DVCC Based K.H.N. Biquadratic Analog Filter with Digitally Controlled Variations

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1 American Journal of Electrical and Electronic Engineering, 2014, Vol. 2, No. 6, Available online at Science and Education Publihing DO: /ajeee DVCC Baed K.H.N. Biquadratic Analog Filter with Digitally Controlled Variation Bilal Arif *, Mohd. Uama mail, Ale mran Department of Electronic Engineering, Aligarh Mulim Univerity, Aligarh, ndia * Correponding author: arifbilal25@gmail.com Received May 07, 2014; Revied November 09, 2014; Accepted November 23, 2014 Abtract n thi paper, a digitally controlled ingle input multi output current-mode K.H.N. Biquad Filter i preented. The filter circuit i compoed of three DVCC together with four grounded reitor and two grounded capacitor. The digital control i incorporated uing a current-umming network (CSN). Tuning of reonant frequency i carried out by 3 bit digital control word. Block by block replacement ha been done to oberve the change in the relationhip between reonant frequency of the band-pa filter with the control word. The filter circuit howed three different variation when the DVCC block were replaced (one by one) with 3-bit DC-DVCC block. PSPCE imulation uing TSMC 0.25 micron CMOS technology have been performed to validate the theoretical reult. Keyword: Current-mode, Differential Voltage Current Conveyor (DVCC), multifunctional filter, digitally controlled DVCC (DC-DVCC), Cut off frequency, K.H.N. Biquad filter Cite Thi Article: Bilal Arif, Mohd. Uama mail, and Ale mran, DVCC Baed K.H.N. Biquadratic Analog Filter with Digitally Controlled Variation. American Journal of Electrical and Electronic Engineering, vol. 2, no. 6 (2014): doi: /ajeee ntroduction n the recent time the current mode filter have gained utility in variou ignal proceing application. Thee filter have revolutionized the modern day ignal proceing and have replaced their voltage mode counterpart in everal of application. Moreover filter which could provide imultaneou realization of the baic filter function have proved themelve ueful in variou application which include touch-tone telephone tone decoder, phae-locked loop FM tereo demodulator and croover network ued in a threeway high-fidelity loudpeaker. With the inception of Current Conveyor (CC), the filter deign ha reached a new height and variou variant of CC have alo gained attraction [1-10]. Variou digitally controlled filter have been propoed and realized in the recent time. n [11] H.P. Chen and S.S. Shen preented a DVCC baed Univeral capacitor grounded voltage mode filter which realized all the five generic filter repone imultaneouly. n [12] H. P. Chen preented tunable current mode univeral filter, the high output impedance of thi filter enable eay cacading in current-mode operation alo in different mode of operation it could realize different filter repone imultaneouly. Two year back. A. Khan and A. M. Nahha preented a CC baed reconfigurable firt order multifunction filter whoe frequency could be changed with a digital control word [13]. n thi paper, the circuit propoed in [14] by Muhammed A. brahim, Shahram Minaei and Hakan Kuntman, ha been ued to deign and implement a digitally controlled current-mode K.H.N. biquad. Uing grounded capacitor, the circuit become uitable for integration a the grounded capacitor circuit can compenate for the tray capacitance at the repective node. PSPCE imulation of the CMOS baed programmable filter are performed to demontrate reult. Figure 1. Symbol repreenting the dual output DVCC [15] 2. DVCC DVCC i a five-terminal active analog building block illutrated in Figure 1, with terminal characteritic decribed by the following matrix equation [15]. Y VY V Y2 Y2 V X = X Z VZ+ Z V Z (1)

