A high power dissipation density in today's miniature electronic/mechanical systems makes on-chip thermal management very important. In order to achieve quick to evaluate, yet accurate electro-thermal models, needed for the thermal management of microsystems, a model order reduction is necessary. In this paper, we present an automatic, Krylov-subspace-based order reduction of a electro-thermal model, which we illustrate by a novel type of micropropulsion device. Numerical simulation results of the full finite element model and the reduced order model, that describes the transient electro-thermal behavior, are presented. A comparison between Krylov-subspace-based order reduction, order reduction using control theoretical approaches and commercially available reduced order modeling has been performed. A Single-Input-Single-Output setup for the Arnoldi reduction algorithm was proved to be sufficient to accurately represent the complete time-dependent temperature distribution of the device.

This report describes a new methodology for the optimal placement of decoupling capacitors on the printed circuit board (PCB). This method searches the optimal position of decoupling capacitor so that the impedance characteristics at the power supply is minimized in the specified frequency range. In this method, the PCB is modeled by the PEEC method to handle the 3-dimensional structures and Krylov-subspace technique is applied to obtain efficiently the impedance characteristics in the frequency domain.