Realization of current-mode KHN-equivalent biquad filter using ZC-CFTAs and grounded capacitors

Transcription

1 Indian Journal of Pure & Applied Physics Vol. 49, December, pp Realiation of current-mode KHN-equivalent biquad filter usin ZC-CFTAs and rounded capacitors Jetsdaporn Satansup & Worapon Tansrirat* Faculty of Enineerin, Kin Monkut s Institute of Technoloy Ladkraban (KMITL),Ladkraban, Bankok 5, Thailand * drworapon@yahoo.com Received 9 Auust ; revised 7 October ; accepted 7 November In this paper, a current-mode Kerwin-Huelsman-Newcomb (KHN) filter structure employin four -copy current follower transconductance amplifiers (ZC-CFTAs) and two rounded capacitors is proposed. The circuit structure has one low-impedance current input and three hih-impedance current outputs and enables realiin lowpass, bandpass and hihpass current responses simultaneously. The bandstop and allpass responses can also be obtained by connectin appropriate output currents directly without additional devices. The proposed filter is capable of providin an independent current-control of the natural anular frequency (ω o ) and quality factor (Q) throuh the transconductance of the ZC-CFTA. Moreover, hih-q value filter can be realied by simply tunin the ratio of ZC-CFTA s transconductance. To support the theoretical results, the properties of the presented filter usin CMOS ZC-CFTA have been verified by simulation results. Keywords: Z-copy current follower transconductance amplifier, Kerwin-Huelsman-Newcomb, Biquad filter, Current-mode circuit Introduction The Kerwin-Huelsman-Newcomb (KHN) biquad, also known as the state variable type filter, is one of the best known multifunction filterin structures. It consists of two interators and a summin amplifier to provide second-order lowpass (LP), bandpass (BP) and hihpass (HP) filterin responses simultaneously. It also provides several advantae features such as low component spread, low passive and active sensitivities and ood stability behaviour. In the current technical literature, various solutions of the KHN biquad structure usin different types of active devices have been reported -. Some of them operate in voltae-mode -7. As is well-known, the currentmode circuits offer certain advantaes such as reater linearity, wider bandwidth, less power consumption, larer dynamic rane and simplicity in circuit implementation compared to their voltae-mode counterparts. Therefore, some current-mode KHN biquads have been studied 7-. However, with three inputs and sinle output, KHN biquads 7,8 cannot realie all the three standard biquadratic filter responses simultaneously. Also, these filters require an excessive number of active and passive elements, i.e., 5 CCCIIs and rounded capacitors 7, and 3 CDBAs, rounded capacitors and 6 resistors 8. Moreover, the output terminal 8 does not exhibit hihoutput impedance. The current-mode KHN-biquad usin differential voltae current conveyors has been reported 9. It provides LP, BP and HP responses simultaneously, but it suffers from hih-input impedance due to a resistor connected to its input. Recently, usin three current follower transconductance amplifiers (CFTAs), the KHNequivalent filter workin in current-mode has been presented. The present circuit provides the three standard biquadratic filter responses simultaneously, while the bandstop (BS) and allpass (AP) responses can be obtained with interconnection of the relevant output currents. In addition, it possesses a low-input impedance and hih-output impedance characteristic, resultin in easy cascadability for current-mode process. However, its natural frequency (ω ) and quality factor (Q) cannot be tuned independently. Recently, the conception of the -copy current follower transconductance amplifier (ZC-CFTA) has been firstly suested in Ref. (). The ZC-CFTA is slihtly modified from the conventional current differencin transconductance amplifier (CDTA) by replacin the current differencin unit with a current follower and complementin the circuit with a simple current mirror for copyin the -terminal current. Thus, the ZC-CFTA element is a combination of the current follower, the current mirror and the multioutput operational transconductance amplifier. As a result, a number of applications based on ZC-CFTAs can be extended 3.

