volume | PIER Journals

Abstract

This paper introduces an original study of low-pass (LP) negative group delay (NGD) circuit. The family of the proposed passive network cross-topology was rarely investigated in the literature. It acts as a tri-port passive circuit presenting a cross-shaped topology. The present study of tri-port passive circuit is originally based on S-matrix modelling. The identification method of LP-NGD function type is established. The considered passive tri-port topology is innovatively constituted by a resistorless LC-passive network. Thanks to the impedance 3-D matrix modelling, the cross-circuit S-parameters are analytically expressed. Then, the NGD analysis at very low-frequencies is presented. The LP-NGD behavior existence condition of the cross-circuit in function of the L and C components is established. The relevance of the tri-port NGD circuit theory is verified by a proof-of-concept of resistorless cross-circuit. Analytical modelling, simulation, and experimentation confirmed the LP-NGD design feasibility with NGD value of about -2 ns and 6.67 MHz cut-off frequency.

1. Chu, S. and S. Wong, "Linear pulse propagation in an absorbing medium," Phys. Rev. Lett., Vol. 48, 738-741, 1982.
doi:10.1103/PhysRevLett.48.738

2. Ségard, B. and B. Macke, "Observation of negative velocity pulse propagation," Phys. Lett. A, Vol. 109, 213-216, 1985.
doi:10.1016/0375-9601(85)90305-6

3. Macke, B. and B. Ségard, "Propagation of light-pulses at a negative group-velocity," Eur. Phys. J. D, Vol. 23, 125-141, 2003.
doi:10.1140/epjd/e2003-00022-0

4. Munday, J. N. and W. M. Robertson, "Observation of negative group delays within a coaxial photonic crystal using an impulse response method," Optics Communications, Vol. 273, No. 1, 32-36, 2007.
doi:10.1016/j.optcom.2006.12.039

5. Eleftheriades, G. V., O. Siddiqui, and A. K. Iyer, "Transmission line for negative refractive index media and associated implementations without excess resonators," IEEE Microw. Wireless Compon. Lett., Vol. 13, No. 2, 51-53, Feb. 2003.
doi:10.1109/LMWC.2003.808719

6. Siddiqui, O. F., M. Mojahedi, and G. V. Eleftheriades, "Periodically loaded transmission line with effective negative refractive index and negative group velocity," IEEE Trans. Antennas Propagat., Vol. 51, No. 10, 2619-2625, Oct. 2003.
doi:10.1109/TAP.2003.817556

7. Bolda, L., R. Y. Chiao, and J. C. Garrison, "Two theorems for the group velocity in dispersive media," Phys. Rev. A, Gen. Phys., Vol. 48, No. 5, 3890-3894, Nov. 1993.
doi:10.1103/PhysRevA.48.3890

8. Macke, B., B. Ségard, and F. Wielonsky, "Optimal superluminal systems," Phys. Rev. E, Vol. 72, 035601(R), 1-4, Sep. 2005.

9. Kandic, M. and G. Bridges, "Asymptotic limits of negative group delay in active resonator-based distributed circuits," IEEE Trans. Circuits Syst. I: Regular Papers, Vol. 58, No. 8, 1727-1735, Aug. 2011.
doi:10.1109/TCSI.2011.2107251

10. Kandic, M. and G. 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, Sep. 2021.
doi:10.2528/PIERB21071209

11. Markley, L. and G. V. Eleftheriades, "Quad-band negative-refractive-index transmission-line unit cell with reduced group delay," Electronics Letters, Vol. 46, No. 17, 1206-1208, Aug. 2010.
doi:10.1049/el.2010.1797

12. Ahn, K.-P., R. Ishikawa, A. Saitou, and K. Honjo, "Synthesis for negative group delay circuits using distributed and second-order RC circuit congurations," IEICE Trans. on Electronics, Vol. E92-C, No. 9, 1176-1181, 2009.
doi:10.1587/transele.E92.C.1176

13. Wu, C.-T.-M. and T. Itoh, "Maximally flat negative group-delay circuit: A microwave transversal filter approach," IEEE Trans. Microw. Theory Techn., Vol. 62, No. 6, 1330-1342, Jun. 2014.
doi:10.1109/TMTT.2014.2320220

14. Zhang, T., R. Xu, and C. M. Wu, "Unconditionally stable non-foster element using active transversal-filter-based negative group delay circuit," IEEE Microw. Wireless Compon. Lett., Vol. 27, No. 10, 921-923, Oct. 2017.
doi:10.1109/LMWC.2017.2745487

15. Qiu, L.-F., L.-S. Wu, W.-Y. Yin, and J.-F. Mao, "Absorptive bandstop filter with prescribed negative group delay and bandwidth," IEEE Microw. Wireless Compon. Lett., Vol. 27, No. 7, 639-641, Jul. 2017.
doi:10.1109/LMWC.2017.2711572

16. Wang, Z., Y. Cao, T. Shao, S. Fang, and Y. Liu, "A negative group delay microwave circuit based on signal interference techniques," IEEE Microw. Wireless Compon. Lett., Vol. 28, No. 4, 290-292, Apr. 2018.
doi:10.1109/LMWC.2018.2811254

17. Liu, G. and J. Xu, "Compact transmission-type negative group delay circuit with low attenuation," Electronics Letters, Vol. 53, No. 7, 476-478, Mar. 2017.
doi:10.1049/el.2017.0328

18. Shao, T., Z. Wang, S. Fang, H. Liu, and S. Fu, "A compact transmission line self-matched negative group delay microwave circuit," IEEE Access, Vol. 5, No. 1, 22836-22843, Oct. 2017.

