New Electronically Tunable Voltage-Mode Lowpass, Highpass, Bandpass Filter Using Simple OTAs

Transcription

1 Internatinal Jurnal f Cmputer and Electrical Engineering, l., N. 5, Octber 0 New Electrnically Tunable ltage-mde Lwpass, Highpass, Bandpass Filter Using Simple OTAs Mntree Kumngern Abstract This paper presents a new electrnically tunable vltage-mde universal biquad filter based n simple CMOS peratinal transcnductance amplifiers (OTAs) and grunded capacitrs. The prpsed filter prvides secnd-rder lwpass, bandpass and highpass vltage respnses at a high impedance input terminal, which enable easy cascadability. The circuit enjys realizatin using a lw number f active and passive cmpnents, n requirement with the cmpnent chice cnditins t realize all filtering functins, and lw active and passive sensitivities perfrmance. The perfrmances f the prpsed filter are simulated with PSPICE t cnfirm the presented cnfiguratin. Index Terms vltage-mde filter, electrnically tunable, peratinal transcnscnductance amplifier, CMOS I. INTRODUCTION Operatinal transcnductance amplifiers (OTAs) have exhibited sme advantages in the circuit design, because its transcnductance gain can be varied electrnically which is especially suitable fr analg circuits. The OTA prvides a wide tunable range and pwerful ability t generate varius circuits. Mrever, OTA based circuits require n resistrs and, therefre, are suitable fr integrated circuit (IC) implementatin []. A biquad filter is very useful blck t realize high-rder filters that plays an imprtant rle in the fields f electrnic measurement, cmmunicatin, autmatic cntrl and neural netwrks. Besides, the vltage-mde active filters with high input impedance are f great interest because several cells f this kind can be directly cnnected in cascade t implement higher rder filters []. On the ther hand, the filters using grunded capacitrs are beneficial frm the pint f view f IC implementatin []. In the literature, several vltage-mde biquad filters using OTAs have been prpsed [4]-[]. Cnsidering the number f input and utput prts, these filters can be divided int fur categries: (i) a single-input, single-utput (SISO) type [4]-[6], (ii) a single-input, multiple-utput (SIMO) type [], [7]-[], (iii) a multiple-input, single-utput (MISO) type []-[6], and (vi) a multiple-input, multiple-utput (MIMO) type [7]-[]. Generally, the SISO filters can realize multi-functin utputs by altering the cnnectin way f the circuits [4]-[6], but altering the cnnectin way can nly realize a filtering utput at a time. The MISO and MIMO filters can realize multifunctin utputs simultaneusly []-[], but they need input signal matching. The SIMO filters can simultaneusly realize standard filters, namely lwpass (LP), bandpass (BP) and highpass (HP) filters at a time withut altering the cnnectin way f the circuits and withut input signal matching. This prperty is interested in this paper. In the prpsed vltage-mde OTA-based SIMO filtering circuits, circuit [] cntains fur OTAs and enjys lw active and passive sensitivities, but the filter structure requires capacitr injectin f excitatin signals in the circuit design, s it is nt suitable fr cascade implementatin, and the resulting flating capacitr are nt ideal fr IC implementatin. The circuits [7], [8], [], [] use grunded capacitrs and enjy a high impedance input terminal, but they suffer frm the use f large active cmpnents. The circuits [9], [0] can realize standard filtering, but the circuits require cmpnent-matching cnditin fr realizing all filter respnses and als use tw kinds f active cmpnents (OTA and p-amp [9] and OTA and DDCC [0]). In this paper, a new electrnically tunable vltage-mde universal biquad filter emplying simple CMOS OTAs and grunded capacitrs, which prvides the advantage f electrnic tuning capability and is especially interest frm the IC implementatin pint f view, is prpsed. It invlves nly a kind f active cmpnent. The circuit can realize LP, BP and HP vltage respnses at a high input impedance terminal, which enable easy cascadability. Als, the natural frequency (ω ) and the quality factr (Q) can be set rthgnally by adjusting the circuit cmpnents. In additin, the bandstp (BS) and allpass (AP) respnses can be btained by intercnnectin f relevant utput vltages by using additinal circuits. PSPICE simulatin results are used t verify the perfrmances f the prpsed circuit. Fig.. Circuit symbl f the OTA. Manuscript received July 6, 0; revised September 0, 0. Mntree Kumngern is with Faculty f Engineering, King Mngkut s Institute f Technlgy Ladkrabang, Bangkk 050, Thailand ( kkmntre@kmitl.ac.th). Fig.. The CMOS implementatin f the simple OTA. 649

