Analytic approximations for multilayer substrate coplanar-plate capacitors

Closed form analytic approximations are proposed for complex impedance (capacitance and Q-factor) of capacitors formed by two coplanar rectangular conducting patches sandwiched between dielectric layers. The computations using proposed formulas are at least an order of magnitude faster in comparison with the commercially available software's, and can be used in optimisation procedures. The formulas are reversible, i.e. from measured impedance one can compute permittivity and losses of one of the dielectric layers.