Analog Integrated Circuits and Signal Processing, 28, 299–307, 2001 C 2001 Kluwer Academic Publishers. Manufactured in The Netherlands.
Current-Mode High Output Impedance Multifunction Filters Employing Minimum Number of FTFNs 2 ˘ ˘ ˘ UGUR C ¸ AM,1 OGUZHAN C ¸ IC ¸ EKOGLU, ALI TOKER3 AND HAKAN KUNTMAN3 1
Sakarya University, Department of Electrical and Electronics Engineering, Engineering Faculty, 54040 Esentepe, Adapazari, Turkey 2 Bo˘gazic¸i University, Institute of Biomedical Engineering, 80815, Bebek, Istanbul, Turkey 3 Istanbul Technical University, Faculty of Electrical and Electronics Engineering, Department of Electronics and Communication Engineering, 80626 Maslak, Istanbul, Turkey. E-mail:
[email protected];
[email protected];
[email protected];
[email protected]
Received September 15, 2000; Revised February 6, 2001; Accepted March 13, 2001
Abstract. In this study, five current-mode FTFN-based multifunction filters are proposed, which realize the same transfer functions in ideal case. All circuits employ two capacitors and three resistors. For each circuit R-C:C-R transformation increases the number of realization possibilities to ten. The proposed topologies simultaneously realize three basic filtering functions using minimum number of FTFNs and provide high output impedances that enable easy cascading in current mode. Sensitivity analysis of the filters show that they have low passive sensitivities, ω0 , Q and ω0 /Q of the filters are insensitive to current tracking errors, furthermore ω0 of the filters are insensitive to voltage tracking errors of the FTFNs. The proposed circuits do not require component matching condition except for notch and allpass responses and permit independent adjustment of ω0 without disturbing ω0 /Q. Experimental and simulation results are given to verify the theoretical analyses. Key Words: four terminal floating nullor, current-mode circuits, active filters
1.
Introduction
Current-mode circuits have been receiving significant attention due to their certain advantages compared to voltage-mode circuits. They offer to the designer several salient features such as inherently wide bandwidth, greater linearity, wider dynamic range, simple circuitry and low power consumption [1–4]. On the other hand, multifunction filters find a wide range of application in communications, analogue signal processing and instrumentation. Second-generation current conveyors (CCII) are widely used as an active element for design of current-mode circuits. CCII based current-mode multifunction filters also exist in the literature [5,6]. ¨ guz et al. [5] proposed a multifunction filter emOzo˘ ploying minimum number of CCIIs and obtained synthesis of an input admittance matrix proposed by Hilberman and Joseph [7]. On the other hand, four terminal floating nullor (FTFN) is a very flexible and versatile building block in active network synthesis, which is especially remarkable when taking the nullor equivalents of the ac-
tive elements into account [8–19]. One terminal of a nullator in nullor equivalent of CCII is connected to one terminal of norator, whereas by the nullor model of FTFN the nullator and norator are isolated from each other, which yields more flexibility in active network synthesis. Some current-mode FTFN-based multifunction filters are available in literature [12–15]. Liu and Lee have proposed an insensitive current-mode multifunction filter, which realizes two basic filtering functions using minimum number of FTFNs and passive components [12]. However this circuit cannot provide two high output impedances, which is important for current mode cascading to realize current-mode high order filters without using any impedance matching device. Abuelma’atti et al. proposed a four input one output active biquad which has a configuration employing four grounded capacitors, three resistors and three FTFNs [13]. This circuit requires parametermatching condition and it cannot simultaneously realize low-pass, band-pass and high-pass filter functions without changing circuit topology and elements. C ¸ am et al. proposed an FTFN-based single input three
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output (SITO) current-mode high output impedance multifunction filter using four active and six passive elements [14], which can simultaneously realize three basic filtering functions without component matching requirements. Toker et al. introduced an FTFN-based multifunction filter employing minimum number of FTFNs [15]. The purpose of this study is to exploit the advantages of FTFN in the design of current-mode multifunction filters. In this paper we present current-mode multifunction filters employing minimum number of FTFNs, which are also based on the principle given in [7]. The presented filters provide the same filter responses in ideal case, but their circuit topologies and nonideal filter responses are different. All the presented circuits employ two capacitors and three resistors. For each circuit R-C:C-R transformation increases the number of realization possibilities to ten. These circuits can realize simultaneously three basic filtering functions using minimum number of FTFNs. All of the presented filters have low passive sensitivities. Natural frequencies (ω0 ), quality factors (Q) and their ratios (ω0 /Q) of the filters are insensitive to current tracking errors. Furthermore ω0 ’s are also insensitive to voltage tracking errors of the FTFNs. The proposed universal filters due to high output impedances enable easy cascading in current mode. They enjoy also independent control of the parameters ω0 and ω0 /Q and permit also the realization of notch and all-pass responses with slight modifications.
