- Email: [email protected]
Multiple-input single-output low-input and high-output impedance current-mode biquadratic filter employing five modified CFTAs and only two grounded capacitors
Microelectronics Journal 44 (2013) 802–806
Contents lists available at ScienceDirect
Microelectronics Journal journal homepage: www.elsevier.com/locate/mejo
Multiple-input single-output low-input and high-output impedance current-mode biquadratic filter employing five modified CFTAs and only two grounded capacitors Xinhua Nie n, Zhongming Pan College of Mechatronics Engineering and Automation, National University of Defense Technology, Changsha, Hunan 410073, PR China
art ic l e i nf o
a b s t r a c t
Article history: Received 17 June 2012 Received in revised form 9 July 2013 Accepted 11 July 2013 Available online 3 August 2013
This paper presents a novel current-mode biquadratic filter with three inputs and a single output. The proposed circuit employs five modified current follower transconductance amplifiers (MCFTAs) and only two grounded capacitors. It can realize all five biquadratic filter functions namely: low-pass (LP), bandpass (BP), high-pass (HP), band-stop (BS) and all-pass (AP) at the output terminal by selecting different input current signals, without requiring any parameter-matching conditions or additional circuits. The filter has an orthogonal electronic adjustment of the natural angular frequency ω0 and the quality factor Q, and it has very low element sensitivities of ω0 and Q. Moreover, the proposed filter has the feature of high output impedance and low input impedance, and the use of only grounded capacitors makes it convenient for integrated circuit implementation. The performances of the proposed circuit are illustrated by PSPICE simulations, and the results are in good agreement with theoretical analysis. & 2013 Elsevier Ltd. All rights reserved.
Keywords: Current-mode circuit Current follower transconductance amplifier (CFTA) Biquadratic filter Multiple-input single-output
1. Introduction Recently, the analog integrated circuits designed in current mode are receiving considerable attention due to their potential performance features such as inherently wide bandwidth, higher slew-rate, greater linearity, wider dynamic range, less circuit complexity and lower power consumption [1,2]. One of the standard research topics in current-mode circuit design is an analog filter, which is an important building block, and widely used for continuous-time signal processing. It can be found in many fields including, communications, measurement, and instrumentation, and control systems [3]. The multiple-input single-output (MISO) current-mode biquadratic filters based on different high-performance current-mode active building blocks, such as current conveyors (CCs) [4,5], current differencing transconductance amplifiers (CDTAs) [6], differential voltage current conveyors (DVCCs) [7], current conveyor transconductance amplifiers (CCTAs) [8], differential difference current conveyors (DDCCs) [9], etc., have been reported in literature. Unfortunately, these mentioned circuits so far suffer from one or more of following disadvantages:
n
Corresponding author. Tel.: +86 138 7599 9854. E-mail addresses: [email protected] (X. Nie), [email protected] (Z. Pan). 0026-2692/$ - see front matter & 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.mejo.2013.07.002
(a) They require some external passive resistors [5,7]. (b) They require parameter-matching conditions or additional circuits to realize all the five standard filter functions such as low-pass (LP), band-pass (BP), high-pass (HP), band-stop (BS) and all-pass (AP) [4,6,8,9]. (c) They do not exhibit independent tuning characteristic of the natural angular frequency ω0 and the quality factor Q [6]. (d) There are non-grounded passive components in the configuration, which make the integration of the filter difficult [5]. (e) There are not both low-impedance input and high-impedance output terminals [4,6–9]. Theoretically, the current-mode filter with low-input impedance can be easily cascaded to synthesis higher-order filters, and the current-mode filter with highoutput impedance can easily drive loads and it facilitates cascading without using a buffering device [10,11]. In this paper, an electronically tunable current-mode biquadratic filter with three inputs and single output is presented which provides all the desirable features (a)–(e) simultaneously. The presented filter employs five modified current follower transconductance amplifiers (MCFTAs) [12–14] and only two ground capacitors, which is important in integration point of view. All the current inputs are applied to the low-input impedance terminals, and the output current is taken directly from the current output terminal, which is the high-output impedance. By selecting different three input current signals, the proposed circuit can realize all five standard biquadratic filter functions, i.e., LP, BP, HP,
X. Nie, Z. Pan / Microelectronics Journal 44 (2013) 802–806
BS and AP, without requiring any parameter-matching conditions or additional circuits. The filter has an orthogonal electronic adjustment of the characteristic parameters ω0 and Q, and it also has very low element sensitivities of ω0 and Q. Moreover, by properly setting the ratio of the bias currents, the high-Q filter can easily be obtained. The performances of the proposed circuit are illustrated by PSPICE simulations, and the results agree well with the theoretical analysis.
2. Modified current follower transconductance amplifier (MCFTA) The schematic symbol of MCFTA and its behavior model are shown in Fig. 1. The MCFTA consists of low-impedance input terminal f, high-impedance output terminal z, zc, z , x+ and x . Assuming the standard notation, the terminal defining relations of the MCFTA can be characterized by the following matrix equation: 32 2 3 2 3 0 0 0 0 0 vf if 6i 7 61 6 7 0 0 0 07 76 v z 7 6 z;zc 7 6 76 6 7 6 7 7 6 iz 7 ¼ 6 1 0 6 7 0 0 0 ð1Þ 76 vz 7 6 7 6 7 6i 7 60 6 þg m 0 0 0 54 vxþ 7 4 xþ 5 4 5 0 g m 0 0 0 ix vx
IB ix+ vx+
x+
if M CFTA
f
ixvx-
xz
zc izc
iz vz
vf
if
ziz-
vzc
gmvz gmvz iz iz if
where gm represents the transconductance gain of the MCFTA. For a MCFTA implemented with bipolar technology, the value of gm can be electronically controllable by the external bias current IB. The relation between the transconductance gm and the bias current IB can be expressed as following: gm ¼
IB 2V T
3. Circuit description The proposed current-mode biquadratic filter with three input terminals and one output terminal, which is based on MCFTA and requires only two grounded capacitors, is shown in Fig. 3. The use of grounded capacitors is attractive from monolithic integration point of view because grounded capacitor circuits can compensate for the stray capacitance at their nodes. By routine circuit analysis based on Eqs. (1) and (2), and I1, I2 and I3 are input currents, the output current Ix at the terminal x or x of the MCFTAs and the output current IO of the proposed filter can, respectively, be derived as: ix1 ¼
g m1 ðI 1 I O Þ sC 1
ð3Þ
ix2 ¼
g m2 ðix1 þ ix3 Þ sC 2
ð4Þ
g m3 ðI 2 þ I O Þ g m4
I O ¼ I 3 þ ix2
ix+ ixizizc iz
vx+ vxvzvzc vz
Fig. 1. MCFTA: (a) schematic symbol and (b) behavioral model.
