Design of a Tunable Active Low Pass Filter by CMOS OTA and a Comparative Study with NMOS OTA with Different Current Mirror Loads

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1 Internatonal Journal of Electroncs and Electrcal Engneerng Vol. 3, No. 5, October 05 Desgn of a Tunable Actve Low Pass Flter by CMOS OTA and a Comparatve Study wth NMOS OTA wth Dfferent Current Mrror Loads T. K. Das and S. Chakrabart Future Insttute of Engg. and Management/ECE Department, Kolkata, Inda Emal: tarun_fem@redffmal.com, sreya.broy@gmal.com Abstract The operatonal amplfers (OPAMP) are basc buldng blocks n mplementng a varety of analog crcuts such as amplfers, flters, ntegrators, dfferentators, summers, oscllators etc. OPAMPs work well for lowfrequency applcatons, such as audo and vdeo systems. For hgher frequences, however, OPAMP desgns become dffcult due to ther frequency lmt. At those hgh frequences, operatonal transconductance amplfers (OTAs) are deemed to be promsng to replace OPAMPS as the buldng blocks. Ths paper llustrates an applcaton of OTA as an actve low pass flter. The prmary buldng block of an OTA s the current mrror. In ths paper dfferent current mrrors are used to desgn the LPF & the correspondng frequency and phase responses are comparatvely studed. Also a comparatve study of CMOS OTA & NMOS OTA s also llustrated n ths paper. Fnally, the applcatons of OTA based LPF are also studed. Index Terms complementary MOSFET, current mrror, low pass flter, operatonal transconductance amplfer I. I out gm (Vn Vn ) Fgure. Macro model of OTA. Fgure. Ideal model of OTA. THEORY AND PRINCIPLES A. Basc Concept of OTA An OTA s a voltage controlled current source, more specfcally the term operatonal comes from the fact Fgure 3. Small sgnal equvalent model of OTA. Manuscrpt receved January 4, 04; revsed October 0, Engneerng and Technology Publshng do: 0.70/jeee () where Vn+=Input voltage appled at the non-nvertng nput termnal of the OTA, Vn-=Input voltage appled at the nvertng nput termnal of the OTA and gm=transconductance of the OTA. An deal OTA has two voltage nputs wth nfnte mpedance (.e. there s no nput current). The common mode nput range s also nfnte, whle the dfferental sgnal between these two nputs s used to control an deal current source (.e. the output current does not depend on the output voltage) that functons as an output. The proportonalty factor between output current and nput dfferental voltage s called transconductance. Fg., Fg. and Fg. 3 show the macro model, deal model and small sgnal equvalent model of OTA respectvely. INTRODUCTION An actve low pass flter s an analog crcut that s wdely used n communcaton systems and sgnal processng to pass a range of frequences & reject the hgher frequency []. It can be easly desgned by a conventonal operatonal amplfer. But CMOS operatonal transconductance amplfer can be used to desgn a LPF resultng reduced power dsspaton & fabrcaton cost []-[5]. Some earler works are enlsted n the references [6]-[] where CMOS OTA s used. But n ths paper we have started our work wth NMOS OTA wth dfferent current mrror loads. Then we have desgned the LPF by CMOS OTA wth dfferent current mrror loads. Fnally a comparatve study was nvestgated to draw the concluson that CMOS OTA s much more superor to NMOS OTA n desgnng analog crcuts. II. that t takes the dfference of two voltages as the nput for the output current converson. The deal transfer characterstc s therefore,