2 84 INDIAN J PURE & APPL PHYS, VOL 49, DECEMBER The desin of the current-mode KHN-equivalent biquad with low-input and hih-output impedances has been studied in the present paper. The developed filter is composed of four ZC-CFTAs and two rounded capacitors, which is suitable for interated circuit (IC) implementation. The circuit realies LP, BP and HP current responses simultaneously with an independent electronic control of ω and Q by means of adjustin the bias current of the ZC-CFTAs. Moreover, the BS and AP responses can be obtained simply by interconnectin their relevant output currents without usin extra active devices. In addition, hih Q-value filters can easily be obtained by adjustin the ratio of two independent bias current. Because of the low-input and hih-output impedances of the circuit, it is easily cascadable. The circuit parameter sensitivities are all low. PSPICE simulation results confirmin the theoretical results are also included. Description of ZC-CFTA The schematic symbol and its ideal behavioral model of the ZC-CFTA are represented in Fis (a and b), respectively. Its operation is defined by the followin expression : vp ip i v i = v i + m v i x m v x () where m is the transconductance ain of the ZC-CFTA, which can be controlled electronically. The CMOS-based internal structure of the ZC-CFTA is shown in Fi.. The circuit is a combination of the current follower with very low input resistance 4, which is the input stae of the device, and the balanced-output transconductance amplifier 5, which forms the output stae. In this case, the m -value of the ZC-CFTA is dependent on the external dc bias current (I O ), which is iven as: v p ZC-CFTA i p v v p p i p v i (a) v i x- i i x- i x- v x- v - m v x- i + m v i v i p i v ip v (b) Fi. ZC-CFTA (a) circuit symbol (b) equivalent circuit Current follower circuit +V Balanced-output transconductance amplifier M 7 M 8 M 9 M M M M 3 M 4 M 5 M i i i M 6 M 7 i x- M 5 M i p I O x- p M 4 M 6 M 8 M 9 M 3 -V M M Fi. Schematic CMOS implementation of the ZC-CFTA

3 SATANSUP & TANGSRIRAT: REALIZATION OF CURRENT-MODE KHN-EQUIVALENT BIQUAD FILTER 843 W = µ () m IO Cox L where µ is the free electron mobility in the channel, C ox is the ate oxide capacitance per unit area and W and L are the channel width and lenth, respectively. 3 Proposed Current-Mode KHN Biquad Filter Fiure 3 shows the block diaram for realiin the proposed current-mode KHN-equivalent biquad. It consists of two lossless interators (/sτ and /sτ ), a summer and proportional ain blocks ( and K). Usin ZC-CFTA as active element for sinal processin, the proposed current-mode KHNequivalent filter is shown in Fi. 4. The circuit structure contains two interators 6 (ZC-CFTA, C and ZC-CFTA, C ) and current-controlled ain block (ZC-CFTA3 and ZC-CFTA4). Note that the circuit uses only rounded capacitors as passive elements, thus, it is advantaeous from interation point of view. Another advantae is that it has a low-input impedance and hih-output impedance property, thereby permittin easy cascadability. Routine analysis of the proposed circuit iven in Fi. 4 ives the followin filter transfer functions: I in K I HP P sτ sτ Fi. 3 Sinal processin block diaram for realiin currentmode KHN biquad I LP I HP ( s) s HP( s) = = (3) I ( s) D( s) BP( s) LP( s) and in m m4 s I ( s) C I ( s) D( s) BP m3 = = (4) in I ( s) C C I ( s) D( s) m m LP = = (5) in m m4 m m D( s) = s + s +. (6) m3c CC Therefore, the proposed filter simultaneously realies second-order HP, BP and LP current responses without requirin any component matchin condition. Moreover, the relevant output currents in Eqs (3)- (5) can be tied toether to obtain the BS and AP responses without any condition or additional circuitry as follows: BS( s) = I ( s) + I ( s) (7) LP HP and AP( s) = I ( s) I ( s) + I ( s) (8) LP BP HP The important parameters ω and Q of this filter are found as: m m ω = (9) CC I in p x- C I HP x- p 3 p x- C P p 4 x- -P I LP C Q = () C m3 m and m4 m where mi and I Oi refer to m and I O of the i-th ZC- CFTA (i =,, 3, 4). Furthermore, for simplicity, substitutin m = m = m (I O = I O = I O ) and C = C = C in Eqs (9) and () yields the followin expressions: m ω = () C Fi. 4 Proposed current-mode KHN biquad filter usin ZC-CFTAs m3 and Q = () m4

