Realization of Tunable Pole-Q Current-Mode OTA-C Universal Filter

Transcription

1 Circuits Syst Signal Process (2010) 29: DOI /s Realization of Tunable Pole-Q Current-Mode OTA-C Universal Filter Pipat Prommee Thanate Pattanatadapong Received: 23 February 2009 / Revised: 22 October 2009 / Published online: 27 April 2010 Springer Science+Business Media, LLC 2010 Abstract A realization of a current-mode operational transconductance amplifiercapacitor (OTA-C) universal filter with tunable pole-q is proposed. A biquadratic band-reject function is used as the initial synthesis function based on three integrator blocks. Consequently, the proposed filter uses a total of three multiple-output OTAs and three grounded capacitors. Five types of transfer functions, namely, low-pass, high-pass, band-pass, band-reject, and all-pass responses, can be obtained without changing the circuit topology. The pole-q (Q 0 ) and the pole-frequency (ω 0 ) parameters are independently tuned. The Q 0 and ω 0 parameters are electronically tuned by adjusting the transconductance gains of the OTAs. Furthermore, Q 0 can be tuned by varying the capacitor manually without affecting ω 0. SPICE simulation results of the proposed filter are presented. Keywords OTA Current-mode circuit Universal filter Tunable pole-q 1 Introduction Current-mode active filters have received much attention due to their many advantages over their voltage-mode counterparts. Because of the simplicity of the building blocks used, current-mode circuits can be very compact and operate with low voltages. This leads to reduced area and power consumption requirements, as well as P. Prommee ( ) T. Pattanatadapong Department of Telecommunications Engineering, Faculty of Engineering, King Mongkut s Institute of Technology Ladkrabang, Bangkok 10520, Thailand pipat@telecom.kmitl.ac.th P. Prommee kppipat@kmitl.ac.th T. Pattanatadapong thanate@telecom.kmitl.ac.th

2 914 Circuits Syst Signal Process (2010) 29: improved high frequency performance. Moreover, the integrated circuit implementation uses grounded capacitors to eliminate the effect of bottom-plate parasitic capacitances. In current-mode circuits, summing of the current signals requires only a circuit node. As a result, current signals can be easily replicated and scaled using current mirrors, and they have the potential to operate at higher signal bandwidths [1]. Previous works that utilize the current-mode technique include those using current followers (CFs) [2], secondgenerationcurrentconveyors (CCIIs) [3 5], andoperational transconductance amplifiers (OTAs) [6 11]. Some OTA-C filters use four OTAs and three grounded capacitors to obtain the five types of standard transfer functions [12]. The analytical synthesis of filter functions based on OTA-C [13, 14] and DDCC [15] has also been introduced. Several current-mode universal biquadratic filters with multiple-input and singleoutput design have been presented in the literature. Chang and Pai [6, 7] haveproposed circuits which use two to three OTAs, where the pole-q(q 0 ) is electronically tunable. However, the pole-frequency (ω 0 ) and Q 0 cannot be tuned independently. Another filter [8] uses three OTAs, wherein the ω 0 and Q 0 parameters can be electronically tuned by adjusting the finite current bias of the OTA. This paper proposes a universal filter with tunable pole-q based on three multipleoutput OTAs (MOOTAs) and three grounded capacitors. A synthesis algorithm for a band-reject function based on lossless integrator building blocks is proposed. The pole-q can be independently tuned by adjusting the transconductance gain of the OTA or by changing a grounded capacitor. Low sensitivities within ±0.5 with respect to the passive and active elements are obtained. The filter characteristic transfer functions including low-pass (LP), high-pass (HP), band-pass (BP), band-reject (BR), and all-pass (AP) can be obtained without changing the circuit topology. 2 Circuit Descriptions 2.1 Multiple-Output OTA and Lossless Integrator A simple MOOTA is realized by bipolar junction transistors (BJTs) as shown in Fig. 1. It is a versatile device that produces multiple positive and negative output currents I O by applying a differential input voltage V in. The transconductance g m is given by ± I O = g m I B (1) V in 2V T where I B is the bias current and V T denotes the thermal voltage ( 26 mv) at room temperature. Consequently, g m can be electronically tuned by varying I B. The current-mode lossless integrator in Fig. 2 is implemented using one MOOTA and a grounded capacitor. The transfer function of the lossless integrator can be expressed as A(s) = i O i in =± g m sc (2)