2 160 American Journal of Electrical and Electronic Engineering DVCC exhibit negligible (ideally zero) input reitance at terminal X, and very high (ideally infinite) reitance at both Y terminal a well a the Z terminal. The output current follow the input current direction with both current flowing either into or out of the device. The CMOS implementation of DVCC i a hown in Figure 2. RCR Q = (6) RRC We can ee that lowpa, bandpa and highpa function can be imultaneouly realized without changing the topology. n imulation, uing PSPCE the DVCC wa realized by the CMOS implementation hown in Figure 2 uing TSMC 0.25-µm proce parameter. The apect ratio of the CMOS tranitor of the DVCC are preented in Table. The upply voltage were taken a, V DD = V SS = 2 V and the biaing voltage were aigned value, V B1 = 1.32 V and V B2 = +0.7 V. The circuit wa deigned for f o = ω o /2π = 100 khz and Q = by chooing R 1 = R 2 =R 3 = R 4 = 1 kω and C 2 =2 C 1 = nf. The repone of the multifunctional filter are hown in Figure 4 (a) and Figure 4 (b). The reult are in full conformity with the theoretical analyi. Figure 2. CMOS realization of the dual-output DVCC [15] MPLEMENTATON OF KHN BQUAD The implemented KHN biquad i illutrated in Figure 3. The analyi of the circuit yield the following equation (2), (3) and (4). Figure 4 (a). Simulated Lowpa and Highpa repone Figure 3. K.H.N. Biquad Filter Realization [14] RRC = 1 R + + N R = 1 R + + HP 2 N 2 1 LP R2R3R4CC 1 2 = 1 R + + N 2 1 (2) (3) (4) The reonant angular frequency o, and the quality factor, Q, are given by (5) and (6) repectively. = (5) Figure 4 (b). Simulated Bandpa repone Table 1. Apect ratio of the cmo tranitor of the dvcc [15] Tranitor W (μm) L (μm) M 1-M M 5-M M 7-M M 9-M 11, M M 12-M M M M DC-DVCC To introduce the programmability in the multifunctional filter we have ued a digitally controlled DVCC (DC-

3 American Journal of Electrical and Electronic Engineering 161 DVCC) hown in Figure 5. The modified terminal characteritic for the ame are a follow Y VY1 Y VY2 V X = X (7) Z+ 0 0 k 0 0 VZ+ Z 0 0 k 0 0 V Z Where: Z k = (8) X For obtaining the digital control in the DVCC current umming network (CSN) are employed at the Z (Z+ and Z-) terminal for controlling the current tranfer gain parameter k. The gain parameter k how a variation from 1 to (2 n 1), where n i the number of tranitor array. The modified circuit of DVCC with the tranitor array i a hown in Figure 5. The CSN conit of n tranitor pair, the apect ratio of whoe PMOS and NMOS tranitor repectively are given by: W i W = 2 (9) L L i 9 W i W = 2 (10) L i L 12 Furthermore, the current at the Z terminal which i aumed to be flowing out of the DC-DVCC, can be expreed by: z n 1 i i2 ( 9 12 ) (11) = d i= 0 Therefore, the propoed DC-DVCC provide a current tranfer gain, k equal to: X n i= 1 i d 2 ( ) 0 ( ) z k = = = (12) i 9 12 n 1 i d 2 i= 0 i 9 12 Where d i are the bit applied to the i-th branch in the CSN. Now the current flow in a particular branch i enabled or diabled depending upon whether d i i a logic 1 or logic 0 [16]. The reonant frequency i now defined a αβγ = (14) A could be clearly een from (14) the reonant frequency of the Bandpa filter can be controlled by changing the value of the gain parameter α, β and γ. Thi variation will not require any change in the value of the paive component. n the analyi that follow it i aumed that if the DVCC i replaced by DC-DVCC the gain parameter for repective block take the value k, however if the DVCC i retained, the gain parameter attain value equal to 1. Figure 5. CMOS realization of the DC- DVCC having gain k Replacing the firt block (correponding to α) by DC- DVCC, therefore for thi configuration we have α= k and β=γ= 1, hence the equation for the band-pa repone and the expreion for the reonant frequency are repectively given by: k RRC kr + k + R C R R R C C N (15) k = (16) The configuration i illutrated in Figure Comparative Study of Variation in Bandpa Filter Reonant Frequency n thi ection the dicuion i retricted to the variation in reonant frequency of Band Pa filter only. The circuit hown in Figure 3 wa modified by replacing a DVCC block with a DC-DVCC block, one by one o that change in relationhip between the reonant frequency and control word can be oberved. Each block i aigned an individual gain α, β and γ repectively. The analyi i done and the following expreion wa obtained for the band pa repone. αβ RRC (13) N 2 1 αβγ + α + Figure 6. Configuration for α= k and β=γ= 1 From (16) it i evident that the reonant frequency varie with the control word k, in a quare root fahion. The configuration hown in Figure 6 i imulated uing PSPCE and the Bandpa ree obtained for the control word ([0 0 1] and [1 1 1]) are hown in Figure 7 (a) and Figure 7 (b).

