Comparisons of algorithms for broadband continuous extraction of complex propagation constant involved in various microwave measurements

Propagation constant characterization plays a key role in various microwave measurement situations such as thru-reflect-line (TRL) calibration, interconnect characterization, fixture de-embedding and measurement of material properties. To differentiate the forward and backward propagating factors, sign-ambiguity problem of square-root searching is inevitable in the process of characterizing the eigenvalue problem associated with electrical measurements of test lines. There are several algorithms proposed for broadband continuous extraction of complex propagation constant. This paper compares the robustness of three algorithms using the experimental data of test lines with both low and high insertion loss.

[1]  A. Ferrero,et al.  Two-port network analyzer calibration using an unknown 'thru' , 1992, IEEE Microwave and Guided Wave Letters.

[2]  J.A. Reynoso-Hernandez.  Reliable method for computing the phase shift of multiline LRL calibration technique , 2002, IEEE Microwave and Wireless Components Letters.

[3]  Lin Li,et al.  On the thru‐reflect‐line (TRL) numerical calibration and error analysis for parameter extraction of circuit model , 2006 .

[5]  Kuen-Fwu Fuh.  Broadband Continuous Extraction of Complex Propagation Constants in Methods Using Two-Line Measurements , 2013, IEEE Microwave and Wireless Components Letters.

[6]  G. F. Engen,et al.  Thru-Reflect-Line: An Improved Technique for Calibrating the Dual Six-Port Automatic Network Analyzer , 1979 .

[7]  John H. Mathews,et al.  Complex analysis for mathematics and engineering , 1995 .

[8]  B. Schiek,et al.  A generalized theory and new calibration procedures for network analyzer self-calibration , 1991 .

[9]  K. Yhland,et al.  A Reformulation and Stability Study of TRL and LRM Using $S$ -Parameters , 2009, IEEE Transactions on Microwave Theory and Techniques.

[10]  J. A. Jargon,et al.  Complex permittivity determination from propagation constant measurements , 1999 .

[11]  Sangwook Nam,et al.  An accurate broadband measurement of substrate dielectric constant , 1996 .

[12]  R. Marks.  A multiline method of network analyzer calibration , 1991 .

[13]  A. Mangan,et al.  De-embedding transmission line measurements for accurate modeling of IC designs , 2006, IEEE Transactions on Electron Devices.

[14]  Andrea Ferrero.  Modern RF and Microwave Measurement Techniques: Two-port network analyzer calibration , 2013 .

[16]  J. P. Mondal,et al.  Propagation constant determination in microwave fixture de-embedding procedure , 1988 .

[17]  D.F. Williams,et al.  Characteristic impedance determination using propagation constant measurement , 1991, IEEE Microwave and Guided Wave Letters.

[18]  Sandro Ridella,et al.  Launcher and microstrip characterization , 1976, IEEE Transactions on Instrumentation and Measurement.

[19]  J. Reynoso‐Hernández.  Unified method for determining the complex propagation constant of reflecting and nonreflecting transmission lines , 2003, IEEE Microwave and Wireless Components Letters.

[20]  Mauro Parodi,et al.  Determination of the propagation constant of uniform microstrip lines , 1976 .

[21]  A. Rumiantsev,et al.  VNA calibration , 2008, IEEE Microwave Magazine.