ð2Þ
Here, VT is the thermal voltage, and the value is about 26 mV at 27 1C. IB is the bias current of the MCFTA. Fig. 2 shows a possible bipolar technology implementation of the MCFTA used in this paper, which is slightly modified from the structure given in literature [15]. The input circuitry is formed by transistors Q1–Q6 and the multiple output-operational transconductance amplifier (MO-OTA) consists of transistors Q7–Q32. The current iz is copied to the current izc by transistors Q9 and Q10, and it is inverted to the current iz by transistors Q11–Q13.
ix3 ¼
vz-
803
Fig. 3. Proposed current-mode biquadratic filter based on MCFTA.
Fig. 2. A possible bipolar implementation of the MCFTA.
ð5Þ ð6Þ
804
X. Nie, Z. Pan / Microelectronics Journal 44 (2013) 802–806
where ixi and gmi (i¼1, 2, 3, 4) denote the current ix and the transconductance gain gm belonging to the ith MCFTA. By substituting Eqs. (3)–(5) into Eq. (6), the output current IO can be obtained as: IO ¼
s2 I 3 sðg m2 g m3 =g m4 C 2 ÞI 2 þ ðg m1 g m2 =C 1 C 2 ÞI 1 s2 þ sðg m2 g m3 =g m4 C 2 Þ þ ðg m1 g m2 =C 1 C 2 Þ
ð7Þ
It can be seen from Eq. (7) that the proposed filter can realize all five types of the standard biquadratic filter, which are summarized as follows: (1) The LP response can be realized, when I2 ¼I3 ¼0, and I1 ¼ a input current signal Iin. (2) The BP response can be realized, when I1 ¼ I3 ¼0, and I2 ¼ Iin. (3) The HP response can be realized, when I1 ¼I2 ¼ 0, and I3 ¼Iin. (4) The BS response can be realized, when I2 ¼0, and I1 ¼ I3 ¼ Iin. (5) The AP response can be realized, when I1 ¼ I2 ¼ I3 ¼Iin. Note that there are not any parameter-matching conditions or additional circuits in the realization of all the filter responses. The natural angular frequency ω0 and the quality factor Q are given by: sffiffiffiffiffiffiffiffiffiffiffiffi rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi g m1 g m2 1 I B1 I B2 ω0 ¼ ð8Þ ¼ 2V T C 1 C 2 C1C2
ω0 ¼
pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi α1 α2 α5 β1 β2 g m1 g m2 =C 1 C 2 ¼ α1 α2 α5 β1 β2 I B1 I B2 =C 1 C 2 2V T ð12Þ
and α4 β4 g m4 Q¼ α3 β3 g m3
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi α1 β1 g m1 C 2 α4 β4 I B4 α1 β1 I B1 C 2 ¼ α2 α5 β2 g m2 C 1 α3 β3 I B3 α2 α5 β2 I B2 C 1
ð13Þ
It is evident that the value of ω0 and Q slightly changes by the effect of the MCFTA non-idealities. In this case, the active and passive sensitivities of ω0 and Q are Sωα10;α2 ;α5 ;β1 ;β2 ;gm1 ;gm2 ;IB1 ;IB2 ¼ SωC 10;C 2 ¼
1 2
ð14Þ
SQα1 ;β1 ;gm1 ;C 2 ;IB1 ¼ SQα2 ;α5 ;β2 ;gm2 ;C 1 ;IB2 ¼
1 2
ð15Þ
SQα4 ;β4 ;gm4 ;IB4 ¼ SQα3 ;β3 ;gm3 ;IB3 ¼ 1
ð16Þ
Based on Eqs. (14)–(16), it can be found that all the sensitivities of ω0 and Q are equal to or smaller than unity in magnitude.
5. SPICE simulation results
and
sffiffiffiffiffiffiffiffiffiffiffi sffiffiffiffiffiffiffiffiffiffiffiffiffi g m4 g m1 C 2 I B4 I B1 C 2 ¼ Q¼ g m3 g m2 C 1 I B3 I B2 C 1
ð9Þ
From Eqs. (8) and (9), it can be seen that the quality factor Q for all the filter responses can electronically be tuned by varying gm3 through the bias current IB3 and/or gm4 through the bias current IB4 without affecting the natural angular frequency ω0. Therefore, the proposed filter provides an attractive feature of independent current-controlled of the natural angular frequency ω0 and the quality Q. In addition, the quality factor Q for the proposed filters is temperature insensitive in theory.
