Electronically Controllable Current-Mode Universal ... - CiteSeerX

Circuits Syst Signal Process (2008) 27: 113–122 DOI 10.1007/s00034-008-9014-2

Electronically Controllable Current-Mode Universal Biquad Filter Using Single DO-CCCDTA Montree Siripruchyanun · Winai Jaikla

Received: 25 December 2006 / Revised: 20 April 2007 / Published online: 17 January 2008 © Birkhäuser Boston 2008

Abstract This article presents a three-input two-output current-mode universal biquadratic filter performing completely standard functions: low-pass, high-pass, bandpass, band-reject and all-pass functions, based-on a dual output current controlled current differencing transconductance amplifier (DO-CCCDTA). The features of the circuit are that the bandwidth and pole frequency can be tuned electronically via the input bias currents and that the circuit description is very simple, consisting of merely a single DO-CCCDTA and two grounded capacitors. Additionally, each function response can be selected by suitably selecting input signals. Without any external resistors and using only grounded elements, the proposed circuit is very suitable to further develop into an integrated circuit. PSPICE simulation results are depicted. The given results agree well with the theoretical anticipation. The maximum power consumption is approximately 1.81 mW at ±1.5 V power supply voltages. Keywords Current-mode · Biquadratic filter · DO-CCCDTA

1 Introduction In electrical engineering, as is well known, an analog filter is an important block and is widely used for continuous-time signal processing. It is found in many fields: for instance, communication, measurement and instrumentation, and control systems [9, M. Siripruchyanun () Department of Teacher Training in Electrical Engineering, Faculty of Technical Education, King Mongkut’s Institute of Technology North Bangkok, Bangkok, 10800, Thailand e-mail: [email protected] W. Jaikla Electric and Electronic Program, Faculty of Industrial Technology, Suan Sunandha Rajabhat University, Dusit, Bangkok, 10300, Thailand e-mail: [email protected]

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15]. One of the most popular analog filters is the universal biquadratic filter since it can provide several functions. Nowadays, a universal filter working in current mode is becoming more popular than a voltage-mode one. Since the last decade, there has been much effort to reduce the supply voltage of analog systems due to the demand for portable and battery-powered equipment. Since a low-voltage operating circuit becomes necessary, the current-mode technique is ideally suited for this purpose. Actually, a circuit using the current-mode technique has many other advantages: for example, larger dynamic range, higher bandwidth, greater linearity, simpler circuitry and lower power consumption [1, 21]. The literature surveys show that a large number of circuit realizations for currentmode universal filters have been reported [2, 5, 6, 8, 12–14, 16–19, 22, 23]. Unfortunately, these reported circuits suffer from one or more of the following weaknesses: (a) Excessive use of active and/or passive elements and the need to change circuit topologies to achieve several functions [6, 18, 19, 22, 23] (b) Lack of electronic adjustability [6, 8, 17, 19, 22, 23, 25] (c) The outputs of the filter responses not being in high output impedance [5, 24], so that cascadability is difficult to achieve (d) Use of the floating capacitor, which is not convenient to further fabricate in ICs [14, 17, 19, 25] (e) Completely standard functions cannot be provided [13, 14, 16–18, 23, 25] A reported 5-terminal active element, namely the current differencing transconductance amplifier (CDTA) [3], seems to be a versatile component in the realization of a class of analog signal processing circuits, especially analog frequency filters [3, 4]. It is really a current-mode element whose input and output signals are currents. In addition, it can also adjust the output current gain. However, the CDTA can not be controlled by the parasitic resistances at two current input ports [3, 4, 20]. Recently, Jaikla and Siripruchyanun have proposed a modified-version CDTA, whose parasitic resistances at two current input ports can be controlled by an input bias current. It is called the current controlled current differencing transconductance amplifier (CCCDTA) [10]. It seems to be a useful building block, since many circuits and systems can be implemented by employing only a single CCCDTA. This work proposes a new three-input two-output current-mode universal biquadratic filter, emphasizing the use of a DO-CCCDTA, which is slightly modified from the proposed CCCDTA to extend its usability. The features of proposed circuit are: the proposed universal filter can provide completely standard functions without changing circuit topology by appropriately selecting the input signals by a digital method; the circuit description is very simple, consisting of a single DO-CCCDTA and two grounded capacitors, suitable for fabricating in a monolithic chip; and the filter does not require any external resistor and passive parameter matching conditions. In addition, the pole frequency and the bandwidth of the proposed circuit can be tuned electronically by adjusting the external bias currents. The performances of proposed circuit are illustrated by PSPICE simulations, they show good agreement with the theory, as mentioned.

