Reflexion coefficient of a magnetized ferrite sphere in a rectangular waveguide

Work on small narrow resonance line-width ferrite spheres in waveguide leads to a need for theoretical quantitative understanding of the interaction between the ferrite and the waveguide fields. Analysis in the literature has previously relied on equivalent circuits with voltage and current, but belief that the concept of electromagnetic fields comes more naturally to waveguides led to the analysis in this paper. The main contribution is the derivation of an expression for the reflaxion coefficient presented by a small transversely magnetized ferrite sphere in a hollow rectangular metal waveguide propagating an H01 mode. The expression is valid for any location of the ferrite in the H-plane transverse dimension (a dimension) of the waveguide. From this general expression are derived subsidiary expressions for the impedance presented by the ferrite at four principal locations, at the centre, at the edge and in the two planes of circular polarization. The derivation of expressions for the H01 mode excited in a rectangular waveguide by a magnetic dipole is of interest outside the field of ferrite technology. Expressions are derived separately fortransverse and longitudinal orientations and hold good for all locations in the a dimension.