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ElectroComponent Science and Technology
Volume 7 (1980), Issue 1-3, Pages 97-105

The Solution of Two-Dimensional Heat Conduction Problems for Predicting Operating Temperature and Power Handling Capabilities of Hybrid Circuits

G.T.E. Telecomunicazioni, S.T. Av., Milan, Cassina De'Pecchi 20060, Italy

Received 10 July 1979

Copyright © 1980 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The problems of heat conduction in hybrid thin and thick film circuits have been investigated using both analytical and numerical approaches.

The calculations were restricted to two dimensions by assuming zero temperature gradient across the thickness of the substrate (slightly more than half millimeter).

All normally recognized parameters were taken into consideration, such as film temperature, power dissipated, substrate area, etc.

Allowances have also been made for lead conduction and connection technology, for horizontal or vertical circuit assembly, and for flush or stand-off mounting on the mechanical support.

The measured results for practical cases show close agreement with the theoretical calculations.

This approach provides a simple tool for the calculation, at an early design stage of power handling capacities of hybrid circuits using composite resistive configurations.

Very little difference was found between temperatures predicted from the theoretical approach and those measured in practical cases of circuits under load.

The availability of such accurate design information means that the stability, life, and reliability of hybrid circuits can be predicted with considerable accuracy at an early design stage.