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2 Principle of Operation 2.1 Dual Output Current Controlled Current Differencing Transconductance Amplifier (DO-CCCDTA) Since the proposed circuit is based on a DO-CCCDTA, a brief review of the DOCCCDTA is given in this section. Basically, the DO-CCCDTA is composed of translinear elements, mixed loops and complementary current mirrors. Generally, DO-CCCDTA properties are similar to those of a conventional CDTA, except that the input voltages of the DO-CCCDTA are not zero and the DO-CCCDTA has finite input resistances Rp and Rn at the p and n input terminals, respectively. These parasitic resistances are equal and can be controlled by the bias current IB1 . The transconductance (gm ) of the CCCDTA can be controlled by the bias current IB2 as shown in the following equation: ⎤ ⎡ Rp Vp ⎢ Vn ⎥ ⎢ 0 ⎥ ⎢ ⎢ ⎣ Iz1,2 ⎦ = ⎣ 1 Ix1,2 0 ⎡

0 Rn −1 0

0 0 0 0

⎤⎡ ⎤ 0 Ip ⎢ ⎥ 0 ⎥ ⎥ ⎢ In ⎥ , ⎦ ⎣ Vx ⎦ 0 Vz1 −gm

(1)

where R p = Rn =

VT , 2IB1

(2)

and gm =

IB2 , 2VT

(3)

where VT is the thermal voltage. The symbol and the equivalent circuit of the CCCDTA are illustrated in Fig. 1(a) and (b), respectively. 2.2 Proposed Current-Mode Universal Biquad Filter The proposed current-mode universal filter is shown in Fig. 2, where IB1 and IB2 are input bias currents of the DO-CCCDTA. Straightforwardly analyzing the circuit in Fig. 2, the output currents can be obtained as IO1 =

 1  2 s C1 C2 Rp + sC2 Iin2 − sC2 Iin1 + D(s)Iin3 D(s)

(4)

 gm  2 s C1 C2 Rp + sC2 Iin2 − sC2 Iin1 , sC2 D(s)

(5)

and IO2 =

where D(s) = s 2 C1 C2 Rn + sC2 + gm . From (4) and (5), the magnitudes of the input currents Iin1 , Iin2 and Iin3 are chosen as in Table 1 to obtain a standard function of the

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Fig. 1 DO-CCCDTA. (a) Symbol, (b) Equivalent circuit

Fig. 2 Proposed current-mode universal filter

second-order network. The circuit of selection can be seen in [12]. From (4), the pole frequency (ω0 ) and quality factor (Q0 ) of each filter response can be expressed as ω0 =

gm , C 1 C 2 Rp

(6)

and

Q0 =

C 1 Rp g m . C2

(7)

Circuits Syst Signal Process (2008) 27: 113–122 Table 1 The Iin1 , Iin2 and Iin3 values selection for each filter function response

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Filter responses IO1

Input IO2

Iin1

Iin2

Iin3

BP

LP

1

0

0

HP

–

1

1

0

BR

LP

1

0

1

AP

–

2

0

1

Substituting the intrinsic resistance and transconductance as depicted in (2) and (3) into (6) and (7) yields