2 Internatonal Journal of Electroncs and Electrcal Engneerng Vol. 3, No. 5, October 05 Therefore, we wll focus on Rout, Rn, Vmn (out), Vmn (n), and A to characterze the current mrror. We can desgn a number of crcuts whch can accomplsh the current mrror functon. The ones mostly used are:. Smple Current Mrror. Wlson Current Mrror 3. Cascode Current Mrror Smple current mrror (Wdlar) Fg. 7 below shows the schematc crcut dagram of a smple current mrror. The amplfer s output voltage s the product of ts output current and ts load resstance: Vout I OUT Rload () The voltage gan s then the output voltage dvded by the dfferental nput voltage: Gm Vout Rload g m Vn Vn (3) B. Current Mrror Fundamentals An OTA s bascally a dfferental amplfer wth actve current mrror load to accomplsh hgh gan. As the name tself suggests a current mrror s used to generate a replca (f necessary t may be attenuated or amplfed) of a gven reference current. If we look at the electrc functon of the crcut, a current mrror s a current controlled current source (CCCS). A current mrror s bascally nothng more than a current amplfer. The deal characterstcs of a current amplfer are: Output current lnearly related to the nput current, Iout=A.Iref Input resstance s zero Output resstance s nfnty In addton, we have the characterstc Vmn whch apples not only to the output but also the nput. Vmn (n) s the range of nput voltage over whch the nput resstance s not small and Vmn (out) s the range of the output voltage over whch the output resstance s not large. Fg. 4, Fg. 5 and Fg. 6 show the block dagram, transfer characterstcs and output characterstcs of a current mrror respectvely. Fgure 7. Schematc crcut dagram of smple current mrror. We assume that VDS>VGS VT then, V VT VDS K ' out LW GS ref LW VGS VT VDS K ' (4) If the transstors are matched, then K =K and VT=VT to gve: VDS out LW ref LW VDS (5) If VDS=VDS then, we have o LW ref LW (6) Therefore the sources of errors are: ) VDS and VDS are not equal. ) M and M are not matched. 3) Channel length modulaton (λ) and 4) Threshold offset. Fg. 8 shows the small sgnal equvalent model of a smple current mrror. Fgure 4. Block dagram of current mrror. Fgure 5. Transfer characterstcs of current mrror. Fgure 8. Small sgnal equvalent model of smple current mrror. Fnally, out g m / g m ref S (Cgs Cgs ) / g m Wlson current mrror Fg. 9 below shows the schematc crcut dagram of a Wlson current mrror. Fgure 6. Output characterstcs of current mrror. 05 Engneerng and Technology Publshng (7) 378

3 Internatonal Journal of Electroncs and Electrcal Engneerng Vol. 3, No. 5, October 05 Fgure 9. Schematc crcut dagram of Wlson current mrror. here, V GS =V GS, so I D s almost equal to I D. Then, W L V L out DS W ref VDS (8) V V V V () DS DS GS 3 GS 4 If V GS3 =V GS4 then, V DS =V DS. Fnally, out ref W W L V L W V W DS L L DS () Fg. below shows the small sgnal equvalent model of a cascode current mrror. Snce, V DS =V DS +V GS3 W out L VDS W ref ( VDS VGS 3) L The output voltage swng s lmted to out,mn,3 GS DSsat Th DSsat (9) V I V V V (0) It uses negatve seres feedback (M3) to acheve hgher output resstance. Fg. 0 shows the small sgnal equvalent model of a Wlson current mrror. Fgure. Small sgnal equvalent model of cascode current mrror. The output swng s lmted to V V V V V (3) out,mn GS GS 4 GS 3 DSsat,3 V V V V V (4) out,mn,3 GS DSsat TH DSsat Hence, the output resstance s ncreased wthout feedback. C. NMOS OTA Desgn wth Current Mrror Loads Fg. 3, Fg. 4 and Fg. 5 show the crcut dagram of NMOS OTA wth smple, Wlson and cascode current mrror loads respectvely. Fgure 0. Small sgnal equvalent model of Wlson current mrror. Cascode current mrror Fg. below shows the schematc crcut dagram of a cascode current mrror. Fgure 3. Crcut dagram of NMOS OTA wth smple current mrror load. Fgure. Schematc crcut dagram of cascode current mrror. An alternatve way to ncrease the output resstance s to use the cascade confguraton. The output stage conssts of two transstors M, M3 n the cascade arrangement. They are bases result from two other transstors M M4 whch are dode connected. Agan, as for the prevously started current mrror the V GS voltage of M and M are set equal. Therefore a replca of current n M s generated by M. The output resstance ncreases because of the cascode arrangement. Here, Fgure 4. Crcut dagram of NMOS OTA wth Wlson current mrror load. 05 Engneerng and Technology Publshng 379