3 Circuits Syst Signal Process (2010) 29: Fig. 1 Top: Basic MOOTA implementation using BJTs. Bottom: Circuit symbol Fig. 2 Implementation of a current-mode lossless integrator using MOOTA and a grounded capacitor 2.2 Band-Reject Biquad Structure Realization A band-reject transfer function with normalized frequency, ω 0 = 1, is written as V O s = V in s 2 (3) + s/q + 1 The transfer function in (3) can be rearranged so that only integrators are required. The integrator form functions are obtained by multiplying both numerator and denominator by 1/s 2, V O [ 1 + 1/(sQ) + 1/s 2 ] = V in ( 1 + 1/s 2 ) (4)

4 916 Circuits Syst Signal Process (2010) 29: Fig. 3 Block diagram of a band-reject filter Fig. 4 Proposed tunable pole-q current-mode universal filter Rewriting (4)as ( Vin V O V O = V in + s 2 ) V O sq we can realize (5) using three lossless integrators to form first-order and second-order lossless integrators, as shown on the block diagram in Fig. 3. Note that the pole-q of the first-order integrator (1/sQ) in the denominator of (3) is completely separated from the second-order integrator (1/s 2 ) block. 2.3 Realization of Proposed Universal Filter The current-mode approach with OTA is used to design the proposed filter in Fig. 3. The OTA is selected due to its simple structure and current-controlled characteristic. Replacing the lossless integrators in the block diagram of Fig. 3 by the OTA integrators in Fig. 2, we obtain the final circuit shown in Fig. 4. The second-order lossless integrator (1/s 2 ) block is implemented using two cascaded lossless integrators OTA 1 -C 1 and OTA 2 -C 2. Likewise, the first-order lossless integrator (1/sQ) block is replaced by a lossless integrator OTA 3 -. Both the positive output of OTA 3 and the negative output of OTA 1 are fed back to OTA 2.The current output is obtained by summing the positive current output of OTA 1 and the negative current output of OTA 3. Another branch of current output is fed back to the input of OTA 3 according to the block diagram. (5)

5 Circuits Syst Signal Process (2010) 29: Using KCL, the current outputs of OTA 1 and OTA 3 can be shown to be the following functions: I O1 = I 1g m1 g m2 g m3 + I 2 (g m1 g m2 g m3 + sg m1 g m2 ) D 1 (s) I O2 = I 1( g m3g m2 C 2 ) + I 2 ( g m3g m2 C 2 + s g m2 C 2 ) D(s) I O3 = I 1(g m1 g m2 g m3 + s 2 g m3 ) I 2 g m1 g m2 g m3 D 1 (s) (6) (7) (8) where D 1 (s) = s 3 + s 2 g m3 + sg m1 g m2 and D(s) = s 2 + s g m3 g m1 g m2. The output current of the proposed filter, I O = I O1 + I O3 + I 3, can be rewritten as I O = I 1s g m3 g + I m1 g m2 2 D(s) + I 3 D(s) + It can be seen that the proposed filter can realize five types of transfer functions under the following conditions. (1) The LP response can be realized when I 1 = I 3 = 0 and I 2 = an input current signal I in. (2) The BP response can be realized when I 2 = I 3 = 0 and I 1 = I in. (3) The HP response can be realized when I 1 = I 2 = I 3 = I in. (4) The BR response can be realized when I 2 = 0 and I 1 = I 3 = I in. (5) The AP response can be realized when I 2 = 0 and I 1 /2 = I 3 = I in. Note that there is no critical component matching conditions in the realization of any of the above filters. Comparing the expression for the denominator D(s) to the characteristic equation D(s) = s 2 + s ω 0 Q 0 + ω0 2, the parameters Q 0 and ω 0 are given by ( ) gm1 g m2 C3 Q 0 = (10) g m3 and gm1 g m2 ω 0 = (11) Using (1), Q 0 and ω 0 in (10) and (11), respectively, can be rewritten in terms of current biases as and Q 0 = ( ) I B1 I B2 C3 I B3 (9) (12) ω 0 = 1 I B1 I B2 (13) 2V T

