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Appendix A TABLES OF FILTER FUNCTIONS 378 Appendix A Tables of Filter Functions 379 380 Appendix A Tables of Filter Functions 381 382 Appendix A Tables of Filter Functions 383 384 Appendix A Tables of Filter Functions 385 386 Appendix A Tables of Filter Functions 387 388 Appendix A Tables of Filter Functions 389 390 Appendix A Tables of Filter Functions 391 In Tables A.15 through A.18, it is assumed that the network functions have the form where represents the real pole when is odd. The pass band has been normalized to unity. In other words, The coefficient K has been calibrated such that 392 Appendix A Tables of Filter Functions 393 394 Appendix A Bibliography [AM] D. Åkerberg and Mossberg, “A versatile active RC building block with inherent compensation for the finite bandwidth of the ampli- fier,” IEEE Trans. Circuits and Systems, vol. CAS-21, pp. 75-78, Jan. 1974. [An] A. Antoniou, “Gyrators using operational amplifiers,” Electron- ics Letters, vol. 3, pp. 350-352, Aug. 1967; and “Realization of gyrators using operational amplifiers and their use in RC-active network synthesis,” Proc. IEE, vol. 116, pp. 1838-1850, Nov. 1969. [Ba] J. R. Bainter, “Active filter has stable notch, and response can be regulated,” Electronics, vol. pp. 115-117, Oct. 2, 1975. [Bo] H. W. Bode, Network Analysis and Feedback Amplifier Design, D. Van Nostrand Co., Inc., New York, 1945. [BGH] R. W. Brodersen, P. R. Gray, and D. A. Hodges, “MOS switched capacitor filters,” Proc. IEEE, vol. 67, pp. 61-75, Jan. 1979. [Br] L. T. Bruton, “Frequency selectivity using positive impedance converter-type networks,” Proc. IEEE, vol. 56, pp. 1378-1379, Aug. 1968; and “Network transfer function using the concept of frequency dependent negative resistance,” IEEE Trans. Circuit Theory, vol. CT-18, pp. 406-408, Aug. 1969. [Bu] S. Butterworth, “On the theory of filter amplifiers,” Wireless Engineering, vol. 7, pp. 536-541, Oct. 1930. [Ca] W. Cauer, Siebschaltungen, V.D.I. Verlag, G.m.b.H., Berlin, 1931. [Da] S. Darlington, “Synthesis of reactance 4-pole which produce pre- scribed insertion loss characteristics,” Journ. Math. Phys., vol. 18, pp. 257-353, Sept. 1939. 396 BIBLIOGRAPHY [De1] T. Delyiannis, “RC active allpass sections,” Electronics Letters, vol. 5, pp. 59-60, Feb. 1969. [De2] T. Delyiannis, “High-Q factor circuit with reduced sensitivity,” Electronics Letters, vol. 4, p. 577, Dec. 1968. [DSF] T. Delyiannis, Y. Sun, and J. K. Fidler, Continuous-Time Active Filter Design, CRC Press LLC, Boca Raton, Florida, 1999. [FT] P. E. Fleischer and J. Tow, “Design formulas for biquad active filters using three operational amplifiers,” Proc. IEEE, vol. 61, pp. 662-663, May 1973. [GG] F. E. J. Girling and E. F. Good, “Active Filters–12 and 13; The leap-frog or active ladder synthesis, Application of the active lad- der synthesis,” Wireless World, vol. 76, pp. 341-345, July 1970, and pp. 445-450, Sept. 1970. [Go] J. Gorski-Popiel, “RC-Active synthesis using positive-immitance converters,” Electronics Letters, vol. 3, pp. 381-382, Aug. 1967. [Gr] A. J. Grossman, “Synthesis of Tchebycheff parameter symmetri- cal filters,” Proc. IRE, vol. 45, pp. 454-473, April, 1957. [GS ] R. L. Geiger and E. Sánchez-Sinencio, “Active filter design us- ing operational transconductance amplifier: a tutorial,” IEEE Circuits and Devices