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Active RC Filters Using Opamps

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VLSI Analog Filters

Abstract

This chapter deals with the realization of active filters using resistors, capacitors and active devices such as opamp. Simple circuits such as amplifiers, integrators, differentiators, and first-order low-pass, high-pass, and all-pass filters are considered. The effect of finite opamp frequency-dependent gain is considered. Various configurations for realizing second-order filters using single opamp such as Sallen–Key filter, Friend’s biquad, multiple-feedback type, and recently derived circuits using differential output opamp are considered. The design equations, practical considerations such as spread in components, sensitivity to non-ideal opamp, and tolerances of components are derived in detail. Second-order filters which use two opamps, such as GIC-based biquads, and which use three opamps, such as Tow-Thomas biquad, KHN biquad, and Tarmy–Ghausi biquad, are described. Techniques for compensating the finite bandwidth of the opamp in order to extend the performance are described. Second-order filters which use only one capacitor and opamp finite pole (bandwidth) are considered, and two opamp-based active R filters which do not use any capacitors are also studied in detail.

The design of active RC filters derived from passive RLC ladder filters based on operational simulation and component simulation and other techniques such as Yoshihoro’s technique have been considered. Design procedures of low-pass, high-pass, and band-pass types are described. The use of FDNR for realizing low-pass filters is also described. The various multiloop feedback techniques are briefly introduced. Techniques for noise analysis and distortion analysis of active RC filters are described. Several SPICE simulation examples are presented to illustrate modeling of various nonidealities of opamps and analysis of total noise.

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References

  1. Sedra, A.S., Brackett, P.O.: Filter Theory and Design: Active and Passive. Matrix, Beaverton, Champaign (1978)

    Google Scholar 

  2. Moschytz, G.S.: Linear Integrated Networks: Fundamentals. Van Nostrand-Reinhold, New York (1974)

    Google Scholar 

  3. Moschytz, G.S.: Linear Integrated Networks: Design. Van Nostrand-Reinhold, New York (1975)

    Google Scholar 

  4. Deliyannis, T., Sun, Y., Fidler, J.K.: Continuous-Time Active Filter Design. CRC Press, Boca Raton (1999)

    Google Scholar 

  5. Tsividis, Y.P., Voorman, J.O. (eds.): Integrated Continuous-Time Filters. IEEE Press, Piscataway (1993)

    Google Scholar 

  6. Schaumann, R., Ghausi, M.S., Laker, K.R.: Design of Analog Filters: Passive, Active RC, and Switched Capacitor. Prentice Hall, Englewood Cliffs (1990)

    Google Scholar 

  7. Ghausi, M.S., Laker, K.R.: Modern Filter Design. Prentice-Hall, Englewood Cliffs (1981)

    Google Scholar 

  8. Temes, G.C., Mitra, S.K. (eds.): Modern Filter Theory and Design. Wiley, New York (1973)

    Google Scholar 

  9. Daryanani, G.: Principles of Active Network Synthesis and Design. Wiley, New York (1976)

    Google Scholar 

  10. Huelsman, L.P., Allen, P.E.: Introduction to the Theory and Design of Active Filters. McGraw-Hill, New York (1980)

    Google Scholar 

  11. Bruton, L.T.: Active RC Circuits. Prentice-Hall, Englewood Cliffs (1980)

    Google Scholar 

  12. Unbehauen, R., Cichocki, A.: MOS Switched-Capacitor and Continuous-time Integrated Circuits and Systems. Springer, Berlin (1989)

    Book  Google Scholar 

  13. Budak, A.: Passive and Active Network Analysis and Synthesis. Waveland Press, Prospect Heights (1991)

    Google Scholar 

  14. Ghausi, M.S.: Analog active filters. IEEE Trans. Circuits Syst. CAS-31, 13–31 (1984)

    Article  Google Scholar 

  15. Soundararajan, K., Ramakrishna, K.: Characteristics of non-ideal operational amplifiers. IEEE Trans. Circuits Syst. CAS-21, 69–75 (1974)

    Article  Google Scholar 

  16. Wilson, G.: Compensation of some operational-amplifier based RC-active networks. IEEE Trans. Circuits Syst. 23, 443–446 (1976)