2 IB1 IB2 ω0 = , (8) VT C1 C2 and

Q0 =

C2 IB2 . C1 IB1

(9)

From (8) and (9), it can be remarked that the pole frequency can be adjusted by IB1 and IB2 without affecting the quality factor by keeping the ratio IB1 and IB2 constant. In addition, the bandwidth (BW) of the system can be expressed by BW =

ω0 2IB1 = . Q0 C2 VT

(10)

We found that the bandwidth can be linearly controlled by IB1 . Moreover, it can be seen that the pole frequency can be adjusted independently from the bandwidth by varying IB2 . 2.3 Circuit Sensitivities The sensitivities of the proposed circuit can be found as 1 ω SC10,C2 = − , 2 1 Q SC20,R1 = ; 2

1 ω SIB10 ,IB2 = , 2 1 Q SC10,Rn2 = − , 2

ω

SVT0 = −1,

(11) (12)

and SCBW = −1, 2 ,VT

SIBW = 1. B1

(13)

Therefore, all the active and passive sensitivities are equal to or less than unity in magnitude.

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Fig. 3 Internal construction of DO-CCCDTA

2.4 Non-ideal Case For the non-ideal case, the Iz and Ix of the DO-CCCDTA can be respectively characterized by [11] Iz1 = αp1 Ip − αn1 In ,

(14)

Iz2 = αp2 Ip − αn2 In ,

(15)

Ix1 = β1 gm Vz1 ,

(16)

and Ix2 = β2 gm Vz1 ,

(17)

where αpi , αni and βi are transferred error values deviated from one. By straightforward analysis of the internal construction of the DO-CCCDTA in Fig. 3, we will obtain the αpi , αni and βi as gm6 gm12 gm22 + gm3 gm23 gm18 αp1 ∼ , = gm12 gm18 (gm6 + gm3 ) αn1 ∼ =

gm5 gm22 gm17 gm16 gm18

+

gm2 gm11 gm23 gm10 gm12

, gm5 + gm2 gm6 gm12 gm19 + gm3 gm13 gm18 , αp2 ∼ = gm12 gm18 (gm6 + gm3 ) αn2 ∼ = β1 ∼ = and β2 ∼ =

gm5 gm19 gm17 gm16 gm18

gm2 gm11 gm13 gm10 gm12

gm5 + gm2

,

(19) (20) (21)

 gm27 gm30 gm32 gm25 gm29 gm27 , − + gm26 (gm29 + gm30 ) gm24 gm31 (gm29 + gm30 ) gm26

(22)

 gm33 gm25 gm29 gm28 gm28 gm30 − + . gm26 (gm29 + gm30 ) gm24 gm31 (gm29 + gm30 ) gm26

(23)





+

(18)

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If gmi  gπi and transistors are matched, we have gm10 = gm11 , gm1 = gm2 = gm3 = gm4 = gm5 = gm6 = gm20 = gm21 , gm12 = gm13 , gm16 = gm17 , gm18 = gm19 , gm24 = gm25 , gm26 = gm27 = gm28 , gm31 = gm32 = gm33 and gm29 = gm30 = gm . The parameters αni ∼ = αpi ∼ =β∼ = 1. In the case of non-ideality and reanalyzing the proposed filter in Fig. 2, it yields the output currents as IO1 =

 1  αn2 D(s) − αn1 αp2 β1 gm Iin2 − αp2 sC2 Iin1 + D(s)Iin3 D(s)

(24)

IO2 =

 gm  αn1 β2 D(s) − αp1 αn1 β1 β2 gm Iin2 − αp1 β2 sC2 Iin1 , sC2 D(s)

(25)

and

while the denominator polynomial is changed to D(s) = s 2 C1 C2 Rp + sC2 + αp1 β2 gm . In this case, ω0 and Q0 are subsequently changed to

αp1 β2 gm ω0 = , C 1 C 2 Rp and

(26)

(27)

Q0 =

αp1 β2 C1 Rp gm , C2

(28)

while BW is still expressed by (10). Practically, the αpi , αni and βi originate from intrinsic resistances and stray capacitances in the DO-CCCDTA. These errors affect the sensitivity to temperature and high frequency response of the proposed circuit; thus a circuit should be carefully designed to make these errors as low as possible. Consequently, these deviations are very small and can be ignored.

