09 Parameter Description Value Units ΘJC Thermal Resistance Junction to Case 0.45 °C/W ΘJB Thermal Resistance Junction to Board 2.6 °C/W TDP Tj Thermal Design Power Maximum Junction Temperature 20 W 105 °C Correlation Table 1. Typical Thermal Package Specifications. Re<900 900<Re<3000 3000<Re<15000 Re>3000 Correlation f= 2g c DPDh Lr fVf 2 DPloss = K r fVf 2 2g c Flow Type Laminar Laminar Flow Type 64 denser,υthere−1is a need to As board layoutsf become = [1 + 30( )] Laminar Re solutions DCthat design optimized thermal use the least a −0.182put, there is no margin amount of spacef possible. Simply Turbulent = 0.140 Re to allow for over-designed heat sinks with tight compo. 0.33 coupling nent spacing. Accounting for the effect Laminar Nu = 0.000972 Re1 17ofPrboard is an important part of this optimization. The possibility for Nu = 3.82 x10 −6 Re1.96 Pr 0.33 Turbulent © Advanced Thermal Solutions, inc. 2007 | 89-27 Access Road Norwood, MA 02062 | T: 781.769.2800 www.qats.com Correlation Flow Type Page THERMAL MINUTES Ta using an oversized heat sink exists only if the junction to case heat transfer path is considered. Ta P1 To ensure a 105°C junction temperature at 55°C ambient a typical component (see Table 1) needs a heat sink resistance of 2.05°C/W (if we ignore board conduction). When board conduction is taken into account, the actual junction temperature could be as low as 74°C, assuming the board temperature is the same as the air temperature. This indicates a heat sink that is larger than necessary. From this example, it is clear that all heat transfer paths from the component junction must be considered. Using just the ΘJC and ΘCA values can lead to a larger than optimal heat sink and may not accurately predict operating junction temperatures. Using the proposed correlation can also predict junction temperature when the board temperature is known from experimentation, as shown in Figure 3. Junction Temperature as a Function of Board Temperature Rise (55°C Ambient) Junction Temperature (°C) 90.0 θb1b2 P2 Tb1 Tb2 Figure 4. Simple Schematic of a PCB with Two Components. Ta Ta θJa1 q1 θJa2 q3 TJ1 TJ2 q4 q2 θb1b2 Tb2 Tb1 q6 θba1 q5 q7 θba2 Ta Ta Figure 5. Simple Resistor Network of the PCB with Two Components. 85.0 80.0 75.0 Applying the energy balances at the nodes J1, J2, b1 and b2 : 70.0 65.0 60.0 0.0 5.0 10.0 15.0 20.0 25.0 30.0 Board Temperature Rise (°C) 1°C/W Heatsink 2°C/W Heatsink Figure 3. Effect of Board Temperature Rise on Junction Temperature. When there is more than one component, the situation becomes much more complex than with just a single component on the board. There is conduction coupling between components through the PCB, and radiation and convective coupling between the components and adjacent cards. A simple PCB with two components is shown in Figure 4. The power dissipation of the two components is assumed to be P1 and P2, and it is assumed that we can neglect the radiation heat transfer. The board temperature under each device is Tb1 and Tb2, respectively. We also assume that the lateral resistance between the two components on the board is θb1b2. T TJ1 − Tb1 j1 − Ta1 + = P1 θJa1 θJb1 Tj2 − Ta2 TJ2 − Tb2 + = P2 θJa2 θJb2 (2) (3) Tj1 − Tb1 Tb1 − Ta (4) T b1 − Tb2 = q6 = q2 − q5 = − θba1 θb1b2 θ jb1 Tb2 − Tb1 T − Tb2 = J2 θb1b2 θJb2 + TJ1 − Tb1 Tb1 − Ta − θJb1 θba1 (5) There are four equations and four unknowns: Tj1, Tj2. Tb1 and Tb2. The unknowns can be determined by solving the simultaneous equations. This simple example demonstrates that by coupling two components through a conduction path, it becomes much more complicated to find the junction temperatures. In a real life application, the situation is much more complicated than the above example when encountering multiple components and multiple PCBs with different conduction planes all inter- © Advanced Thermal Solutions, inc. 2007 | 89-27 Access Road Norwood, MA 02062 | T: 781.769.2800 www.qats.com Page 10 THERMAL MINUTES acting through conduction, convection, and radiation. To obtain reasonable answers it is necessary for the designer to use sound engineering judgment in approximating the coupling between different components. This can be achieved by the following methods: Method 1 - Analytical models, using either a control volume method or a resistor network model. This method requires oversimplification of the problem, otherwise the solution becomes very complicated and impractical. Method 2 - Use of CFD on a simplified geometry, as described by Guenin [4]. This method suggests that an equivalent surface area for a component is found as: (6) Pn An = Ptotal • A Total Where An is the equivalent footprint area of the component n, Pn is the power dissipation of the component n, PTotal is the total power dissipation and ATotal is the total surface area of the PCB. After the equivalent footprint area is calculated, a simple PCB with a single component having the footprint area An and power dissipation of 1 Watt can be simulated using CFD. This process effectively calculates the difference between the board temperature and the ambient (θBA) for a 1 Watt power dissipation. Figure 6 shows the CFD simulation on one such component and Figure 7 shows the θBA as a function of PCB size. Figure 7 can be used to determine the θBA for other components by simply calculating their effective footprint area. It is assumed that all components have the same footprint size. Figure 7. ΘBA Distribution as a Function of PCB Size [4]. The board temperature can then be calculated as: (7) T = P × θ B n BA The junction temperature can then be calculated as: TJ = TB + Pn × ψ JB (8) Where ψJB is the characterization parameter. Method 3 - Measure the board temperature, TB, experimentally, if the PCB is available, and use Equation 8 to find the junction temperature. Again, this is an approximation, as the conditions under which the device is coupled to the PCB might be totally different than those used with the JEDEC test board. References: 1. J oiner, B., Adams, V, Measurement and Simulation of Junction To Board Thermal Resistance and Its Application in Thermal Modeling, Semiconductor Thermal Measurement and Management Symposium, 1999. 2. J ESD51-2, Integrated Circuits Thermal Test Method - Natural Convection, JEDEC, March 1999. 3. J ESD51-6, Integrated Circuit Thermal Test Method Forced Convection, JEDEC, March 1999. Figure 6. CFD Simulation of a Single Component on a PCB [4]. 4. G uenin, B., Characterizing a Package on a Populated Printed Circuit Board, Electronics Cooling Magazine, May 2001 © Advanced Thermal Solutions, inc. 2007 | 89-27 Access Road Norwood, MA 02062 | T: 781.769.2800 www.qats.com Page 11

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