Analog Integr Circ Sig Process (2009) 61:205–209 DOI 10.1007/s10470-009-9298-6
MIXED SIGNAL LETTER
Higher-order immittance functions using current conveyors Jiun-Wei Horng Æ Chun-Li Hou Æ Chun-Ming Chang Æ Hao Yang Æ Woei-Tzer Shyu
Received: 1 February 2007 / Revised: 3 December 2008 / Accepted: 2 March 2009 / Published online: 25 March 2009 Ó Springer Science+Business Media, LLC 2009
Abstract Two configurations for realizing higher-order series and parallel immittance functions using current conveyors are presented. The proposed circuits require only grounded resistors and capacitors. As examples of their applications, highpass and bandpass filters are given with simulation results. Keywords Current conveyor Impedance Admittance Active filter
1 Introduction Current conveyors have been found useful in the synthesis of RC active filters, sinusoidal oscillators and immittance functions. Several circuits for realizing higher-order series and parallel immittance functions have been reported. Higashimura and Fukui proposed two configurations for realizing higher-order series and parallel immittances using second-generation current conveyors (CCIIs) [1]. However, the passive components they employed cannot be all grounded. Weng et al. proposed a configuration for realizing higher-order series impedance function using currentfeedback amplifiers (CFAs) [2]. However, this configuration employs floating resistors and capacitors. Liu and Yang proposed two configurations for realizing higherorder series and parallel immittances using third-generation J.-W. Horng (&) C.-L. Hou H. Yang W.-T. Shyu Department of Electronic Engineering, Chung Yuan Christian University, Chung-Li 32023, Taiwan, ROC e-mail:
[email protected] C.-M. Chang Department of Electrical Engineering, Chung Yuan Christian University, Chung-Li 32023, Taiwan, ROC
current conveyors (CCIIIs) with grounded passive components [3]. However, the active components they used, CCIIIs, are more complicate than CCIIs. In this paper, two configurations are proposed to realize higher-order series and parallel immittances using CCIIs and CCIIIs. The proposed circuits using only grounded passive components. With respect to the previous higherorder immittances circuit configurations in [1–2], the proposed circuits using only grounded passive components. The use of only grounded capacitors and resistors is beneficial from the point of view of integrated circuit fabrications [4–6]. Since one CCIII was constructed by two CCIIs [7] and each proposed basic block circuit is constructed by one CCII and one CCIII. With respect to the previous higherorder immittances circuit configurations in [3] that use two CCIIIs in each basic block circuit, the proposed circuit configurations have a more simple circuit structures.
2 Circuits description The terminal characteristic of the current conveyor can be described by the following matrix equation: 2 3 2 32 3 iy 0 a 0 vy 4 vx 5 ¼ 4 1 0 0 5 4 i x 5 ð1Þ 0 1 0 iz vz For a = 0, the circuit is a second-generation current conveyor (CCII). One possible implementation of the CCII is shown in Fig. 1 [8]. For a = -1, the circuit is a thirdgeneration current conveyor (CCIII). One possible implementation of the CCIII is shown in Fig. 2, which combines two CCII circuits [7]. The multiple current output of the current conveyor can be easily implemented by simply adding output branches.
