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Circuit Elements, Modeling, and Equation Formulation

Most texts on circuits, whether they deal with linear or nonlinear circuits, consider only lumped circuits. If this is not the case, such is normally stated explicitly (see, e.g., Section VI on distributed circuits). A physical circuit is considered to be a lumped circuit, if its size is small enough that for the situation under discussion, electromagnetic waves propagate across the circuit virtually instantaneously. If this is satisfied, voltages across ports and currents through terminals are well defined and, therefore, well suited to describe and analyze the behavior of a circuit. To check whether an actual circuit is lumped or not, the largest extension d of the circuit in any spatial dimension is compared to the shortest wavelength λ of interest or with the shortest time interval τ of interest. If