3 Simulation Results and Discussion To prove the performances of the proposed circuit, the PSPICE simulation program was used for the examinations. The PNP and NPN transistors employed in the proposed circuit were simulated by respectively using the parameters of the PR200N and NR200N bipolar transistors of an ALA400 transistor array from AT&T [7]. Figure 3 depicts the schematic description of the DO-CCCDTA used in the simulations. The circuit was biased with ±1.5 V supply voltages, and C1 = C2 = 10 nF, IB1 = 50 µA and IB2 = 200 µA were chosen to obtain resistance and transconductance values of 260  and 3.846 mS, respectively. This yields a pole frequency of 56.75 kHz. The calculated value of this parameter from (8) is 61.24 kHz. The results shown in Fig. 4 are the gain and phase responses of the proposed biquad filter obtained from Fig. 2, where IB1 and IB2 are equal to 50 µA and 200 µA, respectively. It is clearly seen that the proposed biquad circuit can provide low-pass, high-pass, band-pass, band-reject

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Fig. 4 Gain and phase responses of the biquad filter. (a) LP, (b) HP, (c) BP, (d) BR, (e) AP

and all-pass functions dependent on digital selection as shown in Table 1, without modifying circuit topology. Figure 5 displays magnitude responses of band-pass functions with different IB1 values. It is shown that the bandwidth of the response can be adjusted by the input bias current IB1 . Figure 6 shows magnitude responses of band-pass function with

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Fig. 5 Band-pass responses for different values of IB1

Fig. 6 Band-pass responses for different values of IB2

Fig. 7 Band-pass responses for different values of IB1 and IB2

different IB2 values. It is shown that the quality factor can be adjusted by the input bias current IB2 . Figure 7 shows magnitude responses of band-pass functions where IB1 and IB2 are set equally. It is found that the pole frequency can be adjusted without affecting the quality factor. The maximum power consumption is about 1.81 mW. 4 Conclusions A current-mode universal biquadratic filter based on a DO-CCCDTA has been presented. The advantages of the proposed circuit are that it performs low-pass, highpass, band-pass, band-reject and all-pass functions with two outputs depending on an appropriate selection of three input signals by a digital method; the bandwidth and the pole frequency can be electronically controlled via input bias currents; and it is easily modified to use in control systems using a microcontroller [21]. The circuit description comprises only a single DO-CCCDTA and two grounded capacitors. With these features, it is very suitable to realize the proposed circuit in a monolithic chip for use in battery-powered, portable electronic equipment such as wireless communication system devices. References 1. D.R. Bhaskar, V.K. Sharma, M. Monis, S.M.I. Rizvi, New current-mode universal biquad filter, Microelectronics Journal, vol. 30, pp. 837–839, 1999.