4 Internatonal Journal of Electroncs and Electrcal Engneerng Vol. 3, No. 5, October 05 Fgure 5. Crcut dagram of NMOS OTA wth cascode current mrror load. Prncple of operaton (smple current mrror load) In NMOS OTA the M and M transstors are operated n saturaton regon.e. they satsfy the equatons: V V V & V V V (5) DS GS T DS GS T The current equatons are: The snk current, I 0.5 K ( V V ) (6) D n GS T I 0.5 K ( V V ) (7) D n GS T I I I (8) SS D D M and M are assumed to be perfectly matched.e. K n =K n and V T =V T. Two cases may be possble. Case : If V GS >V GS, then I D ncreases wth respect to I D snce I SS =I D +I D. Ths ncrease n I D mples an ncrease n I D3 and I D4. However, I D decreases when V GS s greater than V GS. Therefore the only way to establsh crcut equlbrum s for I OUT to become postve and V OUT decreases. Case : If V GS >V GS, the accordngly t can be seen that I OUT becomes negatve and V OUT ncreases. In ths way a dfferental voltage s converted to output current and hence the name operatonal transconductance amplfer s justfed. Other confguratons of NMOS OTA can also be explaned accordngly. Fg. 6 shows the small sgnal equvalent model of NMOS OTA wth smple current mrror load. CMRR s low. Slew rate s low. Fabrcaton cost s hgh. Tranconductance s low. D. CMOS OTA Desgn Wth Current Mrror Loads The best suted component for desgn of OTA s CMOS devces as t has the followng advantages: Very less power dsspaton as the feature sze of CMOS processes reduce. CMOS provdes the hghest analog-to-dgtal onchp ntegraton. Overall fabrcaton cost s less. Nose margn s hgh and stablty performance s better. CMRR, Slew rate, and PSRR are mproved. Swtchng speed s very hgh. Fgure 7. Crcut dagram of CMOS OTA wth smple current mrror load. Fgure 8. Crcut dagram of CMOS OTA wth Wlson current mrror load. Fgure 6. Small sgnal equvalent model of NMOS OTA wth smple current mrror load. Lmtatons of NMOS OTA Power dsspaton s hgh. Bandwdth s less. Nose Margn s low. Fgure 9. Crcut dagram of CMOS OTA wth cascode current mrror load. 05 Engneerng and Technology Publshng 380

5 Internatonal Journal of Electroncs and Electrcal Engneerng Vol. 3, No. 5, October 05 III. In CMOS OTA the dfferental amplfer part s exactly same as NMOS OTA, consstng of two NMOS enhancement mode transstors. But the current mrror part (I-V converson) s made of PMOS enhancement mode transstors as shown n the followng fgures. Fg. 7, Fg. 8 and Fg. 9 show the crcut dagram of CMOS OTA wth smple, Wlson and cascode current mrror loads respectvely. Fg. 0 below shows the small sgnal equvalent model of CMOS OTA wth smple current mrror load. PROPOSED ST ORDER LPF DESIGN BY NMOS OTA Fg. shows the crcut dagram of our proposed low pass flter by OTA. Fgure. Crcut dagram of proposed low pass flter. The transfer functon of the flter secton s, Fgure 0. Small sgnal equvalent model of CMOS OTA wth smple current mrror load. A( s) E. Low Pass Flter Fundamentals A flter s a devce that passes electrc sgnals at certan frequences or frequency ranges whle preventng the passage of others. The actve flters dffer from passve flters (smple RC crcuts) by the fact that there s the ablty for gan dependng on the confguraton of the elements n the crcut. It conssts of actve elements lke BJT, Opamp, FET, and MOSFET. In our desgn we have used NMOS OTA & CMOS OTA to desgn an actve Low Pass Flter (LPF). The low pass flter s one that allows low frequences to pass and stops (attenuates) hgher frequences The desgn of a low pass flter needs to take nto consderaton the maxmum frequency that would need to be allowed through. Ths s called