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A theoretical justification is presented of the partial-capacitance (PC) approach, widely exploited in the modeling of coplanar waveguides on finite-thickness and multilayered substrates. The analysis is based on the static spectral-domain approach to the computation of the capacitance of a set of planar conductors embedded into a multilayered substrate. It is shown that the PC method can be derived from approximating the static Green's function of a multilayered dielectric as the sum of partial contributions; such a decomposition can be applied to the Green's function either in parallel (admittance) or series (impedance) form. The resulting (parallel or series) PC approaches are shown to be accurate with substrates having layers of decreasing or increasing permittivity, respectively. Lines backed by magnetic or electric walls are introduced as limiting cases of multilayered structures.