2.
Circuit Description
An FTFN is equivalent to an ideal nullor or is called operational floating amplifier [19]. The port relations of an FTFN as shown in Fig. 1 can be characterized as I1 = I2 = 0 Io1 = Io2 Vx = Vy
(1)
We use the realization method of the current-mode filter according to the input admittance realization scheme given in Fig. 2. Many circuits can be derived from the topology in Fig. 2 [7]. It should be noted that the unity gain voltage buffers in Fig. 2 can be implemented by using the y-x terminals voltage-tracking behavior of the CCIIs in [5]. Considering the nullor models of the CCII and FTFN, the buffer implementation possibili-
Fig. 1. Nullor model and symbol of FTFN.
ties with FTFN increase with the number of the active elements used in the circuit realization compared to the CCII-based realization, since by FTFN-based realizations nullators and norators of FTFNs can be interchanged arbitrarily. Moreover the connections between a-b and c-d in Fig. 2 can be realized also virtually by using the nullators of the FTFN thanks to the zero input current of the voltage buffers. The entire above mentioned considerations yield various implementations of the SITO filter, which are based on the same principle. Considering various practical FTFN implementations the behavior of these circuits is expected to be different in practice. A detailed discussion and comparison of these circuits are out of the scope of this paper. Considering the proposed configurations in Fig. 3, routine analysis yields Q, ω0 and ω0 /Q as given in Table 1. These circuits use three FTFNs and five passive components to simultaneously realize second order current mode low-pass, high-pass and band-pass filter characteristics without changing the circuit configuration. It should be noted that some of the capacitors used in the proposed configuration are floating; they can easily be implemented by using advanced CMOS processes with second poly layer as poly 1-poly 2 (or double-poly) capacitors [20].
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Fig. 2. Realization of Yin = y(1 − T ). (a) T = V2 /V1 , I2 = 0 (b) Equivalent circuit of (a).
Table 1. ω0 /Q, Q and ω0 of the proposed multifunction filters. Figure
ω0 /Q
3a
G1 C1
3b
G1 C2
3c
G1 C1
3d
G1 C1
3e
G3 C2
ω0
Q
filter responses with high output impedance are easily obtained with a slight modification of the proposed circuits.
G 2 C1
G1 G2
G 1 C2
C1 C2
G 1 C1
C1 C2
3.