4. Non-ideal analysis In this section, the influences of the MCFTA non-idealities on the filter performance have been taken into account. In case of non-ideal MCFTA, the relationship of terminal currents and voltages given in Eq. (1) can be rewritten as [16,17] 2 3 2 3 32 0 0 0 0 0 vf if 6i 7 6α 6 7 0 0 0 0 76 vz 7 6 z;zc 7 6 7 6 7 6 7 76 6 iz 7 ¼ 6 α 0 0 0 0 76 vz 7 ð10Þ 6 7 6 7 76 6i 7 60 6 7 þβg m 0 0 0 54 vxþ 7 4 xþ 5 4 5 0 βg m 0 0 0 ix vx where α¼1 ε, and ε (|ε|⪡1) is the current tracking error from f terminal to z, zc and z terminals. β denotes the transconductance gain gm inaccuracy factor. Re-analyzing the proposed filter shown in Fig. 3, with Eq. (10), the output current IO can be re-obtained as: IO ¼
non-ideal case can be re-expressed as
α5 s2 I3 sðα1 α2 α5 β 2 β3 gm2 gm3 =α4 β4 gm4 C 2 ÞI 2 þ ðα1 α2 α5 β1 β2 gm1 g m2 =C 1 C 2 ÞI 1 s2 þ sðα2 α3 α5 β2 β3 g m2 gm3 =α4 β4 g m4 C 2 Þ þ ðα1 α2 α5 β1 β2 gm1 g m2 =C 1 C 2 Þ
ð11Þ where αi ¼1 εi (i ¼1, 2, 3, 4, 5), and εi denotes the current tracking error belonging to the ith MCFTA, βi denotes the transconductance gain gm inaccuracy factor belonging to the ith MCFTA. Then the natural angular frequency ω0 and the quality factor Q for the
To verify the theoretical study, the behavior of the proposed current-mode biquadratic filter has been simulated in PSPICE. The MCFTA was realized using BJT model as shown in Fig. 2, with the transistor model parameters NR200N (NPN) and PR200N (PNP) of bipolar arrays ALA400 from AT&T [18]. The bias current IS ¼ 100 μA has been chosen in Fig. 2, and the DC supply voltages are +VCC ¼ VEE ¼2 V. The SPICE model parameters NR200N and PR200N are listed in Table 1 [18]. As an example to obtain the filter characteristic with the nature frequency of f0 ¼ω0/2π≈1.22 MHz and Q¼1, the active and passive element values were chosen as: IB1 ¼ IB2 ¼IB3 ¼IB4 ¼ IB5 ¼40 μA, and C1 ¼ C2 ¼0.1 nF. The simulated frequency characteristics for the LP, BP, BS and HP filter responses of the proposed current-mode biquadratic filter based on MCFTA are shown in Fig. 4. Similarly, the simulated AP filter responses including the phase response and magnitude response are depicted in Fig. 5. In order to verify the capability of orthogonal adjustment of parameters ω0 and Q, the element values were chosen as:
Table 1 Parameters of the transistors. nPR200N 2X PNP TRANSISTOR
:model PX PNP þRB ¼ 163IRB ¼ 0RBM ¼ 12:27RC ¼ 25RE ¼ 1:5 þIS ¼ 147E18 EG ¼ 1:206XTI ¼ 1:7XTB ¼ 1:866BF ¼ 110:0 þIKF ¼ 4:718E3NF ¼ 1VAF ¼ 51:8ISE ¼ 50:2E16NE ¼ 1:650 þBR ¼ 0:4745IKR ¼ 12:96E3NR ¼ 1VAR ¼ 9:96ISC ¼ 0NC ¼ 2 þTF ¼ 0:610E9 TR ¼ 0:610E8CJE ¼ 0:36E12VJE ¼ 0:5 þMJE ¼ 0:28CJC ¼ 0:328E12VJC ¼ 0:8MJC ¼ 0:4XCJC ¼ 0:074 þCJS ¼ 1:39E12VJS ¼ 0:55MJS ¼ 0:35FC ¼ 0:5 nNR200N 2X NPN TRANSISTOR :model NX NPN þRB ¼ 262:5IRB ¼ 0RBM ¼ 12:5RC ¼ 25RE ¼ 0:5 þIS ¼ 242E18 EG ¼ 1:206XTI ¼ 2XTB ¼ 1:538BF ¼ 137:5 þIKF ¼ 13:94E3NF ¼ 1VAF ¼ 159:4ISE ¼ 72E16NE ¼ 1:713 þBR ¼ 0:7258IKR ¼ 4:396E3NR ¼ 1VAR ¼ 10:73ISC ¼ 0NC ¼ 2 þTF ¼ 0:425E9 TR ¼ 0:425E8CJE ¼ 0:428E12VJE ¼ 0:5 þMJE ¼ 0:28CJC ¼ 1:97E13VJC ¼ 0:5MJC ¼ 0:3XCJC ¼ 0:065 þCJS ¼ 1:17E12VJS ¼ 0:64MJS ¼ 0:4FC ¼ 0:5
X. Nie, Z. Pan / Microelectronics Journal 44 (2013) 802–806
filter can realize LP, HP, BP, BS and AP functions, without requiring any parameter-matching conditions or additional circuits. The proposed filter has an orthogonal electronic adjustment of the natural angular frequency ω0 and the quality factor Q, and it has very low element sensitivities of ω0 and Q. In addition, the proposed filter has the feature of high output impedance and low input impedance, and the use of only grounded capacitors makes it convenient for integrated circuit implementation. The performances of the proposed circuit are illustrated by PSPICE simulations, and the results are in good agreement with analysis.
