Homg et al. [12] presented a high-input impedance voltage- realize AP filter. and one circuit needs voltage inverter to realize AP response.

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1 HighInput Impedance VoltageMode Multifunction Filter with ThreeInput SingleOutput Based on imp e C OTs Montree Kumngem *, Montri Somdunyakanok 8, and Pipat Prommee * Telecommunications Engineering Department, Faculty of Engineering, King Mongkut's Institute of Technology Ladkrabang, Bangkok 10520, Thailand Tel: , , fax: kkmontregkmitl.ac.th, pipatgtelecom.kmitl.ac.th telectrical Engineering Department, Faculty of Engineering, Siam University, Bangkok 10160, Thailand monsom@siam.com AbstractA new voltagemode three inputs and one output output impedance, the highpass (HP), bandstop (BS) and universal biquadratic filter with highinput impedance allpass (AP) responses in [6] require component matching employing six simple operational transconductance amplifiers.. (OTAs) and two grounded capacitors is presented. The proposed conditions responses whileethetap circuit offers the following features: realization of all the component matching conditions and none of their responses standard filter functions, that is, highpass, bandpass, lowpass, have the advantage of highinput impedance in [7], [9]. The bandstop, and allpass filters; electronically tunable of the circuit in [10] employs two plus/minustype CCIIs, two angular frequency through adjusting the bias currents/voltages capacitors and two resistors. However, this circuit needs an of OTAs; no requirements for component matching conditions; i.. ' highinput impedance good for cascadability for the voltage invertlngtype voltage input signal to realiz APe response and mode circuits; the use of only grounded capacitors and require employs both floating capacitors and resistors. The circuit in no resistor; low active and passive sensitivities. PSPICE [11] employs two plustype CCIIs and two capacitors and simulation results that confirm the theoretical predictions are three resistors with four inputs and single output to realize a given. universal biquadratic filter. However, none of its responses have the advantage of highinput impedance and the LP, BS, I. INTRODUCTION and AP responses require componentmatching conditions. Homg et al. [12] presented a highinput impedance voltage Operatisonealtansntasne aifie (OTAs).h.A mode universal biquadratic filter with three inputs and single exviiedso a dvantageslinearele theacircity design.dte Ota output using three plustype CCIIs. However, the circuit provdesanh y lnearfu e ability,to generate a wide tunabe. employs floating capacitors and needs a voltage inverter to range and powerful ability to generate various circuits. relz.pfle esos.tecrut in [1]epo he realize AP filter Morever,OTAasedcircits equie noresitorsand, response. The circuits in [13] employ three Moreover, based circuits resiston plustype CCIIs. However, they employ floating capacitors ter1. and one circuit needs voltage inverter to realize AP response. v... In 2007, Chiu and Horng [14] employed three DDCCs, two Secondorder voltagemode active filters with highinput gruddcpitsantwgonedeitr. impedance are of great interest because several cells of this Mostdof theacirs p res ntedtelittursu kind can be directly connected in cascade to implement higher lack oftelctrcuity [5][14]d B the s order filters [2][3]. On the other hand, the use of grounded applctionscanabelete to the O TrOnA OTA, ota capacitors is beneficial from the point of view of integrated tapplcations can be extended to the domal n of electronically cici imlmntto tunable functions. In the 4. past, several