Voltage Mode-to-Current Mode Transformation

Transcription

1 Tejmal S Rathre et al / nternatnal Jurnal f Engneerng and Technlgy (JET) ltage Mde-t-Current Mde Transfrmatn Tejmal S Rathre 1 and Uday P Kht Electrncs and Telecmmuncatn Engneerng Department, St Francs nsttute f Technlgy, Brval (W), Mumba , nda 1 tsrathr@eetbacn upk@eetbacn Abstract Ths paper prpses a prcedure fr cnvertng a class f Op Amp-, FTFN-, CC- and CFAbased vltage mde crcuts t crrespndng current mde crcuts wthut requrng any addtnal crcut elements and fnally frm Op Amp-based vltage mde crcuts t any f the FTFN, CC and CFA current mde crcuts The latter crcuts perfrm better at hgh frequency than the frmer nes The valdty f the transfrmatn has been checked n smulated crcuts wth PSPCE Keywards ltage mde, Current mde, Transfrmatn, Current feedback amplfer, Current cnveyr, Fur termnal flatng nullr NTRODUCTON Current-mde (CM) flters are attractve because f ther wder bandwdth, hgher slew rate, wder dynamc range and lwer pwer cnsumptn cmpared t vltage-mde (M) cunterparts [1] Hwever, a large number f p-amp (OA)-based M crcuts wth ecellent perfrmance and ther elegant realzatn prcedures were put frward n the past [, 3] t s, therefre, wrthwhle t cnvert them nt CM crcuts FTFN (Fur termnal flatng nullr) [4-10], CC (current cnveyr) [11-14] and CFA (Current Feedback Amplfer) [15-] based CM crcuts have receved cnsderable attentn n many flterng and sgnal prcessng applcatns, partcularly, the CFA-based crcuts are attractve due t the hgh slew rate and bandwdth ndependent f clsed lp gan n ths paper, FTFN- CC- and CFA-based CM crcuts are btaned by transfrmng a class f OAbased M crcuts Obvusly, ne type f crcut can then be cnverted nt the ther type thrugh the prpsed transfrmatn Smlar attempts were made n the past t cnvert OTA-C (peratnal trans-cnductance amplfer) crcuts nt CFA-based RC crcuts [3] and frm SAB (sngle amplfer bquad) crcut t current amplfer based bquad [4] PROPOSED M-TO-CM TRANSFORMATON METHOD Let us eamne the tw crcuts shwn n Fg 1 where N a s the actve netwrk Smpler crcuts are taken fr the sake f cnvenence f analyss and mre general crcuts wll be taken up n the net sectn Analyss f the crcuts shwn n Fg 1 and, respectvely, lead t the fllwng relatns Fg 1 M crcut and CM crcut (1) () SSN : l 4 N 5 Oct-Nv

2 Tejmal S Rathre et al / nternatnal Jurnal f Engneerng and Technlgy (JET) where [ ] and [ ] are the vltage and current at termnal n Fg 1 [] Nte that (1) and () are ndependent f z and z, respectvely Thus, t s mmateral, whether there s a flw f z and [ z ] n the z termnal f the actve devce r nt The tw transfer functns wll be the same, f T(s) (3) whch requres that (4) Ths can be satsfed under the fllwng 3 cases Case A 0, 0 (5) These termnal characterstcs are satsfed when the actve netwrk N a s an Op Amp,, 0, an FFTN,, ± y, y 0 z w r a CC±, y y 0, z ± y y, as shwn n Fgs, 3 and 4, respectvely, wheren termnal (y) s mantaned at vrtual grund by makng y ( ) 0 Fr these crcuts Fg OA-based M crcut and CM crcut Fg 3 FTFN-based M crcut and CM crcut Fg 4 CC-based M crcut and CM crcut 1 (6) SSN : l 4 N 5 Oct-Nv

