Power waves and scattering parameters in magneto-inductive systems

A Voronov,O Sydoruk,R R A Syms

doi:10.1063/5.0049806

Abstract

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.

Highlights

Scattering parameters provide tools to analyze reflection and transmission at discontinuities in electromagnetic systems or media.1,2 it is well known that there may be inconsistencies when port impedances are complex or there is gain or loss.3,4 These arise from the fact that while amplitudes are linear quantities, powers are not
A discrete formulation of power waves has been developed for magneto-inductive waveguides
These waves are analogous to the continuous power waves introduced by Kurokawa for transmissionline systems, satisfy the power conservation relation, and avoid the physical anomalies seen in scattering parameters found using modulus square methods for passive MI systems

Summary

INTRODUCTION

Scattering parameters provide tools to analyze reflection and transmission at discontinuities in electromagnetic systems or media. it is well known that there may be inconsistencies when port impedances are complex or there is gain or loss. These arise from the fact that while amplitudes are linear quantities, powers are not. Conventional definitions may result in anomalies, such as a reflection coefficient being apparently greater than unity even for a passive load.5 These difficulties were resolved for transmissionline systems by Kurokawa and others.. ), forward and backward power flow may be separately described using these “power waves” by the terms This allowed a consistent definition of scattering parameters, for example, for a two-port device as S11 = b1/a1, S12 = b1/a2, S21 = b2/a1, and S22 = b2/a2. Real impedance and low loss render these distinctions largely unimportant for conventional systems. They assume much greater significance for metamaterials, which, due to their periodic arrangement, often have complex impedance and support lossy, band-limited propagation.

POWER CONSERVATION IN MAGNETO-INDUCTIVE SYSTEMS

DISCRETE POWER WAVES AND SCATTERING PARAMETERS

EXAMPLES

CONCLUSIONS