circuit implementation [4]. electronically tunable Recently, many voltagemode universal filters with voltagemode multifunction filters using OTAs were proposed multiple inps sg ad [15][21]. In 1986, Nawrocki and Klein [15] proposed a two multiple inputs and single output based on different design inerao loo unvra biudai fite wit sigl inu techniques are available in literature [5][14]. Early circuits in ingleroup usin eightotas adtw grounded [5][9] employ different types of active devices (three current apaci n 1992,uin et Al [16 p roposed capacitors. In 1992, Khan et al. [ 16] proposed two conveyors and one voltage follower in [5], two plustype secondgeneration current conveyors (CCIIs) in [6], one plus cofgrtns or eaing vlgmd uiesl type CCII and one minustype CCII in [7][8], two plustype bqartcflesec ihtreipt n igeotu ' ~~~~using three OTAs, one voltage follower and two capacitors. CCIIs~~~~ adtomnstpcciin[]. Hoevr onl the. However, only the bandpass (BP) and LP responses have the lowpass (LP) response in [5] enjoys the adlvantage Of high /08/$25.OO 2008 IEEE 426

2 advantage of high output impedance. In 1993, Sun and Fidler where 10 is the output current, VI and V2 denote the non [17] proposed a singleinput and singleoutput voltagemode inverting and inverting input voltage, respectively, of the universal biquadratic filter by using six OTAs and two OTA. Fig. 2 shows the CMOS implementation of simple capacitors. However, it needs componentmatching conditions OTA. It uses only four MOS transistors and one current for the HP, BP, BS and AP responses. Acar et al. [18] source. Assume four MOS transistors operating in saturation proposed some filter structures based on the signal flow graph and require at most six OTAs and two grounded capacitors. It [20] provides only one filtering output simultaneously. Wu and Xie [19] proposed a fiveinput and threeoutput voltagemode region, the transconductance gain (gm) can be expressed by gc =(W/L)Iabc (2) multifunction filter by using four OTAs and two grounded From (2), the gm is proportional to (Iabc) 1/2 capacitors. However, it requires the capacitor injection of excitation signals in the circuit design, so it is not suitable for VDD VDD cascade implementation, and the resulting floating capacitors t T t T are not ideal for IC implementation. MS MM M7 M8 M M In this paper, a new highinput impedance voltagemode MI I multifunction filter with three inputs and one output using six T 1 T simple OTAs (24 MOS transistors and 6 current sources) and OTA1 OTA2 two grounded capacitors is presented. The proposed circuit M1 M2 71 M3 M4 needs neither an invertingtype voltage input signal nor any O X critical componentmatching conditions to realize all five Vic VZ fia V3 generic filter responses, that is, HP, BP, LP, BS and AP filters, labcl labc2 from the same configuration. The parameter coo can be tuned electronically through the bias currents voltages of OTAs. Vss VsS The circuit has low active and passive sensitivities. Addition/Subtraction Ilabc V3 + Ic Vi + lc OTA2 Vc V2 Vi Fig. 1. Circuit symbol of OTA. OTA1 Ici VDD M3 M4 Fig. 3. The addition/subtraction circuit. c From the OTA as shown in Fig. 2, it formed by MOS couple pair and a current mirror. Assume that all MOS devices operate in the saturation region, the transistor drain current ID V1I M 1 M 2 V2 is characterized by a squarelaw model as abc ID =KI(VGS VTH )2 for VGS >VTH, (3) 0 for VGS < VTH J Vss where the transconductance parameter K=[tCO,W/2L, [t is the mobility of the carrier, Co, is the gateoxide capacitance per Fig. 2ThCOimeettnunit area, W is the effective channel width, L is the effective channel length, and