Location: Agricultural Systems Research Unit
Title: Multisection transmission line scatter function theory for measurements of soil dielectric properties
AuthorsShuai, Xiufu   
Green, Timothy  
Ray, Chittaranjan   
Syrmos, Vassilis  
Submitted to: Soil Science Society of America Journal
Publication Type: Peer Reviewed Journal Publication Acceptance Date: April 11, 2014 Publication Date: August 6, 2014 Citation: Shuai, X., Green, T.R., Ray, C., Syrmos, V.L. 2014. Multisection transmission line scatter function theory for measurements of soil dielectric properties. Soil Science Society of America Journal. 78:11391145. doi:10.2136/sssaj2013.11.0505. Interpretive Summary: Vector network analyzers measure both reflection (S11) and transmission (S21) scattering functions, but S21 has not been used to estimate soil dielectric permittivity independently. The mathematical model was derived by integrating the multiple transmissions across a section as a feedback subsystem. Two experiments with three and five sections were carried out to test the model. The transmission scattering functions were measured with a vector network analyzer, and the complex dielectric permittivity values of sand were calculated from these functions. Results using the new theory had lower variation and followed the Debye model more closely than previous methods. Therefore, the complex dielectric permittivity may be estimated more precisely using the derived feedback model than with alternative methods. These results are particularly promising for improving sensor measurements of permittivity in heterogeneous soils. Technical 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: (1) derive the mathematical model for S21 of a multisection transmission line, and (2) 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 ovendried sand and air to examine the S21 model. In the first experiment, a waveguide was filled with one section of sand to form a threesection transmission line; in the second experiment, two sections of sand formed a fivesection 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 lowloss 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 lowloss 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. Vector network analyzers (VNAs) have been used to determine the spectra of soil dielectric properties (Nicolson and Ross, 1970; Shang et al., 1999; West et al., 2003; Huisman et al., 2004; Logsdon and Laird, 2004; Gorriti amd Slob, 2005; Logsdon, 2005; Logsdon, 2006; Logsdon, 2008a, b; Minet et al., 2010). VNAs are also used as a standard method to compare soil dielectric permittivity obtained from different probes and models (Robinson et al., 2005; Shuai et al., 2009; Logsdon et al., 2010). For a twoport VNA, the measurements used are the reflection scatter function S11 and the transmission scatter function S21. Both S11 and S21 are dimensionless complex numbers, which may be logtransformed and expressed in units of dB or dBm, or reported here without transformation. The S11 function describes the reflected wave coming out of port 1 with an incident wave at port 1 while the S21 function describes the transmitted wave coming out of port 2 (Pozar, 2005). Shang et al. (1999) initially used both S11 and S21 to measure soil dielectric permittivity. However, S21 is not widely used to measure soil dielectric properties because the transmission line systems are more difficult to handle such as installation by burying and sample packing. Uniform transmission lines have been used in the measurement of soil dielectric properties by S11 (West et al., 2003; Huisman et al., 2004; Logsdon and Laird, 2004; Logsdon, 2005; Logsdon, 2006; Logsdon, 2008a, b) and both S11 and S21 (BakerJarvis et al., 1990; Shang et al., 1999). Minet et al. (2010) used a multisection transmission line in the measurement of soil dielectric properties by S11. Few multisection transmission lines have been used in the measurement of S21, and there are few reports on the modeling of the scatter function S21 for a multisection transmission line to measure soil dielectric properties (Krupka, 2006). However, impedance mismatches in singlesection transmission lines result in reflectiontransmission feedbacks (Pelletier et al., 2011) similar to those analyzed here. We were motivated to derive a theoretical model of the relationship between complex permittivity of heterogeneous media and the transmission scatter function S21, because (1) S21 provides important information for the measurement of soil dielectric properties; (2) Probes have been developed with the design of multiple nonuniform sections in the time domain reflectometry (TDR) method (Robinson et al., 2003; Blonquist et al., 2005; Pelletier et al., 2012; Casanova et al., 2012) and will become commercially available for the VNA method. The objectives of this study are (1) to derive the theoretical model of transmission scatter function S21 for a multisection transmission line; and (2) to test this model with a multisection transmission line of dry sand and air using the VNA method. As a caveat, model testing using dry sand illustrates the methods, rather than providing comprehensive testing in the permittivity and dielectric loss ranges of field soils.
