Microwave composites filled with thin ferromagnetic films. Part I. Theory

Magnetodielectric Substrates in Antenna Miniaturization: Potential and Limitations

“…It is shown that for bulk laminates ( is the volume fraction of magnetic components in the laminate) in (14), [40]. For sputtered microwave laminates made of iron, the film thickness must not be larger than 0.3 m, and the thickness of substrate may be as low as 10 m [40]. Then % vol.…”

“…and GHz , a value which is about the same as that with hexagonal ferrites. If several magnetic layers separated by nonmagnetic interlayers are sputtered onto a polymer substrate, the volume fraction may be increased by a factor of order of the number of layers [40]. With this method the potentially obtained microwave permeability values are the highest possible among all magnets.…”

Limitations on high-frequency permeability of magnetic materials

“…In both (17) and (18), factors close to unity on the order of magnitude are omitted. Combining (17) and (18), one can get that integral (6) has a constant value in a certain frequency range only if…”

“…For 3D isotropic materials, κ=1/3 in (5). Rigorous derivation of (5) for any form of magnetic dispersion law that can be represented as a sum of Lorentzian terms has been given independently in [16] and [17]. The derivation is analogous to that of the Kramers-Kronig relations and is based on the treatment of complex permeability as an analytic function of complex frequency.…”

Frequency-Dependent Effective Material Parameters of Composites as a Function of Inclusion Shape

“…In composites, this asymptotic behavior is governed by the LLL mixing law. Therefore, integrals I1 and I2 for any composite are equal to the corresponding values for the bulk material of inclusions multiplied by the volume fraction of inclusions [42,43] ,composite ,inclusions . …”