19. Shao, T., S. Fang, Z. Wang, and H. Liu, "A compact dual-band negative group delay microwave circuit," Radio Engineering, Vol. 27, No. 4, 1070-1076, Dec. 2018.

20. Chaudhary, G. and Y. Jeong, "Tunable center frequency negative group delay filter using coupling matrix approach," IEEE Microw. Wireless Compon. Lett., Vol. 27, No. 1, 37-39, 2017.
doi:10.1109/LMWC.2016.2629985

21. Mitchell, M. W. and R. Y. Chiao, "Negative group delay and ``fronts'' in a causal system: An experiment with very low frequency bandpass amplifiers," Phys. Lett. A, Vol. 230, No. 3-4, 133-138, Jun. 1997.
doi:10.1016/S0375-9601(97)00244-2

22. Mitchell, M. W. and R. Y. Chiao, "Causality and negative group-delays in a simple bandpass amplifier," Am. J. Phys., Vol. 66, 14-19, 1998.
doi:10.1119/1.18813

23. Wan, F., J. Wang, B. Ravelo, J. Ge, and B. Li, "Time-domain experimentation of NGD active RC-network cell," IEEE Trans. Circuits and Systems II: Express Briefs, Vol. 66, No. 4, 562-566, Apr. 2019.
doi:10.1109/TCSII.2018.2870836

24. Ravelo, B., "Similitude between the NGD function and filter gain behaviours," Int. J. Circ. Theor. Appl., Vol. 42, No. 10, 1016-1032, Oct. 2014.
doi:10.1002/cta.1902

25. Ravelo, B., "First-order low-pass negative group delay passive topology," Electron. Lett., Vol. 52, No. 2, 124-126, Jan. 2016.
doi:10.1049/el.2015.2856

26. Ravelo, B., "High-pass negative group delay RC-network impedance," IEEE Trans. CAS II: Express Briefs, Vol. 64, No. 9, 1052-1056, Sept. 2017.

27. Fenni, S., F. Haddad, K. Gorshkov, B. Tishchuk, A. Jaomiary, F. Marty, G. Chan, M. Guerin, W. Rahajandraibe, and B. Ravelo, "AC low-frequency characterization of stop-band negative group delay circuit," Progress In Electromagnetics Research C, Vol. 115, 261-276, 2021.
doi:10.2528/PIERC21080508

28. Ravelo, B., O. Maurice, and S. Lalléchère, "Asymmetrical 1 : 2 Y-tree interconnects modelling with Kron-Branin formalism," Electronics Letters, Vol. 52, No. 14, 1215-1216, Jul. 2016.
doi:10.1049/el.2016.1142

29. Ravelo, B., "Behavioral model of symmetrical multi-level T-tree interconnects," Progress In Electromagnetics Research B, Vol. 41, 23-50, 2012.
doi:10.2528/PIERB12040205

30. Wan, F., Y. Liu, J. Nebhen, Z. Xu, G. Chan, S. Lalléchère, R. Vauche, W. Rahajandraibe, and B. Ravelo, "Bandpass negative group delay theory of fully capacitive Δ-network," IEEE Access, Vol. 9, No. 1, 62430-62445, Apr. 2021.
doi:10.1109/ACCESS.2021.3072485

31. Nebhen, J. and B. Ravelo, "Bandpass NGD analysis of symmetric lumped Y-tree via tensorial analysis of networks formalism," Journal of Electromagnetic Waves and Applications, Vol. 35, No. 16, 2125-2140, 2021.
doi:10.1080/09205071.2021.1934570

32. Ravelo, B., F. Wan, J. Nebhen, G. Chan, W. Rahajandraibe, and S. Lalléchère, "Bandpass NGD TAN of symmetric H-tree with resistorless lumped-network," IEEE Access, Vol. 9, 41383-41396, Mar. 2021.
doi:10.1109/ACCESS.2021.3065828

33. Li, N., F. Wan, and B. Ravelo, "Analytical modelling of H-shape distributed topology with bandpass negative group delay behaviour," International Journal of RF and Microwave Computer-Aided Engineering, Vol. 30, No. 9, 1-9, Sept. 2020.

34. Ahn, K.-P., R. Ishikawa, and K. Honjo, "Group delay equalized UWB InGaP/GaAs HBT MMIC amplifier using negative group delay circuits," IEEE Trans. Microw. Theory Techn., Vol. 57, No. 9, 2139-2147, Sept. 2009.
doi:10.1109/TMTT.2009.2027082

35. Ravelo, B., S. Lalléchère, A. Thakur, A. Saini, and P. Thakur, "Theory and circuit modelling of baseband and modulated signal delay compensations with low- and band-pass NGD effects," Int. J. Electron. Commun. (AEÜ), Vol. 70, No. 9, 1122-1127, Sept. 2016.
doi:10.1016/j.aeue.2016.05.009

36. Groenewold, G., "Noise and group delay in active filters," IEEE Trans. CAS I: Regular Papers, Vol. 54, No. 7, 1471-1480, Jul. 2007.

37. Hwang, M.-E., S.-O. Jung, and K. Roy, "Slope interconnect effort: Gate-interconnect interdependent delay modeling for early CMOS circuit simulation," IEEE Trans. CAS I, Vol. 56, No. 7, 1428-1441, Jul. 2009.

Dr. Eric Jean Roy Sambatra

Dr. Antonio Jaomiary

Dr. Samuel Ngoho

Dr. Samar S. Yazdani

Dr. Nour Mohammad Murad

Dr. George Chan

Prof. Blaise Ravelo