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The calculation of the scattering (S) [[parameters]] is usually an important objective of modeling planar structures especially for planar circuits like filters, couplers, etc. As you saw earlier, you can use lumped sources like gaps and probes and even active lumped elements to calculate the circuit characteristics of planar structures. The admittance / impedance calculations based on the gap voltages and currents are accurate at RF and lower microwave frequencies or when the port [[Transmission Lines|transmission lines]] are narrow. In such cases, the electric or magnetic current distributions across the width of the port line are usually smooth, and quite uniform current or voltage profiles can easily be realized. At higher frequencies, however, a more robust method is needed for calculating the port [[parameters]].

One can calculate the scattering [[parameters]] of a planar structure directly by analyzing the current distribution patterns on the port [[Transmission Lines|transmission lines]]. The discontinuity at the end of a port line typically gives rise to a standing wave pattern that can clearly be discerned in the line's current distribution. From the location of the current minima and maxima and their relative levels, one can determine the reflection coefficient at the discontinuity, i.e. the S₁₁ parameter. A more robust technique is Prony’s method, which is used for exponential approximation of functions. A complex function f(x) can be expanded as a sum of complex exponentials in the following form:

where c_i are complex coefficients and γ_i are, in general, complex exponents. From the physics of [[Transmission Lines|transmission lines]], we know that lossless lines may support one or more propagating modes with pure real propagation constants (real γ_i exponents). Moreover, line discontinuities generate evanescent modes with pure imaginary propagation constants (imaginary γ_i 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|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.