Tailoring Antenna Focal Plane Characteristics for a Compact Free-Space Microwave Complex Dielectric Permittivity Measurement Setup

This article presents a compact precision free-space microwave measurement setup with a choice of three dielectric lenses to tailor the antenna focal plane characteristics for extracting complex dielectric permittivity of small samples. Custom designed spot-focusing horn antenna pairs were used to achieve a compact setup with antenna separation distance, 2 f(l) :4 lambda(c)-8 lambda(c) and focal spot size, f(s):1 lambda(c)-1.5 lambda(c), where lambda(c) is the wavelength at center frequency. Using the compact free-space setup, relative complex permittivity (epsilon' - j epsilon") was extracted over 8-12 GHz for low- and high-loss dielectrics with lateral dimensions, 3.3 lambda(c) x 3.3 lambda(c) and 10 lambda(c) x 10 lambda(c). For large materials under test (MUTs), i.e., 10 lambda(c) x 10 lambda(c), measurement accuracy in dielectric constant, Delta epsilon'% was <0.65% and <= 1.14% for low- and high-loss dielectrics, respectively. For smaller MUTs (3.3 lambda(c) x 3.3 lambda(c)), Delta epsilon'% was <0.89% and <= 2.29% for low- and high-loss MUTs, respectively. The error in loss tangent (Delta tan delta) varied over 0.002-0.016 and 0.015-0.056 for large (10 lambda(c) x 10 lambda(c)) and small MUTs (3.3 lambda(c) x 3.3 lambda(c)), respectively. For large MUTs, biconvex lens pair with the smallest f(s)(1 lambda(c)) and f(l) (4 lambda(c)) among the three lenses yielded the best accuracy in dielectric constant (epsilon') due to tight field focusing at the focal plane. The plano-convex lens pair yielded the best accuracy in loss tangent (tan delta = epsilon"/epsilon') for large MUTs due to slow variation in the phase of the local plane wave. By tailoring antenna focal plane characteristics, a compact free-space setup that is 6x-10x smaller than the classical setup for handling MUTs that are 1/5th of the size used in classical setup is demonstrated without compromising the measurement accuracy.