Linearity of bulk-controlled inverter ring VCO in weak and strong inversion



In this paper linearity of frequency modulation in voltage controlled inverter ring oscillators for non feedback sigma delta converter applications is studied. The linearity is studied through theoretical models of the oscillator operating at supply voltages above and below the threshold voltage of a transistor, bringing the transistors in respectively strong and weak inversion. The theoretical results are tested with more advanced models through spectreRF simulations. A soft rail approach implemented to improve linearity in weak inversion is proposed and demonstrated. The influence from voltage noise, process variations and temperature variations have also been simulated to indicate the advantages of having the soft rail bias transistor in the VCO.


Inverter ring Linear modulation Weak inversion VCO FDSM 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    M. Høvin, A. Olsen, T.S. Lande, and C. Toumazou, “Delta-sigma modulators using frequency-modulated intermediate values.” IEEE JSSC, vol. 32, no. 1, pp. 13–22, 1997.Google Scholar
  2. 2.
    A. Hajimiri, S. Limotyrakis, and T.H. Lee, “Jitter and phase noise in ring oscillators.” IEEE JSSC, vol. 34, no. 6, pp. 790–804, 1999.Google Scholar
  3. 3.
    Y.U. Young, J.F. McDonald, and R.P. Kraft. “12–23 GHz ultra wide tuning range voltage-controlled ring oscillator with hybrid control schemes.” In Proc. IEEE Computer Society Annual Symposium on VLSI 2005, 2005, pp. 278–279.Google Scholar
  4. 4.
    S. Aunet, B. Oelmann, T.S. Lande, and Y. Berg, “Multifunction subthreshold gate used for a low power full adder.” In Proc. Norchip Conference 2004, 2004, pp. 44–47.Google Scholar
  5. 5.
    R.R. Pal, H.N. Acharya, S. Kai, and N.B. Chakrabarti, “Voltage controlled oscillators using complementary current mirror inverter.” IEE Electronics Letters, vol. 28, no. 18, pp. 1701–1702, 1992.Google Scholar
  6. 6.
    A. Hajimiri and T.H. Lee, “A general theory of phase noise in electrical oscillators.” IEEE JSSC, vol. 33, no. 2, pp. 179–194, 1998.Google Scholar
  7. 7.
    S.A. Wartenberg and J.R. Hauser, “Substrate voltage and accumulation-mode MOS varactor capacitance.” IEEE Transactions on Electron Devices, vol. 52, no. 7, pp. 1563–1567, 2005.Google Scholar
  8. 8.
    M.J. Deen, M.H. Kazemeini, and S. Naseh, “Performance characteristics of an ultra-low power VCO.” In Proc. International Symposium on Circuits and Systems ISCAS03, May 2003, pp. 697–700.Google Scholar
  9. 9.
    Y. Tsividis, Operation and Modeling of the MOS Transistor, Oxford University Press, Oxford, 1999.Google Scholar
  10. 10.
    W. Fichtner and H.W. Potzl, “MOS modelling by analytical approximations. I. Subthreshold current and threshold voltage.” International Journal of Electronics, vol. 46, no. 1, pp. 33–55, 1979.Google Scholar
  11. 11.
    M. Yoshida, “Mosfet carrier mobility model based on gate oxide thickness, threshold and gate voltages.” Solid-State Electronics, vol. 39, no. 10, pp. 1515–1518, 1996.Google Scholar

Copyright information

© Springer Science + Business Media, LLC 2006

Authors and Affiliations

  1. 1.Centre for Physical Electronics, Ørsted·DTUTechnical University of DenmarkKgs. LyngbyDenmark
  2. 2.Microelectronic Systems, Department of InformaticsUniversity of OsloOsloNorway

Personalised recommendations