2 Internatinal Jurnal f Cmputer and Electrical Engineering, l., N. 5, Octber 0 II. CIRCUIT DESCRIPTION The circuit symbl f the OTA is shwn in Fig.. It is assumed an ideal vltage-cntrlled current surce that has infinite input and utput impedances. Its characteristic f ideal OTA can be given by I m ( ) = g () where I is the utput current, g m is the transcnductance gain, and and dente nn-inverting and inverting input vltage, respectively. Fig. shws the CMOS implementatin f the simple OTA. It uses nly fur MOS transistrs and ne current surce. Assuming fur transistrs are perated in saturatin regin, the transcnductance gain g m f this OTA can be calculated as g = μc W/L I () m x ( ) abc where I abc is the bias current, μ is the carrier mbility, C x is the gate xide capacitance per unit area, and W and L are the channel width and length, respectively. Based n the use f simple CMOS OTA, the additin/subtractin vltage signal can be shwn in Fig.. Referring t [4], [5], this circuit may be called a pl circuit. Assume that all the NMOS devices are biased in the saturatin regin with individual wells cnnected t their surces t eliminate the bdy effect, let the transcnductance parameter and the threshld vltage f M thrugh M 4 be equal t K and TH, respectively, I abc =I abc and I abc =I abc are tw current surces, the currents I and I can be given as [4], [5] I Iabc = K( ) ( ) () K Iabc I ( ) ( ) = K (4) K at the equilibrium state [4], [5] = +. (5) Fig. 4. Prpsed vltage-mde biquad filter using OTAs. This circuit perates as a pl [4], [5] in the sense that the currents flwing in and flwing ut are in equilibrium at the utput nde. Therefre, the additin and subtractin peratin fr vltage signals can be perfrmed by the circuit in Fig.. The prpsed vltage-mde universal biquad filter is shwn in Fig. 4. The buffer circuits must be added at the utput terminals f Fig. 4, because the utput impedances f this circuit are nt zer. By rutine circuit analysis, the vltage transfer functin f Fig. 4 can be given by HP s CC = (6) in s CC + scgm + gmg m BP scg m = (7) in s CC + scg m + g mg m LP g mg m = (8) in s CC + scg m + g mg m Thus, the prpsed circuit can realize a nn-inverting HP signal at HP, an inverting BP signal at BP and a nn-inverting LP signal at LP withut requirement critical cmpnent matching cnditins. In this case, the circuit emplys nly 6 MOS transistrs and 4 current surces (fur simple OTAs) and tw grunded capacitrs. Then, the filter structure is a particularly attractive fr IC implementatin because there is n resistr requirement and using nly grunded capacitr. The natural frequency (ω ) and the quality factr (Q) can be given as gmg m ω = (9) gmc Q = (0) CC gmc Letting g m =g m =g m, the parameters ω and Q can be rewritten as LP Additin/Subtractin OTA5 BS Additin/Subtractin OTA7 AP HP OTA6 BP OTA8 Fig. 5. Adder vltage using OTAs. Iabc Iabc Iabc IabcN Fig.. The additin/subtractin circuit using simple OTAs. M M M MN SS Fig. 6. Multiple-utput current surce. 650

3 Internatinal Jurnal f Cmputer and Electrical Engineering, l., N. 5, Octber 0 ω = gm () C C C Q = () C Frm abve equatins, the parameter Q can be set by C and C whereas the parameter ω can be tuned by adjusting the transcnductance g m thrugh the bias currents/vltages f the OTAs withut disturbing Q, hence the name electrnically tunable filter. In additin, by adding nn-inverting LP and nn-inverting HP filter respnses, a BS filter respnse can be easily btained ( BS = LP + HP ). Similarly, an AP filter respnse can be btained by adding with nn-inverting LP, inverting BP and nn-inverting HP filter respnses ( AP = LP + BP + HP ). Typically, vltage-mde additin circuit can be realized by using peratinal amplifiers and attached t resistrs. Hwever, the authr prvides the adder circuit in Fig. 5 fr suitable IC implementatin as ne chice. The adder circuit f Fig. 5 is cmpsed f fur simple CMOS OTAs, as abve already mentined. By using the circuit in Fig. 5, the BS and AP vltage respnses can be btained as BS in AP in s CC + g mg m = () s C C + sc g + g g m m m m m s CC scgm + g mg m = (4) s C C + sc g + g g Therefre, the prpsed vltage-mde universal biquad filter can realize five standard filtering functins by using nly eight simple CMOS OTAs ( MOS transistrs and 8 current surces). Mrever, the input in is cnnected t the high impedance input ndes f the OTA. S, the circuit enjys the advantage f having high input impedance. Nte frm the prpsed filter that it requires n cmpnent-matching cnditin fr realizatin all filter respnses. In fact, the additin/subtractin circuit is requires current-matching cnditin (i.e. I abc =I abc4 ), but this prblem can be easily slved by using multiple-utput current surce. Hwever, the authr prvides the simple multiple-utput current surce in Fig. 6 as ne example. If mre accuracy current mirrr is required, cascde current mirrr r Wilsn current mirrr may be used t replace the simple current mirrr in Fig. 6. III. CIRCUIT ANALYSIS Taking the nn-idealities f the additin/subtractin circuit, the equatin (5) can be rewritten as m = β β + β (5) where β (s)=β =-ε v and ε v ( ε v «) dentes the vltage tracking errr frm terminal t terminal f the k-th additin/subtractin circuit, β (s)=β =-ε v and ε v ( ε v «) dentes the vltage tracking errr frm terminal t terminal f the k-th additin/subtractin circuit, β (s)=β =-ε v and ε v ( ε v «) dentes the vltage tracking errr frm terminal t terminal f the k-th additin/subtractin circuit. Cnsidering the nn-idealities f the OTA, the transcnductance gain g mni can be given that g g miωgi = (i,) (6) s + ω mni = gi where ω gi dentes the first-rder high frequency ple f the OTA i (i=,). Referring t [], the transcnductance gain g mni can be mdified as g mni ( μ s) = g (7) mi where μ i =/ω gi. Using (5) and (7), the denminatr f the nn-ideal biquad can be expressed as ( ) = s ( CC Cg mμβ + gmg mμμ β ) + sgm( Cβ gmμ β gmμβ ) + g mg mβ D s i (8) The nn-ideal natural frequency (ω n ) and the nn-ideal quality factr (Q n ) can be btained as g mg mβ ω n = (9) C + g mμβ g mg mμμ β CC CC C g mμβ + gmg mμμ β CC gmg mβ CC Q = (0) n g mμ β gmμβ Cg mβ Cg mβ Hwever, due t the parasitic effects, the characteristics depart frm the ideal respnse. But the parasitic effects can be made negligible by satisfying the fllwing cnditins: C g m μβ + gmg mμμ β << C C gmμ β gmμβ << C g β m I. SIMULATION RESULTS () The perfrmances f the prpsed filter in Fig. 4 have been verified using PSPICE simulatins. The simple OTA and additin/subtractin circuit in Figs. and were perfrmed with 0.5μm CMOS technlgy prvided by MOSIS. The aspect ratis f the transistrs used are W/L=μm/μm fr the NMOS devices and W/L=40μm/μm fr the PMOS devices. The bias currents are I abc thrugh I abc8 =5μA and the supply vltages are ± [6]. Fr example design, C =C =00pF and I abc =I abc =50μA (g m =77.5μS) are given. This setting has been designed t btain the filter respnses with the natural frequency f f.7khz and the quality factr (Q)=. The simulated respnse f the HP, BP, and LP f the prpsed filter are shwn in Fig. 7. In this figure, the ple frequency f.84khz is btained. The ple frequency is.84khz instead f.7khz wing t the effect described in Sectin 65

