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Multisection Transmission Line Scatter Function Theory for Measurements of Soil Dielectric Properties
Author(s) -
Shuai Xiufu,
Green Timothy R.,
Ray Chittaranjan,
Syrmos Vassilis L.
Publication year - 2014
Publication title -
soil science society of america journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.836
H-Index - 168
eISSN - 1435-0661
pISSN - 0361-5995
DOI - 10.2136/sssaj2013.11.0505
Subject(s) - permittivity , dielectric , transmission line , debye , computational physics , optics , materials science , dielectric loss , debye–hückel equation , range (aeronautics) , acoustics , physics , computer science , telecommunications , optoelectronics , composite material , condensed matter physics , electrode , quantum mechanics , electrolyte
Vector network analyzers measure both reflection ( S 11 ) and transmission ( S 21 ) functions, but S 21 has not been used to estimate soil dielectric permittivity independently. The objectives of this study were to (i) derive the mathematical model for S 21 of a multisection transmission line and (ii) test this model and demonstrate the method. The mathematical model for S 21 integrates multiple transmissions across a section as a feedback subsystem. Two experiments were conducted using oven‐dried sand and air to examine the S 21 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 S 11 and S 21 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 S 21 were less variable and followed the Debye model more closely than those from the measured S 11 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 S 21 with the derived feedback model than with the widely used method based on S 11 . 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.