volume | PIER Journals

Abstract

A Negative Group Delay (NGD) prototype filter design, based on the ratio of two Chebyshev filter transfer functions, is presented. The two transfer functions are of the same order, but with different in-band ripple amplitudes and different 3 dB-bandwidths. The overall transfer function exhibits both an in-band ripple and an out-of-band steep-slope magnitude transition characteristic of a Chebyshev filter, while also exhibiting an in-band NGD. For high-order designs and in the upper asymptotic limit, the NGD-bandwidth product of the filter is shown to be a linear function of out-of-band gain in decibels. A resonator-based methodology is used to show how frequency upshifted filter designs can be implemented in a Sallen-Key topology or in an all-passive ladder topology. An in-band combined magnitude/phase distortion metric is evaluated for examples of the NGD filter. It is shown that the distortion metric is proportional to the design order, the in-band ripple amplitude, and the out-of-band gain. For a prescribed distortion metric value, it is demonstrated that the proposed design can achieve a higher NGD-bandwidth product than an equivalent Butterworth design, which has a flat in-band magnitude characteristic. Additionally, input waveforms with bandwidths extending to the entire frequency range where the group delay is negative (typically larger than the 3dB-bandwidth) should not be applied to this filter design as it results in strong levels of distortion.

1. Brillouin, L., Wave Propagation and Group Velocity, Vol. 8, Academic Press, New York, 2013.

2. Mojahedi, M., K. J. Malloy, G. V. Eleftheriades, J. Woodley, and R. Y. Chiao, "Abnormal wave propagation in passive media," IEEE Journal of Selected Topics in Quantum Electronics, Vol. 9, No. 1, 30-39, 2003. Google Scholar

3. Stenner, Michael D., Daniel J. Gauthier, and Mark A. Neifeld, "Fast causal information transmission in a medium with a slow group velocity," Physical Review Letters, Vol. 94, No. 5, 053902, 2005. Google Scholar

4. Wang, Youzhen, Yewen Zhang, Li He, Fuqiang Liu, Hongqiang Li, and Hong Chen, "Direct observation of negative phase velocity and positive group velocity in time domain for composite right/left-handed transmission lines," Journal of Applied Physics, Vol. 100, No. 11, 113503, 2006. Google Scholar

5. Mojahedi, Mohammad, Edl Schamiloglu, Frank Hegeler, and Kevin J. Malloy, "Time-domain detection of superluminal group velocity for single microwave pulses," Physical Review E, Vol. 62, No. 4, 5758, 2000. Google Scholar

6. Ibraheem, Ibraheem A., Joerg Schoebel, and Martin Koch, "Group delay characteristics in coplanar waveguide left-handed media," Journal of Applied Physics, Vol. 103, No. 2, 024903, 2008. Google Scholar

7. Bolda, Eric L., Raymond Y. Chiao, and John C. Garrison, "Two theorems for the group velocity in dispersive media," Physical Review A, Vol. 48, No. 5, 3890, Nov. 1993. Google Scholar

8. Kandic, Miodrag and Greg E. Bridges, "Asymptotic limits of negative group delay in active resonator-based distributed circuits," IEEE Transactions on Circuits and Systems I: Regular Papers, Vol. 58, No. 8, 1727-1735, Aug. 2011. Google Scholar

9. Kandic, Miodrag and Greg E. Bridges, "Limits of negative group delay phenomenon in linear causal media," Progress In Electromagnetics Research, Vol. 134, 227-246, 2013. Google Scholar

10. Kandic, Miodrag and Greg E. Bridges, "Negative group delay prototype filter based on cascaded second order stages implemented with Sallen-Key topology," Progress In Electromagnetics Research B, Vol. 94, 1-18, 2021.
doi:10.2528/PIERB21071209 Google Scholar

11. Solli, Daniel, R. Y. Chiao, and J. M. Hickmann, "Superluminal effects and negative group delays in electronics, and their applications," Physical Review E, Vol. 66, No. 5, 056601, 2002. Google Scholar

12. Dorrah, Ahmed H. and Mo Mojahedi, "Nonanalytic pulse discontinuities as carriers of information," Physical Review A, Vol. 93, No. 1, 013823, 2016. Google Scholar

13. Kandic, Miodrag and Greg E. Bridges, "Negative group delay prototype filter based on the reciprocal transfer function of a low-pass Butterworth filter capped at finite out-of-band gain," Progress In Electromagnetics Research B, Vol. 106, 17-38, 2024.
doi:10.2528/PIERB24020602 Google Scholar

14. Macke, Bruno, Bernard Ségard, and Franck Wielonsky, "Optimal superluminal systems," Physical Review E, Vol. 72, No. 3, 035601, Sep. 2005.
doi:10.1103/PhysRevE.72.035601 Google Scholar

15. Macke, Bruno and B. Ségard, "Propagation of light-pulses at a negative group-velocity," The European Physical Journal D --- Atomic, Molecular, Optical and Plasma Physics, Vol. 23, 125-141, 2003. Google Scholar

16. Lucyszyn, S., I. D. Robertson, and A. H. Aghvami, "Negative group delay synthesiser," Electronics Letters, Vol. 29, No. 9, 798-800, Apr. 1993.
doi:10.1049/el:19930533 Google Scholar

17. Nakanishi, T., K. Sugiyama, and M. Kitano, "Demonstration of negative group delays in a simple electronic circuit," American Journal of Physics, Vol. 70, No. 11, 1117-1121, Nov. 2002. Google Scholar

