FULLY INTEGRATED MULTIFUNCTION TRANS-IMPEDANCE MODE BIQUAD FILTER

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1 Journal of Enineerin Science and Technoloy Vol. 3, No. (08) School of Enineerin, Taylor s University FULLY INTEGRATED MULTIFUNCTION TRANS-IMPEDANCE MODE BIQUAD FILTER S. V. SINGH, C. SHANKAR Department of Electronics and Communications, Jaypee Institute of Information Technoloy, Noida-0304 (India) Department of Electronics Enineerin, JSS Academy of Technical Education, Noida 030(India) *Correspondin Author: porwalchandra@mail.com Abstract This paper presents a new trans-impedance-mode biquad filter which simultaneously, realizes the multifunction filterin outputs such as low pass (LP), band pass (BP), hih pass (HP) and band reject (BR). The presented filter topoloy consists of only sinle active element as voltae differencin transconductance amplifier (VDTA) alon with two rounded capacitors and two MOS implemented rounded resistors. So, the proposed filter structure is fully interable and canonical in nature. Apart from these, the proposed filter also enjoys the desirable features such as low active and passive sensitivities, low power consumption and orthoonal tunability of pole frequency and quality factor by electronic means. The presented filter is simulated usin PSPICE in 0.8 µm CMOS process. Keywords: VDTA, Trans-impedance, Biquad, Filter, Tunable.. Introduction In last several decades, active elements based on current-mode (CM) approach to study and synthesis of hih performance continuous-time (CT) filters which form an important part of analoue sinal processin systems such as radios, televisions, stereo systems, raphic equalizers and phase locked loop etc., have attracted sinificant research attention due to havin its inherent advantaes such as wider sinal bandwidth, low power consumption, larer dynamic rane, better linearity, simple circuitry and requirement of lesser on chip area with respect to voltae-mode counterpart []. 80

2 Fully Interated Multifunction Trans-impedance Mode Biquad Filter Nomenclatures C ox G i i I Bi Q 0 V ci V T ate oxide capacitance per unit area Admittance Trans-conductance Bias current Quality Factor biased voltae Threshold voltae Greek Symbols β Trackin error ω 0 Anular Pole Frequency, rad. µ n Mobility of electron Abbreviations BP BR BW CM HP LP VDTA VM Band Pass Band Reject Band Width Current-Mode Hih Pass Low Pass Trans-impedance mode Voltae Differencin Trans-Conductance Amplifier Voltae-Mode Therefore, numbers of such type of CM active elements in which information is processed in term of currents are proposed in the literature. Current conveyors (CCII, CCI, and CCIII) and their variants such as DDCCII, DVCCII, FDCCII and DXCCII etc., are firstly proposed [-8]. Later on other active elements havin the property of inbuilt electronic tunin which may require in the adjustable applications such as music and speech synthesis are also proposed. Few names of them are OTA, CCCII, CCTA, CCCCTA, DDCCTA, CDTA, CCCDTA, CFTA, DVCCTA and VDTA, etc. [9-8]. The detailed properties and reviews of these CM active elements are well described in review published paper [9]. VDTA, a relatively new CM active element, was first introduced in 0 by Yesil et al. [7]. After its inception, various applications of VDTA in analo filters desin have also been reported in literature [0-6]. However, the VDTA based filter circuits proposed in the literature are either voltae-mode (VM) type [0,, 3, 7] or CM type [4, 5, 8] or trans-admittance (TAM) type [,, 6, 7]. Unfortunately, the trans-impedance () type filter(s) usin VDTA, which is the current input voltae output circuit and can be used as interface circuit connectin CM to VM in number of applications such as receiver block, amplifier, analo-to-diital converter (ADC) [6], are bein missed in the available literature. Althouh, quite a few number of biquad filters based on the active elements other than VDTA are found in the literature [6, 9-37]. Out of these, biquads presented in [9, 30, 3-36] use only a sinle current input and provide the simultaneous realization of filterin functions in contrast to those presented in [6, 3, 37] which requires multiple current inputs and realize one output at a time but Journal of Enineerin Science and Technoloy January 08, Vol. 3()

