| Abstract |
In this paper a new formula for the time development of the temperatures of chosen locations in an
electronic system (e.g. the hot spot temperatures of the semiconductor devices usually called junction
temperatures) is presented and an exact physical foundation of thermal equivalent circuits is given. The
formula is derived from the general heat conduction equation and allows the calculation of the thermal
evolution for general power pulses P(t). The essential input value, which characterises the system thermally,
is the transient thermal impedance ZthJA(t) junction-ambient, which is used as input. The method
is generalised for systems with alternating heating of the semiconductors, i.e. multichip-modules in
power converter applications. The results are exemplified by the calculation of the long term time evolution
of the hot spot temperature in an IGBT module under arbitrary load current. The nonlinear temperature
dependence of the heat generation source leads to a nonlinear integral equation, which is solved
by a new and efficient algorithm with high stability and precision. |