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Analog Integr Circ Sig Process (2009) 61:205–209 V+ M4
M5
(a) V in
M7 M8
y
M9
M10 M11
Iin
y
x M1
z-
z+
M14
M12 M13
Vb2
M15 M16
z-
x CCII y2
y1
M2
Vb1
CCIII
x
M6
y
z+
y3
(b)
M3
x V-
V in
Fig. 1 CMOS realization of the CCII
Iin
y
z+
y CCIII
z+
x CCII z3
z1
z2
CCIII Fig. 3 a Basic admittance function circuit. b Basic impedance function circuit
iy vy
y
CCII
x
y
CCII
vx
z+ z+
z+ z+ zvz1
ix x
iz1
Vin
z+ vz2
y Iin
iz2
y
z+
x CCIII y1
z-
x CCII y2
Fig. 2 The implementation for the CCIII y
x CCIII
Considering the first proposed circuit configuration in Fig. 3(a), it consists of a CCIII, a CCII and three grounded admittances. Its driving point admittance function can be expressed as Iin y1 y3 ¼ Yin ¼ y1 þ Vin y2
ð2Þ
The second proposed circuit configuration is Fig. 3(b), it consists of a CCIII, a CCII and three grounded impedances. Its driving point impedance function can be expressed as Vin z1 z3 ¼ Zin ¼ z1 þ ð3Þ Iin z2 It has been found that the circuits of Fig. 3(a) and (b) can simulate two kinds of immittance elements in parallel and in series, respectively, by suitable choosing passive elements. Two methods are proposed to synthesis the higher-order immittance functions by using the basic blocks in Fig. 3(a) and (b). The higher-order admittance function can be realized by using the circuit, which is similar to Fig. 3(a), in place of y3 in Fig. 3(a). For example, the higher-order admittance circuit is shown in Fig. 4 by using the basic block in Fig. 3(a). Its admittance function can be given as
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y3
y
z+ y4
z-
x CCII y5
Fig. 4 Higher-order admittance function using the circuit in Fig. 3(a)
y1 y3 y1 y3 y5 þ ð4Þ y2 y2 y4 By connecting similar stages, we can realize the higherorder admittance function, which can be expressed by the following equation y1 y3 y1 y3 y5 y1 y3 . . .y2n1 Yin ¼ y1 þ þ þ þ ð5Þ y2 y2 y4 y2 y4 . . .y2n2
Yin ¼ y1 þ
Similarly, the higher-order impedance functions can be realized by using the circuit, which is similar to Fig. 3(b), in place of z3 in Fig. 3(b). All the proposed immittances use only grounded capacitors and resistors that are suitable for monolithic integration [4–6]. Since one CCIII was constructed by two CCIIs [7] and each proposed basic block circuit is constructed by one CCII and one CCIII. With respect to the previous higher-order immittances in [3] that using two CCIIIs to construct the basic block circuit, the proposed circuit configurations have more simple circuit structures.
Analog Integr Circ Sig Process (2009) 61:205–209
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Fig. 3(b) with z1 = 1/sC1, z2 = R2 and z3 = 1/sC3. The obtained bandpass circuit is shown in Fig. 6. Its transfer function is
Vo Vin
C4 y x
y
z+ CCIII
C2
R1
z-
s GC34 Vo ¼ 2 4 Vin s þ s GC4 þ GC2 G 1 1 C3
x CCII R3
ð8Þ
Fig. 5 Highpass filter base on the admittance function in Fig. 3(a)
4 Simulation results
x V in
Vo y
z+
R4 y
CCIII
C3
z+
x CCII R2
C1
Fig. 6 Bandpass filter base on the impedance function in Fig. 3(b)
3 Applications to filters To verify the theoretical analysis, a second-order highpass filter can be realized by inserting a capacitor C4 to the admittance function as shown in Fig. 3(a) with y1 = 1/R1, y2 = sC2 and y3 = 1/R3. According to Eq. 2, its driving point admittance can be Yin ¼
1 1 þ Re sLe
PSPICE simulations were carried out to demonstrate the feasibility of the proposed circuit in Figs. 5 and 6 using 0.35 lm, level 3, MOSFET from TSMC (Taiwan Semiconductor Manufacturing Company, Ltd.). The model parameters are given in Tables 1 and 2. The CCII was realized by the CMOS implementation in Fig. 1 whereas the aspect ratios of the MOS transistors are shown in Table 3. The CCIII was realized by two CCII as shown in Fig. 2 [7]. Figure 7 represent the simulated frequency responses for the highpass filter of Fig. 5 designed with C2 = C4 = 80pF, R1 = 10 kX and R3 = 10 kX. Figure 8 represent the simulated frequency responses for the bandpass filter of Fig. 6 designed with C1 = C3 = 80pF and R2 = R4 = 10 kX. The supply voltages are V? = ?1.65 V, V- = -1.65 V, Vb1 = -1 V and Vb2 = -0.6 V. The non-idealities may be due to the ignored parasitic elements of the CCIIs and CCIIIs.