3 8 S. V. Sinh And C. Shankar realization of multiple current inputs which may further require additional hardware. Furthermore, the paper presented in [9, 30] proposed circuits each havin three active elements (CDBA or DVCFAs), two capacitors with both bein rounded, three resistors and also realize three filterin responses. Another paper presented in [3] proposed two different topoloies each havin four CCIIs, four resistors, two capacitors and realizin same number of filterin functions. Two more filter circuits presented in [33, 34] still realizes three filterin functions. In one case [34], the circuit requires only three OTAs in contrast to other case which require 4 OTAs. In addition, each of these circuits uses two op-amps too. Detail comparative study of all these filters requirin only sinle current input are also discussed in Table which reveals the followin points. (i) None of the above proposed filters can be implemented usin only sinle active element. Use of sinle element is beneficial for cost reduction, low power consumption, space savin, simplicity of the circuit point of view [38]. (ii) All the circuits realize at most three filterin functions [9, 30, 3-34]. (iii) Few of the circuits use floatin passive components too which are not favourable for IC interation point of view [9, 30, 3]. (iv) Few of the circuits is lackin electronic tunability feature of filter parameters [9, 30, 3-34] too. (v) Few of the circuits use more number of passive elements [9, 30, 3] too. S. No Table.. A comparative study of various reported sinle input multiple output biquad filters. References Features No. & types of active elements No. & types of passive elements Floatin passive elements Electronic control of filter parameter (ω 0 and Q 0) Realization type Power supply No. of transistors Operatin pole frequency Technoloy used (Feature Sized) [9] [30] [3] [33] [34] Proposed 3 CDBA 3 DVCFA 4 CCII 6 (OP- Amp, OTA) 5 (OP- Amp, OTA) VDTA 3R+C 3R+C 4R+ C NO NO R+ C -R, -C -R -R NO NO NO NO NO NO NO NO YES LP,BP,HP LP,BP,HP LP,BP,HP LP,BP,HP LP,BP,HP LP,BP, HP,BR ±5V ±.5V - ±.5V ±.5V ±.5V KHz.5 MHz - 435KHz- 870KHz 435KHz- 870KHz 5.0 MHz - 0.5µm - 0.5µm 0.5µm 0.36 µm 0 Sensitivity Less than Less than Less than Journal of Enineerin Science and Technoloy January 08, Vol. 3()

4 Fully Interated Multifunction Trans-impedance Mode Biquad Filter Keepin above points in the mind, a new circuit is proposed in this paper which simultaneously realizes four trans-impedance-mode filterin functions by the use of only sinle active element, namely, VDTA. Besides, it also employs two rounded capacitors and two rounded MOS resistors. Moreover, the proposed circuit offers low active and passive sensitivities, low power consumption and orthoonal electronic tunability of pole frequency and quality factor. The validity of proposed filter is also verified by simulatin the circuit in PSPICE.. VDTA Description The symbolic diaram of VDTA is shown in Fi.. Here (Fi. ), P and N are the input ports and Z, Z C, X+ and X- are the output ports. The voltae and current relationship between various input and output ports of VDTA can be characterized by the followin matrix equation [0]. I Z m m 0 VP I - 0 V ZC m m N I 0 0 X m V Z where m and m are the trans-conductance parameters of first stae and second stae, respectively. () Fi.. Symbolic diaram of VDTA. A CMOS model of above VDTA consistin of only eihteen transistors is also shown in Fi.. For the CMOS circuit of VDTA of Fi., the expression of m, m can be derived as [0]. 34, m () m where Wi i I Bi μc is the trans-conductance value of the i th transistor ox Li (i=,...8). Here I Bi is the bias current of the i th transistor, µ is the effective carrier mobility, C ox is the ate oxide capacitance per unit area, and W i & L i are the effective channel width and lenth of the i th MOS transistor, respectively. Journal of Enineerin Science and Technoloy January 08, Vol. 3()