3 Tejmal S Rathre et al / nternatnal Jurnal f Engneerng and Technlgy (JET) Frm these fgures, we see that the M crcut can be cnverted nt the CM crcut by nterchangng the termnals and z n case f OA, the termnals and w n case f FTFN, the termnals y and z n case f CC, and replacng the nput-utput surces Cnnectns f passve elements reman unchanged Let us cnsder a mult-nput ( 1,,, n ) M crcut shwn n Fg 5 and ts transfrmed mult-utput 1,,, n crcut shwn n Fg 5 The utput f the M crcut s gven as n 1 f (7) Fg 5 OA-based mult-nput M crcut and mult-utput CM crcut The n current utputs f the CM crcut are gven as, 1,,, n (8) f These crcuts can be used as the basc buldng blcks fr realzng mre cmple functns Eample 1: Cnsder the Lverng's crcut [5] shwn n Fg 6 Sub-netwrks A and B can be dentfed as the OA based mult-nput blcks Equatn (7) s used fr each buldng blck and then slved fr t yeld ac be (9) bd c f A crrespndng crcut usng the mult-utput CM blcks s shwn n Fg 6 Equatn (8) s used fr each buldng blck n Fg 6 and slved fr where The prcedure can be etended fr cnvertng M crcuts wth n OAs (each wth the nn-nvertng termnal grunded) nt OA based CM crcuts by nterchangng and z termnals f each OA and replacng the npututput surces The abve prcedure can be carred frward t M crcuts wth n FTFN (CC) crcuts n whch all the FTFNs (CCs) have ( ) 0 y SSN : l 4 N 5 Oct-Nv

4 Tejmal S Rathre et al / nternatnal Jurnal f Engneerng and Technlgy (JET) Fg 6 Lverng M OA crcut and CM OA crcut Eample : Akerberg and Mssberg's 3-OA M bquad [6] [7] and Thmas's 4-OA M bquad [3] (pp ), [7] shwn n Fgs 7 and 8, respectvely are cnverted nt CM crcuts shwn n Fgs 7 and 8, respectvely The transfer functn f the crcuts shwn n Fg 7 s be g ace bd h (10) + and that fr the crcut shwn n Fg 8 s ace h b b d d f f k c e c + ad f bd f j ceg j + e g k (11) Fg 7 3-OA M bquad crcut, 3-OA CM bquad crcut t may be mentned that the methd used fr determnng the current transfer functn n the abve eample s mre straght frward than applyng the KCL at each nde f the crcut SSN : l 4 N 5 Oct-Nv 01 35

5 Tejmal S Rathre et al / nternatnal Jurnal f Engneerng and Technlgy (JET) Case B Under these cndtns (4) reduces t Usng (3), we get Fg 8 4-OA M bquad crcut, 4-OA CM bquad crcut 0, 0, 0 Ths cndtn and thse n (1) are satsfed when the actve netwrk N a s a CFA where z, w z, y as shwn n Fg 9 Fr bth the Fgs 9 and, we have z w z (15) where Thus, the current, as desred fr the transfrmatn t hld, satsfes the cndtn n (14) 1 1 z z (1) (13) (14) Fg 9 CFA-based M and CM crcuts Nw, frm (1) 1 1 w 1 + (16) whch leads t 1 (17) + Frm Fg 9, we nte that the CFA based M crcut (wth termnal y grunded and the utput tapped frm the termnal w) can be cnverted nt CFA based CM crcut by nterchangng the termnals and w f the CFA and replacng nput-utput surces Cnnectns f passve elements reman unchanged Thus, the prcedure s the same as that fr the OA based crcuts under case A n a manner smlar t the ne used n case f OA based crcuts, t can be shwn that the prcedure s applcable t CFA based M crcuts havng mre number f CFAs all wth termnal y grunded SSN : l 4 N 5 Oct-Nv

6 Tejmal S Rathre et al / nternatnal Jurnal f Engneerng and Technlgy (JET) Eample 3: Cnsder the M crcut shwn n Fg 10 Fllwng the abve prcedure, the CM crcut btaned as shwn n Fg 10 The tw crcuts have the same transfer functn as gven by (10) n (10), f b c 1S, the transfer functn becmes a e (18) d f Fg 10 M and CM crcuts wth mre number f CFAs s s + 1 ( s) Eample 4: The realzatn f T s btaned usng (18) and s shwn n Fg 11 s + s + 1 n bth the cases A and B, t s requred that all the actve devces shuld have vrtual grund Case C Under these cndtns, (4) results n Fg 11 CM all-pass flter 0, 0, 0, 0 (19) SSN : l 4 N 5 Oct-Nv