the cut off frequency (or the 3dB down frequency). Based on the type of flter that s used (e.g. Butterworth, Bessel etc.) the attenuaton of the hgher frequences can be greater. Ths attenuaton s also based on the order (e.g. st, nd, 3rd ) of the flter that s used. Based on the order of the flter the roll-off of the flter can be calculated usng the formula n*0 db/decade. Ths means that a frst order low pass flter has an attenuaton of -0dB/decade, whle a second order flter should have -40dB/decade roll-off and on down the lst for hgher orders. Fg. shows the typcal frequency response curves of low pass flter for dfferent orders. Vn ( s) / RC Vn ( s) S / RC SRC (8) where the complex frequency varable, s=σ+jw allows for any tme varable sgnals. For pure sne waves, the dampng constant, σ becomes zero and s=jw. For a normalzed presentaton of the transfer functon, s s referred to the flter s corner frequency, or 3 db frequency, wc n rad/sec, and has these relatonshps: s s jw jf wc wc fc (9) The magntude of the gan response s: A( w) w wc (0) At w=wc the magntude of the gan s or -3dB. Hence, the pass band s: 0 w wc, and the stop band s: w>wc. We have wc=/rc. The roll off factor for st order LPF s -0dB/decade. The phase angle of the snusodal transfer functon of the st order LPF s formulated as follows. () A( w) tan ( wrc) At w=wc, the phase angle becomes 45o and as w tends to nfnty, the phase angle tends to -90o whch concludes that the order of the flter s. IV. The workng of the proposed crcut has been verfed usng PSpce smulaton. The PMOS and NMOS transstors have been smulated by respectvely usng the parameters of a 0.5mm TSMC CMOS technology. The aspect ratos of PMOS and NMOS transstors are : dmensonally. Frst we nvestgated dfferent parameters of NMOS OTA and CMOS OTA as defned below and ther measured values are lsted n Table I. Here we have Fgure. Frequency response curves of low pass flter. 05 Engneerng and Technology Publshng RESULTS OF SOFTWARE SIMULATION 38

6 Internatonal Journal of Electroncs and Electrcal Engneerng Vol. 3, No. 5, October 05 set, Vdd=5V, C load =pf for all the crcuts and tuned ISS to get postve output voltage. The calculatons are done accordng to the followng defntons of the parameters. ) Output Offset Voltage (V oo ) s the output voltage, Vout wth Vn+=Vn-=0V ) CMRR( db) 0log Ad () Acm where, Ad=Dfferental Voltage gan and Acm=Common mode voltage gan. 3) VO / Vd( Vdd 0 V ) PSRR( db) 0log (3) V / Vdd ( Vd 0 V ) 4) Sew Rate ( SR) V / s (4) V For Vn+=u(t), unt step sgnal wth Vn-=0V. O V out Fgure 8. Phase angle (degree) vs. frequency (Hz) plot of a st order LPF usng NMOS OTA wth cascode current mrror load Fgure 9. Gan (db) vs. frequency (Hz) plot of a st order LPF usng CMOS OTA wth smple current mrror load Fgure 3. Gan (db) vs. frequency (Hz) plot of a st order LPF usng NMOS OTA wth smple current mrror load Fgure 30. Phase angle (degree) vs. frequency (Hz) plot of a st order LPF usng CMOS OTA wth smple current mrror load Fgure 4. Phase angle (degree) vs. frequency (Hz) plot of a st order LPF usng NMOS OTA wth smple current mrror load Fgure 5. Gan (db) vs. frequency (Hz) plot of a st order LPF usng NMOS OTA wth Wlson current mrror load Fgure 3. Gan (db) vs. frequency (Hz) plot of a st order LPF usng CMOS OTA wth Wlson current mrror load Fgure 6. Phase angle (degree) vs. frequency (Hz) plot of a st order LPF usng NMOS OTA wth Wlson current mrror load Fgure 3. Phase angle (degree) vs. frequency (Hz) plot of a st order LPF usng CMOS OTA wth Wlson current mrror load Fgure 7. Gan (db) vs. frequency (Hz) plot of a st order LPF usng NMOS OTA wth cascode current mrror load Fgure 33. Gan(dB) vs. frequency (Hz) plot of a st order LPF usng CMOS OTA wth cascode current mrror load 05 Engneerng and Technology Publshng 38

