volume | PIER Journals

Abstract

Two approaches to reconstruct the S-matrix of N-port waveguide reciprocal devices from 2-port S-matrix measurements are proposed and discussed. The main advantage of the proposed approaches is that measurements are done always at the same two ports, without moving the device. The remaining N-2 ports are loaded with different loads, either matched or short. The first approach, based on a manipulation of the 2-port S-matrices, requires N-2 matched and two other loads, while the second approach, based on the evaluation of an equivalent circuit, requires N-2 short and two other loads. The measurement technique is based on the standard loads (short, shift and matched) in the waveguide calibration kit of the 2-port VNA.

1. Franzen, N. R. and R. A. Speciale, "A new procedure for system calibration and error removal in automated s-parameter measurements," 5th European Microwave Conference, 69-73, 1975.

2. Speciale, R. A. and C. Tzuang, "Test results on the new TSZ calibration method," 21st ARFTG Conference, Vol. 3, 39-46, Jun. 1983.

3. Rolfes, I. and B. Schiek, "LRR-A self-calibration technique for the calibration of vector network analyzers," IEEE Transactions on Instrumentation and Measurement, Vol. 52, No. 2, 316-319, Apr. 2003.
doi:10.1109/TIM.2003.810040

4. Lenk, F., R. Doerner, and A. Rumiantsev, "Sensitivity analysis of s-parameter measurements due to calibration standards uncertainty," IEEE Transactions on Microwave Theory and Techniques, Vol. 61, No. 10, 3800-3807, Oct. 2013.
doi:10.1109/TMTT.2013.2279774

5. Stumper, U. and T. Schrader, "Calibration method for vector network analyzers using one or two known reflection standards," IEEE Transactions on Instrumentation and Measurement, Vol. 63, No. 6, 1648-1655, Jun. 2014.
doi:10.1109/TIM.2013.2292754

6. Morini, A., M. Guglielmi, and M. Farina, "A technique for the measurement of the generalized scattering matrix of overmoded waveguide devices," IEEE Transactions on Microwave Theory and Techniques, Vol. 61, No. 7, 2705-2714, Jul. 2013.
doi:10.1109/TMTT.2013.2265683

7. Tippet, J. and R. A. Speciale, "A rigorous technique for measuring the scattering matrix of a multiport device with a 2-port network analyzer," IEEE Transactions on Microwave Theory and Techniques, Vol. 30, No. 5, 661-666, May 1982.
doi:10.1109/TMTT.1982.1131118

8. Helton, J. and R. Speciale, "A complete and unambiguous solution to the super-TSD multiport-calibration problem," IEEE MTT-S International Microwave Symposium, 251-252, May 1983.
doi:10.1109/MWSYM.1983.1130874

9. Rautio, J. C., "Techniques for correcting scattering parameter data of an imperfectly terminated multiport when measured with a two-port network analyzer," IEEE Transactions on Microwave Theory and Techniques, Vol. 31, No. 5, 407-412, May 1983.
doi:10.1109/TMTT.1983.1131512

10. Schoon, M., "A semi-automatic 3-port network analyzer," IEEE Transactions on Microwave Theory and Techniques, Vol. 41, No. 6, 974-978, Jun. 1993.
doi:10.1109/22.238511

11. Davidovitz, M., "Reconstruction of the S-matrix for a 3-port using measurements at only two ports," IEEE Microwave and Guided Wave Letters, Vol. 5, No. 10, 349-350, Oct. 1995.
doi:10.1109/75.465040

12. Sercu, S. and L. Martens, "Characterizing n-port packages and interconnections with a 2-port network analyzer," IEEE 6th Topical Meeting on Electrical Performance of Electronic Packaging, 163-166, Oct. 1997.

13. Lu, H.-C. and T.-H. Chu, "Multiport scattering matrix measurement using a reduced-port network analyzer," IEEE Transactions on Microwave Theory and Techniques, Vol. 51, No. 5, 1525-1533, May 2003.
doi:10.1109/TMTT.2003.810134

14. Rolfes, I. and B. Schiek, "An efficient method for the measurement of the scattering-parameters of multi-ports with a two-port network-analyzer," 34th European Microwave Conference, Vol. 2, 797-800, Oct. 2004.

15. Rolfes, I. and B. Schiek, "Multiport method for the measurement of the scattering parameters of n-ports," IEEE Transactions on Microwave Theory and Techniques, Vol. 53, No. 6, 1990-1996, Jun. 2005.
doi:10.1109/TMTT.2005.848823

16. Heuermann, H., "Multiport s-parameter calculation from two-port network analyzer measurements with or without switch matrix," 67th ARFTG Conference, 219-222, Jun. 2006.
doi:10.1109/ARFTG.2006.4734386

17. Will, B., I. Rolfes, and B. Schiek, "Fully automated measurements of calibrated scattering parameters of multi-ports with a two-port network analyzer," European Microwave Conference, 242-245, Oct. 2007.

18. Chen, C.-J. and T.-H. Chu, "Accuracy criterion for S-matrix reconstruction transforms on multiport networks," IEEE Transactions on Microwave Theory and Techniques, Vol. 59, No. 9, 2331-2339, Sept. 2011.
doi:10.1109/TMTT.2011.2160082

19. Rautio, J. and M. Davidovitz, "Comments on ``reconstruction of the s-matrix for a 3-port using measurements at only two ports" [and reply]," IEEE Microwave and Guided Wave Letters, Vol. 6, No. 4, 183, Apr. 1996.
doi:10.1109/75.481082

20. Marcuvitz, N., Waveguide Handbook, Mc-Graw-Hill, 1951.

21. Montgomery, C. G., R. H. Dicke, and E. M. Purcell, Principles of Microwave Circuits, McGraw-Hill, 1948.

22. Zappelli, L., "An equivalent circuit for discontinuities exciting evanescent accessible modes," IEEE Transactions on Microwave Theory and Techniques, Vol. 60, No. 5, 1197-1209, May 2012.
doi:10.1109/TMTT.2012.2187533

23. Zappelli, L., "Circuit approach to the analysis of microwave discontinuities," Progress In Electromagnetics Research B, Vol. 53, 373-397, 2013.
doi:10.2528/PIERB13061004

24. Zappelli, L., "An equivalent circuit for thick centered irises in rectangular waveguide," Proceedings of Numerical Electromagnetic Modelling and Optimization (NEMO), Pavia, 2014.

25. Zappelli, L., "Simple, fast, and effective identification of an equivalent circuit of a waveguide junction with n ports," IEEE Transactions on Microwave Theory and Techniques, Vol. 63, No. 1, 48-55, Jan. 2015.
doi:10.1109/TMTT.2014.2375881

Dr. Leonardo Zappelli