5 84 S. V. Sinh And C. Shankar Fi.. Implementation of VDTA usin CMOS transistors. 3. Proposed Filter And Its Analysis The proposed filter topoloy is shown in Fi. 3 which employs sinle VDTA, two rounded resistors (R and R ) and two rounded capacitors (C and C ). In the proposed topoloy, each rounded resistor (R i, where i=, ) has been realized by usin parallel connection of two NMOS transistors (M Ri and M Ri ) [0]. Thus, the equivalent resistance can be calculated by R i μ C n ox W L MRi (3) MRi (V ci V T ) where V T is the threshold voltae of the NMOS transistor. V ci is the biased voltae and W MRi /L MRi stands for aspect ratio of NMOS transistor used in the resistance realization. V BR(s)= = Iin s + R m m CC (4) D(s) mmr V C C LP(s)= = I D(s) smr V C BP(s)= = I D(s) in 3 in V s R R HP(s)= = - I D(s) 4 m in (5) (6) (7) Journal of Enineerin Science and Technoloy January 08, Vol. 3()

6 Fully Interated Multifunction Trans-impedance Mode Biquad Filter On routine analysis of the circuit in Fi. 3, the transfer functions iven in followin equations can be derived. s R D(s)= s + + C C C where, m m m m It can be noted that from Eqs. (4)-(7) that the proposed topoloy is capable of realizin LP, BP, HP and BR filterin responses and hence, the characterized parameters like pole frequency (ω 0 ),quality factor (Q 0 ) and bandwidth (BW) can be derived as m m ω0, 0 CC m m C Q=, mmr BW (9) R C C It can be concluded from Eq. (9) that by maintainin the condition of m = m =/R = m, ω 0 can be varied electronically and without affectin the Q 0 by varyin m. Similarly, Q 0 can also be varied independent of ω 0 by varyin R which can be further tuned electronically. (8) Fi. 3. Block diaram of proposed multifunction biquad filter. 4. Non-Ideal Effects and Sensitivities Analysis In the previous section, ideal VDTA is considered to derive the various transfer functions and filter parameters. However, the VDTA implemented usin MOS transistors as shown in Fi., will be chacterized by finite non ideal transconductance trackin errors occured due to the mismatchin in the transistors. If we also consider these trackin errors, the current and voltae relationship between various ports of VDTA will be modified and can be rewritten as: I Z βm -β m 0 VP I = β -β 0 V ZC m m N I 0 0 ±β X± m V Z where β and β are the transconductance trackin error for the first and second staes of the VDTA. Considerin the effect of above non-ideal errors, we have (0) Journal of Enineerin Science and Technoloy January 08, Vol. 3()

7 86 S. V. Sinh And C. Shankar further reanalyzed the proposed circuit of Fi. 3. On analyzin, the non-ideal filter transfer functions and its filter parameters can be further derived as follow. V BR(s)= = Iin β β s + R m m CC () D(s) β βmmr V C C LP(s) = = I D(s) in sβ mr V C BP(s)= = I D(s) 3 in V s β R R HP(s)= = I D(s) 4 m in sβ β R β β D(s)= s + + C CC Where, m m m m β β C β Q=, βmmr BW = R C β β C m m ω0, 0 CC m m () (3) (4) (5) It is evident from Eqs. () - (6) that the filter parameters such as pass band ain, ω 0, Q 0, and BW of various filterin responses of the proposed circuit may be slihtly chaned due to effect of trackin errors of VDTA but these deviations can be minimized by adjustin the electronic controllable transconductance parameters. (6) The active and passive sensitivities of ω 0 and Q 0 for the proposed filter in Fi. 3 are also derived as follow. ω 0 ω0 ω S β S m S m, S 0 S C C (7) Q Q 0 0 Q0 Q S β S m S m SC, S 0 Q, S 0 C R (8) ω0 ω0 S β Q0 Q0 S β From above equations, it can be observed that all the active and passive sensitivities of ω 0 and Q 0 are low and less than in manitude. 5. Non-Ideal Parasitics Analysis In this section, the effect of VDTA parasitic on the performance of presented filter is considered. In the presence of various ports parasitic in the form of parasitic capacitors and resistors, the circuit of Fi. 3 has been chaned to Fi. 4. Here, C P R P at ports (X+, V N ), C P R P at port Z, C P3 R P3 at ports (X-, V P ) and C P4 R P4 at port Z C are combined parasitic impedance in the form of parallel combination of parasitic capacitances and resistances. The external resistance R, R and parasitic resistances R Pi (i=,, 3, 4) can be represented in terms of admittances as G, G and G Pi (i=,, 3, 4), respectively (where G i =/R i, G Pi =/R Pi ). Practical value of parasitic capacitances C Pi are in the rane of Journal of Enineerin Science and Technoloy January 08, Vol. 3()