VGS and VTH are the gatetosource and the threshold voltages, respectively. Let Vin is the differential The circuit symbol of the OTA is shown in Fig. 1. Ideally, input voltage (Vin=VlV2), I is the output current, labc is the the OTA is assumed an ideal voltagecontrolled current bias current, Ml and M2 are perfectly matched and the current source and can be described by following equation, mirrors have unity current gain. By using (3), the differential output current (Io=ID IDT) of the circuit in Fig. 2 can be given Io = gm(v1 V2) (1) b[ International Symposium on Communications and Information Technologies (ISCIT 2008) 427

3 2I~~KV~11 1KVj~~J2IabC 0 The BS response can be obtained when 0 in (4) ~~~~~~~~~~VinI=Vin2=Vin3=Vin. for Ilabc/K <Vin < Iabc/K Therietrnsonutaknte geiatinvg of OTA euthsimpl canhbespc the biquadratic filtering function without component b aingthdeiaieoeqain()whrspc matching condition requirements as well as require no an derviv,yeld The tanscnductnce ain of he smple TA cn be Thus, the proposed filter can realize all the standard types of to V~~~~11, yielding ~~~~~invertingtype voltage input signal hence the name "universal g= 2IabcK for Ilabc/K. Vi. Ilabc/K (5) biquadratic filter". It requires the minimum number of passive components. Moreover, the three input signals Vini1, V1112 and Equation (5) shows that the transconductance gain gm of the Vin13, are connected to the high input impedance input nodes of OTA can be varied by the bias current Iabc in the form of the OTAs. So the circuit enjoys the advantage of having high square root function. In addition, in order to operate in the input impedance thus permitting easy cascadability. Note that low distortion range, where all the transistors are operated in the high input impedance makes the proposed circuit easy to saturation, the input voltage Vi11 should be in the range of [22] be connected to next stage without any buffer. Furthermore, the new circuit uses only two grounded capacitors and require Vin. Clabc /K (6) on resistor, which are suitable for integrated circuit implementation. The employs of only simple OTA simplify III. CIRCUIT REALIZATION the circuit configuration. It should be noted that the proposed universal filter is suitable for a high impedance load. If the By usng thsimpe OTAas shwn infig. the Byd usiongsuthcio simpletotan, shown in Fig.3.I 2,2th low impedance load is applied, it needs a voltage buffer at an p roleof proposedifilterrareogivenqby: ain)the teplso h rpsdfle r ie y [23], this circuit may be called pool circuit. Assume all the othet NMOS devices in Fig. 3 are biased in the saturation region with individual wells connected to their sources to eliminate 1m the body effect. Let the transconductance parameter and the wo f~2(1) = threshold voltage of MI through M4 be equal to K and VT, GIG2 respectively. Let labc=iabc1=1abc2, the currents 101 and 102 in the mc addition/subtraction circuit in Fig. 3 can be given as Q (12) K(V1 0) 21ac (1 v0 2 (7) It can be seen from equation (11) that the parameter oo~is tunable by adjusting the transconductances gm and gm2 1,=K(V V2) 2ac (V3 V2)2 (8) through the bias currents of the OTAs hence the name K )2 ~~~~~~~"electronically tunable biquadratic filter". Therefore, at the equilibrium state [2l][22] IV. NONIDEAL EFFECTS Vo0 VI V2 + V3. (9) The effects of addition/subtraction circuit nonidealities and This circuit operates as a pool [22] in the sense that the OTA on the filter performance have been considered. By currents flowing in and flowing out are in equilibrium at the considering the nonideal addition/subtraction circuit, Eq. (9) output node V0. Therefore, the