4 162 American Journal of Electrical and Electronic Engineering Figure 7(a). Simulated magnitude repone (in db) for band pa filter with control word [d 2 d 1 d 0 = 0 0 1] elected for circuit of Figure 6 Figure 9(a). Simulated magnitude repone (in db) for band pa filter with control word [d 2 d 1 d 0 = 0 0 1] elected for circuit of Figure 8 Figure 7(b). Simulated magnitude repone (in db) for band pa filter with control word [d 2 d 1 d 0 = 1 1 1] elected for circuit of Figure 6. The imulation how a gradual increae in the reonant frequency when the control word i increaed, the obervation are recorded in Table. Now when the econd block i replaced the value of the gain parameter change to α= β=k and γ= 1 hence the equation for the band-pa repone and the expreion for the reonant frequency are repectively given by: 2 1 k R RRC N 2 1 k + k + R C R R R C C 2 1 (17) = k (18) The configuration i illutrated in Figure 8 Figure 9(b). Simulated magnitude repone (in db) for band pa filter with control word [d 2 d 1 d 0 = 11 1] elected for circuit of Figure 6 The imulation how an increae in the reonant frequency when the control word i increaed, the obervation are recorded in Table 2. When the third block i replaced the value of the gain parameter change to α= β=γ=k hence the equation for the band-pa repone and the expreion for the reonant frequency are repectively given by: 2 1 k R RRC N 2 1 k + k + R C R R R C C 2 1 (19) 3/2 = k (20) The configuration i illutrated in Figure 10 Figure 8. Configuration for α= k and β=γ= k From (18) it i evident that the reonant frequency varie with the control word k, in a linear fahion. The configuration hown in Figure 8 i imulated uing PSPCE and the Bandpa ree obtained for the control word ([0 0 1] and [1 1 1]) are hown in Figure 9 (a) and Figure 9 (b). Figure 10. Configuration for α= β=γ= k From (20) it i evident that the reonant frequency varie with the control word k, in a k 3/2 fahion. The

5 American Journal of Electrical and Electronic Engineering 163 configuration hown in Figure 10 i imulated uing PSPCE and the Bandpa ree obtained for the control word ([0 0 1] and [1 1 1]) are hown in Figure 11 (a) and Figure 11 (b). Figure 12, Figure 13 and Figure 14 are the plot howing variation in reonant frequency of the Bandpa filter configuration hown in Figure 6, Figure 8, Figure 10. Figure 11(a). Simulated magnitude repone (in db) for band pa filter with control word [d 2 d 1 d 0 = 0 0 1] elected for circuit of Figure 10 Figure 12. Variation in reonant frequency of F with digital control word for circuit of Figure 6 Figure 11(b). Simulated magnitude repone (in db) for band pa filter with control word [d 2 d 1 d 0 = 1 1 0] elected for circuit of Figure 10 The imulation how an increae in the reonant frequency when the control word i increaed, the obervation are recorded in Table 2. The circuit preented in [14] for a particular deign worked only for a ingle frequency but uing the modification uggeted in thi paper the utility of the circuit i increaed. Now the circuit when elected for a particular variation and deigned for a particular et of value of reitance and capacitance can work for even different frequencie. Table 2. Variation in reonant frequency of bandpa repone with the control word Reonant Reonant frequency Reonant frequency of of F of Circuit of frequency of F Control F of Circuit Figure 10 (khz) of Circuit of word, k of Figure 8 3 Figure 6 (khz) (ω k 2 (khz) ) (ω k) (ω k) Figure 13. Variation in reonant frequency of F with digital control word for circuit of Figure 8 Figure 14. Variation in reonant frequency of F with digital control word for circuit of Figure 10 The plot for the variation in reonant frequency obtained by imulation upport the theoretical analyi. For the circuit in Figure 6 we have obtained a quare root variation then linear variation i oberved for the circuit of Figure 8 finally a variation directly proportional to k 3/2 i oberved for circuit of Figure 10.