6 918 Circuits Syst Signal Process (2010) 29: Fig. 5 Generic small signal OTA macromodel Observe that because of the /I B3 factor in (12), the pole-q (Q 0 ) can be tuned without affecting the pole-frequency ω 0 in (13). For Q 0 = 1, it is recommended to use g m1 = g m2 = g m3 = g m and C 1 = C 2 = = C. Then the pole-frequency can be electronically tuned by adjusting the transconductance (g m ) gain of the MOOTAs. The pole-q can be tuned by one of two approaches: electronic tuning, or varying the capacitance. For electronic tuning we let = C and g m1 = g m2 = g m. The pole-q becomes g m /g m3. For tuning of pole-q by varying the capacitance, C 1 = C 2 = C and g m = g m3. In this case the pole-q becomes /C. The active and passive sensitivities with respect to ω 0 and pole-q are given by S ω 0 g m1 = S ω 0 g m2 = S Q 0 g m1 = S Q 0 g m2 = 0.5 (14) S ω 0 C 1 = S ω 0 C 2 = S Q 0 C 1 = S Q 0 C 2 = 0.5 (15) S ω 0 g m3 = S ω 0 = 0 (16) S Q 0 g m3 = S Q 0 = 1 (17) 3 Effects of Nonidealities of the OTAs The characteristics of the nonideal OTA play an important role when dealing with a wide frequency range of operation. The simple but practical small signal OTA macromodel in Fig. 5 is used to facilitate filter performance characterization. The macromodel components are characterized by (i) the differential and common-mode input capacitances, denoted by C d and C c, respectively; (ii) the output capacitance C O and resistance (conductance) R o (g o ); and (iii) the frequency-dependent transconductance g m.from[16], the frequency dependence of g m can be approximated as g m = g m0 ( ωp2 s + ω p2 ) = g m0 ( sτ ) g m0 (1 sτ) ωτ 1 (18) where g m0 is the transconductance of the ideal OTA, ω p2 denotes the second pole of the OTA, and τ = 1/ω p2. Consequently, in the frequency range of interest, ω 0 ω p2, the nonideal transfer function A n (s) of the OTA lossless integrators may be approximated as A n (s) = g m (1 sτ) (19) sc

7 Circuits Syst Signal Process (2010) 29: Now we reanalyze the proposed circuit in Fig. 4 using (19), with τ i = 1/ω p2i representing the delay of the ith OTA-C integrator. The nonideal transfer functions become T LP n (s) = g m1 g m2 [s 2 τ 1 τ 2 s(τ 1 + τ 2 ) + 1] D n1 (s) (20) s2 T HPn (s) = D n1 (s) T BPn (s) = g m3 (s s 2 τ 3 ) D n1 (s) T BRn (s) = s2 + g m1g m2 [s 2 τ 1 τ 2 s(τ 1 + τ 2 ) + 1] D n1 (s) T AP n (s) = s2 g m3 [s s 2 τ 3 ]+ g m1g m2 [s 2 τ 1 τ 2 s(τ 1 + τ 2 ) + 1] D n1 (s) (21) (22) (23) (24) where D n1 (s) = s 2 ( 1 g m3 τ 3 + g m1g m2 ) (τ 1 τ 2 ) ( gm3 + s g m1g m2 (τ 1 + τ 2 ) ) + g m1g m2 (25) Comparing (25)toD(s) = s 2 + s ω 0 Q 0 + ω0 2, the parameters of the nonideal multifunction filter are then expressed as ω 0n1 = g m1 g m2 1 g m3 τ 3 + g m1g m2 (τ 1 τ 2 ) (26) Q 0n1 = gm1 g m2 g m3 [1 g m3 τ 3 + g m1g m2 (τ 1 τ 2 )] g m1g m2 (τ 1 + τ 2 ) (27) Equations (26) and (27) show how the parasitic delays τ i of the OTA i affect the filter performance. In the case where τ i satisfy the following conditions: ( ) gm3 τ 3 + g m1g m2 C 1 C 2 (τ 1 τ 2 ) 1 ( ) ( ) (28) gm1 g m2 gm3 (τ 1 + τ 2 ) the effect of the parasitic delay is negligible. Next we consider the effects of the other parasitic elements (resistances and capacitances) while taking g m as ideal (g m = g m0 ) and neglecting the parasitic delay.

