In most published experimental studies, these differences are not very large and the missing/underestimated terms are balanced by lower

effective permeability values obtained from the fitting of the calibration curves.

Assuming that the dielectric spheres are located in the host medium randomly and homogeneously, in the quasistatic limit, we can derive the relative effective permittivity [[epsilon].sub.eff]([omega]) and the relative

effective permeability [[mu].sub.eff] ([omega]) from the extended Maxwell-Garnett theory (EMG), as shown in [14]

The

effective permeability coefficient, like the suction powered function, could be presented as the following:

Common metal has

effective permeability below 1, such as 0.5, at the MHz level, and resistance becomes low due to the generated [E.sub.B].

For Knudsen numbers greater than 0.01, an

effective permeability must be computed to compensate for the Knudsen diffusion and/or the slippage flow.

under this assumption, the

effective permeability is an average value over the subdomains that reflects the comprehensive effects of cracks and matrix [12,13].

The ratio of output signal y(t) to input signal x(t) varies directly to wavelength A while its constant of proportionality K defines the links parameters (electrical properties of the channel) such as

effective permeability [[mu].sub.e], and it is the effective dielectric constant, effective permittivity [[epsilon].sub.e] which implies the dielectric constant of a homogeneous medium that replaces air, depending on the nature of the material, signal source core/chip gain [G.sub.t], and receiving core/chip gain [G.sub.m].

In Figures 2 and 3,

effective permeability and permittivity tensors perpendicular components [[epsilon].sub.eff] = [[epsilon].sub.xx] = [[epsilon].sub.yy] and [[mu].sub.eff] = [[mu].sub.xx] = [[mu].sub.yy] behavior is showed versus magnetic inclusion filling fraction (f = [d.sub.a]/a, where [d.sub.a] is the magnetic layer thickness).

At this frequency, the effective permittivity is [epsilon] = -9111.7 - i5655.8, and the

effective permeability is [mu] = -4.7 + i6.7.

(2011) find that the maximum value of

effective permeability enhancement is 5 x 10-16 [m.sup.2] and the maximum enhanced permeability is 1.5 x [10.sup.-15] [m.sup.2].

where [K.sub.p] is

effective permeability, [K.sub.p] = K/[R.sub.k] [R.sub.k] being permeability reduction coefficient; [[phi].sub.p] is effective porosity, [[phi].sub.p = [phi](1 - IPV).

MTM sample consisting of hexaferrite slab and metallic array of parallel wires ensures the corresponding negative values for the

effective permeability in a frequency domain which overlaps the domain with negative permittivity [3] as in Figure 2(c).