10 0 Current Gain (dB)
IB1 ¼ IB2 ¼IB3 ¼IB5 ¼40 μA, and C1 ¼ C2 ¼ 0.1 nF. The bias current IB4 was taken as 40 μA, 80 μA, 120 μA and 160 μA respectively for obtaining Q¼1, 2, 3 and 4. The simulation results are shown in Fig. 6. And it can be easily concluded from Fig. 6 that the adjustment of factor Q is achieved without affecting the center frequency of the proposed filter. In other words, the high values of the factor Q of the proposed filter can be easily obtained by increasing the ratio of IB4/IB3. On the other side, the sensitivities of ω0 and Q for the temperature are also simulated. As an example, the results of the BP responses with Q¼ 1 simulated at 0 1C, 15 1C, 30 1C, 45 1C, 60 1C, and 70 1C, respectively, are illustrated in Fig. 7. It can be obtained that the change of the nature frequencies ω0 is very small while the temperature changes from 0 1C to 70 1C. At the same time, the bandwidths BW are nearly changeless. Consequently, the quality factor Q¼ ω0/BW would be much slightly changed with the temperature. Then the quality factor Q can be considered as nearly temperature insensitive in practice.
6. Conclusion
805
In this paper, a novel multiple-inputs single-output biquadratic filter based on modified current follower transconductance amplifier (MCFTA) has been presented. The proposed biquadratic filter consists of five MCFTAs and only two grounded capacitors. By selecting different three input current signals, the proposed
-10 -20 -30 -40 -50 -60 104
105
106
107
Frequency (Hz)
Fig. 6. Simulated results of the BP response with different Q values.
10 0
-10
Current Gain (dB)
Current Gain (dB)
0
-20 -30 -40 -50
-5 -10 -15 -20 -25 -30 -35
-60 104
105
106
-40 104
107
105
106 Frequecny (Hz)
Frequency (Hz)
Fig. 4. Simulated frequency characteristics for LP, BP, HP and BS responses of the proposed filter in Fig. 3.
Fig. 7. Simulated results of the BP response with different temperatures when Q¼ 1.
Curren Gain (dB)
4 2 0 -2 -4 104
105
106
107
106
107
Frequency (Hz)
Phase (dB)
0 -90 -180 -270 -360 104
107
105 Frequency (Hz)
Fig. 5. Simulated AP phase and magnitude responses of the proposed filter.
806
X. Nie, Z. Pan / Microelectronics Journal 44 (2013) 802–806
Acknowledgments The paper has been supported by National University of Defense Technology (NUDT) Innovation Sustentation Foundation for Excellent Postgraduate (No. B110302) and Hunan Provincial Innovation Foundation for Postgraduate (No. CX2011B012). The authors also would like to thank the anonymous reviewer for his constructive comments that substantially improved the quality of this paper. References [1] C. Toumazou, F.J. Lidgey, D.G. Haigh, Analogue IC Design: The Current-Mode Approach, Peter Peregrinus, London, 1990. [2] D.R. Bhaskar, V.K. Sharma, M. Monis, S.M.I. Rizvi, New current-mode universal biquad filter, Microelectron. J. 30 (1999) 837–839. [3] M.A. Ibrahim, S. Minaei, H.A. Kuntman, A 22.5 MHz current-mode KHN-biquad using differential voltage current conveyor and grounded passive elements, Int. J. Electron. Commun. (AEÜ) 59 (2003) 311–318. [4] Worapong Tangsrirat, Current-tunable current-mode multifunction filter based on dual-output current-controlled conveyors, Int. J. Electron. Commun. (AEÜ) 61 (2007) 528–533. [5] Jiun-Wei Horng, High output impedance current-mode universal biquadratic filters with five inputs using multi-output CCIIs, Microelectron. J. 42 (2011) 693–700. [6] Worapong Tangsrirat, Teerasilapa Dumawipata, Wanlop Surakampontorn, Multiple-input single-output current-mode multifunction filter using current differencing transconductance amplifiers, Int. J. Electron. Commun. (AEÜ) 61 (2007) 209–214.
[7] Hua-Pin Chen, Tunable versatile current-mode universal filter based on plustype DVCCs, Int. J. Electron. Commun. (AEÜ) 66 (2012) 332–339. [8] Sajai Vir Singh, Sudhanshu Maheshwari, Current-processing current-controlled universal biquad filter, Radioengineering 21 (1) (2012) 317–323. [9] Pipat Prommee, Montri Somdunyakanok, CMOS-based current-controlled DDCC and its applications to capacitance multiplier and universal filter, Int. J. Electron. Commun. (AEÜ) 65 (2011) 1–8. [10] A.M. Soliman, New current mode filters using current conveyors, Int. J. Electron. Commun. (AEÜ) 51 (1997) 275–278. [11] W. Tangsrirat, W. Surakampontorn, Systematic realization of cascadable current-mode filters using CDTAs, Frequenz 60 (2006) 241–245. [12] D. Biolek, R. Senani, V. Biolkova, Z. Kolka, Active elements for analog signal processing: classification, review, and new proposals, Radioengineering 17 (2008) 15–32. [13] Yong-an Li, A series of new circuits based on CFTAs, Int. J. Electron. Commun. (AEÜ) 66 (2012) 587–592. [14] Jetsdaporn Statansup, Worapong Tangsrirat, Single-input five-output electronically tunable current-mode biquad consisting of only ZC-CFTAs and grounded capacitors, Radioengineering 3 (2011) 650–655. [15] N. Herencsar, K. Vrba, J. Koton, A. Lahiri, Realisations of single-resistance -controlled quadrature oscillators using generalised current follower transconductance amplifier and unity-gain voltage-follower, Int. J. Electron. 97 (8) (2010) 897–906. [16] Worapong Tangsrirat, Single-input three-output electronically tunable universal current-mode filter using current follower transconductance amplifiers, Int. J. Electron. Commun. (AEÜ) 65 (2011) 783–787. [17] Bhopendra Singh, Abdhesh Kumar Singh, Raj Senani, New universal currentmode biquad using only three ZC-CFTAs, Radioengineering 21 (1) (2012) 273–280. [18] D.R. Frey, Log-domain filtering: an approach to current-mode filtering, IEE Proceeding G (Circuits, Devices and Systems) 140 (6) (1993) 406–416.
