For the GSOLT calibration algorithm of n-port vector network analyzers (VNA), the sensitivity coefficients for the S-parameters of the n-port device under test (DUT) are developed as functions of the S-parameter deviations of SOLT standards. By introducing the generalized flow graph of the 3n-term error model, analytic formulas for the S-parameter deviations of the n-port DUT with respect to the error terms have been deduced. In addition, expressions for the deviations of the error terms in regard to the nonideal calibration elements are given by a series of matrix operations. Finally, the analytic expressions of the sensitivity coefficients are concluded, which can be used for establishing the type-B uncertainty budget for S-parameter measurements.
1. Ferrero, A., V. Teppati, E. Fledell, B. Grossman, and T. Ruttan, "Microwave multiport measurements for the digital world," IEEE Microwave Magazine, Vol. 12, No. 1, 61-73, 2011. doi:10.1109/MMM.2010.939305
3. Rytting, D., "Network analyzer error models and calibration methods," RF & Microwave Measurement for Wireless Application (ARFTG/NIST Short Course Notes) , 1996.
4. Heuermann, H., "GSOLT: The calibration procedure for all multiport vector network analyzers," MTT-S International Microwave Symposium, 1815-1818, 2003.
5. Zhao, W., Y. J. Zhao, and H. B. Qin, "Calibration of the three-port VNA using the general 6-term error model," Journal of Electromagnetic Wave and Application,", Vol. 24, No. 2--3, 319-326, 2010.
6. Zhao, W., et al., "Calibration algorithm of the n-port vector network analyzer using the general node equation," IET Science, Measurement & Technology, Vol. 4, No. 6, 298-302, 2010. doi:10.1049/iet-smt.2009.0091
7. Stumper, U. and T. Schrader, "Influence of different configurations of nonideal calibration standards on vector network analyzer performance," IEEE Transactions on Instrumentation and Measurement, Vol. 61, No. 7, 2034-2041, 2012. doi:10.1109/TIM.2012.2182889
8. Stumper, U., "Influence of nonideal calibration items on S-parameter uncertainties applying the SOLR calibration method," IEEE Transactions on Instrumentation and Measurement, Vol. 58, No. 4, 311-315, 2009. doi:10.1109/TIM.2008.2006962
9. Stumper, U., "Influence of TMSO calibration standards uncertainties on VNA S-parameter measurements ," IEEE Transactions on Instrumentation and Measurement, Vol. 52, No. 2, 311-315, 2003. doi:10.1109/TIM.2003.810041
10. Zhao, W., et al., "Zhao, W., X. D. Yang, J. K. Xiao, et al., \Uncertainties of multiport VNA S-parameter measurements applying the GSOLT calibration method," IEEE Transaction on Instrument and Measurement, Vol. 61, No. 12, 3251-3258, 2012. doi:10.1109/TIM.2012.2210332
11. Mason, S. J., "Feedback theory: Further properties of signal flow graphs," Proceedings of The Institute of Radio Engineers, Vol. 44, No. 7, 920-926, 1956.
12. Da Silva, E., "High Frequency and Microwave Engineering,", 2001.
13. Kurokawa, K., "Power waves and the scattering matrix," IEEE Transactions on Microwave Theory and Techniques, Vol. 13, No. 2, 194-202, 1965. doi:10.1109/TMTT.1965.1125964
14. Henderson, H. V. and S. R. Searle, "On deriving the inverse of a sum of matrices," Siam Review, Vol. 23, No. 1, 53-60, 1981. doi:10.1137/1023004
15. Petersen, K. B. and M. S. Pedersen, The Matrix Cookbook, Technical University of Denmark, 2006.