New in the Theory of Periodic Structures

New results in the theory of periodic structures (PSs), obtained on the basis of stepped transmission line model, are presented. It is shown that PSs peculiarly transform the wave impedance, inducing unusual properties of the wave medium. Stepped transmission line model makes it possible to determine the fundamental relationships of physics and mathematics for PSs. Model of impedance delta-inhomogeneities allows to get simple analytical expressions for PS characteristics. Two-phase PSs for which band gap frequencies are twice lower than those for traditional single-phase PSs are considered.