Capacity extraction in physical equivalent networks

Physical Equivalent Circuits of electronic devices are very useful for EMC root-cause analysis, because they boil down complex coupling paths into rather simple circuit schematics, displaying only relevant inductive and capacitive structures. However, their derivation can be extremely time-consuming and requires thorough understanding of the device under test. Recently, a method was proposed to derive such a circuit with the aid of a computer. Whereas the design of an inductive network is relatively straight forward, correct placement of only the relevant capacities is difficult. In frequency range of interest, there are often too few resonances to determine capacitances uniquely, revealing that capacity placement has typical properties of an ill-posed problem. Engineering intuition states that often, only few capacitances dominate the root-causes of an EMC spectrum. We present a regularization method that allows to quickly determine the C matrix with fewest number of entries via an iterative least squares minimization. We are thus able to compute a unique physically meaningful capacitance matrix of a physical equivalent circuit.