A Variational Approach for Propagation in Ferromagnetic Nanowired Composite

This article presents a variational approach for ferromagnetic nanowired composites to determine material parameters, which are important for the development of microwave devices. It permits faster and easier calculation than numerical methods. The influence of ferromagnetic nanowires on the effective permittivity and the effective permeability is presented. For this purpose an analytical permittivity model has been developed by considering geometrical parameters of the substrate such as the porosity of the membrane and the height of the nanowires and is discussed briefly. For the effective permeability we have developed two analytical models, volumetric and variational. We will show that the variational approach agrees better with experiment and is able to take lossy gyro-magnetic media, such as ferromagnetic nanowires, into account. The models have been validated by S-parameter measurements of microstrip lines on a substrate filled with cobalt nanowires.