Dynamic modeling of tunable analog integrated filters for a stability study of on-chip automatic tuning loops

Abstract

Continuous-time filters with automatic tuning loops are nonlinear feedback systems that are potentially unstable. To ensure stability, particularly if the design of the loop controllers is to be improved, the appropriate linear dynamic modeling of the tunable filter, including control inputs, should be attained. This work aims to present a general dynamic modeling of continuous-time analog filters with automatic tuning capability. The general analysis leads to an equivalent small-signal linearized incremental model, from which transfer functions between output variables and control voltages are obtained. Subsequent to the analysis, it is possible to design compensated loops with enhanced stability and dynamic performance. By way of example, the modeling of a particular band-pass CMOS continuous-time analog filter is presented in this paper. Two transfer functions are derived: the transfer function between the output phase shift and the central frequency control voltage, and that between the output amplitude and the quality factor control voltage. These functions are required to properly tune the central frequency and quality factor parameters. This modeling makes it possible to propose an adaptive controller with improved stability and a possible implementation for such a controller. Finally, experimental results are shown for a CMOS 0.8 μm technology.

This is a preview of subscription content, access via your institution.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16

References

  1. 1.

    Tsividis, Y. P., & Voorman, J. O. (1993). Integrated continuous-time filters: Principles, design and applications. A selected reprints volume. IEEE Press.

  2. 2.

    Tsividis, Y. P. (1981). Self-tuned filters. Electronics Letters, 17(12), 406–407.

    Article  Google Scholar 

  3. 3.

    Schaumann, R., & Mehmet, A. T. (1989, May). The problem of on-chip automatic tuning in continuous-time integrated filters. Proceedings of the IEEE International Symposium on Circuits and Systems (ISCAS’89) (pp. 106–109).

  4. 4.

    Sümesaglam, T., & Karsilayan, A. I. (2003). A digital approach for automatic tuning of continuous-time high-Q filters. IEEE Transactions on Circuits and Systems-II: Analog And Digital Signal Processing, 50(10), 755–761.

    Article  Google Scholar 

  5. 5.

    Banu, M., & Tsividis, Y. (1985). An elliptic continuous-time CMOS filter with on-chip automatic tuning. IEEE Journal of Solid–State Circuits, 20(6), 1114–1121.

    Article  Google Scholar 

  6. 6.

    Karsilayan, A. I., & Schaumann, R. (1998, June). Automatic tuning of frequency and Q-factor of bandpass filters based on envelope detection. Proceedings of the IEEE International Symposium on Circuits and Systems (ISCAS’98) (pp. I–65–I–68).

  7. 7.

    Kallam, P., Sinencio, S. E., & Karsilayan, A. I. (2003). An enhanced adaptive Q-tuning scheme for a 100-MHz fully symmetric OTA-based bandpass filter. IEEE Journal of Solid-State Circuits, 38(4), 585–593.

    Article  Google Scholar 

  8. 8.

    Kozma, K. A., Johns, D. A., & Sedra, A. S. (1995, April). An approach for tuning high-Q continuous-time bandpass filters. Proceedings of the IEEE International Symposium on Circuits and Systems (ISCAS’95) (pp. 1037–1040).

  9. 9.

    Wada, K., Takagi, S., & Fujii, N. (1998). Automatic tuning system for integrator-based continuous-time filters. Analog Integrated Circuits and Signal Processing, 16(3), 225–238.

    Article  Google Scholar 

  10. 10.

    Wyszynski, A., & Schaumann, R. (1994, May). Frequency and phase tuning of continuous-time integrated filters using common mode signals. Proceedings of the IEEE International Symposium on Circuits and Systems (ISCAS’94), 5, 269–272.

  11. 11.

    Yamazaki, H., Oishi, K., & Gotoh, K. (1999). An accurate center frequency tuning scheme for 450-kHz CMOS Gm–C bandpass filters. IEEE Journal of Solid-State Circuits, 34(12), 1691–1697.

    Article  Google Scholar 

  12. 12.

    Yoo, C., Lee, S.-W., & Kim, W. (1998). A ±1.5-V, 4-MHz CMOS continuous-time filter with a single-integrator based tuning. IEEE Journal of Solid-State Circuits, 33(1), 18–27.