    Article  Google Scholar 

  17. Soliman, A.N., Ismail, M.: Active compensation of Opamps. IEEE Trans. Circuits Syst. 26, 112–117 (1979)

    Article  Google Scholar 

  18. Ravichandran, S., Rao, K.R.: A novel active compensation scheme for active-RC filters. Proc. IEEE 68, 743–744 (1980)

    Article  Google Scholar 

  19. Boutin, N.: Active compensation of op-amp inverting amplifier using NIC. Electron. Lett. 17, 978–979 (1981)

    Article  Google Scholar 

  20. Ananda Mohan, P.V.: Active compensation of Opamp Inverting Amplifier using NIC. AEU 42, 192–194 (1988)

    Google Scholar 

  21. Brackett, P.O., Sedra, A.S.: Active compensation for high-frequency Op-Amp circuits with applications in active RC filters. IEEE Trans. Circuits Syst. 23, 68–72 (1976)

    Article  Google Scholar 

  22. DeBoo, G.J.: A novel integrator results by grounding its capacitor. Electron. Des. 15 (1967)

    Google Scholar 

  23. Thomas, L.C.: The biquad: part-I- some practical design considerations. IEEE Trans. Circuit Theory CT-18, 350–361 (1971)

    Article  Google Scholar 

  24. Akerberg, D., Mossberg, K.: A versatile active RC building block with inherent compensation for the finite bandwidth of the amplifier. IEEE Trans. Circuits Syst. 21, 75–78 (1974)

    Article  Google Scholar 

  25. Tsividis, Y.P.: Integrated continuous-time filter design-an overview. IEEE J. Solid-State Circuits 29, 166–176 (1994)

    Article  Google Scholar 

  26. Ponsonby, J.E.B.: Active all-pass filter using a differential operational amplifier. Electron. Lett. 2, 134–135 (1966)

    Article  Google Scholar 

  27. Sallen, R.P., Key, W.L.: A practical method of designing active RC filters. IEEE Trans. Circuit Theory CT-2, 74–85 (1955)

    Google Scholar 

  28. Gray, P.R., Meyer, R.G.: Analysis and Design of Analog Integrated Circuits, 2nd edn. Wiley, New York (1982)

    Google Scholar 

  29. Friend, J., Harris, C.A., Hilberman, D.: STAR: an active biquadratic filter section. IEEE Trans. Circuits Syst. 22, 115–121 (1975)

    Article  Google Scholar 

  30. Fleischer, P.E.: Sensitivity minimization in a single amplifier biquad circuit. IEEE Trans. Circuits Syst. CAS-23, 45–55 (1976)

    Article  Google Scholar 

  31. Deliyannis, T.: High Q-factor circuit with reduced sensitivity. Electron. Lett. 4, 577 (1968)

    Article  Google Scholar 

  32. Moschytz, G.S.: Gain sensitivity product – a figure of merit for hybrid integrated filters using single operational amplifiers. IEEE J. Solid-State Circuits SC- 6, 103–110 (1971)

    Article  Google Scholar 

  33. Moschytz, G.S., Horn, P.: Reducing non-ideal opamp effects in active filters by minimizing the gain-sensitivity product. IEEE Trans. Circuits Syst. CAS-24, 437–445 (1977)

    Article  Google Scholar 

  34. Ford, R.L., Girling, F.E.J.: Active filters and oscillators using simulated inductance. Electron. Lett. 2, 52 (1966)

    Article  Google Scholar 

  35. Chandra, G., Tadeparthy, P., Easwaran, P.: Single amplifier bi-quadratic filter topologies in transimpedance configuration. IEEE Trans. Circuits Syst. 55, 502–507 (2008)

    Article  Google Scholar 

  36. Ananda Mohan, P.V.: On single amplifier bi-quadratic topologies in transimpedance configuration. In: Proceedings of TENCON 2009-IEEE Region 10 Conference. doi:10.1109/TENCON.2009.5395967, pp. 1–6 (2009)

  37. Antoniou, A.: Realization of gyrators using operational amplifiers and their use in RC active network synthesis. Proc. IEE 116, 1838–1850 (1969)

    Google Scholar 

  38. Ananda Mohan, P.V., Ramachandran, V., Swamy, M.N.S.: New General Biquadratic Active RC and SC Filters. Proc. IEE, Part G, ECS 131, 51–55 (1984)

    Google Scholar 

  39. Kerwin, W.J., Huelsman, L.P., Newcomb, R.W.: State-variable synthesis for insensitive integrated circuit transfer functions. IEEE J. Solid-State Circuits 2, 87–92 (1973)

    Article  Google Scholar 

  40. Ananda Mohan, P.V., Ramachandran, V., Swamy, M.N.S.: Formulas for dynamic-range evaluation of second-order discrete-time filter. IEEE Trans. Circuits Syst. 30, 321 (1983)

