Crossing transmission lines on a ferrite substrate: A TEM model

Summary form only given. The saturated ferrite is a novel material that is commonly used to create a non-reciprocal device or network, such as a circulator or isolator. For example, when two crossing microstrip traces are placed on a ferrite slab it is possible to couple electromagnetic energy from trace one to trace two in a completely different fashion than from trace two to trace one. The mechanism for quasi-static coupling has been adequately explained using lumped-element circuit techniques. A TEM wave investigation of this same coupling is explored in this presentation.The presentation commences with a transmission line model of three crossing microstrip lines on a uniformly biased, infinitely extended, fully saturated ferrite slab. The series impedances of this model are obtained from a quasi-static analysis that treats the wire-to-wire coupling effect as an anisotropic, inductive transformer. The shunt admittances account for capacitive coupling. The circuit analysis of the resulting configuration yields a set of telegrapher´s matrix equations with a non-symmetrical impedance matrix Z and symmetrical admittance matrix Y. The matrix product of Z and Y equals the wave matrix k that quantifies the non-reciprocal propagation characteristics of the coupled lines. The telegrapher´s equations can be decoupled using modal matrix methods, thus allowing one to obtain a wave solution in terms of scalar characteristic impedances and wave numbers. The properties of these impedances and wave numbers are explored to give a better understanding of the cut-off effect near ferromagnetic resonance due to both distributive and capacitive coupling. As the frequency is reduced the classical, quasi-static solution emerges as a special case thus providing validation of the approach taken herein.