G 1 C2
C1 C2
Taking into consideration the FTFN nonidealities the port relations in equation (1) can be expressed as:
G 3 C2 G 3 C1 G 3 C1 G 1 C2 G 1 C2 G 3 C1
G1 G3 G1 G3 G1 G3 C1 C2 G1 G3 C1 C2
The ideal transfer functions of the filter circuit shown in Fig. 3a can be given as follows: IL P G2G3 = 2 Iin s C1 C2 + sC2 G 1 + G 1 G 2 IH P C1 C2 s 2 =− 2 Iin s C1 C2 + sC2 G 1 + G 1 G 2 IB P sC2 G 2 = 2 Iin s C1 C2 + sC2 G 1 + G 1 G 2
Tracking Errors Analysis and Sensitivity
(2) (3) (4)
It can be easily seen from equations (2–4) that if we replace FTFN2 with an OMA, which performs current inversion of the one of the output port in Fig. 3a and connecting low-pass and high-pass output terminals yields a notch filter transfer function by matching R1 = R3 . Similarly, replacing FTFN1 with an OMA connecting low-pass, high-pass and band-pass output terminals yields a second order all-pass filter transfer function by matching R1 = R2 = R3 . Thus universal current-mode
Vx = βVy Io2 = α Io1
(5)
where β = 1 − εv , and εv denotes voltage tracking error and α = 1 − εi , εi denotes current tracking error of the FTFN. Reanalysis of the filter circuit yields the modified ω0 , Q and ω0 /Q as in Table 2 where βk , k = 1, 2, 3 are the voltage tracking error of the kth FTFN. Sensitivity analysis of Fig. 3a with respect to passive elements yields: S Rω10 = S Rω20 = SCω10 = SCω20 = S RQ2 = SCQ2 = − 12
(6)
S RQ1 = SCQ1 =
(7)
1 2
It is clearly observed from equations (6–7) that ω0 and Q passive sensitivities are low. It is easy to show that ω0 , Q and ω0 /Q are insensitive to current tracking errors of the FTFNs and ω0 is also insensitive to voltage tracking errors of the FTFNs. Furthermore, voltage tracking error sensitivities of Q remain low only for low Q realizations. The sensitivity performances of the other topologies in Fig. 3 are similar.
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Fig. 3. The proposed multifunction filters for realizing three functions simultaneously.
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Fig. 3. (Continued )
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Fig. 3. (Continued )
4.
Experimental Results and Discussion
To verify theoretical analysis the proposed circuits are experimentally tested. The proposed circuits are also simulated using PSPICE program. As an example, experimental and simulation results of the circuit shown in Fig. 3b is given in Fig. 5. The circuit was conTable 2. ω0 /Q, Q and ω0 of the proposed multifunction filters with non-ideal FTFN. Figure
ω0 /Q β
3a 3b
C2 G 1 +C1 G 2 (1− β1 ) 3
C1 C2 C1 G 1 +C2 G 3 (1−β1 β2 β3 ) C1 C2 β
3c 3d 3e
ω0
Q
C2 G 1 +C1 G 3 (1− β1 ) 3
C1 C2 β β C2 G 1 +C1 G 3 (1− 1β 2 ) 3
√
C1 C2
√
β C2 G 1 +C1 G 2 (1− β1 3
√
G1 G2
√
)
C1 C2 G 1 G 3 C1 G 1 +C2 G 3 (1−β1 β2 β3 )
√
C1 C2
√
G1 G3 β
C2 G 1 +C1 G 3 (1− β1 )
√
C1 C2
√
C1 C2 C1 G 3 +C2 G 1 (1−β1 β2 ) C1 C2
C1 C2 G 1 G 3 C1 G 3 +C2 G 1 (1−β1 β2 )
√
3
G1 G3
β β C2 G 1 +C1 G 3 (1− 1β 2 3
√
)
G1 G2 C1 C2 G1 G3 C1 C2 G1 G3 C1 C2 G1 G3 C1 C2 G1 G3 C1 C2
Fig. 4. Realization of an FTFN with the commercial AD844 IC.
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Fig. 5. PSPICE simulation and experimental results of the proposed multifunction filter in Fig. 3b (R1 = R2 = R3 = 10 k , C1 = C2 = 1 nF).
structed with the commercial current feedback op-amp IC AD844 of Analog Devices. The FTFN was implemented with of two AD844 IC as shown in Fig. 4 [12–14]. PSPICE simulations were performed using AD844 macromodel of Analog Devices. The supply voltages were taken as VD D = 15 V and −VSS = −15 V. The passive elements of the filter were chosen as R1 = R2 = R3 = 10 k , C1 = C2 = 1 nF ( f o = 15.9 kHz, Q = 1). The experimental and simulation results given in Fig. 5 for the lowpass, highpass and bandpass filter characteristics verify the theoretical analysis. Other multifunction filters shown in Fig. 3 have also very similar results.