7 Tejmal S Rathre et al / nternatnal Jurnal f Engneerng and Technlgy (JET) The cndtns gven n (19) and (0) are satsfed when N a s an amplfer f gan and gan A n current mde as shwn n Fg 1 + z z (0) A n vltage mde Fg 1 M crcut and CM crcut wth actve devce havng n nput termnal at vrtual grund n the M crcut, the amplfer gan s cmple (a functn f 1 and ) whereas t s pstve real n the CM crcut Hence, the M crcut wll requre a larger number f passve elements than the CM crcut Mrever, bth these crcuts are mre cmple than thse shwn n Fgs, 3, 4, and 9 Fr these crcuts A 1 (1) A 1 Ths relatn des nt ffer any specal advantage f these crcuts ver thse f Fgs, 3, 4, and 9 Hence, ths case wll nt be dealt wth any mre APPLCATONS OF TRANSFORMATON METHOD TO GENERAL CRCUTS Mre general crcuts n vltage mde and ther transfrmed crcuts n current mde crrespndng t the cases A and B are btaned frm Fgs and 9, by replacng -termnal passve elements by 3-termnal passve netwrks N A and N B r N and these crcuts are shwn n Fgs 13 and 14, respectvely Analyss f these tw B crcuts gves Fg 13 Generalzed OA based M and CM crcuts wth 3 termnal passve netwrk SSN : l 4 N 5 Oct-Nv

8 Tejmal S Rathre et al / nternatnal Jurnal f Engneerng and Technlgy (JET) and and Respectvely, where 1 A, 1 B and and 1 B B 1 Fg 14 Generalzed CFA based M and CM crcuts 1 B 1A ( + ) () (3) are the transfer admttances f netwrks N A, N B and N, respectvely Specal features 1 A clse eamnatn f () and (3) shws that the fllwng prcedure can be used fr cnvertng OA based M/CM crcut f Fg 13 nt CFA based crcut shwn n Fg 14 wthut ncreasng the number f passve cmpnents Take ut a sutable drvng pnt admttance frm 1B f the OA based crcut and realze the remanng admttance 1 B as transfer admttance by the netwrk N Eample 5: Fr eample, the OA based M lw-pass flter shwn n Fg 15 s cnverted nt fur CFA based CM lw-pass flters shwn n Fg 15 One can nw easly vsualze that CFA based CM crcut f Fg 10 s dervable frm the OA based M crcut f Fg 6 All the lnear peratns perfrmed by sngle-nput OA crcuts can als be perfrmed by CFA crcuts n bth vltage and current mdes Eample 6: A CM phase shft scllatr shwn n Fg 16 s derved frm the OA based ne 3 t may be nted frm () that T(s) beng a rat f tw transfer admttances, any stable vltage r current transfer functn wth zers ff the pstve real as can be realzed usng just ne OA [] and hence by ne CFA Eample 7: Fr the ntch functn fllwng the prcedure n [] (p 474) (after makng crrectns), s gven n Fg 17 1B 1A 1B s +, s + 0s + 1A 1B, B B SSN : l 4 N 5 Oct-Nv

9 Tejmal S Rathre et al / nternatnal Jurnal f Engneerng and Technlgy (JET) Fg 15 OA based M lw-pass flter and fur CFA based CM lw-pass flters Fg 16 CM phase shft scllatr Fg 17 CM ntch flter SSN : l 4 N 5 Oct-Nv

10 Tejmal S Rathre et al / nternatnal Jurnal f Engneerng and Technlgy (JET) Fg 18 Generalzed OA based M and CM crcuts wth 4 termnal passve netwrk The prcedure utlned s als applcable t mre generalzed OA based M and CM crcuts shwn n Fg 18 where N s a 4-termnal passve netwrk Eample 8: The OA based crcut f the M band-pass flter [3] s transfrmed nt fur CM crcuts shwn n Fg 19 The prpsed technque leads t the transfrmatn wthut any addtnal elements SENSTT TO NONDEALTES Cnsderng the nn-dealtes arsng frm the physcal mplementatn f the CFA, ts termnal relatnshp can be gven as 0 γ 0 0 y y (4) z α z w 0 0 β 0 w where α s the current gan and β and γ are the vltage gans whch can be epressed as α 1 ε1, β 1 ε, and γ 1 ε Here, ε 3 1 ( ε 1 << 1) dentes the current trackng errr f the CFA and ε (ε << 1), ε 3 ( ε 3 << 1) are the vltage trackng errrs There s n effect f the vltage trackng errr ε 3 as the y termnal f the CFA s grunded The transfer functn / f the lw-pass flter shwn n Fg 15 can be wrtten as αβg1 C (5) αβg s + C As the y termnal f CFA s grunded, the vltage gan γ des nt appear n the transfer functn Applyng the usual defntn f senstvty t s fund that the passve and actve senstvtes f these lw-pass flters are ω G S y G1 yδ δy 0 ω0 ω0 ω0 ω0 S S 1, S 0, S S 1 C Thus the passve and actve senstvtes fr the presented flters are lw, n mre than unty n magntude α β (6) (7) SSN : l 4 N 5 Oct-Nv