6 164 American Journal of Electrical and Electronic Engineering 5. Concluion n thi paper, a digitally programmable current mode K.H.N. biquad filter baed on three DVCC wa preented. Digital control ha been achieved with the introduction of CSN and variation of 3-bit digital control word (k). Now thi circuit can be tuned for even different frequencie for a particular deign and variation. Thi multi frequency tenability within the ame deign i the contribution for thi circuit The circuit wa configured in three different way to provide different relation between reonant frequency of the Bandpa filter and the digital control word (k). The variation obtained were dependent upon the number of DC-DVCC ued. When a ingle DVCC wa replaced with a DC-DVCC quare root relation between reonant frequency and k wa obtained, thi variation became linear on replacement of econd DVCC block and when the final block wa replaced the reonant frequency became directly proportional to k 3/2. The obervation upport the fact that the reonant frequency of Bandpa filter i directly proportional to k a/2, where a i the number of DVCC replaced with DC-DVCC. Hence we obtained a circuit whoe variation (relationhip) of reonant frequency can be controlled. PSPCE imulation were carried out to verify the working of the digitally controlled K.H.N. Biquad Filter. Reference [1] H. O. Elwan, A. M. Soliman. "A novel CMOS current conveyor realization with an electronically tunable current mode filter uitable for VLS." Circuit and Sytem : Analog and Digital Signal Proceing, EEE Tranaction, vol. 43, iue. 9, pp , Sep [2] C.M. Chang, M.J. Lee. Voltage-mode multifunction filter with ingle input and three output uing two compound current conveyor. Circuit and Sytem : Fundamental Theory and Application, EEE Tranaction, vol. 46, iue. 11, pp , Nov [3] O. Cicekoglu. Current-mode biquad with a minimum number of paive element. Circuit and Sytem : Analog and Digital Signal Proceing, EEE Tranaction, vol. 48, iue. 2, pp , Feb [4] H. Y. Wang, C. T. Lee. Veratile inenitive current-mode univeral biquad implementation uing current conveyor. Circuit and Sytem : Analog and Digital Signal Proceing, EEE Tranaction, vol. 48, iue. 4, pp , Apr [5] A.S. Sedra, K.C. Smith. A econd generation current conveyor and it application. EEE Tranaction on circuit theory, vol. 17, pp , Feb [6] W. Chiu, S.. Liu, H. W. Tao, J. J. Chen. CMOS differential difference current conveyor and their application. EE Proceeding-Circuit, Device and Sytem, vol. 143, iue. 2, pp , Apr [7] H.O. Elwan, A. M. Soliman. Novel CMOS differential voltage current conveyor and it application. EE Proceeding-Circuit, Device and Sytem, vol. 144, iue. 3, pp , Jun [8] T. Dotal, D. Biolek, K. Vrba. Adjoint voltage-current mode tranformation for circuit baed on modern current conveyor. Device, Circuit and Sytem, Proceeding of the Fourth EEE nternational Caraca Conference, 2002, pp. T [9] B. Wilon, Recent development in current conveyor and current-mode circuit. Circuit, Device and Sytem, EE Proceeding G, vol. 137, iue. 2, pp , Apr [10] H. Hakan Kuntman. New Advance and Poibilitie in Active Circuit Deign. in Proc. 10th nternational Conference on Development and Application Sytem, 2010, pp [11] H. P. Chen and S. S. Shen. "A veratile univeral capacitorgrounded voltage-mode filter uing DVCC." ETR journal, vol. 29, iue. 4, pp , Aug [12] H. P. Chen. "Tunable veratile current-mode univeral filter baed on plu-type DVCC." AEU-nternational Journal of Electronic and Communication, vol. 66, iue. 4, pp , [13]. A. Khan and A. M. Nahha. "Reconfigurable Voltage Mode Firt Order Multifunctional Filter uing Single Low Voltage Digitally Controlled CMOS CC." nternational Journal of Computer Application, vol. 45, iue. 5, pp , May [14] M.A. brahim, S. Minaei, H. Kuntman. A 22.5 MHz currentmode KHN biquad uing differential voltage current conveyor and grounded paive element." AEU-nternational Journal of Electronic and Communication, vol. 59, iue. 5, pp , [15] W. Tangrirat, O. Chaannumin. Voltage -mode multifunctional biquadratic filter uing ingle DVCC and minimum number of paive element. ndian Journal of Pure and Applied Phyic, vol. 49, pp , Oct [16] S. A. Mahmoud, M.A. Hahieh. and A.M. Soliman. Lowvoltage digitally controlled fully differential current conveyor. Circuit and Sytem : Regular Paper, EEE Tranaction, vol. 52, iue. 10, pp , Oct