    Article  Google Scholar 

  13. 13.

    Groeneworld, G. (2000). Low-power MOSFET-C 120 MHz bessel allpass filter with extended tuning range. IEE Proc Circuits Devices System, 147(1), 28–34.

    Article  Google Scholar 

  14. 14.

    Mingdeng, C., Silva–Martínez, J., Rokhsaz, S., & Robinson, M. (2003). A 2-Vpp 80–200-MHz fourth-order continuous-time linear phase filter with automatic frequency tuning. IEEE Journal of Solid-State Circuits, 38(10), 1745–1749.

    Article  Google Scholar 

  15. 15.

    Liu, H., & Karsilayan, A. I. (2003). An Accurate automatic tuning scheme for high-Q continuous-time bandpass filters based on amplitude comparison. IEEE Transactions on Circuits and Systems–II: Analog and Digital Signal Processing, 50(8), 415–423.

    Article  Google Scholar 

  16. 16.

    Yoshizawa, A., & Tsividis, Y. P. (2002). Anti-blocker design techniques for MOSFET-C filters for direct conversion receivers. IEEE Journal of Solid-State Circuits, 37(3), 357–364.

    Article  Google Scholar 

  17. 17.

    Silva–Martínez, J., Adut, J., Rocha–Perez, J. M., Robinson, M., & Rokhsaz, S. (2003). A 60-mW 200-MHz continuous-time seventh-order linear phase filter with on-chip automatic tuning system. IEEE Journal of Solid-State Circuits, 38(2), 216–225.

    Article  Google Scholar 

  18. 18.

    Liu, H., & Karsilayan, A. I. (2002, May). An automatic tuning scheme for high frequency bandpass filters. Proceedings of the IEEE International Symposium on Circuits and Systems (ISCAS’02) (pp. III-551–III-554).

  19. 19.

    Karsilayan, A. I., Huang, S.-L., & De Lima, J. A. (2002, May). Automatic tuning of linearly tunable high-Q filters. Proceedings of the IEEE International Symposium on Circuits and Systems (ISCAS’02), (V-177–V-180).

  20. 20.

    Erickson, R. W., & Maksimovic, D. (2001). Fundamentals of power electronics. The Netherlands: Kluwer.

    Google Scholar 

  21. 21.

    Carlosena, A., & Cabral, E. (1997). Novel transimpedance filter topology for instrumentation. IEEE Transactions on Instrumentation and Measurement, 46(4), 862–867.

    Article  Google Scholar 

  22. 22.

    Tsividis, Y., Banu, M., & Khoury, J. (1986). Continuous-time MOSFET-C filters in VLSI. IEEE Journal of Solid-State Circuits, 21(1), 15–30.

    Article  Google Scholar 

  23. 23.

    Tsividis, Y., Banu, M., & Khoury, J. (1986). Continuous-time MOSFET-C filters in VLSI. IEEE Transactions on Circuits and Systems, CAS-33(2), 125–140.

    Article  Google Scholar 

  24. 24.

    Schaumann, R., Ghausi, M. S., & Laker, R. L. (1990). Design of analog filters. Passive, active RC, and switched capacitor. USA: Prentice–Hall.

    Google Scholar 

  25. 25.

    Kozma, K. A., Johns, D. A., & Sedra, A. S. (1991). Automatic tuning of continuous-time integrated filters using an adaptive filter technique. IEEE Transactions on Circuits and Systems, 38(11), 1241–1248.

    Article  Google Scholar 

  26. 26.

    Sanders, S. R., Noworolski, J. M., Liu, X. Z., & Verghese, G. C. (1991). Genereralized averaging method for power conversion circuits. IEEE Transactions on Power Electronics, 6(2), 251–259.

    Article  Google Scholar 

  27. 27.

    Ogata, K. (1997). Modern control engineering (3rd ed.). USA: Prentice–Hall.

    Google Scholar 

  28. 28.

    Omeni, O., Rodríguez–Villegas, E., & Toumazou, C. (2005). A micropower CMOS continuous-time filter with on-chip automatic tuning. IEEE Transactions on Circuits and Systems–I: Regular Papers, 52(4), 695–705.

    Article  Google Scholar 

  29. 29.