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2. M. Bhusan, R.W. Newcomb, Grounding of capacitors in integrated circuits, Electronics Letters, vol. 3, pp. 148–149, 1967. 3. D. Biolek, CDTA–building block for current-mode analog signal processing, In Proceedings of the European Conference on Circuit Theory and Design 2003—ECCTD’03, Krakow, Poland, pp. 397– 400, 2003. 4. D. Biolek, V. Biolkova, Universal biquads using CDTA elements for cascade filter design, In 13th Int. Multi Conference CSCC2003, Corfu, Greece, pp. 8–12, 2003. 5. S. Celma, J. Sabadell, P. Martinez, Universal filter using unity-gain cells, Electronics Letters, vol. 31, pp. 1817–1818, 1995. 6. C.M. Chang, T.S. Liao, T.Y. Yu, E.S. Lin, C.H. Teng, C.L. Hou, Novel universal current-mode filters using unity-gain cells, Int. Journal of Electronics, vol. 86, pp. 23–30, 2001. 7. D.R. Frey, Log-domain filtering: an approach to current-mode filtering, IEE Proc. Circuit Devices Syst., vol. 140, pp. 406–416, 1993. 8. J.W. Horng, Current-conveyors based allpass filters and quadrature oscillators employing grounded capacitors and resistors, Computers and Electrical Engineering, vol. 31, pp. 81–92, 2005. 9. 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, AEU International Journal of Electronics and Communications, vol. 59, pp. 311–318, 2005. 10. W. Jaikla, M. Siripruchyanun, Current controlled current differencing transconductance amplifier (CCCDTA): A new building block and its applications, Proceedings of ECTI Conference 2006, Ubonratchathani, Thailand, pp. 348–351, May 2006. 11. A.U. Keskin, D. Biolek, E. Hancioglu, V. Biolkova, Current-mode KHN filter employing current differencing transconductance amplifiers, AEU International Journal of Electronics and Communications, vol. 60, pp. 443–446, 2006. 12. Y. Maruyama, A. Hyogo, K. Sekine, A digitally programmable CMOS biquad filter using currentmode integrators, IEICE Trans. on Fundamentals, vol. E85-A, no. 2, pp. 316–323, 2002. 13. N. Pandey, S.K. Paul, A. Bhattacharyya, S.B. Jain, A novel current controlled current mode universal filter: SITO approach, IEICE Electronics Express, vol. 2, pp. 451–457, 2005. 14. M. Sagbas, K. Fidanboylu, Electronically tunable current-mode second-order universal filter using minimum elements, Electronics Letters, vol. 40, pp. 2–4, 2004. 15. A.S. Sedra, K.C. Smith, Microelectronic Circuits, 3rd ed., Florida: Holt, Rinehart and Winston, 1991. 16. R. Senani, V.K. Singh, A.K. Singh, D.R. Bhaskar, Novel electronically controllable current-mode universal biquad filter, IEICE Electronics Express, vol. 1, pp. 410–415, 2004. 17. N.A. Shah, M.A. Malink, High impedance voltage and current-mode multifunction filters, AEU International Journal of Electronics and Communications, vol. 59, pp. 262–266, 2005. 18. N.A. Shah, M.A. Malik, Voltage/current-mode universal filter using FTFN and CFA, Analog Integrated Circuits and Signal Processing, vol. 45, pp. 197–203, 2005. 19. R.K. Sharma, R. Senani, Universal current-mode biquad using a single CFOA, Int. J. Electronics, vol. 91, pp. 175–183, 2004. 20. W. Tangsrirat, W. Surakampontorn, Systematic realization of cascadable current-mode filters using current differencing transconductance amplifiers, Frequenz, vol. 60, pp. 241–245, 2006. 21. C. Toumazou, F.J. Lidgey, D.G. Haigh, Analogue IC Design: The Current-Mode Approach, London: Peter Peregrinus, 1990. 22. S.H. Tu, C.M. Chang, K.P. Liao, Novel versatile insensitive universal current-mode biquad employing two second-generation current conveyors, Int. J. Electronics, vol. 89, pp. 897–903, 2002. 23. H.Y. Wang, C.T. Lee, Versatile insensitive current-mode universal biquad implementation using current conveyors, IEEE Trans. on. Circuits and Systems II, vol. 48, pp. 409–413, 2001. 24. R.M. Weng, J.R. Lai, M.H. Lee, New universal biquad filters using only two unity-gain cells, Int. J. Electronics, vol. 87, pp. 57–61, 2000. 25. J. Wu, E.I. El-Masry, Universal voltage and current-mode OTAs based biquads, Int. J. Electronics, vol. 85, pp. 553–560, 1998.