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

TLDR: 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 dielectrics permittivity of small samples.

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, ${2}{f}_{l}$ : $4{\lambda }_{c}$ – $8{\lambda }_{c}$ 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 ( ${\varepsilon '-j\varepsilon ''}$ ) was extracted over 8–12 GHz for low- and high-loss dielectrics with lateral dimensions, $3.3{\lambda }_{c}\times 3.3{\lambda }_{c}$ and $10{\lambda }_{c}\times 10{\lambda }_{c}$ . For large materials under test (MUTs), i.e., $10{\lambda }_{c}\times 10{\lambda }_{c}$ , measurement accuracy in dielectric constant, ${\Delta \varepsilon '}$ % was $3.3{\lambda }_{c}\times 3.3{\lambda }_{c}$ ), ${\Delta \varepsilon '}$ % was ${\Delta }\text {tan}{\delta }$ ) varied over 0.002–0.016 and 0.015–0.056 for large ( $10{\lambda }_{c}\times 10{\lambda }_{c}$ ) and small MUTs ( $3.3{\lambda }_{c}\times 3.3{\lambda }_{c}$ ), 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 ( ${\varepsilon '}$ ) due to tight field focusing at the focal plane. The plano-convex lens pair yielded the best accuracy in loss tangent ( $\text {tan}{\delta =\varepsilon ''/\varepsilon '}$ ) 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\times $ – $10\times $ 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.