Magazine, vol. 1, no. 2, pp. 20-32, March, 1985. [Gu] E. A. Guillemin, Synthesis of Passive Networks, John Wiley and Sons, Inc., New York, 1957. [HBG] B. J. Hosticka, R. W. Brodersen, and P. R. Gray, “MOS sampled date recursive filters using switched capacitor integrators,” IEEE Journ. Solid-State Circuits, vol. SC-12, pp. 600-608, Dec. 1977. [Hu] G. Hurtig, III, U. S. Patent 3,720,881, March 1973. [Ka] T. Kailath, Linear Systems, Prentice Hall, Englewood Cliffs, NJ, 1980. [KHN] “W. J. Kerwin, L. P. Huelsman, and R. W. Newcomb, “State- variable synthesis for insensitive integrated circuit transfer func- tions,” IEEE Journ. Solid-State Circuits, vol. SC-2, pp. 87-92, Sept. 1967. [Ma] K. Martin, “Improved circuit for the realization of switched- capacitor filters,” IEEE Trans. Circuits and Systems, vol. CAS- 27, pp. 237-244, April 1980. BIBLIOGRAPHY 397 [Mi] S. K. Mitra, Analysis and Synthesis of Linear Active Networks, John Wiley and Sons, Inc., New York, 1969. [Ri] R. H. S. Riordan, “Simulated inductor using differential ampli- fiers,” Electronics Letters, vol. 3, pp. 50-51, Feb. 1967. [SK] R. P. Sallen and E. L. Key, “A practical method of designing RC- active filters,” MIT Lincoln Laboratory Technical Report No. 50, May 6, 1954; also IEEE Trans. Circuit Theory, vol. CT-2, pp. 74-85, March 1955. [Sa] W. Saraga, “Sensitivity of 2nd-order Sallen-Key-type active RC filters,” Electronics Letters, vol. 3, pp. 442-444, October 10, 1967. [Ste] J. J. Friend, C. A. Harris, and D. Hilberman, “STAR: An active biquadratic filter section,” IEEE Trans. Circuits and Systems, vol. CAS-22, pp. 115-121, Feb. 1975. [Sto] L. Storch, “Synthesis of constant-time-delay ladder networks us- ing Bessel polynomials,” Proc. IRE, vol. 42, pp. 1666-1675, 1954. [Su1] K. L. Su, Active Network Synthesis, McGraw-Hill Book Com- pany, New York, 1965. [Su2] K. L. Su, Time-Domain Synthesis of Linear Networks, Prentice- Hall, Inc., New Jersey, 1971. [Su3] K. L. Su, Handbook of Tables for Elliptic-Function Filters, Kluwer Academic Publishers, Boston/Dordrecht/London, 1990. [SV] R. Schaumann and M. Van Valkenburg, Design of Analog Filters, Oxford University Press, New York, 2001. [Sz] G. Szentirmai, “Synthesis of multiple-feedback active filters,” Bell System Tech. Journ., vol. 52, pp. 527-555, Apr. 1973. [Ths] L. C. Thomas, “The Biquad: Part I— Some practical design considerations,” IEEE Trans. Circuit Theory, vol. CT-18, pp. 350-357, May 1971. [Thn] W. E. Thomson, “Delay networks having maximally flat fre- quency characteristics,” Proc. IEE, pt. 3, vol. 96, pp. 487-490, 1949. [To] J. Tow, “Active RC filters—A state-space realization,” Proc. IEEE, vol. 56, pp. 1137-1139, June 1968. Index Akerberg, D., 249, 395 Biquad, see Op amp-RC biquad, Akerberg-Mossberg biquad, 249 OTA-C biquad, Allpass biquad characteristic, 208 Switched-capacitor biquad Allpass characteristics, 5 Biquad magnitude characteristics Allpass networks, 70 allpass, 208 delay of, 73 bandpass, 208 All-pole function, 68, 70, 149, 272 bandreject, 208 Amplifier highpass, 208 208 buffer, 193 lowpass, 208 differential, 327, 332 parameters of, Biquads, 189 inverting voltage, 192, 327 cascade of, 189, 253 noninverting voltage, 192 coupled, 274 OTA 347, 350 sequencing of, 264 unity-gain, 193 switched-capacitor, 334-337 Analysis two-integrator, 238-247 ladder, 10 see also Op amp-RC Biquad, node, 9 OTA Biquad, Switched- Antoniou, A., 