4 844 INDIAN J PURE & APPL PHYS, VOL 49, DECEMBER It should be noted from Eqs () and () that the filter parameters ω and Q are independently controllable. This means that the ω for all filter responses can electronically be tuned without disturbin the Q-value by adjustin m. Also, the parameter Q can be tuned independently by the ratio of m3 and m4. Therefore, the hih-q filters can be obtained by settin this ratio properly. 4 Trackin Errors and Sensitivity Analysis By takin the ZC-CFTA non-idealities into consideration, the port relation in Eq. () can be rewritten as: vp ip i αi v i = α i v i + m v i x m v x (3) where α i = -ε i and ε i ( ε i << ) represents the current trackin error from p to or terminals of the i-th ZC-CFTA. Re-analyin the proposed circuit of Fi. 4 with Eq. (3) yields the followin non-ideal parameters : = α α m m ω (4) CC are presented in Table. The supply voltaes are +V = V = 3 V, and all the biasin currents ( ) which are realied by the simple current mirror circuits are set to 5 µa. For all simulations, the capacitance values were chosen as: C = C = pf. In order to realie the filter responses with a natural frequency of f = ω /π 3.3 MH and a quality factor of Q =, the followin settin for the presented filter of Fi. 4 have been selected as : m = m = m3 = m4 = 45 µa/v (I O = I O = I O3 = I O4 = 4 µa), which results in total power consumption of about 9 mw. Fi. 5 shows the simulation results for HP, BP, LP and BS filter characteristics. The ain and phase responses of the AP filter confiuration are also shown in Fi. 6. In addition, time domain simulation results for the LP, BP and HP responses of the proposed filter in Fi. 4, are shown in Fi. 7, in which a 3.-MH sinusoidal input current sinal with µa peak value is applied to the filter. In Fi. 7, the dotted lines represent ideal response while the solid lines denote simulated responses. It can be observed form Fis 5-7 that the proposed filter performs all the standard biquadratic filterin functions well and the simulation results are close to ideal responses. To demonstrate the electronic controllability of f, the tunin bias currents m (= m = m ) were Table Transistor dimensions of the CMOS ZC-CFTA circuit in Fi. Transistors W (µm) L (µm) C Q = α α α α C 3 m3 m and 4 m4 m. (5) M M M 7 M M 6 M 4.7 It is evident that the values ω and Q slihtly chane by the effect of the ZC-CFTA current trackin error. However, these deviations may be compensated by re-adjustin the m -value appropriately. Thus, the desired parameter values can still be satisfied. From Eqs (4) and (5), all the active and passive sensitivities are within unity in manitude. Gain (db) LP(s) BP(s) HP(s) BS(s) 5 Simulation Results To prove the theoretical validity of the filter proposed in Fi. 4, this filter was simulated with PSPICE proram. The ZC-CFTAs were simulated usin the CMOS implementation iven in Fi. based on the.35 µm Taiwan Semiconductor Manufacturin Company (TSMC) process parameters. The aspect ratios of the MOS transistors - -4 k M M M Frequency (H) Fi. 5 Simulated LP, BP, HP and BS responses for the proposed filter in Fi. 4

