Coupled Magnetostatic/Electromagnetic Studies of Nonuniformly Biased $Y$-Junction Circulator: Application to Transmission Bandwidth Increase

The electromagnetic analysis of a Y-junction circulator proposed here is more realistic than the conventional one, as it accounts for two aspects that are usually neglected despite their frequent occurrence in practice: 1) the nonuniformity of the dc-bias field met in planar technology and 2) the introduction of a tensor to take into account all the magnetization states of the ferrite material. Slicing the ferrite sample into concentric zones allows us to consider the radial variation of the bias field in the electromagnetic calculation. A magnetostatic calculation of the internal field provides the true internal field within each region of the ferrite disk. We replace the Polder tensor, which describes only one specific magnetization state of the material, with another tensor that allows the true magnetization of the ferrite rings to be taken into account.