8 Fully Interated Multifunction Trans-impedance Mode Biquad Filter fraction of picofarads and that of G pi (i=, ) are less than 0 of micro mho. So, the external capacitances C and C can be chosen as much reater than the parasitic capacitances. Therefore, min (C, C )>> (C P, C P, C P3, C P4 ). Similarly, the external admittances can also be chosen much reater than the parasitic admittances. Therefore, min (G, G )>> (G P, G P, G P3, G P4 ). To see the effects of various parasitic impedances on the performance of the proposed filter circuit, the circuit of Fi. 4 is aain reanalyzed. On reanalyzin the circuit of Fi. 4, we et the followin transfer functions for the filterin functions. Fi. 4. Proposed biquad filter in the presence of various ports parasitic. sc s + + V G C C (s)= = P3 m m BR Iin sc P3 " G + D (s) G m m V CCG LP(s) I in scp3 " D (s) G m G P s V C G C 3 BP (s) I in scp3 " D (s) G sm V4 GG HP(s)= = - Iin sc P3 sc P4 " + + D (s) G G where " m m m m D (s) s s sc P3 sc C G CC G G P3 (9) (0) () () (3) Journal of Enineerin Science and Technoloy January 08, Vol. 3()

9 88 S. V. Sinh And C. Shankar As a result, the expressions of pole frequency and quality factor have been chaned to ω = ω ' 0 0 C + s G P3 C, ' P3 Q 0= Q0 + s G where, ω 0 and Q 0 are the pole frequency and quality factor of the filter in ideal case. It can be clearly seen from Eqs. (9) - (4) that additional first order pole or zero are yielded in the expression of transfer functions and filter parameters due to various port parasitic of VDTA which may deviate undesirably the pass band ain, pole frequency and quality factor of the proposed filter. However, these undesirable factors can be eliminated or minimized and hence, the proposed filter may approach towards ideal response, if we choose the operatin frequency (ω 0 ) in the desin criterion as follows: G G G << ω << min, C C C P 0 P3 P4 6. Simulation Results In order to check the performance, the presented filter circuit was desined usin CMOS implementation of VDTA with aspect ratio of transistor as described in Table and simulations were carried out usin PSPICE in ORCAD 6.5 with model of 0.8µm CMOS process parameter from TSMC []. The circuit was biased with V DD =-V SS =.5V DC power supply. To desin the proposed filter of pole frequency 5.0 MHz and Q 0 =, the passive components value was set to R =R =KΩ, C =C =5pF and biasin current were chosen so that m = m 473.5µA/V (I B =I B =53µA). Fiure 5 shows the simulated versus ideal (theoretical or analytical) ain responses of LP, HP, BP, and BR for the proposed biquad filter. It is clear from Fi. 5 that simulated results are in ood areements with the ideal or theoretical results. Moreover, the simulated pole frequency was obtained 5.0 MHz which is closed to the theoretical value of 5.0 MHz. The total power consumption of the filter was obtained as. mw. (4) (5) Table.Transistors aspect ratios of CMOS implementation of VDTA of Fi. 3. Transistor W(µm)/L(µm) M-M,M5-M6 8.8/0.36 M3-M4,M7-M8 4.4/0.36 M9-M 0.8/0.36 M3,M8 3.6/0.36 M4-M7 4.37/0.36 Journal of Enineerin Science and Technoloy January 08, Vol. 3()

