Estimation of Electronic Circuit Temperature Solving an Inverse Problem

This paper presents an approach to estimation of electronic circuit temperature solving an inverse problem. The main goal of the simulations presented in this paper is to investigate the possibility of improving the quality of circuit temperature estimates applying the function specification algorithm. Given information on circuit layout as well as typical working conditions and material thermal properties, a mathematical model of the circuit is created. Based on the model, sensitivity coefficients relating the amount of dissipated power to the temperature rise at chosen temperature sensor locations are determined. For arbitrary values of power dissipated in the circuit, the coefficients are employed to compute temperature rise values at chosen temperature sensor locations. Next, these values are contaminated with noise and used as input data for the function specification algorithm, which produces estimates of the power dissipated in heat sources. In the simulations, different configurations of temperature sensors and algorithm parameter values are considered. NOMENCLATURE A – vector of identity matrices J number of sensors T sensor temperatures T̂ structure temperature X coefficients relating temperature to heat fluxes g interlayer thermal conductance h heat exchange coefficient q heat flux q̂ unknown heat flux estimate p – number of heat sources r number of "future values" x, y, z – co-ordinates φ temperature rise for unitary heat flux change λ thermal conductivity i, j series indexes k sampling instant INTRODUCTION The growth in the density of power dissipated in modern electronic circuits has induced still increasing interest in circuit thermal analysis. In many applications, continuous monitoring of circuit temperature is required. The best solution would be to place temperature sensors, e.g. p-n junctions directly where heat is generated. This solution, however, usually cannot be realised in practice. Therefore, it is necessary to estimate the temperature of heat sources from remote temperature sensor measurements solving an inverse problem. As the thermal response is damped, the problem is extremely sensitive to measurement errors and special techniques must be applied to obtain robust estimates of circuit temperature. In most cases encountered in electronics, heat is generated only on structure surface, thus the problem of determining heat generation density can be reduced to the problem of unknown surface heat flux estimation. Then, having the number of temperature sensors greater than the number of heat sources, the corrupted with noise sensor temperature readings are supplied to the function specification algorithm, which is adapted for multiple surface