[[File:PMOM73.png]]
where c<sub>i</sub> are complex coefficients and ?γ<sub>i</sub> are, in general, complex exponents. From the physics of transmission lines, we know that lossless lines may support one or more propagating modes with pure real propagation constants (real ?γ<sub>i</sub>exponents). Moreover, line discontinuities generate evanescent modes with pure imaginary propagation constants (imaginary ?γ<sub>i</sub> exponents) that decay along the line as you move away from the location of such discontinuities.
In practical planar structures for which you want to calculate the scattering parameters, each port line normally supports one, and only one, dominant propagating mode. Multi-mode transmission lines are seldom used for practical RF and microwave applications. Nonetheless, each port line carries a superposition of incident and reflected dominant-mode propagating signals. An incident signal, by convention, is one that propagates along the line towards the discontinuity, where the phase reference plane is usually established. A reflected signal is one that propagates away from the port plane. Prony's method can be used to extract the incident and reflected propagating and evanescent exponential waves from the standing wave data. From a knowledge of the amplitudes (expansion coefficients) of the incident and reflected dominant propagating modes at all ports, the scattering matrix of the multi-port structure is then calculated. In Prony's method, the quality of the S parameter extraction results depends on the quality of the current samples and whether the port lines exhibit a dominant single-mode behavior. Clean current samples can be drawn in a region far from sources or discontinuities, typically a quarter wavelength away from the two ends of a feed line.