5.
Conclusion
In this paper we propose five current-mode multifunction filters using minimum number of FTFNs. The filter circuits can realize simultaneously three basic filtering functions using a low number of passive components. The proposed filters do not require any parameter matching condition except for notch and allpass responses and have low passive sensitivities. Furthermore, ω0 , Q and ω0 /Q of the filters are insensitive to current tracking errors of the FTFNs and ω0 of the filters are also insensitive to voltage tracking errors of the FTFNs. All outputs of the filters exhibit high
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output impedances so that this property makes the circuits very attractive from the viewpoint of cascading in current mode. The proposed filter circuits have also the possibility of independent adjustment of ω0 without disturbing ω0 /Q. If component matching is allowed the circuits permit also the realization of notch and allpass responses with a slight modification. Experimental and simulation results are in very close agreement with theory. References 1. Toumazou, C., Lidgey, F. J. and Haigh, D., “Analog IC design: The current-mode approach.” Exeter, UK, Peter Peregrinus, 1990. 2. Wilson, B., “Tutorial review: Trends in current conveyor and current-mode amplifier design.” Int. J. Electronics 73, pp. 573– 583, 1992. 3. Arbel, A., “Current-mode signal processing.” In Proc. of the 17th Convention of Electrical and Electronics Eng. in Israel, pp. 309–312, 1991. 4. Asserud, O. and Nielsen, I. R., “Trends in current analogue design-A panel debate.” Analog Integrated Circuits and Signal Processing 7, pp. 5–9, 1995. ¨ guz, S., Toker, A. and C¸i¸ceko˘glu, O., “High output 5. Ozo˘ impedance current-mode multifunction filter with minimum number of active and reduced number of passive components.” Electronics Letters 34, pp. 1807–1808, 1998. 6. Chang, C. M., “Multifunction biquadratic filters using current conveyors.” IEEE Trans. Circuits and Syst.-II 44, pp. 956–958, 1997. 7. Hilberman, D., Joseph, R. D., “Analysis and synthesis of admitances matrices of RLC:VGUGA common ground networks.” IEEE Trans. on Circuit Theory CT-15(1), pp. 426–430, 1968. 8. Higashimura, M., “Current-mode allpass filter using FTFN with grounded capacitor.” Electronics Letters 27, pp. 1182–1183, 1991. 9. Higashimura, M., “Current-mode lowpass, bandpass and highpass filter using an FTFN.” Microelectronics Journal 24, pp. 659–662, 1993. 10. Higashimura, M., “Realisation of current-mode transfer function using four terminal floating nullor.” Electronics Letters 27, pp. 170–171, 1991. 11. Liu, S. I., “Cascadable current-mode filters using single FTFN.” Electronics Letters 31, pp. 1965–1966, 1995. 12. Liu, S. I. and Lee, J. L., “Insensitive current/voltage mode filters using FTFNs.” Electronics Letters 32, pp. 1079–1080, 1996. 13. Abuelma’ atti, M. T., Al-Zaher, H. A. and Al-Qahtani, M. A., “Active biquads using FiTFNs” Microelectronics Journal 29(3), pp. 123–132, 1998. 14. C ¸ am, U., C¸i¸ceko˘glu, O., Kuntman, H., “A new FTFN-based single input three output (SITO) current-mode filter.” Microelectronics Journal 30(2), pp. 155–188, 1999. ¨ guz, S. and C 15. Toker, A., Ozo˘ ¸ i¸ceko˘glu, O., “High Output Impedance Current-Mode Multifunction Filter Using FTFNs.” In Proc. of 1999 IEEE. Int. Symp. on Circuits and Systems (ISCAS’99) 2, pp. 267–269, Orlando, USA, 30 May–2 June, 1999.