7 Internatonal Journal of Electroncs and Electrcal Engneerng Vol. 3, No. 5, October 05 Fgure 34. Phase angle(degree) vs. frequency (Hz) plot of a st order LPF usng CMOS OTA wth cascode current mrror load Fg. 3-Fg. 8 show the gan (db) vs. frequency (Hz) and phase angle (degree) vs. frequency (Hz) plots for st low pass flter desgned by NMOS and Fg. 9-Fg. 34 those for CMOS OTA wth dfferent current mrror loads OTA NMOS CMOS TABLE I. as dscussed earler. For the desgn we have chosen R=0kΩ and C=0.0μF, Vn=Vpp sne wave. The theortcal value of hgh cut-off frequency, f H =/π.r.c=.59khz. We assume the pass band gan as unty. In Fg. 3 the maxmum pass band gan n db, hgh cut-off frequency and ts correspondng gan n db are ndcated. In Fg. 4 the phase angel at hgh cut-off frequency and also that as frequency tends to nfnty are ndcated. In Table I a parameter values of NMOs OTA and CMOS OTA are lsted. In Table II all the specfcatons of the desgned low pass flter are lsted for all the crcuts. In Table III the statc power dsspatons for all the crcuts are lsted. PARAMETERS OF NMOS OTA AND CMOS OTA current mrror load Output offset voltage CMRR (db) PSRR (db) Slew Rate (V/μs) Bas Voltage (Vdd) (Volts) Snk Current (ISS) Smple.95nV μa Wlson 57.86mV μa Cascode 57.86mV μa Smple 3.57nV μA Wlson.8mV pA Cascode 57.86mV uA TABLE II. SPECIFICATIONS OF NMOS AND CMOS OTA BASED ST ORDER LPF OTA NMOS CMOS current mrror load Hgh cut-off frequency (f H) (khz) Maxmum pass-band gan (db) Slope of the magntude plot (db/decade) Phase angle at f H (degree) Phase angle as frequency tends to nfnty (degree) Smple Wlson Cascode Smple m Wlson m Cascode m OTA NMOS CMOS TABLE III. STATIC POWER DISSIPATION current mrror load Bas voltage, Vdd (Volts) Snk Current ISS Statc Power Dsspaton Smple 5 500μA.5mW Wlson 5 μa 0.6mW Cascode 5 43μA 0.mW Smple pW Wlson pW Cascode 5.86.Pw Fgure 35. Basc block dagram of PLL V. APPLICATIONS OF OTA BASED LPF A. In Phase Locked Loop The Phase locked loop (PLL) s a frequency-selectve feedback system whch can synchronze wth a selected nput sgnal and track the frequency changes assocated wth t. It s the basc buldng block of FM demodulators, stereo demodulators, tone decoders, frequency syntheszers, televson dsplay systems & many other crcuts. Fg. 35 shows the basc block dagram of a PLL wth our proposed OTA based LPF as the loop flter. B. In DSB-SC Demodulator In Double Sde Band Suppressed Carrer (DSB-SC) demodulator crcut our proposed OTA based LPF can be used as shown n Fg. 36 below. Fgure 36. Basc block dagram DSB-SC demodulator(synchronous detecton method) Here we have only shown two applcatons of OTA based LPF. There are many crcuts n communcaton systems and sgnal processng systems where the conventonal OPAMP based LPF can be replaced by our proposed OTA based LPF to get better result. 05 Engneerng and Technology Publshng 383

8 Internatonal Journal of Electroncs and Electrcal Engneerng Vol. 3, No. 5, October 05 VI. CONCLUSIONS From Table III we can conclude that the CMOS based OTA reduces the statc power dsspatons drastcally & also the pass band gan s nearer to 0dB.e. unty gan whch s our objectve. It may be further noted that the bas voltage for CMOS OTA s reduced greatly. We call our proposed OTA based LPF as tunable because by adjustng the values of power supply and snk current we can get dfferent pass band gan less than unty. Agan, the hgh cut-off frequency can be adjusted by changng smply the values of resstor, R and capactor, C of the nput RC secton. The other advantages of our desgn over conventonal OPAMP based LPF are () a sngle power supply s requred, () CMRR, PSRR, slew rate are better. (3) nose margn s hgh, (4) desgn s very smple, (5) fabrcaton cost s reduced greatly. VII. FUTURE SCOPE Here we have desgned a st order LPF wth dfferent current mrror loads and a comparatve study was analyzed. The OTA