4 Internatinal Jurnal f Cmputer and Electrical Engineering, l., N. 5, Octber 0 III. Accrding t equatin (9), this drp-ff wuld be caused by vltage tracking errrs. Fig. 8 shws the simulated a BP filter respnse f the prpsed filter when the bias currents I abc (I abc =I abc =I abc ) were simultaneusly adjusted fr the value, 0, 0 and 00μA, respectively. This result is cnfirmed by (). By using adder circuit in Fig. 5, the simulatin results fr the BS ( LP + HP ) and AP ( LP + BP + HP ) vltage respnses are shwn in Figs. 9 and 0, respectively. It is evident frm Figs. 7, 9 and 0 that HP, BP, LP, BS and AP vltage respnses can be achieved by using eight simple CMOS OTAs and tw grunded capacitrs. A sine wave signal (.84kHz) was supplied t the input f the BP respnse. When the amplitude is increased, it has been fund that the input signal level is lwer than 0.8 P-P and the ttal harmnic distrtin (THD) is abut 0.7%. Hwever, the THD is rapidly increased when the input signal is increased beynd 0.8 P-P. These simulatin results are shwn in Figs. and, respectively. Fig. 0. Simulated frequency and phase respnses f the AP filter. Fig. 7. Simulated frequency respnses f the HP, BP and LP vltage respnses f the prpsed filter. Iabc= A Iabc=0 A Iabc=0 A Iabc=00 A Fig.. The input and utput wavefrms f the BP respnses fr a.84khz sinusidal input vltage f 0.8P-P. Fig. 8. Simulated frequency respnses f the BP filter when I abc is varied Fig.. Ttal harmnic distrtin f BP filter n input vltage amplitude. Fig. 9. Simulated frequency and phase respnses f the BS filter. It shuld be nted that in rder t cnfirm the peratin f the prpsed filter, this paper has been simulated by using capacitr value f 00pF. Hwever, fr n chip capacitr, the capacitance value shuld be ranged between 0.5 t 50pF [7], 65

5 Internatinal Jurnal f Cmputer and Electrical Engineering, l., N. 5, Octber 0 [8]. If lw value capacitance is used, the transcnductance gain must be reduced fr the prpsed circuit t wrk within the bandwidth f the OTA.. CONCLUSION In this paper, a new electrnically tunable vltage-mde universal biquad filter based n simple CMOS OTAs and grunded capacitrs, which is very suitable fr IC implementatin, is prpsed. The prpsed filter can realize LP, BP, HP, BS and AP filter respnses. The ω f the filter can electrnically be cntrlled. Als, the Q can rthgnally be set by cntrlling the circuit cmpnents. The circuit requires n cmpnent matching cnditins and n inverting-type vltage input signals and has lw active and passive sensitivities. Fr realizing five standard filter respnses, the filter emplys nly MOS transistrs and 8 current surces (8 simple CMOS OTAs). REFERENCES [] E. Sanchez-Sinenci, R. L. Geiger, and H. 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