Empirical formulas of the effective lumped parameters for planar artificial transmission lines

The novel planar artificial transmission line (PATL) is a type of slow-wave structure composed of microstrip quasi-lumped elements like meandered-line inductor and interdigital capacitors. This paper investigates on the relations between the physical parameters and the effective lumped parameters of the meandered-line inductor and interdigital capacitor and concludes the corresponding empirical formulas. Those formulas are then generalized considering the influences of substrate thickness and substrate permittivity. The modified formulas are then applied to the design procedure of PATL-based Wilkinson power divider. It is expected that the empirical formulas proposed in this paper would improve both design efficiency and design accuracy of the novel planar artificial transmission line, and are also useful in designing other microstrip discontinuous or slow-wave structures.