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, <inline-formula> <tex-math notation="LaTeX">${2}{f}_{l}$ </tex-math></inline-formula>:<inline-formula> <tex-math notation="LaTeX">$4{\lambda }_{c}$ </tex-math></inline-formula>–<inline-formula> <tex-math notation="LaTeX">$8{\lambda }_{c}$ </tex-math></inline-formula> and focal spot size, <inline-formula> <tex-math notation="LaTeX">${f}_{s}$ </tex-math></inline-formula>:<inline-formula> <tex-math notation="LaTeX">$1{\lambda }_{c}$ </tex-math></inline-formula>–<inline-formula> <tex-math notation="LaTeX">$1.5{\lambda }_{c}$ </tex-math></inline-formula>, where <inline-formula> <tex-math notation="LaTeX">${\lambda }_{c}$ </tex-math></inline-formula> is the wavelength at center frequency. Using the compact free-space setup, relative complex permittivity (<inline-formula> <tex-math notation="LaTeX">${\varepsilon '-j\varepsilon ''}$ </tex-math></inline-formula>) was extracted over 8–12 GHz for low- and high-loss dielectrics with lateral dimensions, <inline-formula> <tex-math notation="LaTeX">$3.3{\lambda }_{c}\times 3.3{\lambda }_{c}$ </tex-math></inline-formula> and <inline-formula> <tex-math notation="LaTeX">$10{\lambda }_{c}\times 10{\lambda }_{c}$ </tex-math></inline-formula>. For large materials under test (MUTs), i.e., <inline-formula> <tex-math notation="LaTeX">$10{\lambda }_{c}\times 10{\lambda }_{c}$ </tex-math></inline-formula>, measurement accuracy in dielectric constant, <inline-formula> <tex-math notation="LaTeX">${\Delta \varepsilon '}$ </tex-math></inline-formula>% was <0.65% and ≤1.14% for low- and high-loss dielectrics, respectively. For smaller MUTs (<inline-formula> <tex-math notation="LaTeX">$3.3{\lambda }_{c}\times 3.3{\lambda }_{c}$ </tex-math></inline-formula>), <inline-formula> <tex-math notation="LaTeX">${\Delta \varepsilon '}$ </tex-math></inline-formula>% was <0.89% and ≤2.29% for low- and high-loss MUTs, respectively. The error in loss tangent (<inline-formula> <tex-math notation="LaTeX">${\Delta }\text {tan}{\delta }$ </tex-math></inline-formula>) varied over 0.002–0.016 and 0.015–0.056 for large (<inline-formula> <tex-math notation="LaTeX">$10{\lambda }_{c}\times 10{\lambda }_{c}$ </tex-math></inline-formula>) and small MUTs (<inline-formula> <tex-math notation="LaTeX">$3.3{\lambda }_{c}\times 3.3{\lambda }_{c}$ </tex-math></inline-formula>), respectively. For large MUTs, biconvex lens pair with the smallest <inline-formula> <tex-math notation="LaTeX">${f}_{s}$ </tex-math></inline-formula>(<inline-formula> <tex-math notation="LaTeX">$1{\lambda }_{c}$ </tex-math></inline-formula>) and <inline-formula> <tex-math notation="LaTeX">${f}_{l}$ </tex-math></inline-formula>(<inline-formula> <tex-math notation="LaTeX">$4{\lambda }_{c}$ </tex-math></inline-formula>) among the three lenses yielded the best accuracy in dielectric constant (<inline-formula> <tex-math notation="LaTeX">${\varepsilon '}$ </tex-math></inline-formula>) due to tight field focusing at the focal plane. The plano-convex lens pair yielded the best accuracy in loss tangent (<inline-formula> <tex-math notation="LaTeX">$\text {tan}{\delta =\varepsilon ''/\varepsilon '}$ </tex-math></inline-formula>) 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 <inline-formula> <tex-math notation="LaTeX">$6\times $ </tex-math></inline-formula>–<inline-formula> <tex-math notation="LaTeX">$10\times $ </tex-math></inline-formula> 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.

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