10 Fully Interated Multifunction Trans-impedance Mode Biquad Filter Fi. 5. Ideal and PSPICE simulated response of LP, HP, BP, and BR Filter. Further simulations of the proposed circuit were also done to show the electronic tunin capability of the circuit by plottin various BP filterin responses. Fiure 6(a) shows the electronic tunability feature of ω 0 independent of Q 0 by ettin the simulation results at different value of ω 0 as 3.40 MHz, 5.5 MHz, 6.74 MHz, and 0.5 MHz at constant Q 0 =, which were further obtained by varyin m and m in such a way so that m = m =/R (for example, m = m = µa/v, µa/v, µa/v, 08.5 µa/v and R =.80 KΩ (V ci =.694),.98 KΩ (V ci =.88),.53 KΩ (V ci =.96) and 97 Ω (V ci =.303)). On the hand, Fiure 6(b) shows the electronic tunability of Q 0 independent of ω 0 by chanin R which can be further varied by V ci as mentioned in Fi. 6(b). The correspondin Q 0 value was obtained as 0.63, 0.8,. and.5 at various R = 3.4 KΩ (V ci =0.65),.6 KΩ (V ci =0.7),.65 KΩ (V ci =0.9) and 788 Ω (V ci =.5). The lare sinal behavior of the proposed circuit is also investiated by applyin an input sinusoidal current sinal and measurin LP and HP voltae output. (a) (b) Fi. 6. Electronic tunin feature of (a) ω 0 independent of Q 0 (Q 0 =) (b) Q 0 independent of ω 0 (at ω 0 =5.0MHz) for BP filter. Journal of Enineerin Science and Technoloy January 08, Vol. 3()

11 90 S. V. Sinh And C. Shankar Fiure 7(a) shows the time domain sinusoidal input current sinal of frequency of 500 KHz havin peak to peak amplitude of 900 µa and correspondin LP voltae output while Fiure 7(b) shows the time domain sinusoidal input current sinal of frequency of 4000 khz havin peak to peak amplitude of 90 µa and correspondin HP voltae output. Furthermore, the total harmonic distortions (THDs) results for LP voltae responses with respect to sinusoidal input current sinal of constant peak to peak amplitude of 00 µa and havin variable frequency in the rane of 600 khz to 600 khz are also shown in Fi. 8. The THDs results shown in Fi. 8 indicate that THDs value of the circuit are within acceptable limits of 4% which shows a fairly moderate THD performance of the circuit. To observe the effect of passive component mismatchin on the filter s performance, Monte-Carlo analysis has been performed. For this, The BP output was simulated with 0% Gaussian deviation in C = C = 5 pf for 500 concurrently runs where first run is done with nominal values of capacitor while the subsequent runs are done with values enerated randomly by PSPICE. The statistical results in the form of historam plots are shown in Fi. 9. From these plots, the simulated mean, median and standard deviation were obtained as 5.3 MHz; 5.3 MHz, KHz, respectively which conclude that with respect to the simulated pole frequency of 5.0 MHz, the proposed filter is less sensitive to the chane in capacitive value and thus offers ood passive sensitivity. Further, to check the circuit immunity with respect to circuit noise, the noise analysis of LP filter has been performed and correspondin simulation results in term of input noise and LP output noise at different frequencies are shown in Fi. 0. The maximum output noise spectral density obtained from Fi. 0 is equal to 8.7nV/Hz / which is small and acceptable rane [7]. (a) (b) Fi. 7. Transient response of (a) LP filter (b) HP filter. Journal of Enineerin Science and Technoloy January 08, Vol. 3()

12 Fully Interated Multifunction Trans-impedance Mode Biquad Filter Fi. 8. % THDs of LP filter at constant peak to peak input current of 00µA and variable frequency. Fi. 9. Monte Carlo analysis. Fi. 0. Input-Output noise spectral density of LP filter. 7. Conclusion In this paper a new VDTA based biquad filter topoloy is presented which realizes four filterin functions such as the LP, BP, HP and BR, simultaneously usin only sinle active element. In addition of usin only sinle CMOS based active element, it also employs two rounded capacitors and two MOS implemented rounded resistors which can be easily realize usin MOS Journal of Enineerin Science and Technoloy January 08, Vol. 3()

