Theory of the measurement of the elements of the permeability tensor of a ferrite by means of a resonant cavity

The `intrinsic¿ and `external¿ permeabilities of a ferrite are defined, and the relationship between the elements of these tensors is discussed. The derivation from Maxwell´s equations is given of the magnetic field in a ferrite sphere when this is placed in a uniform microwave field perpendicular to the polarizing field. This result is used in the calculation of the frequency shift which takes place when a ferrite sphere is placed in a resonant cavity. From the frequency shift, the elements of either permeability tensor can be calculated. Also, regarding the frequency shift as complex, the change in the Q-factor on introducing the ferrite sphere can be used to calculate the imaginary parts of these elements. Finally, the derivations of the frequency shift given by previous authors are reviewed, and certain misconceptions and mistakes cleared up in the light of the theory given in the present paper.