    Article  Google Scholar 

  41. Ananda Mohan, P.V., Ramachandran, V., Swamy, M.N.S.: Nodal voltage simulation of active RC networks. IEEE Trans. Circuits Syst. 32, 1085–1088 (1985)

    Article  Google Scholar 

  42. Soliman, A.M.: History and progress of the Tow–Thomas bi-quadratic filter. Part I: generation and Op amp realizations. J. Circuits Syst. Comput. 17, 33–54 (2008)

    Article  Google Scholar 

  43. Moustakas, E., Chan, S.: Sensitivity considerations in a multiple-feedback universal active filter. IEEE Trans. Circuits Syst. 24, 695–703 (1977)

    Article  MATH  Google Scholar 

  44. Tarmy, R., Ghausi, M.S.: Very high-Q insensitive active RC networks. IEEE Trans. Circuit Theory CT-17, 358–366 (1970)

    Article  Google Scholar 

  45. Moschytz, G.S.: High-Q factor insensitive active RC network similar to the Tarmy-Ghausi circuit, but using single-ended operational amplifiers. Electron. Lett. 8, 458–459 (1972)

    Article  Google Scholar 

  46. Mulawka, J., Bialko, M.: Modifications of Tarmy-Ghausi active filter. Electron. Lett. 10(18), 380–381 (1974)

    Article  Google Scholar 

  47. Toker, A., Ozoguz, S., Cicekoglu, O., Acar, C.: Current-mode all-pass filters using current differencing buffered amplifier and a new high-Q band-pass filter configuration. IEEE Trans. Circuits Syst.-II: Analog Digit. Signal Process. 47, 949–954 (2)

    Article  Google Scholar 

  48. Soliman, A.M., Fawzy, M.: A bandpass filter using the operational amplifier pole. IEEE J. Solid-Sate Circuits SC-12, 429–430 (1977)

    Article  Google Scholar 

  49. Ananda Mohan, P.V.: A novel band-pass filter using the amplifier pole. IEEE J. Solid-State Circuits 14, 649–651 (1979)

    Article  Google Scholar 

  50. Tobey, T.E., Greame, J.G., Huelsman, L.P.: Operational Amplifier: Design and Applications. McGraw-Hill, New York (1971)

    Google Scholar 

  51. Rao, K.R., Srinivasan, S.: A bandpass filter using the operational amplifier pole. IEEE J. Solid-State Circuits SC-8, 245–246 (1973)

    Article  Google Scholar 

  52. Ananda Mohan, P.V.: Low-pass and notch filters using the operational amplifier pole. Proc. IEEE 67, 1160–1162 (1979)

    Article  Google Scholar 

  53. Ananda Mohan, P.V.: Novel active filters using the amplifier pole. Electron. Lett. 16, 378–380 (1980)

    Article  Google Scholar 

  54. Mitra, A.K., Aatre, V.K.: Low sensitivity high-frequency active R filters. IEEE Trans. Circuits Syst. 23, 670–676 (1976)

    Article  Google Scholar 

  55. Rao, K.R., Srinivasan, S.: Low-sensitivity active filters using the operational amplifier pole. IEEE Trans. Circuits Syst. CAS-21, 260–262 (1974)

    Article  Google Scholar 

  56. Schaumann, R.: Low-sensitivity High-frequency tunable active filters without external capacitors. IEEE Trans. Circuits Syst. CAS-22, 39–44 (1974)

    Google Scholar 

  57. Orchard, H.J.: Inductorless filters. Electron. Lett. 2, 24–25 (1966)

    Article  Google Scholar 

  58. Riordan, R.H.S.: Simulated inductors using differential amplifiers. Electron. Lett. 3(2) (1967)

    Google Scholar 

  59. Bruton, L.: Network transfer functions using the concept of frequency dependent negative resistance. IEEE Trans. Circuit Theory 16, 406–408 (1969)

    Article  Google Scholar 

  60. Allstot, D.J., Brodersen, R.W., Gray, P.R.: Design techniques for MOS switched capacitor ladder filters. IEEE Trans. Circuits Syst. CAS-25, 1014–1021 (1978)

    Google Scholar 

  61. Yoshihoro, M., Nishihra, A., Yanagisawa, T.: Low-sensitivity active and digital filters based on the node voltage simulation of LC ladder structures. In: Proceedings of IEEE International Symposium on Circuits and Systems, AZ, pp. 446–449 (1977)