Contents lists available at ScienceDirect
Microelectronics Journal journal homepage: www.elsevier.com/locate/mejo
Multiple-input single-output low-input and high-output impedance current-mode biquadratic filter employing five modified CFTAs and only two grounded capacitors Xinhua Nie n, Zhongming Pan College of Mechatronics Engineering and Automation, National University of Defense Technology, Changsha, Hunan 410073, PR China
art ic l e i nf o
a b s t r a c t
Article history: Received 17 June 2012 Received in revised form 9 July 2013 Accepted 11 July 2013 Available online 3 August 2013
This paper presents a novel current-mode biquadratic filter with three inputs and a single output. The proposed circuit employs five modified current follower transconductance amplifiers (MCFTAs) and only two grounded capacitors. It can realize all five biquadratic filter functions namely: low-pass (LP), bandpass (BP), high-pass (HP), band-stop (BS) and all-pass (AP) at the output terminal by selecting different input current signals, without requiring any parameter-matching conditions or additional circuits. The filter has an orthogonal electronic adjustment of the natural angular frequency ω0 and the quality factor Q, and it has very low element sensitivities of ω0 and Q. Moreover, the proposed filter has the feature of high output impedance and low input impedance, and the use of only grounded capacitors makes it convenient for integrated circuit implementation. The performances of the proposed circuit are illustrated by PSPICE simulations, and the results are in good agreement with theoretical analysis. & 2013 Elsevier Ltd. All rights reserved.
Keywords: Current-mode circuit Current follower transconductance amplifier (CFTA) Biquadratic filter Multiple-input single-output
1. Introduction Recently, the analog integrated circuits designed in current mode are receiving considerable attention due to their potential performance features such as inherently wide bandwidth, higher slew-rate, greater linearity, wider dynamic range, less circuit complexity and lower power consumption [1,2]. One of the standard research topics in current-mode circuit design is an analog filter, which is an important building block, and widely used for continuous-time signal processing. It can be found in many fields including, communications, measurement, and instrumentation, and control systems [3]. The multiple-input single-output (MISO) current-mode biquadratic filters based on different high-performance current-mode active building blocks, such as current conveyors (CCs) [4,5], current differencing transconductance amplifiers (CDTAs) [6], differential voltage current conveyors (DVCCs) [7], current conveyor transconductance amplifiers (CCTAs) [8], differential difference current conveyors (DDCCs) [9], etc., have been reported in literature. Unfortunately, these mentioned circuits so far suffer from one or more of following disadvantages:
n
Corresponding author. Tel.: +86 138 7599 9854. E-mail addresses: [email protected] (X. Nie), [email protected] (Z. Pan). 0026-2692/$ - see front matter & 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.mejo.2013.07.002
(a) They require some external passive resistors [5,7]. (b) They require parameter-matching conditions or additional circuits to realize all the five standard filter functions such as low-pass (LP), band-pass (BP), high-pass (HP), band-stop (BS) and all-pass (AP) [4,6,8,9]. (c) They do not exhibit independent tuning characteristic of the natural angular frequency ω0 and the quality factor Q [6]. (d) There are non-grounded passive components in the configuration, which make the integration of the filter difficult [5]. (e) There are not both low-impedance input and high-impedance output terminals [4,6–9]. Theoretically, the current-mode filter with low-input impedance can be easily cascaded to synthesis higher-order filters, and the current-mode filter with highoutput impedance can easily drive loads and it facilitates cascading without using a buffering device [10,11]. In this paper, an electronically tunable current-mode biquadratic filter with three inputs and single output is presented which provides all the desirable features (a)–(e) simultaneously. The presented filter employs five modified current follower transconductance amplifiers (MCFTAs) [12–14] and only two ground capacitors, which is important in integration point of view. All the current inputs are applied to the low-input impedance terminals, and the output current is taken directly from the current output terminal, which is the high-output impedance. By selecting different three input current signals, the proposed circuit can realize all five standard biquadratic filter functions, i.e., LP, BP, HP,
X. Nie, Z. Pan / Microelectronics Journal 44 (2013) 802–806
BS and AP, without requiring any parameter-matching conditions or additional circuits. The filter has an orthogonal electronic adjustment of the characteristic parameters ω0 and Q, and it also has very low element sensitivities of ω0 and Q. Moreover, by properly setting the ratio of the bias currents, the high-Q filter can easily be obtained. The performances of the proposed circuit are illustrated by PSPICE simulations, and the results agree well with the theoretical analysis.
2. Modified current follower transconductance amplifier (MCFTA) The schematic symbol of MCFTA and its behavior model are shown in Fig. 1. The MCFTA consists of low-impedance input terminal f, high-impedance output terminal z, zc, z , x+ and x . Assuming the standard notation, the terminal defining relations of the MCFTA can be characterized by the following matrix equation: 32 2 3 2 3 0 0 0 0 0 vf if 6i 7 61 6 7 0 0 0 07 76 v z 7 6 z;zc 7 6 76 6 7 6 7 7 6 iz 7 ¼ 6 1 0 6 7 0 0 0 ð1Þ 76 vz 7 6 7 6 7 6i 7 60 6 þg m 0 0 0 54 vxþ 7 4 xþ 5 4 5 0 g m 0 0 0 ix vx
IB ix+ vx+
x+
if M CFTA
f
ixvx-
xz
zc izc
iz vz
vf
if
ziz-
vzc
gmvz gmvz iz iz if
where gm represents the transconductance gain of the MCFTA. For a MCFTA implemented with bipolar technology, the value of gm can be electronically controllable by the external bias current IB. The relation between the transconductance gm and the bias current IB can be expressed as following: gm ¼
IB 2V T
3. Circuit description The proposed current-mode biquadratic filter with three input terminals and one output terminal, which is based on MCFTA and requires only two grounded capacitors, is shown in Fig. 3. The use of grounded capacitors is attractive from monolithic integration point of view because grounded capacitor circuits can compensate for the stray capacitance at their nodes. By routine circuit analysis based on Eqs. (1) and (2), and I1, I2 and I3 are input currents, the output current Ix at the terminal x or x of the MCFTAs and the output current IO of the proposed filter can, respectively, be derived as: ix1 ¼
g m1 ðI 1 I O Þ sC 1
ð3Þ
ix2 ¼
g m2 ðix1 þ ix3 Þ sC 2
ð4Þ
g m3 ðI 2 þ I O Þ g m4
I O ¼ I 3 þ ix2
ix+ ixizizc iz
vx+ vxvzvzc vz
Fig. 1. MCFTA: (a) schematic symbol and (b) behavioral model.
