Design and analysis of the dynamic frequency divider using the BiCMOS–NDR chaos-based circuit

  • Kwang-Jow Gan
  • Chun-Yi Guo
  • Ping-Feng Wu
  • Yaw-Hwang Chen


A dynamic frequency divider using a negative-differential-resistance (NDR) circuit combined with an inductor and a capacitor was demonstrated. This NDR circuit was made of Si-based metal-oxide-semiconductor field-effect transistor (MOS) and SiGe-based heterojunction bipolar transistor devices. The operation of this frequency divider circuit was based on the long-period behavior of the nonlinear NDR circuit generating chaos phenomena. This circuit was analyzed by numerical simulation and the results showed that different dividing ratio could be obtained by modulating the input signal frequency using the MATLAB program and the HSPICE program. Some measured results were shown to verify our analyses. This application was designed based on a standard 0.18 μm BiCMOS technique.


Dynamic frequency divider Negative differential resistance Long-period behavior Chaos circuit BiCMOS technique 



The authors would like to thank the Chip Implementation Center (CIC) of Taiwan for its great effort and assistance in arranging the fabrication of this chip. This work was financially supported by the Ministry of Science and Technology of Taiwan under contract no. NSC101-2221-E-415-026.


  1. 1.
    Lorenz, E. (1963). Deterministic non-periodic flow. Journal of the Atmospheric Sciences, 20, 130–141.CrossRefzbMATHGoogle Scholar
  2. 2.
    Ivancevic, V. G., & Ivancevic, T. T. (2008). Complex nonlinearity: Chaos, phase transitions, topology change and path integrals. New York: Springer.zbMATHGoogle Scholar
  3. 3.
    Hilborn, R. C. (2004). Sea gulls, butterflies, and grasshoppers: A brief history of the butterfly effect in nonlinear dynamics. American Journal of Physics, 72(4), 425–427.CrossRefGoogle Scholar
  4. 4.
    Chua, L. O., Kocarev, L., Eckert, K., & Itoh, M. (1992). Experimental chaos synchronization in Chua’s circuit. International Journal of Bifurcation and Chaos, 2(03), 705–708.CrossRefzbMATHGoogle Scholar
  5. 5.
    Chen, L., & Aihara, K. (1995). Chaotic simulated annealing by a neural network model with transient chaos. Neural Networks, 8(6), 915–930.CrossRefGoogle Scholar
  6. 6.
    Kawano, Y., Ohno, Y., Kishimoto, S., Maezawa, K., & Mizutani, T. (2002). High-speed operation of a novel frequency divider using resonant tunneling chaos circuit. Japanese Journal of Applied Physics, 41(2B), 1150–1153.CrossRefGoogle Scholar
  7. 7.
    Quintana, J. M., & Avedillo, M. J. (2005). Analysis of frequency divider RTD circuits. IEEE Transactions on Circuits and Systems I: Regular Papers, 52(10), 2234–2247.MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Kawano, Y., Ohno, Y., Kishimoto, S., Maezawa, K., & Mizutani, T. (2002). 50 GHz frequency divider using resonant tunnelling chaos circuit. Electronics Letters, 38(7), 305–306.CrossRefGoogle Scholar
  9. 9.
    Romeira, B., Figueiredo, J. M. L., Slight, T. J., Wang, L., Wasige, E., Ironside, C. N., et al. (2008). Synchronization and chaos in a laser diode driven by a resonant tunneling diode. IET Optoelectronics, 2(6), 211–215.CrossRefGoogle Scholar
  10. 10.
    Kaddoum, G., & Shokraneh, F. (2015). Analog network coding for multi-user multi-carrier differential chaos shift keying communication system. IEEE Transactions on Wireless Communications, 14(3), 1492–1505.CrossRefGoogle Scholar
  11. 11.