5 SATANSUP & TANGSRIRAT: REALIZATION OF CURRENT-MODE KHN-EQUIVALENT BIQUAD FILTER 845 f =.6 MH f = 3. MH f = 6.45 MH G ain (db ) - -4 k M M M Frequency (H) I i n ( µa ) Fi. 6 Ideal and simulated ain and phase responses of the AP filter confiuration in Fi Fi. 8 Simulated frequency responses of the BP filter when f is varied and Q = Q = Q = Q = 4 I L P (µa ) 4 Gain (db) - P (µa ) k M M M Frequency (H) Fi. 9 Simulated frequency responses of the BP filter when Q is varied and f 3. MH I H P (µa ) Time (µs) Fi.7 Time domain responses of LP, BP and HP filters for the proposed filter in Fi. 4 respectively varied to, 4 and 6 µa, while keepin I O3 = I O4 = 4 µa for Q =. In this settin, the f -values calculated from Eq. () are approximated to.6, 3. and 6.45 MH, respectively. The resultin responses of the BP filter correspondin to different bias currents I O are shown in Fi. 8. From the simulations, the correspondin f are found as.6, 3.3 and 6. MH, respectively. Fi. 9 shows the simulated BP responses with Q-tunin (i.e., Q =, and 4). In this case, the bias T H D ( % ) Input current (µa) (peak) Fi. THD variations of the proposed filter versus amplitude of the applied sinusoidal current sinal at 3. MH currents were chosen as: I O = I O = 4 µa, I O4 = µa, and I O3 = µa, 4 µa, 6 µa, respectively. Note that the hih-q filter can be realied from hih value of I O3. Furthermore, the total harmonic distortion (THD) variations of BP response on the

6 846 INDIAN J PURE & APPL PHYS, VOL 49, DECEMBER amplitude of the sinusoidal input current sinal at 3. MH are shown in Fi.. 6 Conclusions The realiation of current-mode KHN-equivalent biquad usin ZC-CFTAs has been described. The circuit structure employs four ZC-CFTAs and two rounded capacitors, which is convenient for interation. The filter simultaneously realies LP, BP and HP current responses from the same topoloy and it can easily be modified to realie BS and AP functions. The circuit also provides independent current control of ω and Q, and the filter with hih Q value can be obtained by simply tunin the ratio of ZC-CFTA s bias currents. It has both low-input and hih-output impedance, thereby permittin easy cascadability. Also, the described circuit requires no component matchin conditions and has low sensitivities. Acknowledement This work was supported by the Office of the Hiher Education Commission, Ministry of Education, Thailand, under the research project title Hiher Education Research Promotion. References Kerwin W, Huelsman L & Newcomb R, IEEE J Solid-State Circuits, SC- (967) 87. Koton J, Herencsar N & Vrba K, Int J Electron, 97 () Soliman A M, Electron Lett, 3 (994 )9, 4 Senani R & Sinh V K, Electron Lett, 3 (995) Khaled N S & Soliman A M, Frequen, 54 ()9. 6 Koton J, Herencsar N & Vrba K, Int J Electron Commun (AEU), 65() Altuntas E & Toker A, Int J Electron Commun (AEU), 56 () Toker A, Oou S & Acar C, Electron Lett, 35 (999) Ibrahim M A, Minaei, S & Kuntman H, Int J Electron Commun (AEU), 59 (5) 3. Herencsar N, Koton J & Vrba K, IEICE Trans Fundamentals, E93-A () 86. Biolek D, Senani R, Biolkova V & Kolka Z, Radioenineerin, 7 (8) 5. Biolek D, Proc ECCTD 3, Vol III, Poland; pp 397-4, 3. 3 Herencsar N, Koton J, Vrba K & Lattenber I, J Active and Passive Electronic Devices, 6 ()7. 4 Tansrirat W, Klahan K, Dumawipata T & Surakampontorn W, Int J Electron, 93 (6) Bhaskar D R, Sinh A K, Sharma R K & Senani R, IEICE Electronics Express, (5) 8. 6 Tansrirat W & Tanjaroen W, Circuits, Syst Sinal Process, 7 (8) 8.