Biological Tissue Complex Permittivity Measured From $S_{21}$ —Error Analysis and Error Reduction by Reference Measurements

Our analysis and measurements of a custom-designed two-port microstrip test fixture for biological tissue characterization at microwave and millimeter-wave frequencies demonstrated that the transmission parameter S ₂₁ would provide a better sensitivity to the complex permittivity change than the reflection coefficient S ₁₁. However, the standard through-reflect-line (TRL) calibration method employed for the extraction of the tissue complex permittivity did not fully remove the coaxial-to-microstrip adaptors\´ induced errors, which were manifested by ripple artifacts on the measured two-port S parameters. A simple deconvolution method was demonstrated wherein these errors were removed by postcalibration correction of the measured S ₂₁ of the tissue under test (TUT) by using water as a reference material. This paper provides a theoretical analysis of this method based on a model presented for postcalibration adaptors. Our detailed analysis shows that the error for S ₂₁ using the deconvolution method linearly depends on the difference between the S ₁₁ of the TUT and the reference material. Measurement and error estimation are also provided for various biological tissues and are consistent with analytical expectations. Our analysis provides support that systematic errors of numerically modeled S ₂₁ utilized for complex permittivity extraction can significantly be reduced by the deconvolution method. On the other hand, the analysis also shows that the S ₂₁ numerical modeling errors and the postcalibration adaptors\´ error terms have a similar impact on the extracted complex permittivity using the standard time-gating technique and are irreducible, unless the deconvolution method is used. Our analysis also identifies water as a better reference sample than methanol for accurate extraction of the complex permittivity of tissues in the range of epsiv- - \´ > 9 and epsiv" > 7 at 30 GHz.