The system follows a series model of material core reluctance plus air gap reluctance. Reference article from Alan Payne “Inductance derived from capacitance” makes an analogy of the coil magnetic field to a dipole antenna electric field, expressed by formula 1:
Where Rin air and Rout air is reluctance of a coil inside and outside the coil respectively, k is the apparent permeability of the outside path, μf is the permeability of the ferrite, lc is the coil length and dc is the diameter of the coil.
The magnetic field in the edge of an antenna and at a point larger than it radius is governed respectively by formula 2:
Where N is the number of coil turns, μ0 is the air permeability, μrod is the relative rod permeability, I is the current passing through the wire, a radius of the coil, r transversal distance from the center of the coil.
It is easy to deduce from the above equation that to reach higher Bz greater μrod is required. Therefore, the higher the core length to diameter ratio the better magnetic field is accomplished.
An experimentally deduced graph provided by Ferroxcube makes evident the significant impact of the mechanical core dimension with respect to the final core permeability. Our new solution almost double the aspect ratio from previous product which could result in a ten fold relative rod permeability improvement according to this graph. The material permeability is another parameter to take into account, with greater material permeability greater is the effect and treshold of the aspect ratio and consequently better rod permeability is obatined. Amorphous microwire can reach up to 100.000 realtive permeability so that this makes them really good candidates.
Current manufacturing relies on uniaxial pressure sinterization process which limits the length of the bar to 120 mm. Ferrites are ceramic, similarly to glass, extremely brittle and fragile. In order to avoid fatal damage of the core, protective coating and plastic overmolding are essential. A crack in a ferrite inside an antenna or inductor produces a high reluctance magnetic path of the field thus reducing the effective permeability and dropping the inductance, that if the application is a resonant tank for an antenna, leads to a higher self-resonant frequency of the tank and makes the circuit operate out of specifications or even do not operate at all as the energy transmitted to or by a not tuned tank can be too low to let the circuit operate as a signal transceiver.