1 CALCULATION LIMITS of THE HOMOGENEOUS EFFECTIVE THERMAL CONDUCTIVITY APPROACH in MODELING of PRINTED CIRCUIT BOARD Minh-Nhat NGUYEN 1* , Eric MONIER-VINARD 2 , Najib LARAQI 1 , Cheikh-Tidiane DIA 1,2 , Valentin BISSUEL 2 1 Laboratoire Thermique Interfaces Environnement (LTIE), 92410 Ville d’Avray – France 2 Thales Global Services, 92366 Meudon la foret Cedex – France *Corresponding Author : paulminhnhat.nguyen@gmail.com Abstract Electronic components are continuously getting smaller. They embed more and more powered functions which exacerbate the temperature rise in component/board interconnect areas. Their design optimization is henceforth mandatory to control the temperature excess and to preserve component reliability. To allow the electronic designer to early analyze the limits of their power dissipation, an analytical model of a multi-layered electronic board was established with the purpose to assess the validity of conventional board modeling approaches. For decades, a vast majority of authors have been promoting a homogenous single layer model that lumped the layers of the board using effective orthotropic thermal properties. The work presents the thermal behavior comparison between a detailed multi-layer representation and its deducted equivalent lumped model for an extensive set of variable parameters, such as effective thermal conductivities calculation models or source size. The results highlight the fact that the conventional practices for Printed Circuit Board modeling can dramatically underestimate source temperatures when their size is very small. 1. Introduction More than ever, electronic board designers are aware of magnified cooling stakes. Powered devices are constrained on high density electronic board, which leads to potential reliability issues due to excessive temperature beyond manufacturer limit. Last generation of miniaturized electronic component is reinforcing the need to simulate in more details the board architectures in order to manage their contribution to heat transfer. If detailed numerical simulations are mandatory to deliver an optimized design, the sensitivity of component temperatures to early conception changes of design parameters is today a crucial concern. The ability to eliminate bad concept candidates with a minimum of setup, relevant assumptions and low computation time is henceforth required. Thus the conventional assumptions for electronic board thermal modeling are discussed with the aim to check the pertinence of existing methods and to quantify the inherent uncertainty of thermal effective conductivity determination of Printed Circuit Board (PCB acronym). The PCB effective thermal conductivity is a major parameter for electronic thermal analysis so its conventional calculation technique was investigated. This study is based on the use of an analytical thermal model for better discerning the sensitive parameters and managing the solution accuracy. The main objective of this work is to promote a systematic characterization of the design of electronic boards, at an early stage. Analytical methods are easy to use, effortless to implement, and do not have complex meshing nor convergence rules to master. Moreover, the proposed analytical formulation allows fast evaluation of temperature profile of constitutive dielectric or conductive layers under steady state conditions. 2. Descriptions and Solutions of the problems The multi-layer electronic board is considered cooled by coupled convection and radiation heat exchanges to enable potential infrared measurement validation at laboratory boundary conditions. The heat of the planar source is only transfer through these external surfaces to the ambient T ∞ . The planar source can be located on upper or lower board external surfaces. Its heat flow rate qs is assumed uniform over the source. The board shape is always approximated by a rectangular or a square geometry. Each interface of adjacent layer is considered in perfect thermal contact. Its overall length (Lb), width (Wb) and thickness (Hb) are depicted on Figure 1. Figure 1: Geometric parameters of the analytical model The set of equations describing the proposed conduction model and its boundary conditions are summarized below. The generalized steady-state heat transfer governing equation in each layer i (i=1...nl) is given as Laplace’s equation: ! ",$ ∙ & ’ ( $ )*, +, ,- &* ’ . ! /,$ ∙ & ’ ( $ )*, +, ,- &+ ’ . ! 0,$ ∙ & ’ ( $ )*, +, ,- &, ’ 1 0 (1) Where ( $ )*, +, ,- 1 3 $ )*, +, ,- 4 3 5 The four lateral sides of each layer are assumed to be adiabatic due to their very low thickness: ! ",$ ∙ 7( $ )*, +, ,- 7* 8 "9:,;< 1 0 and ! /,$ ∙ 7( $ )*, +, ,- 7+ 8 /9:,A< 1 0 (2) z x y Layer 1 z 1 = t 1 Hb Lb Wb Upper source ( xc, yc, zc) Ls Ws q h t Layer nl z nl = Hb h r