ð2Þ
Here, VT is the thermal voltage, and the value is about 26 mV at 27 1C. IB is the bias current of the MCFTA. Fig. 2 shows a possible bipolar technology implementation of the MCFTA used in this paper, which is slightly modified from the structure given in literature [15]. The input circuitry is formed by transistors Q1–Q6 and the multiple output-operational transconductance amplifier (MO-OTA) consists of transistors Q7–Q32. The current iz is copied to the current izc by transistors Q9 and Q10, and it is inverted to the current iz by transistors Q11–Q13.
ix3 ¼
vz-
803
Fig. 3. Proposed current-mode biquadratic filter based on MCFTA.
Fig. 2. A possible bipolar implementation of the MCFTA.
ð5Þ ð6Þ
804
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where ixi and gmi (i¼1, 2, 3, 4) denote the current ix and the transconductance gain gm belonging to the ith MCFTA. By substituting Eqs. (3)–(5) into Eq. (6), the output current IO can be obtained as: IO ¼
s2 I 3 sðg m2 g m3 =g m4 C 2 ÞI 2 þ ðg m1 g m2 =C 1 C 2 ÞI 1 s2 þ sðg m2 g m3 =g m4 C 2 Þ þ ðg m1 g m2 =C 1 C 2 Þ
ð7Þ
It can be seen from Eq. (7) that the proposed filter can realize all five types of the standard biquadratic filter, which are summarized as follows: (1) The LP response can be realized, when I2 ¼I3 ¼0, and I1 ¼ a input current signal Iin. (2) The BP response can be realized, when I1 ¼ I3 ¼0, and I2 ¼ Iin. (3) The HP response can be realized, when I1 ¼I2 ¼ 0, and I3 ¼Iin. (4) The BS response can be realized, when I2 ¼0, and I1 ¼ I3 ¼ Iin. (5) The AP response can be realized, when I1 ¼ I2 ¼ I3 ¼Iin. Note that there are not any parameter-matching conditions or additional circuits in the realization of all the filter responses. The natural angular frequency ω0 and the quality factor Q are given by: sffiffiffiffiffiffiffiffiffiffiffiffi rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi g m1 g m2 1 I B1 I B2 ω0 ¼ ð8Þ ¼ 2V T C 1 C 2 C1C2
ω0 ¼
pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi α1 α2 α5 β1 β2 g m1 g m2 =C 1 C 2 ¼ α1 α2 α5 β1 β2 I B1 I B2 =C 1 C 2 2V T ð12Þ
and α4 β4 g m4 Q¼ α3 β3 g m3
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi α1 β1 g m1 C 2 α4 β4 I B4 α1 β1 I B1 C 2 ¼ α2 α5 β2 g m2 C 1 α3 β3 I B3 α2 α5 β2 I B2 C 1
ð13Þ
It is evident that the value of ω0 and Q slightly changes by the effect of the MCFTA non-idealities. In this case, the active and passive sensitivities of ω0 and Q are Sωα10;α2 ;α5 ;β1 ;β2 ;gm1 ;gm2 ;IB1 ;IB2 ¼ SωC 10;C 2 ¼
1 2
ð14Þ
SQα1 ;β1 ;gm1 ;C 2 ;IB1 ¼ SQα2 ;α5 ;β2 ;gm2 ;C 1 ;IB2 ¼
1 2
ð15Þ
SQα4 ;β4 ;gm4 ;IB4 ¼ SQα3 ;β3 ;gm3 ;IB3 ¼ 1
ð16Þ
Based on Eqs. (14)–(16), it can be found that all the sensitivities of ω0 and Q are equal to or smaller than unity in magnitude.
5. SPICE simulation results
and
sffiffiffiffiffiffiffiffiffiffiffi sffiffiffiffiffiffiffiffiffiffiffiffiffi g m4 g m1 C 2 I B4 I B1 C 2 ¼ Q¼ g m3 g m2 C 1 I B3 I B2 C 1
ð9Þ
From Eqs. (8) and (9), it can be seen that the quality factor Q for all the filter responses can electronically be tuned by varying gm3 through the bias current IB3 and/or gm4 through the bias current IB4 without affecting the natural angular frequency ω0. Therefore, the proposed filter provides an attractive feature of independent current-controlled of the natural angular frequency ω0 and the quality Q. In addition, the quality factor Q for the proposed filters is temperature insensitive in theory.