11 Tejmal S Rathre et al / nternatnal Jurnal f Engneerng and Technlgy (JET) Fg 19 OA based M band-pass flter and fur CM band-pass flters SMULATON RESULTS All the lw-pass flters shwn n Fg 15 were smulated fr 3-dB cut-ff frequency f 159 khz, usng CFA AD844 and hgh frequency OA AD817 wth supply vltages f ±15, and emplyng PSPCE sftware [8] The crcut cmpnents were RR 1 1 kω, C10 nf All the flters gave nearly the same magntude respnse as shwn n Fg 0 The lw-pass flters were als smulated fr cut-ff frequency as hgh as 159 MHz The crcut cmpnents used fr ths purpse were RR 1 1 kω, C 100 pf The crrespndng magntude respnses are shwn n Fg 0 The phase shft scllatr f Fg 16 was als smulated and the utput wavefrm, as shwn n Fg 1, has peak-t-peak ampltude f 10 ma t may be nted that, the scllatr crcut des nt have a separate ampltude stablzer and the scllatn levels are lmted by the supply vltages Fr supply vltages f ±6, the smulatn resulted n peak-t-peak ampltude f ma PRACTCAL RESULTS T valdate the transfrmatn at hgh cut-ff frequences f the flters, the crcut fr lw-pass flter shwn n Fg 15 was assembled usng a hgh frequency OA AD817 and that fr lw-pass flter shwn n Fg 15() was assembled usng CFA AD844 n case f CFA, t generate the nput current, 1 kω resstr was cnnected n seres wth the nput vltage surce The ther crcut elements chsen fr the cut-ff frequency f 159 MHz are R R 1 1 kω and C 100 pf Bth the lw-pass flters perfrmed almst dentcally fr the cut-ff frequency as hgh as 159 MHz as shwn n Fg SSN : l 4 N 5 Oct-Nv

12 Tejmal S Rathre et al / nternatnal Jurnal f Engneerng and Technlgy (JET) Fg 0 Smulatn results: Frequency respnses f the lw-pass flters fr f khz and fr f MHz Fg 1 wavefrm f the phase shft scllatr wth R Ω, C 1 nf, R f 5 kω SSN : l 4 N 5 Oct-Nv

