Capacitance and

relative permittivity values were measured using Hewlett Packard 4194A impedance analyzer (50 Ohms, Refurbished).

The next equation can be used to calculate the

relative permittivity:

and the total electric field, where [[epsilon].sub.r] is the

relative permittivity. The scattered electric field can be obtained [21] as follows:

In the second layer, the substrate properties for the 50-[micro]m PEN film substrate are introduced by assigning the loss tangent to 0.01 and the

relative permittivity to 3.35.

where [bar.E], [bar.B], [bar.D], and [bar.H] are electromagnetic fields, and [[epsilon].sub.r] and [[mu].sub.r] are

relative permittivity and permeability of the material, while [kappa] is the chirality parameter which describes electromagnetic coupling and c is speed of light in vacuum.

The

relative permittivity of the Engineering Quartz is about 3.9-j0.0001 [18] in the C band, so the proposed method for measuring the permittivity under the condition that the composite sample [S.sub.6] as showed in Figure 4 with mass ratio 2 : 1 and thickness is 8.56 mm is of very high accuracy.

The

relative permittivity of water, about 70-80, is much higher than that of most civil construction materials, which are generally less than 5 [21].

The medium of the the slits and the ring (white area) is assumed to be air whose

relative permittivity [[epsilon].sub.d] is set to be 1.

It is external non-magnetic dielectric layer (an upper index "d"), characterized by the real

relative permittivity [[epsilon].sup.d.sub.r] and the relative permeability [[mu].sup.d.sub.r] = 1.

Given the

relative permittivity and loss tangent of the dielectric, the attenuation constant can he determined using

For the Rogers 4350 substrate, the

relative permittivity [[epsilon].sub.r] is 3.45, the value of tangent for the loss angle is 0.004, and the thickness of the metal is 50 microns.

The sample consists of a layer of material with thickness [DELTA] and

relative permittivity [[epsilon].sub.r] = 10 embedded and centered within a layer of

relative permittivity [[epsilon].sub.r] = 2, as shown in Figure 1.