circuit can be obtained the can be rewritten as addition/subtraction circuit. It uses simple OTAs to obtain with simple circuitry. Using the simple OTA in Fig. 2 and the Vo0 f3kivl f3k2v2 + f3k3v3 (13) addition/subtraction circuit in Fig. 3, the proposed where f3ki(s)=f3ki=l8kiv and 4k14(1vJ«1) denotes the voltage configuration can be shown in Fig. 4. The transfer functions taknerrfo Itria ov emnl k()p2l can be expressed as trcigerrfo 1tria t 0tria,fk()fk=1 2 42v~~~~~~~~~~ and 4k24(2vJ«1) denotes the voltage tracking error from ou.i2i3simvi2+gimvn (10) V2 terminal to V0 terminal, f3k3(s)=f3k3=l8k3v and 44k3v( k3o«) from eqation(1) that:terminal of the kth addition/subtraction circuit. Considering vout s2c1 C2 + scigm2 + gm1gm2 denotes the voltage tracking error from V3 terminal to V0 It is clarlysee It s cleal see (10 fresoms eqatin otaiehat: ilvi the nonidealities of the OTA, the transconductance gain gmi * Th HPrespnsecanbe otaied wen ~11=V~12=0and can be assumed as [24] Is The BP response can be obtained when Vi111=Vi113=0 and mcg Vin2=Vin 9mi s + W ~~~~~~~~~(i 1,2) (14)

4 Vi n OTA z + iota2 1C Fig. 4. Proposed three inputs and single output multifunction biquadratic filter. Referencing to [24], the transconductance gain gmi may be AlA\/KA modified to VO = V1±+(V3 V2 1 (20) 2cabc 2K) gm1 gmj(1htis) 'l (15) where di=l/ogi. Using (13) and (15), the transfer function in Equation (20) implies that the mismatch of the dc current Fig. 4 becomes sources and the aspect ratio K cause of the voltage tracking error. The changing of K may be increased the linearity error. 2CC (1 C1gm2f323f33 +gm1m2p12p22p32~112 The gain error of the addition/subtraction circuit can be S C1 24 improved by increasing the bias current babc and K or by Referencig C 2 decreasing the W/L ratio of M6b +scig to Vmo=m2P12P22I32I1 gm1gm2p12p22p322 TABLE I. 1m2232yt C1gm ) SENSITIVITIES OF CIRCUIT COMPONENTS +gm1gm2(12i22p32 I x I abc (16) gl From (16), the nonidealities of the addition/subtraction gm circuits and OTAs affect the circuit characteristics, which ck depart from ideal values. For the parasitic effects from the P OTAs, it can be made negligible by satisfying the following I condition: d a ±gm1gm2p12p22p32[l1 2 «1 P l C1C2 1 V. SIMULATION RESULTS. mlg2m1222m31.4<< (17 The proposed circuit was simulated using PSPICE. The Cg2323f32 «ij simple OTA was realized by the CMOS implementation in Fig. 2 using 0.5pm CMOS technology process parameters as Therefore, the nonideal natural frequency a o and quality shown in Table II. The power supplies are selected as factor Q can be obtained by VDD=VSS=2.5V. gsigitanb) = gmlgm0l2d2202 (18) For example deiggn, the aspect ratios of the MOS transistors are W/L=4pm/4m for all NMOS and W/L= C1C2 40pnm/2m for all PMOS. C1=C2=l0OpF and Iabc =KIabc2=5A 1 gm2c1j312j22. 1) (gm=77.524ps) are given. The bias currents for OTA3 to 23 gmc2j32 (19) OTA6 are chosen as 25A. This setting has been designed to obtain the LP, BP, HP, BS and AP filter responses with The incremental sensitivities of the parameters o<and Q are fs= khz and Q=1. The simulated response of the HP, calculated as Table I. Considering the addition/subtraction LP, and BP of the proposed filter are shown in Fig. 5. In this circuit shown in Fig. 3, assume that the aspect ratios of Ml figure, the pole frequency of kHz is obtained. The pole and M2 are equal Kb to AK/2 and those of M3 and M4 are frequency is kHz instead of kHz owing to the equal to AK/2. If the dc current sources Iabcl=JabcAI/2 and effect described in Section 4. According to (18), this error IabcT=IabcAI/22one can obtain. would be caused by voltage tracking errors International Symposium on Communications and Information Technologies (ISCIT 2008) 429