4. Non-ideal analysis In this section, the influences of the MCFTA non-idealities on the filter performance have been taken into account. In case of non-ideal MCFTA, the relationship of terminal currents and voltages given in Eq. (1) can be rewritten as [16,17] 2 3 2 3 32 0 0 0 0 0 vf if 6i 7 6α 6 7 0 0 0 0 76 vz 7 6 z;zc 7 6 7 6 7 6 7 76 6 iz 7 ¼ 6 α 0 0 0 0 76 vz 7 ð10Þ 6 7 6 7 76 6i 7 60 6 7 þβg m 0 0 0 54 vxþ 7 4 xþ 5 4 5 0 βg m 0 0 0 ix vx where α¼1 ε, and ε (|ε|⪡1) is the current tracking error from f terminal to z, zc and z terminals. β denotes the transconductance gain gm inaccuracy factor. Re-analyzing the proposed filter shown in Fig. 3, with Eq. (10), the output current IO can be re-obtained as: IO ¼
non-ideal case can be re-expressed as
α5 s2 I3 sðα1 α2 α5 β 2 β3 gm2 gm3 =α4 β4 gm4 C 2 ÞI 2 þ ðα1 α2 α5 β1 β2 gm1 g m2 =C 1 C 2 ÞI 1 s2 þ sðα2 α3 α5 β2 β3 g m2 gm3 =α4 β4 g m4 C 2 Þ þ ðα1 α2 α5 β1 β2 gm1 g m2 =C 1 C 2 Þ
ð11Þ where αi ¼1 εi (i ¼1, 2, 3, 4, 5), and εi denotes the current tracking error belonging to the ith MCFTA, βi denotes the transconductance gain gm inaccuracy factor belonging to the ith MCFTA. Then the natural angular frequency ω0 and the quality factor Q for the
To verify the theoretical study, the behavior of the proposed current-mode biquadratic filter has been simulated in PSPICE. The MCFTA was realized using BJT model as shown in Fig. 2, with the transistor model parameters NR200N (NPN) and PR200N (PNP) of bipolar arrays ALA400 from AT&T [18]. The bias current IS ¼ 100 μA has been chosen in Fig. 2, and the DC supply voltages are +VCC ¼ VEE ¼2 V. The SPICE model parameters NR200N and PR200N are listed in Table 1 [18]. As an example to obtain the filter characteristic with the nature frequency of f0 ¼ω0/2π≈1.22 MHz and Q¼1, the active and passive element values were chosen as: IB1 ¼ IB2 ¼IB3 ¼IB4 ¼ IB5 ¼40 μA, and C1 ¼ C2 ¼0.1 nF. The simulated frequency characteristics for the LP, BP, BS and HP filter responses of the proposed current-mode biquadratic filter based on MCFTA are shown in Fig. 4. Similarly, the simulated AP filter responses including the phase response and magnitude response are depicted in Fig. 5. In order to verify the capability of orthogonal adjustment of parameters ω0 and Q, the element values were chosen as:
Table 1 Parameters of the transistors. nPR200N 2X PNP TRANSISTOR
:model PX PNP þRB ¼ 163IRB ¼ 0RBM ¼ 12:27RC ¼ 25RE ¼ 1:5 þIS ¼ 147E18 EG ¼ 1:206XTI ¼ 1:7XTB ¼ 1:866BF ¼ 110:0 þIKF ¼ 4:718E3NF ¼ 1VAF ¼ 51:8ISE ¼ 50:2E16NE ¼ 1:650 þBR ¼ 0:4745IKR ¼ 12:96E3NR ¼ 1VAR ¼ 9:96ISC ¼ 0NC ¼ 2 þTF ¼ 0:610E9 TR ¼ 0:610E8CJE ¼ 0:36E12VJE ¼ 0:5 þMJE ¼ 0:28CJC ¼ 0:328E12VJC ¼ 0:8MJC ¼ 0:4XCJC ¼ 0:074 þCJS ¼ 1:39E12VJS ¼ 0:55MJS ¼ 0:35FC ¼ 0:5 nNR200N 2X NPN TRANSISTOR :model NX NPN þRB ¼ 262:5IRB ¼ 0RBM ¼ 12:5RC ¼ 25RE ¼ 0:5 þIS ¼ 242E18 EG ¼ 1:206XTI ¼ 2XTB ¼ 1:538BF ¼ 137:5 þIKF ¼ 13:94E3NF ¼ 1VAF ¼ 159:4ISE ¼ 72E16NE ¼ 1:713 þBR ¼ 0:7258IKR ¼ 4:396E3NR ¼ 1VAR ¼ 10:73ISC ¼ 0NC ¼ 2 þTF ¼ 0:425E9 TR ¼ 0:425E8CJE ¼ 0:428E12VJE ¼ 0:5 þMJE ¼ 0:28CJC ¼ 1:97E13VJC ¼ 0:5MJC ¼ 0:3XCJC ¼ 0:065 þCJS ¼ 1:17E12VJS ¼ 0:64MJS ¼ 0:4FC ¼ 0:5
X. Nie, Z. Pan / Microelectronics Journal 44 (2013) 802–806
filter can realize LP, HP, BP, BS and AP functions, without requiring any parameter-matching conditions or additional circuits. The proposed filter has an orthogonal electronic adjustment of the natural angular frequency ω0 and the quality factor Q, and it has very low element sensitivities of ω0 and Q. In addition, the proposed filter has the feature of high output impedance and low input impedance, and the use of only grounded capacitors makes it convenient for integrated circuit implementation. The performances of the proposed circuit are illustrated by PSPICE simulations, and the results are in good agreement with analysis.