    Google Scholar 

  62. Ananda Mohan, P.V.: Operational simulation of high-pass RLC filters. Electron. Lett. 24, 779–780 (1988)

    Article  Google Scholar 

  63. Martin, K., Sedra, A.S.: Exact design of Switched capacitor band-pass filters using coupled biquad structures. IEEE Trans. Circuits Syst. CAS-27, 469–475 (1980)

    Article  Google Scholar 

  64. Laker, K.R., Schaumann, R., Ghausi, M.S.: Multiple-loop feedback topologies for the design of low-sensitivity active filters. IEEE Trans. Circuits Syst. 26, 1–21 (1979)

    Article  Google Scholar 

  65. Bruton, L.T., Trofimenkoff, F.N., Treleaven, D.H.: Noise performance of low-sensitivity active filters. IEEE J. Solid-State Circuits SC-8, 85–91 (1973)

    Article  Google Scholar 

  66. Trofimenkoff, F.N., Treleaven, D.H., Bruton, L.T.: Noise performance of RC active quadratic filter sections. IEEE Trans. Circuits Syst. CT-5, 524–532 (1973)

    Google Scholar 

  67. Bachler, H.J., Guggenbuhl, W.: Noise analysis and comparison of second-order networks containing a single amplifier. IEEE Trans. Circuits Syst. 27, 85–91 (1980)

    Article  Google Scholar 

  68. Bachler, H.J., Guggenbuhl, W.: Noise and Sensitivity optimization of a single-amplifier biquad. IEEE Trans. Circuits Syst. 26, 30–36 (1979)

    Article  Google Scholar 

  69. Billam, P.J.: Practical optimization of noise and distortion in Sallen and Key filter sections. IEEE J. Solid-State Circuits 14, 768–771 (1979)

    Article  Google Scholar 

  70. Allen, P.E.: Slew-induced distortion in operational amplifiers. IEEE J. Solid-State Circuits 12, 39–44 (1977)

    Article  Google Scholar 

  71. Allen, P.E.: A model for Slew-induced distortion in single-amplifier active RC filters. IEEE Trans. Circuits Syst. 25, 565–572 (1978)

    Article  Google Scholar 

  72. Borys, A.: A relationship between different measures of non-linear distortion in single-amplifier active filters. IEEE Trans. Circuits Syst. 30, 842–846 (1983)

    Article  Google Scholar 

  73. Borys, A.: A note on general Gain-sensitivity product and complementary transformation. IEEE Trans. Circuits Syst. 37, 1324–1325 (1990)

    Article  Google Scholar 

  74. Borys, A.: Slew-induced distortion of single-amplifier active filters using the gain-sensitivity-product concept. IEEE Trans. Circuits Syst. CAS-31, 306–308 (1984)

    Article  Google Scholar 

  75. Hilberman, D.: Input and ground as complements in active filters. IEEE Trans. Circuit Theory CT-20, 540–547 (1973)

    Google Scholar 

  76. Mikhael, W.B., Bhattacharyya, B.B.: A practical design for insensitive RC-filters. IEEE Trans. Circuits Syst. CAS-22, 407–425 (1975)

    Article  Google Scholar 

  77. Padukone, P.R., Mulawka, J., Ghausi, M.S.: An active biquadratic section with reduced sensitivity to operational amplifier imperfections. J. Franklin Inst. 310, 27–40 (1980)

    Article  Google Scholar 

  78. Wilson, G., Bedri, Y., Bowron, P.: RC-active networks with reduced sensitivity to amplifier gain-bandwidth product. IEEE Trans. Circuits Syst. CAS-21, 618–626 (1974)

    Article  Google Scholar 

  79. Sedra, A.S., Brown, L.: A simple all-pass network with complex poles and zeros. IEEE Trans. Circuit Theory. CT-, 445–446 (1973)

    Google Scholar 

  80. Bach, R.E.: Selecting RC values for active filters. Electronics 33, 82–85 (1960)

    Google Scholar 

  81. Moschytz, G.S.: A note on pole, frequency and Q – sensitivity. IEEE J. Solid-State Circuits SC-6, 267–269 (1871)

    Google Scholar 

  82. Geiger, R.L.: Amplifiers with maximum bandwidth. IEEE Trans. Circuits Syst. 24, 510–512 (1977)

    Article  Google Scholar 

  83. Michael, S., Mikhael, W.B.: Inverting integrator and active filter applications of composite operational amplifiers. IEEE Trans. Circuits Syst. CAS-34, 461–470 (1987)

