Computerized Thermal Analysis of Hybrid Circuits

A computer program was written to perform steady-state analysis for hybrid circuits. The output of the program gives the temperature of each power dissipating element in the hybrid. The program is based upon solution of Laplace's equation in three dimensions using Fourier techniques. The assumptions made are: no convection or radiation, constant and isotropic thermal conductivity for any single material, and constant temperature at the bottom of the hybrid package. Bessel's inequality allows one to input the desired accuracy and to determine where the infinite series should be truncated. Theoretically, the program will attain any desired accuracy less than 100 percent, but practical considerations of computer run times limit accuracies to the 90- to 95-percent region. The program has been tested by comparing computer results to known theoretical exact solutions and to actual measurements on sample hybrids. When compared to known theoretical exact solutions, the computer result accuracy is between 95 and 100 percent. When compared to actual measurements on sample hybrids, the computer result accuracy is between 90 and 95 percent. This program has been used successfully on over twenty circuit designs. It has also been used to evaluate simpler types of thermal anal- yses.