10 0 Current Gain (dB)
IB1 ¼ IB2 ¼IB3 ¼IB5 ¼40 μA, and C1 ¼ C2 ¼ 0.1 nF. The bias current IB4 was taken as 40 μA, 80 μA, 120 μA and 160 μA respectively for obtaining Q¼1, 2, 3 and 4. The simulation results are shown in Fig. 6. And it can be easily concluded from Fig. 6 that the adjustment of factor Q is achieved without affecting the center frequency of the proposed filter. In other words, the high values of the factor Q of the proposed filter can be easily obtained by increasing the ratio of IB4/IB3. On the other side, the sensitivities of ω0 and Q for the temperature are also simulated. As an example, the results of the BP responses with Q¼ 1 simulated at 0 1C, 15 1C, 30 1C, 45 1C, 60 1C, and 70 1C, respectively, are illustrated in Fig. 7. It can be obtained that the change of the nature frequencies ω0 is very small while the temperature changes from 0 1C to 70 1C. At the same time, the bandwidths BW are nearly changeless. Consequently, the quality factor Q¼ ω0/BW would be much slightly changed with the temperature. Then the quality factor Q can be considered as nearly temperature insensitive in practice.
6. Conclusion
805
In this paper, a novel multiple-inputs single-output biquadratic filter based on modified current follower transconductance amplifier (MCFTA) has been presented. The proposed biquadratic filter consists of five MCFTAs and only two grounded capacitors. By selecting different three input current signals, the proposed
-10 -20 -30 -40 -50 -60 104
105
106
107
Frequency (Hz)
Fig. 6. Simulated results of the BP response with different Q values.
10 0
-10
Current Gain (dB)
Current Gain (dB)
0
-20 -30 -40 -50
-5 -10 -15 -20 -25 -30 -35
-60 104
105
106
-40 104
107
105
106 Frequecny (Hz)
Frequency (Hz)
Fig. 4. Simulated frequency characteristics for LP, BP, HP and BS responses of the proposed filter in Fig. 3.
Fig. 7. Simulated results of the BP response with different temperatures when Q¼ 1.
Curren Gain (dB)
4 2 0 -2 -4 104
105
106
107
106
107
Frequency (Hz)
Phase (dB)
0 -90 -180 -270 -360 104
107
105 Frequency (Hz)
Fig. 5. Simulated AP phase and magnitude responses of the proposed filter.
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Acknowledgments The paper has been supported by National University of Defense Technology (NUDT) Innovation Sustentation Foundation for Excellent Postgraduate (No. B110302) and Hunan Provincial Innovation Foundation for Postgraduate (No. CX2011B012). The authors also would like to thank the anonymous reviewer for his constructive comments that substantially improved the quality of this paper. References [1] C. Toumazou, F.J. Lidgey, D.G. Haigh, Analogue IC Design: The Current-Mode Approach, Peter Peregrinus, London, 1990. [2] D.R. Bhaskar, V.K. Sharma, M. Monis, S.M.I. Rizvi, New current-mode universal biquad filter, Microelectron. J. 30 (1999) 837–839. [3] M.A. Ibrahim, S. Minaei, H.A. Kuntman, A 22.5 MHz current-mode KHN-biquad using differential voltage current conveyor and grounded passive elements, Int. J. Electron. Commun. (AEÜ) 59 (2003) 311–318. [4] Worapong Tangsrirat, Current-tunable current-mode multifunction filter based on dual-output current-controlled conveyors, Int. J. Electron. Commun. (AEÜ) 61 (2007) 528–533. [5] Jiun-Wei Horng, High output impedance current-mode universal biquadratic filters with five inputs using multi-output CCIIs, Microelectron. J. 42 (2011) 693–700. [6] Worapong Tangsrirat, Teerasilapa Dumawipata, Wanlop Surakampontorn, Multiple-input single-output current-mode multifunction filter using current differencing transconductance amplifiers, Int. J. Electron. Commun. (AEÜ) 61 (2007) 209–214.
[7] Hua-Pin Chen, Tunable versatile current-mode universal filter based on plustype DVCCs, Int. J. Electron. Commun. (AEÜ) 66 (2012) 332–339. [8] Sajai Vir Singh, Sudhanshu Maheshwari, Current-processing current-controlled universal biquad filter, Radioengineering 21 (1) (2012) 317–323. [9] Pipat Prommee, Montri Somdunyakanok, CMOS-based current-controlled DDCC and its applications to capacitance multiplier and universal filter, Int. J. Electron. Commun. (AEÜ) 65 (2011) 1–8. [10] A.M. Soliman, New current mode filters using current conveyors, Int. J. Electron. Commun. (AEÜ) 51 (1997) 275–278. [11] W. Tangsrirat, W. Surakampontorn, Systematic realization of cascadable current-mode filters using CDTAs, Frequenz 60 (2006) 241–245. [12] D. Biolek, R. Senani, V. Biolkova, Z. Kolka, Active elements for analog signal processing: classification, review, and new proposals, Radioengineering 17 (2008) 15–32. [13] Yong-an Li, A series of new circuits based on CFTAs, Int. J. Electron. Commun. (AEÜ) 66 (2012) 587–592. [14] Jetsdaporn Statansup, Worapong Tangsrirat, Single-input five-output electronically tunable current-mode biquad consisting of only ZC-CFTAs and grounded capacitors, Radioengineering 3 (2011) 650–655. [15] N. Herencsar, K. Vrba, J. Koton, A. Lahiri, Realisations of single-resistance -controlled quadrature oscillators using generalised current follower transconductance amplifier and unity-gain voltage-follower, Int. J. Electron. 97 (8) (2010) 897–906. [16] Worapong Tangsrirat, Single-input three-output electronically tunable universal current-mode filter using current follower transconductance amplifiers, Int. J. Electron. Commun. (AEÜ) 65 (2011) 783–787. [17] Bhopendra Singh, Abdhesh Kumar Singh, Raj Senani, New universal currentmode biquad using only three ZC-CFTAs, Radioengineering 21 (1) (2012) 273–280. [18] D.R. Frey, Log-domain filtering: an approach to current-mode filtering, IEE Proceeding G (Circuits, Devices and Systems) 140 (6) (1993) 406–416.