18. Kitano, Masao, Toshihiro Nakanishi, and Kazuhiko Sugiyama, "Negative group delay and superluminal propagation: An electronic circuit approach," IEEE Journal of Selected Topics in Quantum Electronics, Vol. 9, No. 1, 43-51, Jan.-Feb. 2003. Google Scholar

19. Siddiqui, Omar F., M. Mojahedi, and George V. Eleftheriades, "Periodically loaded transmission line with effective negative refractive index and negative group velocity," IEEE Transactions on Antennas and Propagation, Vol. 51, No. 10, 2619-2625, Oct. 2003. Google Scholar

20. Ravelo, Blaise, AndrÉ PÉrennec, Marc Le Roy, and Yann G. Boucher, "Active microwave circuit with negative group delay," IEEE Microwave and Wireless Components Letters, Vol. 17, No. 12, 861-863, Dec. 2007.
doi:10.1109/LMWC.2007.910489 Google Scholar

21. Mirzaei, Hassan and George V. Eleftheriades, "Realizing non-Foster reactive elements using negative-group-delay networks," IEEE Transactions on Microwave Theory and Techniques, Vol. 61, No. 12, 4322-4332, Dec. 2013. Google Scholar

22. Chaudhary, Girdhari, Yongchae Jeong, and Jongsik Lim, "Microstrip line negative group delay filters for microwave circuits," IEEE Transactions on Microwave Theory and Techniques, Vol. 62, No. 2, 234-243, Feb. 2014. Google Scholar

23. Wu, Chung-Tse Michael and Tatsuo Itoh, "Maximally flat negative group-delay circuit: A microwave transversal filter approach," IEEE Transactions on Microwave Theory and Techniques, Vol. 62, No. 6, 1330-1342, Jun. 2014. Google Scholar

24. Wu, Yongle, Handing Wang, Zheng Zhuang, Yuanan Liu, Quan Xue, and Ahmed A. Kishk, "A novel arbitrary terminated unequal coupler with bandwidth-enhanced positive and negative group delay characteristics," IEEE Transactions on Microwave Theory and Techniques, Vol. 66, No. 5, 2170-2184, 2018. Google Scholar

25. Wan, Fayu, Ningdong Li, Blaise Ravelo, and Junxiang Ge, "O=O shape low-loss negative group delay microstrip circuit," IEEE Transactions on Circuits and Systems II: Express Briefs, Vol. 67, No. 10, 1795-1799, Oct. 2020. Google Scholar

26. Ravelo, Blaise, Fayu Wan, and Junxiang Ge, "Anticipating actuator arbitrary action with a low-pass negative group delay function," IEEE Transactions on Industrial Electronics, Vol. 68, No. 1, 694-702, Jan. 2021. Google Scholar

27. Wang, Zhongbao, Shipeng Zhao, Hongmei Liu, and Shaojun Fang, "A compact dual-band differential negative group delay circuit with wideband common mode suppression," IEEE Journal of Microwaves, Vol. 2, No. 4, 720-725, Oct. 2022. Google Scholar

28. Nair, Rekha G. and S. Natarajamani, "Design theory of compact power divider with reconfigurable power division and negative group delay characteristics," Scientific Reports, Vol. 13, No. 1, 7222, May 2023. Google Scholar

29. Palson, Chithra Liz, Deepti Das Krishna, and Babita Roslind Jose, "Planar tunable negative group delay circuit with low reflection loss," Progress In Electromagnetics Research Letters, Vol. 113, 53-59, 2023.
doi:10.2528/PIERL23090902 Google Scholar

30. Ravelo, Blaise, Habachi Bilal, Sylcolin Rakotonandrasana, Mathieu Guerin, Fayrouz Haddad, Samuel Ngoho, and Wenceslas Rahajandraibe, "Transient characterization of new low-pass negative group delay RC-network," IEEE Transactions on Circuits and Systems II: Express Briefs, Vol. 71, No. 1, 126-130, Jan. 2024. Google Scholar

31. Zhang, Awei, Jinping Xu, and Zhiqiang Liu, "A microstrip linear-phase BPF using dual-band negative group delay equalizers," IEEE Microwave and Wireless Technology Letters, Vol. 34, No. 4, 387-390, Apr. 2024. Google Scholar

32. Chang, Niannan, Aixia Yuan, Ying Wang, and Junzheng Liu, "Multi-band pass negative group delay circuit with low insertion loss," International Journal of Circuit Theory and Applications, Jul. 2024. Google Scholar

33. Nako, Julia, Costas Psychalinos, Ahmed S. Elwakil, and Brent J. Maundy, "A note on the bandwidth of negative group delay filters," International Journal of Circuit Theory and Applications, 2024. Google Scholar

34. Nako, Julia, Costas Psychalinos, Brent J. Maundy, and Ahmed S. Elwakil, "Elementary negative group delay filter functions," Circuits, Systems, and Signal Processing, Vol. 43, No. 6, 3396-3409, 2024. Google Scholar

35. Maundy, B. J., A. S. Elwakil, and C. Psychalinos, "Systematic design of negative group delay circuits," AEU --- International Journal of Electronics and Communications, Vol. 174, 155060, 2024. Google Scholar

36. Nako, Julia, Costas Psychalinos, Ahmed S. Elwakil, and Brent J. Maundy, "Power-law negative group delay filters," Electronics, Vol. 13, No. 3, 522, 2024. Google Scholar

37. United States Patent Office (USPTO) application number: 18/491922.

Dr. Miodrag Kandic

Prof. Greg E. Bridges