ð6Þ
where Re = R1 and Le = R1C2R3. The obtained highpass circuit is shown in Fig. 5. Its transfer function is
5 Conclusion
Vo s2 ¼ 2 G 3 Vin s þ s C1 þ GC1 G 4 2 C4
Two configurations for realizing higher-order series and parallel immittance functions using current conveyors are presented. The proposed circuit configurations have more simple circuit structures with previous higher-order series and parallel immittance functions in [3]. As examples of
ð7Þ
A second-order bandpass filter can be realized by inserting a resistor R4 to the impedance function as shown in
Table 1 TSMC NMOS parameters for 0.35 lm process .MODEL Mbreakn NMOS (LEVEL = 3 ? TOX = 7.9E-9 NSUB = 1E17 GAMMA = 0.5827871 ? PHI = 0.7 VTO = 0.5445549 DELTA = 0 ? UO = 436.256147 ETA = 0 THETA = 0.1749684 ? KP = 2.055786E-4 VMAX = 8.309444E4 KAPPA = 0.2574081 ? RSH = 0.0559398 NFS = 1E12 TPG = 1 ? XJ = 3E-7 LD = 3.162278E-11 WD = 7.046724E-8 ? CGDO = 2.82E-10 CGSO = 2.82E-10 CGBO = 1E-10 ? CJ = 1E-3 PB = 0.9758533 MJ = 0.3448504 ? CJSW = 3.777852E-10 MJSW = 0.3508721)
Table 2 TSMC PMOS parameters for 0.35 lm process .MODEL Mbreakp PMOS (LEVEL = 3 ? TOX = 7.9E-9 NSUB = 1E17 GAMMA = 0.4083894 ? PHI = 0.7 VTO = -0.7140674 DELTA = 0 ? UO = 212.2319801 ETA = 9.999762E-4 THETA = 0.2020774 ? KP = 6.733755E-5 VMAX = 1.181551E5 KAPPA = 1.5 ? RSH = 30.0712458 NFS = 1E12 TPG = -1 ? XJ = 2E-7 LD = 5.000001E-13 WD = 1.249872E-7 ? CGDO = 3.09E-10 CGSO = 3.09E-10 CGBO = 1E-10 ? CJ = 1.419508E-3 PB = 0.8152753 MJ = 0.5 ? CJSW = 4.813504E-10 MJSW = 0.5)
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Analog Integr Circ Sig Process (2009) 61:205–209
Table 3 Aspect ratios of the MOS in Fig. 1 MOS transistors
Aspect ratio (W/L)
M1, M2
28/0.7
M3
49/0.7
M4, M5
42/0.7
M6, M7, M8, M9, M10, M11,
14/0.7
M12, M13, M14, M15, M16
References
7/0.7
10 180
0
-20 90
-30
Phase, deg
Gain, dB
-10
-40
Theo. Simu. o o o Gain
-50 -60 4 10
-.-.-.- x x x
Phase 10
5
6
0
10
Frequency, Hz
Fig. 7 Simulated frequency responses of the second-order highpass filter in Fig. 5
0
Gain, dB
0
-15
Phase, deg
-10
-20 Theo. Simu.
-30 10 4
o o o Gain -.-.-.- x x x Phase
10 5
-90 10 6
Frequency, Hz
Fig. 8 Simulated frequency responses of the second-order bandpass filter in Fig. 6
their applications, a second-order highpass and a secondorder bandpass filters are given with simulation results.
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1. Higashimura, M., & Fukui, Y. (1998). Novel method for realizing higher-order immittance function using current conveyors. IEEE ISCAS, pp. 2677–2680. 2. Weng, R. M., Lai, J. R., & Lee, M. H. (2000). Realization of nthorder series impedance function using only (n-1) current-feedback amplifiers. International Journal of Electronics, 87(1), 63–69. doi: 10.1080/002072100132453. 3. Liu, S. I., & Yang, C. Y. (1996). Higher-order immittance function synthesis using CCIIIs. Electronics Letters, 32(25), 2295–2296. doi:10.1049/el:19961538. 4. Abuelma’atti, M. T., Al-ghumaiz, A. A., & Khan, M. H. (1995). Novel CCII-based single-element controlled oscillators employing grounded resistors and capacitors. International Journal of Electronics, 78(6), 1107–1112. 5. Bhusan, M., & Newcomb, R. W. (1967). Grounding of capacitors in integrated circuits. Electronics Letters, 3(4), 148–149. doi: 10.1049/el:19670114. 6. Gupta, S. S., & Senani, R. (2003). Realisation of current-mode SRCOs using all grounded passive elements. Frequenz, 57(1–2), 26–37. 7. Fabre, A. (1995). Third-generation current conveyor: a new helpful active element. Electronics Letters, 31(5), 338–339. doi: 10.1049/el:19950282. 8. Surakampontorn, W., Riewruja, V., Kumwachara, K., & Dejhan, K. (1991). Accurate CMOS-based current conveyors. IEEE Transactions on Instrumentation and Measurement, 40(4), 699– 702. doi:10.1109/19.85337.
