The circular homogeneous-ferrite microwave circulator - an asymptotic Green´s function and impedance analysis

A detailed analysis of the circular, homogeneous ferrite microwave circulator is provided. Particular emphasis is on the circulator´s Green´s function and the impact of the asymptotic term within the Green´s function on convergence, data quality, and design methodology. The asymptotic term is shown to be logarithmic, which suggests that the Green´s function is weakly singular when the source and observation points occupy the same location. With the Green´s function properly understood, two techniques - one analytical and one numerical - are then offered to integrate that function in order to obtain Z-parameter data and, subsequently, S-parameter data. Data are provided to show rapid convergence of all parameters of interest. A small coupling angle approximation is then given for the Z-parameters and, from that approximation, a first-order design equation is obtained that relates the coupling angle to circulator radius. A circulator design example is presented and compared to a design associated with the Wu and Rosenbaum method; the comparison substantiates the small coupling angle approximation and design formula.