An Improved Rectangular Cavity Approach for Measurement of Complex Permeability of Materials

An improved rectangular cavity (RC) approach is proposed for the accurate complex permeability determination of materials in the microwave frequency band. The proposed approach assumes the bar-shaped magnetic specimen to be placed along the width of the cavity to increase the sensitivity of the measurement. A generalized closed-form formula is derived accordingly to determine the complex permeability of these bar-shaped samples in terms of the cavity parameters measured under both loaded and unloaded conditions. The proposed formula is found to improve the accuracy of the original RC approach where samples are placed in the H-plane traversing the maximum width of the cavity for permeability measurement. The improvement in accuracy is facilitated by considering the sinusoidal magnetic field variation over the test sample, which is otherwise neglected in most of the earlier approaches. The modified formula is numerically tested for a number of samples having wide range of permeability variations, and the obtained results are typically 40% more accurate than the values obtained using the original formula. Finally, the synthesized magnetic samples, viz., the carbonyl iron-epoxy composite and the manganese ferrite, are measured by placing them inside the fabricated X-band cavity with the help of a vector network analyzer. The proposed approach is quite advantageous for magnetic materials as finite-size samples having sample to cavity volume ratio of less than 3e-3 can be characterized quite accurately with typical errors of 2% and 3% in the real and imaginary parts of the complex permeability, respectively.