Comparison of Techniques for Microwave Characterization of Percolating Dielectric -Metallic Media and Resolution of Disc
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ABSTRACT The measured microwave effective dielectric properties of metal-dielectric composites show discrepancies when data from free space, resonant cavity or transmission line measurements are compared. Discrepancies are especially evident for materials where the metallic concentration is near the percolation threshold. This paper presents theory and measured data which highlight and resolve these discrepancies. Electrical correlation length is the relevant parameter which must be considered in choice of measurement technique. Agreement between effective medium models and measurement are best when focussed beam measurement techniques are utilized so as to produce planar wave-fronts whose extent is 3-4 freespace wavelengths when incident on the sample.
INTRODUCTION AND PROBLEM STATEMENT Electromagnetic transmission line measurement techniques have been the preferred methods to perform constitutive parameter measurements (E, y, a') of iso or anisotropic scale invariant homogeneous materials '2 for frequencies from 50 MHz to 18 GHz. However, constitutive parameter measurements are often found to depend on the dimensionality of the test fixture, sample (sample thickness and/or sample-test fixture cross sectional dimensions) and electromagnetic wavelength when the transmission line techniques are applied in the of dielectric matrices, are composed artificial materials. Composites measurement of Ed (f) = Edr + lad / 27rfe0 and metallic or semi-conducting inclusions of conductivity a,1 . The measurement of their effective electromagnetic properties applies only when the electromagnetic wavelength within the material, AM, is much greater than characteristic dimensions of sample inhomogeneity. The sources of observed measurement variation derive from electrical percolation threshold and
relative electrical conductor correlation, ý(f) = ;E 0(f)j/1(f)aoIp- pcj a.
percolation threshold; the frequency
f
E,(f).t(f)
/A.,0,within the material. Here
is the inclusion volumetric concentration; P, is the electrical
is the conducting inclusion size; p
are permittivity and permeability of the media surrounding the inclusion at
with free space wavelength /1 0 and 1) is the characteristic critical exponent 3 (4/3 in 2D and
0.88 in 3D). Measurement errors which result from the correlation length and wavelength dependence are discussed below.
Measurement variations deriving from sample finite thickness, 2 vs 3 dimensions Unlike homogeneous electrically lossy dielectric materials, the effective complex conductivity, 1(f) or permittivity
e(f) =
jC0oE0 ,(f) can vary with thickness or sample cross section. For p near but less that
PC,
l2ff'p)= (atif-lOi 0))}jY{IPPo1i(ljJ The characteristic frequencies are f = a,
f
7rEEo, fo
=
Cd
/ 21rE•o. Y is a conductivity scaling functional 3
of reference 3 with s and t critical transport exponents
J-- (I - j fo) is
f
2
I.
1
w9 335
Mat. Res. Soc. Symp. Proc. Vol. 500 ©1998 Materials Research Society
4 The value of p, is known to be a function of sample scaled thickness a0 / T
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