16. Liu, S. I., “Single-resistance-controlled sinusoidal oscillator using two FTFNs.” Electronics Letters 33(14), pp. 1185–1186, 1997. 17. Liu, S. I. and Yu-Hung, L., “Current-mode quadrature sinusoidal oscillator using single FTFN.” Int. J. Electronics 81(2), pp. 171– 175, 1996. 18. Senani, R., “A novel application of four terminal floating nullors.” In Proc. of IEEE 35(11), pp. 1544–1546, 1987. 19. Huijsing, J. H., “Operational floating amplifier (OFA).” In IEE Proc. 137(2), part G, pp. 131–136, 1990. 20. Baker, R. J., Li, H. W. and Boyce, D. E., CMOS Circuit Design, Layout, and Simulation, Chap. 7. New York, USA, IEEE Press, 1998.
U˘gur C ¸ am was born in Afyon, Turkey, on October 10, 1972. He received B.Sc., M.Sc. and Ph.D. Degree from Istanbul Technical University at 1993, 1996 and 2000 respectively. He is working as a research assistant at Sakarya University, Department of Electrical and Electronic Engineering. His research interest includes analog integrated circuit design, analog signal processing, current-mode circuits and electronic device modelling. He is author or co-author of 13 journal papers. Dr. C¸am is a member of the Chamber of Turkish Electrical Engineers (EMO).
O˘guzhan C ¸ i¸ceko˘glu was born in 1963 in Istanbul, Turkey. He received the B.Sc. and M.Sc. degrees from Bo˘gazi¸ci University and the Ph.D. degree from Istanbul
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Technical University all in Electrical and Electronics Engineering in 1985, 1988 and 1996 respectively. He served as teaching assistant in Computer Engineering department, as lecturer at the School of Advanced Vocational Studies Electronics Prog. of Bo˘gazi¸ci University where he held various administrative positions between 1993 and 1999, and as part time lecturer at various institutions. He is currently Associate Professor at the Biomedical Engineering Institute of Bo˘gazi¸ci University. His current research interests include analog circuits, active filters, analog signal processing applications and current-mode circuits. He is the author or coauthor of more than 80 papers published or accepted for publishing in scientific journals or conference proceedings. O˘guzhan C ¸ i¸ceko˘glu is a member of the IEEE.
Ali Toker was born in Istanbul, Turkey, 1951. He received the B.Sc. and M.Sc. degrees in electrical engineering from the Faculty of Electrical and Electronics Eng., Istanbul Technical University, Turkey in 1973 and 1975, respectively. He received the Ph.D. degree in 1986 from the Institute of Science and Technology of the same university. He is currently an associate professor in electronics, teaching graduate and undergraduate courses. He is also the author or co-author of about 45 papers published in scientific reviews or conference
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proceedings. His main research interests are design of current-mode circuits and analog signal processing applications.
H. Hakan Kuntman received his B.Sc., M.Sc. and Ph.D. degrees from Istanbul Technical University in 1974, 1977 and 1982, respectively. In 1974 he joined the Electronics and Communication Engineering Department of Istanbul Technical University. Since 1993 he is a professor of electronics in the same department. His research interest include design of electronic circuits, modeling of electron devices and electronic systems, active filters, design of analog IC topologies. Dr. Kuntman has authored many publications on modeling and simulation of electron devices and electronic circuits for computer-aided design, analog VLSI design and active circuit design. He is the author or the coauthor of 61 journal papers published or accepted for publishing in international journals, 55 conference papers presented or accepted for presentation in international conferences, 70 turkish conference papers presented in national conferences and 10 books related to the above mentioned areas. Furthermore he advised and completed the work of 5 Ph.D. students and 24 M.Sc. students. Currently, he acts as the advisor of 7 Ph.D. and 14 M.Sc. students. Dr. Kuntman is a member of the Chamber of Turkish Electrical Engineers (EMO).
