Power waves and scattering parameters in magneto-inductive systems

Difficulties arise in the definition of power flow in transmission-line systems with a complex propagation constant. These were resolved by Kurokawa using quantities known as “power waves,” which contain both voltage and current terms and correctly separate power flow into forward- and backward-traveling components. Similar difficulties must arise for electromagnetic metamaterials since any discrete, periodic structure leads to band-limited propagation, with a complex propagation constant both inside and outside the bands due to loss and cutoff, respectively. Here, discrete power waves are defined for magneto-inductive (MI) systems, metamaterials based on chains of magnetically coupled LC resonators. These waves are shown to satisfy the discrete power conservation equation for MI waves and are used to calculate scattering parameters for multi-port MI devices without the anomalous predictions of conventional methods. The results will allow correct evaluation of internal scattering parameters in MI systems.