2019-01-22
Pole-Zero Analysis of Microwave Filters Using Contour Integration Method Exploiting Right-Half Plane
By
Progress In Electromagnetics Research M, Vol. 78, 59-68, 2019
Abstract
This paper presents the pole-zero analysis of microwave filters using contour integration method exploiting right-half plane (RHP). The poles and zeros can be determined with only S21 by exploiting contour integration method on the RHP along with certain S matrix properties. The contour integration in the argument principle is evaluated numerically via the finite-difference method. To locate the poles or zeros, the contour divide and conquer approach is utilized, whereby the contour is divided into smaller sections in stages until the contour enclosing the pole or zero is sufficiently small. The procedures to determine the poles and zeros separately are described in detail with the aid of pseudocodes. To demonstrate the effectiveness of the proposed method, it is applied to determine and analyze the poles and zeros of various microwave filters.
Citation
Eng Leong Tan, and Ding Yu Heh, "Pole-Zero Analysis of Microwave Filters Using Contour Integration Method Exploiting Right-Half Plane," Progress In Electromagnetics Research M, Vol. 78, 59-68, 2019.
doi:10.2528/PIERM18102301
References

1. Pozar, D. M., Microwave Engineering, 4th Ed., Wiley, 2011.

2. Matthaei, G. L., L. Young, and E. M. T. Jones, Microwave Filters, Impedance Matching Network and Coupling Structure, Artech House, 1980.

3. Hong, J. S. and M. J. Lancaster, Microstrip Filter for RF/Microwave Application, 2nd Ed., Wiley, 2011.
doi:10.1002/9780470937297

4. Collin, R. E., Foundations for Microwave Engineering, 2nd Ed., IEEE Press, 2001.
doi:10.1109/9780470544662

5. Cameron, R. J., C. M. Kudsia, and R. R. Mansour, Microwave Filters for Communication Systems, John Wiley and Sons, 2007.

6. Wang, X., Y. Di, P. Gardner, and H. Ghafouri-Shiraz, "Frequency transform synthesis method for cross-coupled resonator bandpass filters," IEEE Microw. Wireless Compon. Lett., Vol. 15, No. 8, 533-535, Aug. 2005.
doi:10.1109/LMWC.2005.852799        Google Scholar

7. Liu, A.-S., T.-Y. Huang, and R.-B. Wu, "A dual wideband filter design using frequency mapping and stepped-impedance resonators," IEEE Trans. Microw. Theory Tech., Vol. 56, No. 12, 2921-2929, Dec. 2008.
doi:10.1109/TMTT.2008.2007357        Google Scholar

8. Xue, S. J., W. J. Feng, H. T. Zhu, and W. Q. Che, "Microstrip wideband bandpass filter with six transmission zeros using transversal signal-interaction concepts," Progress In Electromagnetics Research C, Vol. 34, 1-12, 2013.
doi:10.2528/PIERC12092814        Google Scholar

9. Xu, J. and W. Wu, "Compact microstrip dual-mode dual-band band-pass filters using stubs loaded coupled line," Progress In Electromagnetics Research C, Vol. 41, 137-150, 2013.
doi:10.2528/PIERC13052204        Google Scholar

10. Sun, X. and E. L. Tan, "Dual-band filter design with pole-zero distribution in the complex frequency plane," 2016 IEEE MTT-S Int. Microw. Symp. Dig., 2016, doi:10.1109/MWSYM.2016.7540174.        Google Scholar

11. Tan, E. L. and D. Y. Heh, "Application of Belevitch theorem for pole-zero analysis of microwave filters with transmission lines and lumped elements," IEEE Trans. Microw. Theory Tech., Vol. 66, No. 11, 4669-4676, Nov. 2018.
doi:10.1109/TMTT.2018.2865928        Google Scholar

12. Belevitch, V., Classical Network Theory, Holden-Day, 1968.

13. Ahlfors, L., Complex analysis: An Introduction to the Theory of Analytic Functions of One Complex Variable, McGraw-Hill, 1979.

14. Wong, S. W., K. Wang, Z. Chen, and Q. Chu, "Rotationally symmetric coupled-lines band-pass filter with two transmission zeros," Progress In Electromagnetics Research, Vol. 135, 641-656, 2013.
doi:10.2528/PIER12112405        Google Scholar