8 920 Circuits Syst Signal Process (2010) 29: Table 1 Model parameters of AT&T CBIC-R transistors.model PR100N PNP (IS = 73.5E 18 BF = 110 NF = 1VAF= 51.8 IKF= 2.359E 03 + ISE = 25.1E 16 NE = BR = VAR = 936 IKR = 6.478E 03 + NR = 1ISC= 0NC= 2RE= 3RB= 327 IRB = 0 RBM = RC = 50 + CJE = 0.180E 12 VJE = 0.5 MJE = 0.28 CJC = 0.164E 12 VJC = MJC = 0.4 XCJC = CJS = 1.03E 12 VJS = 0.55 MJS = 0.35 FC = TF = 0.610E 09 TR = 0.610E 08 EG = XTB = XTI = 1.7).MODEL NR100N NPN (IS = 121E 18 BF = IRB = 0NF= 1NR= 1 + VAF = IKF = 6.974E 03 ISE = 36E 16 ISC = 0NE= BR = VAR = IKR = 2.198E 03 RE = 1RB= RBM = 25 RC = 50 + CJE = 0.214E 12 VJE = 0.5 MJE = 0.28 CJC = 0.983E 13 VJC = 0.5 MJC = XCJC = CJS = 0.913E 12 VJS = 0.64 MJS = 0.4 FC = 0.5 TF = 0.425E 09 + TR = 0.425E 08 EG = XTB = XTI = 2) In this case, the denominator of the proposed filter is approximated as [ (gm1 ) D n2 (s) g m2 = C 1 + g ( m3 1 C 2 C 3 R ) C 1 R 2 C 2 ] s R 2 R 3 C 2 C 3 [ (gm3 C 3 R 1 R 3 C 1 C 3 R 1 R 2 C 1 C 2 ) ( 1 + R C 1 R ) ] C 2 R 3 + s 2 (29) C 3 where R 1 = R O2, R 2 = R 3 = R O1 R O3, C 1 = C 1 + C O2 + C c1 + C d1, C 2 = C 2 + C O1 + C O3 + C c2 + C d2 and C 3 = + C O1 + C O3 + C c3 + C d3. Assuming that every OTA is matched based on the identical output resistances (R Oi = R O ),the parameters of the nonideal multifunction filter are expressed as ω 0n2 = g m1 g m2 C 1 C 2 + g ( m3 1 C 3 R O C ) C 2 (30) Q 0n2 = gm1 g m2 C 1 + g m3 C 2 R ( 1 O C C 2 ) ( g m3 ) + R 1 O ( 1 C C ) (31) Equations (30) and (31) show how the parasitic resistances and capacitances of the OTAs affect the filter performances. For the specific case where it is assumed that the parasitic capacitances C Oi = C O, C di = C d, and C ci = C c, the parasitic effects on the pole-frequency and pole-q can be avoided by choosing C 1 (C O + C c + C d ) (32) C 2, (2C O + C c + C d ) (33)

9 Circuits Syst Signal Process (2010) 29: Simulation Results We investigate the characteristics and performance of our proposed current-mode OTA-C universal filter using a SPICE simulation. The simple BJT MOOTA is constructed with ±2 V power supplies. Model parameters of the AT&T CBIC-R process realizing the MOOTA are listed in Table 1. For Q 0 = 1, the pole-frequency of the proposed filter is electronically controlled by the identical conditions of MOOTA transconductances and capacitors, i.e., g m1 = g m2 = g m3 = g m and C 1 = C 2 = = C. Example values of bias currents and capacitors are given in Table 2 for Q 0 > 1. Figure 6 depicts the simulated current-mode amplitude responses for the BR, LP, BP, and HP filters based on the input current conditions in Sect The filters are designed for f 0 = 1 MHz by choosing C 1 = C 2 = 2 nf and g m1 = g m2 = g m3 = Table 2 Example and I B3 values for tunable pole-q at 100 khz Q 0 I B1 = I B2 = I B3 = 70 µa I B1 = I B2 = 70 µa C 1 = C 2 = 2nF C 1 = C 2 = = 2nF (nf) I B3 (µa) Fig. 6 Filter amplitude response characteristics for the BR, LP, BP, and HP filters with I B = 70 µa and C = 0.2 nf

10 922 Circuits Syst Signal Process (2010) 29: Fig. 7 All-pass amplitude and phase response characteristics at 1 MHz Fig. 8 Tuning the pole-q of the BP response by changing capacitor g m = 1.35 ms (I B = 70 µa). The simulated current-mode amplitude and phase responses for the AP filter are shown in Fig. 7. Figure 8 depicts the tunable pole-q obtained using the approach of varying a capacitor. We assign C 1 = C 2 = 2nF, I B1 = I B2 = I B3 = 70 µa, and vary the capacitor between 2 and 128 nf. Alternatively, the electronic tunability of pole-q is illustrated in Fig. 9 by assigning C 1 = C 2 = 2nF,I B1 = I B2 = 70 µa, and varying the bias current I B3 from to 70 µa. Note that in both Figs. 8 and 9 the tunable pole-q values, Q 0 = 1, 2, 4, 8, 16, 32, and 64, are obtained without affecting the ω 0 parameter. Figure 10 depicts the BP amplitude response characteristics with tunable polefrequency. The bias current I B is varied from 7 to 70 µa and C 1 = C 2 = = 0.2nF. Consequently, f 0 is varied from 100 khz to 1 MHz.