can be used to desgn hgher order flters to get more deal frequency response by smply ncludng more RC sectons at the non-nvertng termnal of the OTA. Also the hgher pass band can be obtaned by changng the value of R and C. Agan, pass band gan can be ncreased by addng a feedback resstor voltage dvder secton at the nvertng nput termnal of the OTA. The OTA can be desgned practcally n IC fabrcaton lab and the practcal applcatons of OTA based LPF can be studed. In our desgn for the CMOS OTA we have used NMOS transstors to desgn the dfferental amplfer wth PMOS transstors for the current mrror secton. These transstors can be nterchanged & the change at the output can be studed. REFERENCES [] C.-L. Hsu, M.-H. Ho, Y.-K. Wu, and T.-H. Chen, Desgn of lowfrequency low-pass flters for bomedcal applcatons, n Proc. IEEE Asa Pacfc Conference on Crcuts and Systems, Dec. 006, pp [] E. R. Vllegas, A. J. Casson, and P. Corbshley, A subhertz nanopower low-pass flter, IEEE Transactons on Crcuts and Systems II, vol. 58, no. 6, pp , Jun. 0. [3] H. Lu, X. Peng, and W. Wu, Desgn of a Gm-C low pass flter wth low cutoff frequency, n Proc. Asa Pacfc Conference on Postgraduate Research n Mcroelectroncs and Electroncs, Jan. 009, pp [4] P. K. Mahapatra, M. Sngh, and N. Kumar, Realzaton of actve flters usng operatonal transconductance amplfer (OTA), Journal of the Instrument Socety of Inda, vol. 35, no., pp -9, 009. [5] R. L. Geger and E. Sánchez-Snenco, Actve flter desgn usng operatonal transconductance amplfers: A tutoral, IEEE Crcuts and Devces Magazne, vol., pp. 0-3, Mar [6] H. S. Malvar, Electroncally controlled actve flters wth operatonal transconductance amplfer, IEEE Transactons on Crcuts and Systems, vol. CAS 9, pp , May 98. [7] F. Rezz, A. Bashrotto, and R. Castello, A 3V -55MHz BCMOS pseudo-dfferental contnuous-tme flter, IEEE Transactons on Crcuts and System I, vol. 4, pp , Nov [8] A. Tmar and M. Rencz, Desgn ssues of a low frequency lowpass flter for medcal applcatons usng CMOS technology, n Proc. IEEE Desgn and Dagnostcs of Electronc Crcuts and Systems, Apr. 007, pp. -4. [9] S. Sols-Bustos, J. S. Martnez, F. Malobert, and E. Sanchez- Snenco, A 60-dB dynamc-range CMOS sxth-order.4-hz low-pass flter for medcal applcatons, IEEE Transactons on Crcuts and Systems, vol. 47, no., pp , Dec [0] T.-Y. Lo and C. C. Hung, A -V Gm-C low-pass flter for uwb wreless applcaton, n Proc. IEEE Asan Sold-State Crcuts Conference, Nov. 008, pp [] W. R. Grse. Applcaton of the operatonal transconductance amplfer to voltage controlled amplfers and actve flters. TECHNOLOGY INTREFACE: The Electronc Journal for Engg. Technology [Onlne]. Avalable: Tarun Kumar Das was born n Kolkata, Inda n 979. He receved the B.Tech. degree n Electroncs & Communcaton Engneerng from Murshdabad College of Engg. & Technology under West Bengal Unversty of Technology, Inda n 003, M.Tech. degree n software engneerng from West Bengal Unversty of Technology, Inda n 008. Currently he s an assstant professor n Electroncs & Communcaton Engneerng Department at Future Insttute of Engneerng & Management under West Bengal Unversty of Technology. Hs research nterest ncludes mcroelectroncs & VLSI technology, control system and sgnal processng. Sreya Chakrabart was born n Barakar, Inda n 983. She receved the B.Tech. degree n Electroncs & Communcaton Engneerng from Dr.B.C. Roy Engneerng College under Burdwan Unversty, Inda n 004, M.Tech. degree n computer scence & engneerng from West Bengal Unversty of Technology, Inda n 007. Currently she s an assstant professor n Electroncs & Communcaton Engneerng Department at Future Insttute of Engneerng & Management under West Bengal Unversty of Technology. Hs research nterest ncludes mcroelectroncs & VLSI technology, embedded systems and satellte communcaton. 05 Engneerng and Technology Publshng 384