Anti-Reciprocal Motional Impedance and its Properties

Abstract

We investigate a classical notion denoted as ‘Motional impedance (Zmot)’ first developed by Kennelly in 1912, then explored by many other researchers early in the 20th century. Due to long history to establish impedance properties, Zmot has not been clearly understood with respect to classical impedance properties which makes retroactive study of the Zmot worthy. In this study, we project Zmot’s unique characteristics onto anti-reciprocity where every electro-mechanical system as modeled by a gyrator. This work also clarifies that Zmot is a type of transfer impedance, thus is not necessarily to be a minimum-phase nor a Positive-Real function. Based on simulation, this study shows a shunt eddy current loss on the electrical side of the system is one possible source of the negative real part of Zmot which leads negative real part in Zmot plots. By taking a Balance Armature Receiver (BAR) as a specific example of the electro-mechanical systems, we also explore the (non)linear approximation principal of the BAR based on the magnetic force and hysteresis characteristics. We believe that this study puts anti-reciprocal physics on both the empirical and theoretical basis.