volume | PIER Journals

Abstract

A Negative Group Delay (NGD) filter prototype design based on cascaded identical 2nd-order baseband stages is presented. The prototype design achieves an NGD-bandwidth product that in the upper asymptotic limit for a distributed design is a function of out-of-band gain in decibels raised to the power 3/4. This is an improvement of previous cascaded first-order designs that have an NGD-bandwidth functional dependency of out-of-band gain in decibels to the power of 1/2. The bandwidth is taken as the 3 dB amplitude response bandwidth. The corresponding NGD design upshifted to a non-zero center frequency, i.e. a Band-Stop Filter (BSF) design, is shown to be possible to implement with Sallen-Key topology, and an example is presented for a 500 MHz center frequency and a 100 MHz (20%) 3 dB bandwidth. The filter shows a 4.05 ns negative group delay with a 1.28 ns in-band variation and a 3-dB amplitude response over the bandwidth of 100 MHz, achieving an NGD-bandwidth product of 0.405. An in-band distortion metric is presented, which can be evaluated for any specified time-domain input waveform. It is shown that the bandwidth, order of filter and desired distortion for a particular input waveform are interrelated. Therefore, the proposed in-band distortion metric constitutes another trade-off quantity to be checked for any type of NGD design.

1. Brillouin, L., Wave Propagation and Group Velocity, Academic Press, 1960.

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.
doi:10.1109/JSTQE.2002.807971

3. Stenner, D., D. J. Gauthier, and M. A. Neifeld, "Fast causal information transmission in a medium with a slow group velocity," Phys. Rev. Lett., Vol. 94, No. 5, 053902, 2005.
doi:10.1103/PhysRevLett.94.053902

4. Mojahedi, M., E. Schamiloglu, F. Hegeler, and K. J. Malloy, "Time-domain detection of superluminal group velocity for single microwave pulses," Phys. Rev. E, Vol. 62, No. 4, 2000.
doi:10.1103/PhysRevE.62.5758

5. Wang, Y., Y. Zhang, L. He, F. Liu, H. Li, and H. 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, 113503, 2006.
doi:10.1063/1.2372573

6. Ibraheem, A., J. Schoebel, and M. Koch, "Group delay characteristics in coplanar waveguide left-handed media," Journal of Applied Physics, Vol. 103, 024903, 2008.
doi:10.1063/1.2832750

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

9. Kandic, M. and G. Bridges, "Limits of negative group delay phenomenon in linear causal media," Progress in Electromagnetics Research, Vol. 134, 227-246, Jan. 2013.
doi:10.2528/PIER12082915

10. Solli, D., R. Y. Chiao, and J. M. Hickmann, "Superluminal effects and negative group delays in electronics, and their applications," Phys. Rev. E, Vol. 66, No. 5, 056601, 2002.
doi:10.1103/PhysRevE.66.056601

11. Dorrah, A. H. and M. Mojahedi, "Nonanalytic pulse discontinuities as carriers of information," Phys. Rev. A, Vol. 93, 013823, 2016.
doi:10.1103/PhysRevA.93.013823

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

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

14. 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

15. Nakanishi, T., K. Sugiyama, and M. Kitano, "Demonstration of negative group delays in a simple electronic circuit," Am. J. Phys., Vol. 70, No. 11, 1117-1121, Nov. 2002.
doi:10.1119/1.1503378

16. Kitano, M., T. Nakanishi, and K. Sugiyama, "Negative group delay and superluminal propagation: An electronic circuit approach," IEEE J. Sel. Topics Quantum Electron., Vol. 9, No. 1, 43-51, Feb. 2003.
doi:10.1109/JSTQE.2002.807979

17. 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 Propag., Vol. 51, No. 10, 2619-2625, Oct. 2003.
doi:10.1109/TAP.2003.817556

18. Ravelo, B., A. Perennec, M. Le Roy, and Y. G. Boucher, "Active microwave circuit with negative group delay," Microwave and Wireless Components Letters, Vol. 17, No. 12, 861-863, Dec. 2007.
doi:10.1109/LMWC.2007.910489

19. Choi, H., Y. Jeong, C. D. Kim, and J. S. Kenney, "Bandwidth enhancement of an analog feedback amplier by employing a negative group delay circuit," Progress In Electromagnetics Research, Vol. 105, 253-272, 2010.
doi:10.2528/PIER10041808

20. Mirzaei, H. and G. V. Eleftheriades, "Realizing non-Foster reactive elements using negative group delay networks," IEEE Trans. Microw. Theory Techn., Vol. 61, No. 12, 4322-4332, Dec. 2013.
doi:10.1109/TMTT.2013.2281967

21. Chaudhary, G., Y. Jeong, and J. Lim, "Microstrip line negative group delay filters for microwave circuits," IEEE Trans. Microw. Theory Techn., Vol. 62, No. 2, 234-243, Feb. 2014.
doi:10.1109/TMTT.2013.2295555

22. 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

23. Chaudhary, G. and Y. Jeong, "Transmission-type negative group delay networks using coupled line doublet structure," IET Microw. Antennas Propag., Vol. 9, No. 8, 748-754, 2015.
doi:10.1049/iet-map.2014.0351

24. Chaudhary, G. and Y. Jeon, "Negative group delay phenomenon analysis using finite unloaded quality factor resonators," Progress In Electromagnetics Research, Vol. 156, 55-62, Jan. 2016.
doi:10.2528/PIER16041111

25. Wu, Y., H. Wang, Z. Zhuang, Y. Liu, Q. Xue, and A. Kishk, "A novel arbitrary terminated unequal coupler with bandwidth-enhanced positive and negative group delay characteristics," IEEE Trans. Microw. Theory Techn., Vol. 66, No. 5, 2170-2184, 2018.
doi:10.1109/TMTT.2018.2809516

26. Wan, F., N. Li, B. Ravelo, and J. Ge, "O=O shape low-loss negative group delay microstrip circuit," IEEE Trans. Circuits Syst. II, Exp. Briefs, Vol. 67, No. 10, 1795-1799, Oct. 2020.
doi:10.1109/TCSII.2019.2955109

Dr. Miodrag Kandic

Prof. Greg E. Bridges