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2025-01-26
Maximally Flat Negative Group Delay Prototype Filter Based on Capped Reciprocal Transfer Function of Classical Bessel Filter
By
Progress In Electromagnetics Research B, Vol. 110, 91-105, 2025
Abstract
A prototype filter design exhibiting Negative Group Delay (NGD) is presented, based on the ratio of two low-pass classical Bessel filter transfer functions of the same order, but with different 3dB-bandwidths. The resulting design is a reciprocal-Bessel filter transfer function, capped at a finite out-of-band gain. The proposed capped reciprocal-Bessel design is based on a similar concept applied to previously reported capped reciprocal-Butterworth and reciprocal-Chebyshev NGD designs, which use ratios of corresponding classical low-pass filter transfer functions. It is shown that within the in-band frequency range, the synthesized NGD transfer function exhibits a maximally flat group delay characteristic (Bessel-like property). Due to its near-flat in-band group delay characteristic, the design is suitable for constant phase shifter applications. For high design orders, it is shown that the achieved NGD-bandwidth product has an upper asymptotic limit, given by the square root of the out-of-band gain in decibels. When the prototype baseband transfer function is translated to a non-zero center frequency, it is demonstrated that resonator-based implementations are feasible via Sallen-Key, as well as all-passive ladder topologies. A combined in-band magnitude/phase distortion metric is evaluated for selected design examples and applied Gaussian and sinc input waveforms, and it is shown to be proportional to the design order and out-of-band gain. The proposed design's distortion metric is also shown to be generally lower than the previously reported capped reciprocal-Butterworth and reciprocal-Chebyshev designs.
Citation
Miodrag Kandic, and Greg E. Bridges, "Maximally Flat Negative Group Delay Prototype Filter Based on Capped Reciprocal Transfer Function of Classical Bessel Filter," Progress In Electromagnetics Research B, Vol. 110, 91-105, 2025.
doi:10.2528/PIERB24121308
References

1. 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.

2. 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.

3. 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.

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

5. 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.

6. 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.

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.

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.

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.

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

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.

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

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

14. Kandic, Miodrag and Greg E. Bridges, "Negative group delay prototype filter based on the ratio of two classical Chebyshev filter transfer functions," Progress In Electromagnetics Research B, Vol. 107, 139-153, 2024.
doi:10.2528/PIERB24071304

15. Macke, Bruno, Bernard Ségard, and Franck Wielonsky, "Optimal superluminal systems," Physical Review E, Vol. 72, No. 3, 035601(R), Sep. 2005.

16. Macke, B. 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.

17. Ravelo, B., M. Le Roy, and A. Pérennec, "Application of negative group delay active circuits to the design of broadband and constant phase shifters," Microwave and Optical Technology Letters, Vol. 50, No. 12, 3078-3080, 2008.

18. Meng, Yuwei, Zhongbao Wang, Shao-Jun Fang, and Hongmei Liu, "Broadband phase shifter with constant phase based on negative group delay circuit," Progress In Electromagnetics Research Letters, Vol. 103, 161-169, 2022.
doi:10.2528/PIERL22031301

19. Ravelo, Blaise, "Similitude between the NGD function and filter gain behaviours," International Journal of Circuit Theory and Applications, Vol. 42, No. 10, 1016-1032, 2014.

20. Lucyszyn, S., I. D. Robertson, and A. H. Aghvami, "Negative group delay synthesiser," Electronics Letters, Vol. 29, No. 9, 798-800, Apr. 1993.

21. 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.

22. 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.

23. Siddiqui, O. F., M. Mojahedi, and G. 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.

24. Ravelo, Blaise, Andre Perennec, 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.

25. Choi, Heungjae, Yongchae Jeong, Chul Dong Kim, and James Stevenson Kenney, "Bandwidth enhancement of an analog feedback amplifier by employing a negative group delay circuit," Progress In Electromagnetics Research, Vol. 105, 253-272, 2010.

26. Choi, Heungjae, Yongchae Jeong, Chul Dong Kim, and J. Stevenson Kenney, "Efficiency enhancement of feedforward amplifiers by employing a negative group-delay circuit," IEEE Transactions on Microwave Theory and Techniques, Vol. 58, No. 5, 1116-1125, May 2010.

27. 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.

28. 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.

29. 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.

30. 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.

31. 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. 2019.

32. 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.

33. 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.

34. 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.

35. 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

36. 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.

37. 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.

38. 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.

39. 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.

40. 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.

41. 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.

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

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

44. United States Patent Office (USPTO) application number: 19/017634.

45. Goodman, Thomas J. and Maurice F. Aburdene, "Pascal filters," IEEE Transactions on Circuits and Systems I: Regular Papers, Vol. 55, No. 10, 3090-3094, Nov. 2008.