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Acknowledgment The National Science Council, Republic of China supported this work under grant number NSC 97-2221-E-033056.
Jiun-Wei Horng was born in Tainan, Taiwan, Republic of China, in 1971. He received the B.S. degree in Electronic Engineering from Chung Yuan Christian University, Chung-Li, in 1993, and the Ph.D. degree from National Taiwan University, Taipei, in 1997. From 1997 to 1999, he served as a SecondLieutenant in China Army Force. From 1999 to 2000, he joined CHROMA ATE INC. where he worked in the area of video pattern generator technologies. From 2000 to 2005, he was with the Department of Electronic Engineering, Chung Yuan Christian University, Chung-Li, Taiwan as an Assistant Professor. Since 2005, he is an Associate Professor. His teaching and research interests are in the areas of Circuits and Systems, Analog and Digital Electronics, Active Filter Design and Current-Mode Signal Processing.
Analog Integr Circ Sig Process (2009) 61:205–209 Chun-Li Hou was born in Taipei, Taiwan, Republic of China, in 1951. He received the B.S degree, M.S. degree, and Ph.D degree in Electrical Engineering from National Taiwan University, Taipei, in 1974, 1976, and 1991, respectively. From 1977 to 1979, he taught as a lecture in Tamkang College. From 1981 to 1991, he taught as a lecture in the department of Electronic Engineering, Chung Yuan Christian University, Chung-Li, Taiwan. From 1992 until now, he taught there as an Associate Professor. His teaching and research interests are in the areas of Current-Mode Analog Circuit Analysis and Design, Active Network Synthesis Circuit theory and Applications.
Chun-Ming Chang obtained his bachelor and master degrees, both in the field of Electrical Engineering, from National Cheng Kung University, Tainan, Taiwan, R.O.C., and his Ph.D degree in the field of Electronics and Computer Science from the University of Southampton, U.K. He had been an Associate Professor in Chung Yuan Christian University in Taiwan from 1985 to 1991, and has been a full Professor in the same University since 1991. His research interest is divided by two relative fields, network synthesis before 1991 and analog circuit design after 1991. He had been a chairman of the electrical engineering department in Chung Yuan Christian University from 1995 to 1999. He has published over 70 journal papers, in which the most famous is the invention of a new analytical synthesis method for the design of analog circuits which can, for the first time, simultaneously achieve three important criteria for the design of OTA-C filters without trade-offs. Using a succession of innovative algebra manipulation operations, a complicated nthorder transfer function can be decomposed into a set of simple equations feasible using the single-ended-input OTAs and grounded capacitors. He is in the process of writing his professional textbook: ‘‘Analog Circuit Design-Analytical Synthesis Method’’. Professor Chang is a senior member of the IEEE Circuits and Systems Society.
209 Hao Yang was born in Taichung, Taiwan, Republic of China, in 1985. He received the B.S. degree in Electronic Engineering from Chung Yuan Christian University, Chung-Li, in 2008. Presently, he is working toward the M.S. degree in Electronic Engineering at Chung Yuan Christian University, Chung-Li. His research interests are in the area of voltage mode filter, current mode filter and analog integrated circuit design and simulation.
Woei-Tzer Shyu was born in Taipei, Taiwan, Republic of China, in 1983. He received the B.S. degree in Electronic Engineering, in 2007. Presently, he is working toward the M.S. degree in Electronic Engineering, both from Chung Yuan Christian University, Chung-Li. His research interests are in the area of voltage/current mode filter, and mixed analog/digital system integrated circuit design and simulation.
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