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

Abstract

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 <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">l</sub> :4λ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">c</sub> -8λ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">c</sub> and focal spot size, f <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">s</sub> :1λ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">c</sub> -1.5λ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">c</sub> , where λ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">c</sub> is the wavelength at center frequency. Using the compact free-space setup, relative complex permittivity (e' - je'') was extracted over 8-12 GHz for lowand high-loss dielectrics with lateral dimensions, 3.3λ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">c</sub> × 3.3λ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">c</sub> and 10λ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">c</sub> × 10λ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">c</sub> . For large materials under test (MUTs), i.e., 10λ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">c</sub> × 10λ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">c</sub> , measurement accuracy in dielectric constant, Δe'% was <; 0.65% and <; 1.14% for low- and high-loss dielectrics, respectively. For smaller MUTs (3.3λ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">c</sub> × 3.3λ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">c</sub> ), Ae'% was <; 0.89% and <; 2.29% for low- and high-loss MUTs, respectively. The error in loss tangent (Δtanδ) varied over 0.002-0.016 and 0.015-0.056 for large (10λ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">c</sub> × 10λ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">c</sub> ) and small MUTs (3.3λ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">c</sub> × 3.3λ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">c</sub> ), respectively. For large MUTs, biconvex lens pair with the smallest f <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">s</sub> (1λ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">c</sub> ) and f <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">l</sub> (4λ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">c</sub> ) among the three lenses yielded the best accuracy in dielectric constant (e') due to tight field focusing at the focal plane. The plano-convex lens pair yielded the best accuracy in loss tangent (tanδ = e''/e') 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 6×-10× 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.