13 Tejmal S Rathre et al / nternatnal Jurnal f Engneerng and Technlgy (JET) Fg Epermental results Frequency respnses f lw-pass flters shwn n Fg 15 wth R R 1 1 kω, C 100 pf fr f MHz CONCLUDNG REMARKS A prcedure fr cnvertng a class f M crcuts, whch have all the actve devces wth vrtual grund, nt CM crcuts wthut alterng the transfer functn and wthut requrng any addtnal cmpnents has been develped t cvers the crcuts havng actve devces lke OA, FTFN, CC, and CFA Snce vltage and current transfer functns (assumng the same actve devces) are the same, the characterstcs such as stablty, tunablty, senstvty etc reman unaltered The prcedure has been demnstrated by eamples Thus, a sngle crcut can be used n ether mde The valdty f the prpsed transfrmatn prcedure has been tested by smulatng the transfrmatn f the lw-pass flter and phase shft scllatr wth the help f PSPCE The epermental results shw that the frequency respnses f bth the M and CM lw-pass flters are dentcal The actve and passve senstvtes fr the presented flters are very lw t has been shwn that a sngle FTFN, CC, and CFA based crcuts can realze bth stable vltage and current transfer functns wth zers ff the pstve real as REFERENCES [1] B Wlsn, Recent develpments n current cnveyrs and current-mde crcuts, EE Prc, vl 137, (Pt G), n, pp 63-77, 1990 [] S K Mtra, Analyss and Synthess f Lnear Actve Netwrks, New rk: Jhn Wley, 1969 [3] G Daryanan, Prncples f Actve Netwrk Synthess and Desgn, New rk: Jhn Wley & Sns, 1976 [4] S Lu and J L Lee, nsenstve current/vltage mde flters usng FTFNs, Electrn Lett, vl 3, pp , 1996 [5] O Ççekğlu, Current-mde Bquad wth a mnmum number f passve elements, EEE Trans Crcuts and Syst, vl 48, n 1, pp 1-, 001 [6] M T Abuelma'att, Cascadable current-mde flters usng sngle FTFN, Electrn Lett, vl 3, n 16, pp , 1996 [7] M Hgashmura, Current-mde allpass flter usng FTFN wth grunded capactr, Electrn Lett, vl 7, n 13, pp , 1991 [8] S Lu and C S Hwang, Realzatn f current-mde flters usng sngle FTFN, nt J Electrn, vl 8, n 5, pp , 1997 [9] S Lu and H La, Current-mde quadrature snusdal scllatr usng sngle FTFN, nt J Electrn, vl 81, n, pp , 1996 [10] M Hgashmura, Current-mde lwpass, bandpass and hghpass flters usng an FTFN, Mcrelectrn J, vl 4, pp , 1993 [11] A Tker, S Őzcan, H Kuntman,, and O Ççekğlu, Supplementary all-pass sectns wth reduced number f passve elements usng a sngle current cnveyr, nt J Electrn, vl 88, n 9, pp , 001 [1] A Khan and S Maheshwar, Smple frst rder all-pass sectn usng a sngle CC, nt J Electrn, vl 87, n 3, pp , 000 [13] O Ççekğlu, H Kuntman, and S Berk, All-pass flters usng a sngle current cnveyr, nt J Electrn, vl 86, n 8, pp , 1999 [14] A Tker, S Őzcan, H Kuntman, and O Ççekğlu, Supplementary allpass sectns wth reduced number f passve elements usng a sngle current cnveyr, nt J Electrn, vl 88, n 9, pp , 001 [15] A Fabre, Unsenstve M and CM flters frm cmmercally avalable trans-mpedance p amps, EE Prc, vl 140, (Pt G), pp , 1993 [16] S Lu and S Hwang, Realzatn f RL and CD mpedances usng current feedback amplfer and ts applcatns, Electrncs Letters, vl 30, pp , 1994 [17] S Lu and D S Wu, New current feedback amplfer-based unversal bquadratc flter, EEE Trans nstru Meas, vl 44, pp , 1995 [18] S Lu, Unversl flter usng tw current feedback amplfers, Electrn Lett, vl 31, pp , 1995 SSN : l 4 N 5 Oct-Nv