5 TABLE II. MODEL PARAMETERS FROM 0.5}tm MOSIS. 20_.MODEL CMOSN NMOS LEVEL=3 PHI= TOX=9.6000E09 +XJ= U TPG=1 VTO= DELTA=1.0700E+00 +LD=4.2030E08 KP=1.7748E04 UO=493.4 THETA=1.8120E01 +RSH=1.6680E+01 GAMMA= NSUB=1.1290E+17 +NFS=7.1500E+ 1I VMAX=2.7900E+05 ETA= E02 +KAPPA=1.6100E01 CGDO=4.0920E10 CGSO=4.0920E10 +CGBO=3.7765E10 CJ=5.9000E04 MJ= CJSW=2.OOOOE11 +MJSW= PB= abc1oa 0 co 20 ICDbc1A \ I1labC=3O0AA IabC=300J1A.MODEL CMOSP PMOS LEVEL=3 PHI= TOX=9.6000E09 +XJ= U TPG=1 VTO= DELTA=1.2380E02 +LD=5.2440E08 KP=4.4927E05 UO=124.9 THETA=5.7490E02 +RSH=1.1660E+00 GAMMA= NSUB=8.0710E+16 +NFS=5.9080E+11 VMAX=2.2960E+05 ETA=2.1930E02 +KAPPA=9.3660E+00 CGDO=2.1260E10 CGSO=2.1260E10 +CGBO=3.6890E10 CJ=9.3400E04 MJ= CJSW=2.51OOE10 +MJSW= PB= Fig. 6 shows the simulated frequency responses of the gain and phase characteristics of the AP filter. It is clear from Figs. 56, that the proposed filter performs five standard biquadratic filtering functions well KHZ 1 KHz I 1 00KHz Frequency Fig. 7. ± 1.0MHz 1 0MHz Simulated frequency responses of the BP filter when Io is varied. Fig. 7 shows the simulated a BP filter response when the dc bias currents abc (i.e. IabcIabc1Iabc2) were simultaneously adjusted for the values IA, 1OpA, 3OpA and 3OOiA while keeping the capacitors C1 and C2 are loopf. VI. CONCLUSIONS In this paper, a new three inputs and single output voltagemode universal biquadratic filter with highinput impedance is presented. The proposed circuit uses simple OTAs and / vg Xh \' 20grounded capacitors and offers following advantages: high / X \ \ input impedance, low active and passive sensitivities, the use of only eight simple OTAs (32 MOS transistors and eight current sources), the use of only two grounded capacitors and ~BP on resistors, the versatility to synthesize LP, BP, HP, HP require A/ABS BS and AP responses without component matching conditions 100KHz 1.OMHz 10MHz 1 AKHz and electronically tunable of parameter (O. PSPICE simulations confirm the theoretical predictions. Frequency A 0 mco o O KHz REFERENCES Fig. 5. Simulated LP, BP, HP, and BS responses of the proposed filter. Gain, db Phase, degree 10d_ 0 50_ d =[ dr_ gain 00 phase 300d 400d K 1. OKHz a E C l l l 10OKHz 1 00KHz 1 0MHz Frequency Fig. 6 Simulated AP response ofthe proposed filter. [1] E. SanchezSinencio, R. L. Geiger, and H. NevarezLozano, "Generation of continuoustime two integrator loop OTA filter structure," IEEE Transactions on Circuits and Systems, vol. CAS35, pp , [2] S. F. H. Naqshbendi and R. S. Sharma, "High input impedance current conveyor filters," International Journal of Electronics, vol. 55, pp , [3] A. Fabre, F. Dayoub, L. Duruisseau, and M. Kamoun, "High input impedance insensitive secondorder filters implemented from current conveyors," IEEE Transactions on Circuits and SystemsI, vol. 41, pp , [4] M. Bhusan and R. W. Newcomb, "Grounding of capacitors in integrated circuits," Electronics Letters, vol. 3, pp , 1 11Hz [5] C.M. Chang and M.S. Lee, "Comment: Universal voltagemode with three inputs and one output using three current conveyors and one voltage follower," Electronics Letters, vol. 31, pp , [6] 0. Ozoguz and E. 0. Gunes, "Universal filter with three inputs using CCII+s," Electronics Letters, vol. 32, pp , [7] J.W. Homng, C.G. Tsai, and M.H. Lee, "Novel universal voltagemode biquad filter with three inputs and one output using only two current conveyors," International Journal of Electronics, vol. 80, pp , International Symposium on Communications and Information Technologies (ISCIT 2008)

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