    Serra-Graells, F., Gómez, L., & Huertas, J. L. (2004). A True-1-V 300 μW CMOS-subthreshold log-domain hearing-aid-on-chip. IEEE Journal of Solid–State Circuits, 39(8), 1271–1281.

    Article  Google Scholar 

  30. 30.

    Sunyoung, K., Lee, J.-Y., Song, S.-J., Cho, N., & Yoo, H.-J. (Jun. 2005). An energy-efficient analog front-end circuit for a sub-1 V digital hearing aid chip. Symposium on VLSI Circuits 2005. Digest of Technical Papers, (pp. 176–179).

  31. 31.

    Ahmadi S., & Zaghloul, M. (2001, May). Signal conditioning for fabry-perot sensor. Proceedings of the IEEE International Symposium on Circuits and Systems (ISCAS’01) (2, 277–280).

  32. 32.

    Czarnul, Z. (1986). Novel MOS resistive circuit for synthesis of fully integrated continuous-time filters. IEEE Transactions on Circuits and Systems, CAS-33(7), 718–721.

    Article  Google Scholar 

  33. 33.

    Ismail, M., Smith, S. V., & Beales, R. G. (1988). A New MOSFET-C Universal Filter Structure for VLSI. IEEE Journal on solid-State Circuits, 23(1), 183–194.

    Article  Google Scholar 

  34. 34.

    Osa, J. I., Porta, S., & Carlosena, A. (1998, May). The most resistive model for the MOS resistive circuit. Proceedings of the IEEE International Symposium on Circuits and Systems (ISCAS’98) (pp. 208–211).

  35. 35.

    Vidal, E., Martínez, H., Alarcón, E., & Poveda, A. (1999, August). Nonlinear analytical model of the MRC (MOS Resistive Circuit). Proceedings of the 42th IEEE Midwest Symposium on Circuits and Systems (MWSCAS’99) (pp. 1122–1125). USA: Las Cruces.

  36. 36.

    Vidal, E., Porta, S., Martínez, H., Alarcón, E., & Poveda, A. (2000, June). Complete nonlinear model of the MRC (MOS Resistive Circuit). Proceedings of the IEEE International Symposium on Circuits and Systems (ISCAS’00) (pp. 140–143). Geneva, Switzerland.

  37. 37.

    Martínez, H., Vidal, E., Alarcón, E., & Poveda, A. (2001, August). Design and implementation of an MRC-C TQE filter with on-chip automatic tuning. Proceedings of the 44th IEEE Midwest Symposium on Circuits and Systems (MWSCAS’01). USA: Dayton.

  38. 38.

    Martínez, H., Vidal, E., Alarcón, E., & Poveda, A. (2006, May). Improving the stability of on-chip automatic tuning loops for continuous-time filters with analog adaptive controller. Proceedings of the IEEE International Symposium on Circuits and Systems (ISCAS’06). Greece: Isle of Kos.

  39. 39.

    Alzaher, H. A., Elwan, H., & Ismail, M. (2000). CMOS digitally programmable filter for multi-standard wireless receivers. Electronics Letters, 36(2), 133–135.

    Article  Google Scholar 

  40. 40.

    Alzaher, H. A., Elwan, H., & Ismail, M. (2000). CMOS baseband filter for WCDMA integrated wireless receivers. Electronics Letters, 36(18), 1515–1516.

    Article  Google Scholar 

  41. 41.

    Smith, J. (1986). Modern communication circuits. New York: McGraw–Hill.

    Google Scholar 

Download references

Acknowledgment

This work has been partially funded by project TEC2004-05608-C02-01 (-02) from the Spanish MCYT and EU FEDER funds.

Author information

Affiliations

Authors

Corresponding author

Correspondence to Herminio Martínez.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Martínez, H., Vidal, E., Alarcón, E. et al. Dynamic modeling of tunable analog integrated filters for a stability study of on-chip automatic tuning loops. Analog Integr Circ Sig Process 61, 231 (2009). https://doi.org/10.1007/s10470-009-9314-x

Download citation

Keywords

  • Analog integrated circuits
  • CMOS technology
  • Continuous-time filters (CTF)
  • Dynamic modeling
  • Self-tuning circuits