    Article  Google Scholar 

  84. Natarajan, S., Bhattacharyya, B.B.: Design of actively compensated finite gain Amplifiers for high-frequency applications. IEEE Trans. Circuits Syst. CAS-27, 1133–1139 (1980)

    Article  Google Scholar 

  85. Prescott, A.J.: Loss compensated active gyrator using differential-input operational amplifiers. Electron. Lett. 2, 283–284 (1966)

    Article  Google Scholar 

  86. Berndt, D., Dutta Roy, S.C.: Inductor simulation using a single unity gain amplifier. IEEE J. Solid-State Circuits SC-4, 161–162 (1969)

    Article  Google Scholar 

  87. Dutta Roy, S.C., Nagarajan, V.: On inductor simulation using a unity-gain amplifier. IEEE J. Solid-State Circuits SC-5, 95–98 (1970)

    Google Scholar 

  88. Molo, F.: Parallel resonator with a resistance and a frequency dependent negative resistance realized with a single operational amplifier. IEEE Trans. Circuits Syst. CAS-21, 783–788 (1974)

    Article  Google Scholar 

  89. Ahuja, B.K.: Implementation of active distributed RC anti-aliasing/smoothing filters. IEEE J. Solid-State Circuits SC-17, 1076–1080 (1982)

    Article  Google Scholar 

  90. Mitra, S.K.: Synthesizing active filters. IEEE Spectr. 46–63 (1969)

    Google Scholar 

  91. Soderstand, M.A., Mitra, S.K.: Gain and sensitivity limitations of active RC filters. IEEE Trans. Circuit Theory CT-18, 600–609 (1971)

    Article  Google Scholar 

  92. Comer, D.J., McDermid, J.E.: Inductorless bandpass characteristics using all-pass networks. IEEE Trans. Circuit Theory 15, 501–503 (1968)

    Article  Google Scholar 

  93. Dalpadado, R.N.G.: A class of high-Q high-frequency two amplifier active RC networks. IEEE Trans. Circuits Syst. CAS-25, 1099–1101 (1978)

    Article  Google Scholar 

  94. Kim, H.K., Ra, J.B.: An active biquadratic building block without external capacitors. IEEE Trans. Circuits Syst. CAS-24, 689–694 (1977)

    Google Scholar 

  95. Carlosena, A.V., Cabral, E.: Novel transimpedance filter topology for instrumentation. IEEE Trans. Instrum. Meas. 46, 862–867 (1997)

    Article  Google Scholar 

  96. Higashimura, M., Fukui, Y.: Realization of current-mode all-pass networks using a single current conveyor. IEEE Trans. Circuits Syst. 37, 660–661 (1990)

    Article  Google Scholar 

  97. Abuelmaatti, M.T.: Two minimum component CC II based RC oscillators. IEEE Trans. Circuits Syst. 34, 980–981 (1987)

    Article  Google Scholar 

  98. Abuelmaatti, M.T., et al.: Novel RC oscillators using current feedback operational amplifiers. IEEE Trans. Circuits Syst. 43, 155–157 (1996)

    Article  Google Scholar 

  99. Bhaskar, D.R.: Single resistance controlled sinusoidal oscillator using single FTFN. Electron. Lett. 35, 190 (1999)

    Article  Google Scholar 

  100. Ananda Mohan, P.V.: Grounded capacitor based grounded and floating inductance simulation using current conveyors. Electron. Lett. 34, 1037–1038 (1998)

    Article  Google Scholar 

  101. Singh, V.K., Senani, R.: New multifunction active filter configuration employing current conveyors. Electron. Lett. 26, 1814–1816 (1990)

    Article  Google Scholar 

  102. Sedra, A.S., Ghorab, M.A., Martin, K.: Optimum configurations for single amplifier biquadratic filters. IEEE Trans. Circuits Syst. 27, 1155–1163 (1980)

    Article  Google Scholar 

  103. Allen, P.E., Holberg, D.R.: CMOS Analog Circuit Design. Oxford University Press, New York (2002)

    Google Scholar 

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  1. Electronics Corporation of India, Ltd., Bangalore, India

    P. V. Ananda Mohan

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Mohan, P.V.A. (2013). Active RC Filters Using Opamps. In: VLSI Analog Filters. Modeling and Simulation in Science, Engineering and Technology. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-0-8176-8358-0_2

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