Modified Nodal Analysis Using Measurement Data Instead of Lumped Models

A standard circuit solver is based on modified nodal analysis (MNA), resolving Kirchhoffs voltage law explicitly by defining nodal potentials and enforcing Kirchhoffs current law as a differential algebraic system of equations [1] (Fig. 1a). Thereby, the lumped elements are represented by lumped models, from which chord or differential conductances, capacitances and inductances are derived and entered in the system. Many lumped elements are, however, only known through a set of measurement data. The selection of an appropriate lumped model and the determination of the parameters thereof may be cumbersome, and in any case add an additional source of uncertainties and errors. This contribution constructs a MNA circuit solver refraining from constructing such lumped models, but instead uses the available measurement data directly [2] (Fig. 1b). The idea has already been successfully applied in the field simulation context [3, 4, 5]. For each lumped element defined by measurement data, the data-driver solver minimizes the distance between the actual operating point and the set of measurement points according to an appropriate norm (Fig. 1b). Thereby, Kirchhoff laws serve as constraints [6]. The approach has been tested for two academic examples. It has been found that the data-driven MNA circuit solver converges to the true solution for sets of synthetic measurement data with increasing cardinality. The method allows to consider combinations of exactly known lumped elements and data-defined lumped elements [4]. For highly nonlinear lumped elements, the minimization should be carried out with an adaptive norm [5].