13 9 S. V. Sinh And C. Shankar technoloy [0] and hence, the presented circuit can be made fully interable in CMOS technoloy and provide canonical structure. Moreover, the presented filter enjoys the feature of simultaneously outputs, all rounded passive elements, low active and passive sensitivities, low power consumption, independent electronic tunin of filter parameters. The above distinuished features of the circuit make hope that this work will add to the body of knowlede on classical filter desin. References. Toumazou, C.; Lidey, F.J.; and Makris, C.A. (990). Extendin voltaemode op amps to current-mode performance. IEEE Proceedins G - Circuits, Devices and Systems, 37(), Smith, K.C.; and Sedra, A. (968). The current conveyor - A new circuit buildin block. Proceedins of IEE, 56(8), Sedra, A.S.; and Smith, K.C. (970). A second-eneration current conveyor and its application. IEEE Transaction on Circuit Theory, 7(), Fabre, A. (995). Third eneration current conveyor: A new helpful active element. Electronics Letter, 3(5), Elwan, H.O.; and Soliman, A.M. (997). Novel CMOS differential voltae current conveyor and its applications. IEE Proceedins - Circuits, Devices and Systems, 44(3), Chiu, W.; Liu, S.I.; Tsao, H.W.; and Chen, J.J. (996). CMOS differential difference current conveyors and its applications. IEE Proceedin - Circuits, Devices and Systems, 43(), El-Adaway, A.A.; Soliman, A.M.; and Elwan, H.O. (000). A novel fully differential current conveyor and applications for analo VLSI. IEEE Transactions on Circuits and Systems II: Analo and Diital Sinal Processin, 47(4), Maheshwari, S.; and Ansari, M.S. (0). Catalo of realizations for DXCCII usin commercially available ICs and applications. Radioenineerin,, Park, C.-S.; and Schaumann, R. (986). A hih frequency CMOS linear trans-conductance element. IEEE Transactions on Circuits and Systems, 33(), Fabre, A.; Saaid, F.; Wiest, F.; and Boucheron, C. (996). Hih frequency application based on a new current controlled conveyor. IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications, 43(), Tomar, R.S.; Sinh, S.V.; and Chauhan, D.S. (03). Current-processin current tunable universal biquad filter employin two CCTAs and two rounded capacitors. Circuits and Systems, 4(6), Maheshwari, S.; Sinh, S.V.; and Chauhan, D.S. (0). Electronically tunable low-voltae mixed-mode universal biquad filter. IET Circuits, Devices & Systems, 5(3), Journal of Enineerin Science and Technoloy January 08, Vol. 3()

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15 94 S. V. Sinh And C. Shankar 8. Satansup. J; Tanrirat. W (0). Sinle VDTA based current mode Electrical tunable multifunction filter. 4 th international conference on Science, Social Science, Enineerin and Enery (I-SEEC0,) th -4 th December, 0, Sabal, M.; and Köksal, M. (005). A New multi-mode multifunction filter usin CDBA. Circuit Theory and Desin, Proceedins of the European Conference,, II/5-II/ Ibrahim, M.A. (007). A trans-impedance type multifunction filter suitable for MOSFET-C technoloy. Proceedins of the 5 th IEEE International Conference on Electrical and Electronics Enineerin (ELECO) Bursa, Turkey, Sinh, S.V.; Maheshwari, S.; and Chauhan, D.S. (0). Sinle MO- CCCCTA-based electronically tunable current/ trans-impedance -mode biquad universal filter. Circuits and systems, (), Soliman, A.M. (996). Mixed-mode biquad circuits. Microelectronics Journal, 7(6), Minaei, S.; Topcu, G.; and Cicekolu, O. (005). Low input impedance transi-mpedance type multifunction filter usin only active elements. International Journal of Electronics, 9(7), Abuelma atti, M.T. (008). Comment on low input impedance transimpedance type multifunction filter usin only active elements. International Journal of Electronics, 95(), Carlosena, A.; and Cabral, E. (997). Novel transimpedance filter topoloy for instrumentation. IEEE Transactions on Instrumentation and Measurement, 46(4), Chandra, G.; Tadeparthy, P.; and Easwaran, P. (008). Sinle amplifier biquadratic filter topoloies in transimpedance confiuration. IEEE Transactions on Circuits and Systems-II: 55(6), Kilinç, S.; and Çam, U. (006). Transimpedance type fully interated biquadratic filters usin operational transresistance amplifiers. Analo Interated Circuits and Sinal Processin, 47(), Be, P.; and Maheshwari, S. (04). Generalized filter topoloy usin rounded components and sinle novel active element. Circuits, Systems, and Sinal Processin, 33(), Journal of Enineerin Science and Technoloy January 08, Vol. 3()