    Quyen, N. X., Van Yem, V., & Duong, T. Q. (2015). Design and analysis of a spread-spectrum communication system with chaos-based variation of both phase-coded carrier and spreading factor. IET Communications, 9(12), 1466–1473.CrossRefGoogle Scholar
  12. 12.
    Wang, S., Kuang, J., Li, J., Luo, Y., Lu, H., & Hu, G. (2002). Chaos-based secure communications in a large community. Physical Review E, 6(6), 065202(R).CrossRefGoogle Scholar
  13. 13.
    Sudirgo, S., Nandgaonkar, R. P., Curanovic, B., Hebding, J. L., Saxer, R. L., Islam, S. S., et al. (2004). Monolithically integrated Si/SiGe resonant interband tunnel diode/CMOS demonstrating low voltage MOBILE operation. Solid-State Electronics, 48, 1907–1910.CrossRefGoogle Scholar
  14. 14.
    Chung, S. Y., Jin, N., Berger, P. R., Yu, R., Thompson, P. E., Lake, R., et al. (2004). 3-terminal Si-based negative differential resistance circuit element with adjustable peak-to-valley current ratios using a monolithic vertical integration. Applied Physics Letters, 84(14), 2688–2690.CrossRefGoogle Scholar
  15. 15.
    Balthasar, V. D. P. (1934). Nonlinear theory of electric oscillations. Proceedings of the Institute of Radio Engineers, 22(9), 1051–1086.Google Scholar
  16. 16.
    Gan, K. J., Tsai, C. S., Hsien, C. W., Li, Y. K., & Yeh, W. K. (2011). Design of monostable-bistable transition logic element using the BiCMOS-based negative differential resistance circuit. Analog Integrated Circuits and Signal Processing, 68(3), 379–385.CrossRefGoogle Scholar
  17. 17.
    Gan, K. J., Tsai, C. S., Chen, Y. W., & Yeh, W. K. (2010). Voltage-controlled multiple-valued logic design using negative differential resistance devices. Solid-State Electronics, 54(12), 1637–1640.CrossRefGoogle Scholar
  18. 18.
    Núñez, J., Avedillo, M. J., & Quintana, J. M. (2011). RTD–CMOS pipelined networks for reduced power consumption. IEEE Transactions on Nanotechnology, 10(6), 1217–1220.CrossRefGoogle Scholar
  19. 19.
    Hanafusa, Hiroaki, Hirose, Nobumitsu, Kasamatsu, Akifumi, Mimura, Takashi, Matsui, Toshiaki, Harold, M. H., et al. (2011). Si/Ge hole-tunneling double-barrier resonant tunneling diodes formed on sputtered flat Ge layers. Applied Physics Express, 4(2), 024102.CrossRefGoogle Scholar
  20. 20.
    Nagase, M., & Tokizaki, T. (2014). Bistability characteristics of GaN/AlN resonant tunneling diodes caused by intersubband transition and electron accumulation in quantum well. IEEE Transactions on Electron Devices, 61(5), 1321–1326.CrossRefGoogle Scholar
  21. 21.
    Chua, L. O., Wu, C. W., Huang, A., & Zhong, G. Q. (1993). A universal circuit for studying and generating chaos. I. Routes to chaos. IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications, 40(10), 732–744.MathSciNetCrossRefzbMATHGoogle Scholar
  22. 22.
    Zou, F., & Nossek, J. A. (1993). Bifurcation and chaos in cellular neural networks. IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications, 40(3), 166–173.MathSciNetCrossRefzbMATHGoogle Scholar
  23. 23.
    Rand, R. H., & Holmes, P. J. (1980). Bifurcation of periodic motions in two weakly coupled van der Pol oscillators. International Journal of Non-Linear Mechanics, 15(4–5), 387–399.MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  • Kwang-Jow Gan
    • 1
  • Chun-Yi Guo
    • 1
  • Ping-Feng Wu
    • 1
  • Yaw-Hwang Chen
    • 2
  1. 1.Department of Electrical EngineeringNational Chiayi UniversityChiayi CityTaiwan, ROC
  2. 2.Department of Electronic EngineeringKun Shan UniversityTainan CityTaiwan, ROC

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