This paper presents an algorithm for thermal optimization for distributed heat sources of integrated circuit (ICs) electronic devices on printed circuit board (PCB). Random thermal placement method is used for the initial population of components placement. Genetic algorithm (GA) tool search strategy from Matlab is used for optimization process to evaluate the performance of individuals, do selection, crossover and mutation for producing new sample design. The objective of the optimization is to minimize the total thermal distribution and the maximum operating temperature of ICs components by considering a few thermal design constraint. The operating temperature of each component should be in a suggested range proposed by the manufacturers in order to increase the components lifetime and system reliability. Nodal thermal resistance network is used in this work to predict the temperature of each component at any location on PCB. Results show the thermal distribution of each component on PCB is minimized. Finally, new design of arrangement is proposed based on the optimization results.
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There are a few main concerning issues for PCB assembly need to be tackled in order to increase components reliability and minimizing the failure rate [1, 2]. Component placement optimization is one of the best techniques to reduce the thermal problem and package size or dimension for multi-chip-module (MCM) and PCB design. Placement strategies that do not consider heat dissipation would choose to place two or more chips that emit a significant amount of heat next to one another. This would result a 'hot spot' on the board or any IC components and would cause one more components malfunction ideally . A few methods have been applied such as forced-directed algorithm  and simulated annealing  for routability, to minimize the total net length, wire crossovers and vias for MCM and printed wiring board design. Forced-directed placement algorithm based on heat conduction analogy is also widely studied for MCM placement . Recently, a thermal forced directed based on fuzzy model artificial intelligent (AI) technique has been introduced to manage the thermal placement problem for MCM [7,8].
Components optimal placement on printed circuit board (PCB) requires multiple design objectives such as geometry of physical dimension, electrical networks design, maximum temperature allowed of thermal problem, mechanical properties, cost and time of manufacturing, as shown in Figure 1. Various techniques and approaches have been developed to optimize the design of PCB under thermal and electrical constraints.
Figure 1. PCB design consideration
Application of evaluation process like GA is the most popular recently. GA acts on a set of solutions rather than a single solution. Genetic placement  presented earlier has been proved by many researchers as a good search engine if a well formulated fitness function is applied. MCM thermal management under thermal constraint currently has been done using finite element method and GA [10,11]. Many researchers interested on thermal optimization for MCM placement, but some works are limited to one single size and constant properties.
The objective of this paper is to minimize the total temperature of thermal distribution and operating temperature of ICs components on PCB using genetic algorithm. The operating temperature of each component should be in a suggested range proposed by the manufacturers in order to increase the components lifetime and system reliability.
2. Thermal network model
More works have been done [12,13,14] in the past in developing thermal models of different electronic packages using the first principles of heat conduction equation where the temperature distribution T(r, t) inside the IC component is
Where (kg m-3) is material mass density, (J kg-1 K-1) is material specific heat, (WK-1m-1) is the thermal conductivity at any location inside the component and (Wm-3) is a distributed power density.
Today, almost all IC components produced by manufacturers come with datasheets. All parameters can be found easily such as junction to ambient resistance (), power dissipation (P) and maximum temperature allowed. These parameters can be used to predict the initial temperature of individual component (Ti) using (2)
On PCB there are a few components act as individual heat source with are connected. Thermal resistance of interconnect is:
Heat flow is proportional to the temperature difference (DT) between the heat sources
Where constant a = kA [(W/Km)(m2)] , DT is the temperature difference (°C), D is the distance (m) between components and is the heat flow (watt or J/s).
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The heat equation (1) can be solved using equivalent electrical network for component on PCB. If the testing component is ICx, then electrical network of heat flow from the neighbouring components can be solved as
Steady state heat conduction equation of component ICx on PCB is
The model of nodal thermal network of heat flow model for multiple components (6) on PCB is shown in Figure 2.
Figure 2. Heat flow model
3. Thermal Optimization Method Using Genetic Algorithm
Genetic Algorithm (GA) is a numerical search and optimization techniques based on the mechanism of natural selection and natural genetics . A theory of evolution act on a population of individuals, the so-called chromosomes and not an isolated individual. Each chromosome is constituted by a number of individual structures called genes. Each gene is associated with a specific parameter or variable of the search space.
Chromosomes are usually constant length sequences, and traditionally binary numbers, however in practice they can be anything including a mix of integers and real numbers, or a mix of numbers and character strings. Where, each chromosome represents a possible solution to a given problem.
The populations initially chosen at random will evolve thank to three operators: reproduction, crossover and permutation. Thermal optimization for IC devices on PCB is stated with random placement and interconnects. There are ten components will be placed on PCB as listed in Table 1. Components position on PCB is
Table 1. IC Parameters
Initial Tj (°C)
Random thermal connections are created for all components in Figure 3. After that, the programme will calculate the distance between components.
Furthermore, the fitness performance is evaluated and the various sample design are sorted by the performance criteria such as distance from one component to others, thermal resistance or thermal conductance, heat transfer by conduction, maximum temperature of component and interconnect at steady state.
Figure 3. Thermal interconnect
Define temperature T as
= Temperature of component i at population j for generation k
k = 1, 2, …., 50 (for 50 generations)
j = 1, 2, …., 20 (for 20 populations)
i = 1, 2, …., 10 (for 20 components)
Objective function for optimization processes is given by (8), derived from of a few parameters such as power dissipation, component dimension and PCB, and the distance among the components are located on PCB. All these components are placed randomly on PCB and the process of optimization has been programme using Matlab as summarized in Figure 4.
The procedure of generation can be repeated as many times as desired until the best value of the objective function is satisfied or set up generation is completed.
Figure 4. Optimization process using GA
4. Results and Analysis
There are 10 components to be placed on PCB. Figure 5(a) shows one of the 20 samples of random initial placement. The programme plots the center of component position on (10 x 20) cm2 PCB under Cartesian coordinate. The components interconnects are also randomly generated.
Total temperature, minimum and maximum temperature are calculated for each individual population. The lowest solution implies the highest fitness of the solution. Optimization is the process of minimizing the total temperature of components on PCB. New components placement for each generation based on fitness proportional selection process.
Elitism concept has been used where the best two individuals are keep during the cross over and mutation processes. However, for the following generation the elites must go through the process of fitness and selection. Figure 5(b) and 5(c) are the best or the minimum total temperature distribution for the particular generations.
The total temperature per generations for elites is shown in Figure 6(a). The temperature is minimized up to 2% after going through 50 generations. Figure 6(b) and 6(c) are shown the variations of total temperature over 50 generations for the selected populations. These individuals have to undergo the cross over and mutations in order to produce new child string until the new population of 20 individuals are formed.
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Finally, the best, average and the poorest total temperature over generations are plotted in Figure 7. The results show that genetic algorithm is one of the best evaluation methods for optimization process. Although the actual thermal PCB profile is not analyzed but the profile of components temperature can be predicted before the design process. This is the best way to increase the components reliability and cost of production for PCB design process.
Generation : 1
(b) Generation : 10
(c) Final Generation : 50
Figure 5. Placement arrangement for a few generations
Figure 6. Individual population analysis
Figure 7. Analysis the best, average and the lowest temperature over generations
Optimized the components placement on certain dimension of PCB under total temperature consideration has been done for ten various power dissipation components. Elitism and proportional selection process have been proposed for the PCB designed. The results and analysis show that application of genetic algorithm can propose new PCB design and components placement as well as to improve the temperature distribution.