Multisection Transmission Line Scatter Function Theory for Measurements of Soil Dielectric Properties

Abstract

Vector network analyzers measure both reflection (S11) and transmission (S21) functions, but S21 has not been used to estimate soil dielectric permittivity independently. The objectives of this study were to (i) derive the mathematical model for S21 of a multisection transmission line and (ii) test this model and demonstrate the method. The mathematical model for S21 integrates multiple transmissions across a section as a feedback subsystem. Two experiments were conducted using oven-dried sand and air to examine the S21 model. In the first experiment, a waveguide was filled with one section of sand to form a three-section transmission line; in the second experiment, two sections of sand formed a five-section transmission line. The S11 and S21 functions were measured with a vector network analyzer, and the complex dielectric permittivity values were calculated. Results of Debye model fitting and sensitivity analysis demonstrated that the complex dielectric permittivity of low-loss sand estimated from the measured S21 were less variable and followed the Debye model more closely than those from the measured S11 in the frequency range from 45.0 MHz to 3.0 GHz. Therefore, the complex dielectric permittivity of low-loss materials may be estimated more precisely using measurements of S21 with the derived feedback model than with the widely used method based on S11. These general behaviors are also expected for more lossy media within a limited frequency range, but the present theory and testing methods should be used to evaluate permittivity measurements under field conditions in moist heterogeneous soils.