289, 395 capacitor Biquad Antoniou GIC, 289 Bode, H. W., 174, 395 Approximation, 21, 25 Bode sensitivity, see First-order Attenuation, stopband, 6 sensitivity Available power, 146 Brodersen, R. W., 322, 324, 395, 396 Bainter, J. R., 250, 395 Bruton, L. T., 299, 395 Bainter biquad, 250 Buffer amplifier, see Voltage Band center, 82 follower Bandpass characteristics, 5 Butterworth, S., 26, 55, 395 of biquads, 82 Butterworth filter, 27 Bandreject characteristics, 5 delay characteristic of, 71 of biquads, 208 Butterworth lowpass character- Bandwidth, 81 istics, 26 Bessel polynomial, 69 application of, 29 Bessel-Thomson filters, 66 high-frequency behavior, 27 network functions for, 67-69, network function, 53, 389-390 377-378 400 Index Butterworth polynomial, 54, 57 Differential sensitivity, see First- order sensitivity Canonic realization of lossless func- Differential weighted summer, 194 tion, 98, 104, 107 Digital signal processing, 1 Capacitances, parasitic, 326 Doubly-terminated lossless Cascade of biquads, 182, 253 twoport, 145, 167 Cauer, W., 41, 395 Cauer filter, see Elliptic filter Elliptic filter, 41, 62 Cauer’s realizations of lossless func- delay characteristic of, 71 tion, 106 lowpass characteristic of an, Center frequency, 82 41 Chebyshev filter, 30 network functions, 391-394 delay characteristic of, 71 Equalizer, delay, 71 network function, 58, 379- 388 FDNR, 299 , Chebyshev lowpass characteris- Fidler, J. K., 347, 396 tic, 26, 30, 31 Filter high-frequency behavior, 35 active, 2, 182, 187 inverse, 38, 46 active bandpass, 308 Chebyshev polynomial, 31 analog, 1, 3 Chebyshev rational functions, 40 Bessel-Thomson, 66 Circuit analysis, 9 Butterworth, 27 Classical sensitivity, see First-order Cauer, 41 sensitivity Chebyshev, 30 Conformal transformation, 62 comparison of active and Controller canonic form, 265 passive, 182,187 Converters, impedance, 287 digital, 1 Coupled biquads, 274 elliptic, 41, 62 first-order active, 195 Darlington, S., 148, 149, 159, 395 insertion, 145-167 Darlington’s realization, 148 maximally-flat delay, 66 Delay characteristics, 70 MOS, 323, 346 of allpass functions, 73 optimal, 1 of Bessel-Thomson filters, 70 OTA, 345-374 of standard lowpass filters, passive, 2, 182, 187 71 simulation of, 290-314, 337, Delay, group, 4 360 Delay equalization, 71 specification, 16 Delay equalizer, 4 switched-capacitor, 321-340 Delyiannis, T., 250, 374, 396 with equal terminations, 149- Delyiannis biquad, 250, 396 158 Denormalization, 13, 16, 21 with unequal terminations, Differential amplifier, 332, 350 156-165 Differential lossy integrator, 332 First-order section, 195, 333,353 Index 401 First-order sensitivity Gains, change of internal, 277, definition of, 173 305, 364 properties of, 174-175 Generalized impedance converter, see also Sensitivity see GIC Fleischer, P. E., 245, 396 GIC, 288 Fleischer-Tow biquad, 245 Antoniou, 289 Foster’s expansion, 96 Girling, F. E. J., 305, 396 Foster’s preamble, 115 Good, E. F., 305, 396 Foster’s realizations of lossless Gorski-Popiel, J., 296, 396 function, 99 Gray, P. R., 322, 395, 396 Frequency scaling, 13 Grossman, A. J., 62, 396 Frequency transformation, 77-88 Group delay, 4 element replacement, 87 Guillemin, E. A., 93, 95, 111, Frequency-dependent negative re- 395 sistors, see FDNR Gyrator, 93n, 288 Friend, J.
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