14 Tejmal S Rathre et al / nternatnal Jurnal f Engneerng and Technlgy (JET) [19] S Lu, Hgh nput mpedance flters wth lw cmpnent spread usng current feedback amplfers, Electrn Lett, vl 31, pp , 1995 [0] M T Abuelmaat and S M Al-Shaharan, New unversal flter usng tw current feedback amplfers, nt J Electrn, vl 80, pp , 1996 [1] J W Hrng and M H Lee, Hgh nput mpedance vltage-mde lwpass, bandpass and hgh pass flters usng current feedback amplfers, Electrn Lett, vl 33, pp , 1997 [] C L Hu, C C Huang, S Lan, J J Shaw, and C M Chang, Current mde and vltage mde unversal bquads usng a sngle current feedback amplfer, nt J Electrn, vl 86, pp 99-93, 1999 [3] C L Hu and W Wang, Crcut transfrmatn methd frm OTA-C crcuts nt CFA-based RC crcuts', EE Prc, vl 144, n 4, pp 09-1, 1997 [4] G W Rberts, A General class f current amplfer-based bquadratc crcuts, EEE Trans Crcuts and Syst, vl 39, n 4, pp 57-63, 199 [5] W F Lverng, Analg cmputer smulatn f transfer functn, EEE Prc, vl 53, pp 306, 1965 [6] A Akerberg and K Mssberg, A versatle actve RC buldng blck wth nherent cmpensatn fr the fnte bandwdth f the amplfer, EEE Trans Crcut Thery, vl CAS-1, n 1, pp 75-78, 1974 [7] L C Thmas, The bquad, Part - Sme practcal desgn cnsderatns, EEE Crcut Thery, vl CT-18, pp , 1974 [8] 'Electrnc Desgn Sftware', OrCAD 100, Cadence Desgn Systems, nc, USA, 003 AUTHORS PROFLE T S Rathre was brn n Jhabua (M P, nda) n Oct 9, 1943 He receved the B Sc (Electrcal Engneerng), M E (Appled Electrncs & Servmechansms), and Ph D (by research n Passve and Actve Crcuts) degrees n Electrcal Engneerng frm ndre Unversty, ndre, nda n 1965, 1970 and 1975, respectvely He served SGSTS, ndre frm 1965 t 1978 befre jnng the EE Department f T Bmbay frm where he retred as a Prfessr n superannuatn n June 006 Currently, frm July 006, he s the Dean (R&D) and Head f Electrncs & Telecmmuncatn Department at St Francs nsttute f Technlgy, Brval He was a pst-dctral fellw ( ) at the Cncrda Unversty, Mntreal, Canada and a vstng researcher at the Unversty f Suth Australa, Adelade (March-June 1993) He was an STE vstng prfessr ( ) He has publshed and presented ver 00 research papers n varus natnal/nternatnal jurnals and cnferences He has authred the bk Dgtal Measurement Technques, New Delh: Narsa Publshng Huse, 1996 and Alpha Scence nternatnal Pvt Ltd, U K, 003 and translated n Russan language n 004 He was the Guest Edtr f the specal ssue f Jurnal f E n nstrumentatn Electrncs (199) He s a member n the edtral bards f STE Natnal Jurnal f Techncal Educatn and ETE Jurnal f Educatn He has wtnessed, rganzed and chared many natnal/nternatnal cnferences and n sme he was als the Chef Edtr f the prceedngs Prf Rathre s a Senr Member f EEE (USA), Fellw f ETE (nda), Fellw f E (nda), Member f STE (nda), Member f nstrument Scety f nda, Member f Cmputer Scety f nda He has been lsted n Asa s Wh s Wh f Men and Wmen f achevement (1991) He has played a very actve rle as Fellw f ETE and has served ts Mumba Centre as lunteer member ( ), C-pted member ( ), Secretary ( ), Charman (001-0), ce Charman (003-06) and Charman (006-08) He has receved ETE M N Saha Memral Award (1995), EEE Slver Jublee Medal (001), STE U P Gvernment Natnal Award (00), STE Maharashtra State Natnal Award (003), ETE Prf S C Aya Memral Award (004), ETE BR Batra Memral Award (005), ETE Prf K Sreenvasan Memral Award (005) ETE K S Krshnan Memral Award (009), ETE - Har Ramj Tshnwal Gld Medal Award (010), and ETE best paper award publshed n ETE J f Educatn (011) Uday P Kht was brn n Klhapur (MS) n June 15, 1970 He btaned B E (nd Electrncs) frm Amaravat Unversty n 1991, and M Tech (Cntrl and nstrumentatn) and Ph D (by research n Synthess f Analg Crcuts Emplyng Current-Mde Buldng Blcks) bth n Electrcal Engneerng frm T Bmbay, nda, n 1999 and January 010, respectvely He served Bharat dyapeet's nsttute f Technlgy, Nav Mumba frm as a lecturer and Thadmal Shahan Engneerng Cllege, Mumba, as an Assstant Prfessr frm He was an Asscate Prfessr n Thadmal Shahan Engneerng Cllege, Mumba, snce January 006 t July 01 Frm January 010, he was the Head f Electrncs & Telecmmuncatn Department at Thadmal Shahan Engneerng Cllege, Mumba tll July 01 July 01 nwards, he s a Prfessr n Electrncs and Telecmmuncatn Engneerng Department f St Francs nsttute f Technlgy, Mumba, nda SSN : l 4 N 5 Oct-Nv 01 36

15 Tejmal S Rathre et al / nternatnal Jurnal f Engneerng and Technlgy (JET) Dr Kht s a Fellw Member f ETE (nda), Member f STE (nda), Member f EEE (USA) and Member f E (nda) He has been lsted n the nternatnal Wh s Wh f Prfessnals Hstrcal Scety havng demnstrated eemplary achevement and dstngushed cntrbutns t the busness cmmunty, edtn He has served ETE Mumba Centre as a Member ( ) He has publshed mre than 5 research papers n Natnal/nternatnal jurnals and cnferences Hs areas f research nterest are: Synthess f analg current-mde crcuts, fault dagnss n analg/dgtal crcuts, and mcrwave crcuts SSN : l 4 N 5 Oct-Nv