11 Circuits Syst Signal Process (2010) 29: Fig. 9 Tuning the pole-q of the BP response by varying I B3 Fig. 10 Tuning the frequency (f 0 ) of the BP filter through OTA current bias I B 5 Conclusion This paper presents an approach for multiple-input single-output filter synthesis using the biquadratic BR function. The proposed filter is realized using MOOTAs. Five types of current-mode standard transfer functions are obtained without changing the circuit topology. The filter can independently tune the pole-frequency and the pole-q. The pole-frequency and the pole-q can be electronically tuned through the OTA bias currents. Alternatively, the pole-q can also be tuned by varying a particular capacitor in the circuit. We investigate the parasitic effects of nonideal OTAs on the filter characteristics. We show that these effects can be made negligible if the design sat-

12 924 Circuits Syst Signal Process (2010) 29: isfies certain circuit conditions. Lastly, the proposed circuit configuration is suitable for implementation using either bipolar or CMOS technologies. Acknowledgements The authors would like to thank Dr. M.N.S. Swamy and Dr. Ananda Mohan and the anonymous reviewers who gave us valuable comments and suggestions. The authors would also like to thank our colleagues Dr. Tulaya Limpiti, Dr. Att Kruafak, and Mr. Natapong Wongprommoon for their editorial comments which significantly improved the manuscript. References 1. R.F. Ahmed, I.A. Awad, A.M. Soliman, A transformation method from voltage-mode OP-amp-RC circuits to current-mode Gm-C circuits. Circuits Syst. Signal Process. 25, (2006) 2. S.I. Liu, J.J. Chen, Y.S. Hwang, New Current mode biquad filters using current follower. IEEE Trans. Circuits Syst. 42, (1995) 3. E.O. Gunes, A. Toker, S. Ozoguz, Insensitive current-mode universal filter with minimum component using dual-output current conveyors. Electron. Lett. 35, (1999) 4. A. Fabre, O. Saaid, F. Wiest, C. Boucheron, Current controlled bandpass filter based on translinear conveyors. Electron. Lett. 31, (1995) 5. A.M. Soliman, New current-mode biquad filters using current conveyors. Int. J. Electron. Commun. (AEÜ) 51, (1997) 6. C. Chang, New multifunction OTA-C biquads. IEEE Trans. Circuits Syst. 46, (1999) 7. C. Chang, S. Pai, Universal current-mode OTA-C biquad with the minimum components. IEEE Trans. Circuits Syst. 47, (2000) 8. C. Chang, B.M. Al-Hashimi, J.N. Ross, Unified active filter biquad structure. IEE Proc. Circuits Dev. Syst. 151, (2004) 9. J. Wu, Current-mode high-order OTA-C filter. Int. J. Electron. 76, (1994) 10. M.T. Abuelma atti, A. Bentrcia, New universal current-mode multiple-input multiple-output OTA-C filter. In: IEEE Asia Pacific Conference on Circuits and Systems, APCCAS 2004, pp (2004) 11. E. Sanchez-sinencio, R.L. Geiger, H. Nevarez-Lozano, Generation of continuous-time two integrator loop OTA filter structures. IEEE Trans. Circuits Syst. 35, (1988) 12. J. Wu, E. El-Masry, Design of current-mode ladder filters using coupled-biquads. IEEE Trans. Circuits Syst. 45, (1998) 13. C.M. Chang, C.L. Hou, W.Y. Chung, J.W. Horng, C.K. Tu, Analytical synthesis of high-order singleended-input OTA-grounded C all-pass and band-reject filter structures. IEEE Trans. Circuits Syst. 53, (2006) 14. S.H. Tu, C.M. Chang, J.N. Ross, M.N.S. Swamy, Analytical synthesis of current-mode high-order single-ended-input OTA and equal-capacitor elliptic filter structures with the minimum number of components. IEEE Trans. Circuits Syst. 54, (2007) 15. C.M. Chang, A.M. Soliman, M.N.S. Swamy, Analytical synthesis of low-sensitivity high-order voltage-mode DDCC and FDCCII-grounded R and C all-pass filter structures. IEEE Trans. Circuits Syst. 54, (2007) 16. H. Pevarez-Lozano, E. Sanchez-Sinencio, Minimum parasitic effects biquadratic OTA-C filter architectures. Analog Integr. Circuits Signal Process. 1, (1991)