1. Ideal OP Amps. +V cc. R o. v 1 v 2. v o. R d 2 1. V cc. Ideal Characteristics A = (gain is infinite) (no offset voltage) R

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1 . Ideal OP Amps Op amp Hgh-gan d dfferental amplfer ( ) D pwer supples are requred Usually used wth external negate feedbak Assume deal p amp desgn rut hek nn-deal haratersts are mprtant mdfy f neessary V V A ( ) d Ideal Charatersts A = (gan s nfnte) = when = (n ffset ltage) d = (nput mpedane s nfnte) = (utput mpedane s zer) Bandwdth = (n frequeny respnse lmtatn wth n phase shft) Tw Bas ules ule When the p amp utput s n ts lnear regn, the tw nput termnals are at the same ltage. ule N urrent flws nt ether nput termnal f the p amp. Saturatn f utput at slghtly lwer than pwer supply ltages. Inertng Amplfers ( ) Inertng amplfer and nput-utput haraterst - - BME, KHU

2 f Vrtual grund: = Analyss: n f = f = r = and = ut f = Summng amplfer: = f f 3. Nnnertng Amplfers ( ) Unty-gan fllwer r buffer: =, n =, and ut = Nnnertng amplfer and nput-utput haraterst = Analyss: n ( ) f f = = = and = ut - - BME, KHU

3 f 4. Dfferental Amplfers ( ) One-p-amp dfferental amplfer 4 Analyss: 5 = 4 3 4, = =, = ( ) Gd Cmmn-mde rejetn rat (CM): CM = r lg G d G G 4 Dfferental mde gan, Gd = Cmmn mdel gan, G : gan fr 3 = 4 < (uld be small) and = n ut 3 Three-p-amp dfferental amplfer (nstrumentatn amplfer, ) Analyss: ( ) =, 3 4 db =, = ( ) 3 4, BME, KHU

4 ( ) 4 = 3 Gd Cmmn-mde rejetn rat (CM): CM = r lg G d G G db 4 Dfferental mde gan, Gd = 3 Cmmn mdel gan, G : gan fr = = and = n ut 5. Cmparatrs ( ) Smple mparatr r Shmtt trgger V sat ref V sat ref ref > = Vsat and < ref = Vsat mnmzes erdrng p amp nput. Senste t nse at nput and an be nterhanged. ref Cmparatr wth hysteress Pste feedbak wth and 3 hysteress nsenste t nput nse Analyss 3 = V = V sat 3 ref V 3 sat 3 sat t prdue = V sat must be greater than BME, KHU

5 3 3 = V = V sat ref 3 V 3 sat 3 sat t prdue = V ntrls the wdth f the hysteress. sat must be smaller than ref 3 V sat 3 3 = V sat ref 6. etfers ( ) x ( x) D D V sat D 4 D 3 = x Full-wae presn retfer ( ) > D and D 3 ON, D and D 4 OFF upper p amp rut bemes a nnnertng amplfer wth gan f x, lwer p amp rut has n effet BME, KHU

6 n utput < D and D 3 OFF, D and D 4 ON upper p amp rut has n effet n utput bemes a nnnertng amplfer wth gan f x, lwer p amp rut bemes an nertng amplfer wth gan f x Varable gan and hgh nput mpedane Half-wae presn retfer ( ) Upper r lwer p amp rut = kω f = kω L = 3kΩ One p-amp full-wae retfer Gan s a funtn f lad nstant lad s requred 7. Lgarthm Amplfers f 9 f V sat Wthut bstng I C Fr a transstr, VBE =.6lg IS wth reerse saturatn urrent 3 I S = A at 7 C BME, KHU

7 Transdde nfguratn: IC = and = VBE =.6lg IS Fr < <,.66 V < <.36 V 7 A I C A Wth bstng: same as nnnertng amplfer Temperature mpensatn fr auray Antlg (expnental) rut: nterhange resstr wth transstr Applatns Multplatn, dsn, pwer Dynam range mpressn Lnealzatn 8. Integratrs ( ) S C S Integratr Intal ndtn settng: S pen and S lsed = (nertng amplfer) and () = Integratn: S lsed and S pen t = dt C t and = dt C = Hld: S pen and S pen s hld Frequeny respnse: V ( jω) Z f jωc = = = = V( jω ) Z jωc jωτ BME, KHU

8 Drft and saturatn prblem Charge amplfer ( ) Vrtual grund = = lng able an be used s dx = K dt sc s Kx = K dt = Drft and saturatn prblem Large feedbak resstr Preents saturatn Hgh-pass flter wth er ltage amplfer t dx C dt C f = n frequeny respnse mprement π C s C = dq dt = K dx dt s Pezeletr sensr s sc s FET 9. Dfferentatrs ( ) C Dfferentatr d d = C and = = C dt dt BME, KHU

9 Frequeny respnse: V ( jω ) Z f = = = jω C = jωτ V( jω) Z jωc Dfferentatr utput: tends t sllate and nsy due t amplfatn f hgh frequeny mpnents. Ate Flters ( ) Lw-Pass Flter ( ) C f f Frequeny respnse: f jωc ( jωcf ) f V ( jω ) Z f f f f = = = = V( jω ) Z j ( jω fcf ) ( ωτ ) If ω << τ r f << f wth f = πc f f rut bemes nertng amplfer wth gan f If ω >> τ r f >> f, rut bemes ntegratr Cutff frequeny r rner frequeny: f = πc f f Hgh-Pass Flter ( ) C f BME, KHU

10 Frequeny respnse: V ( jω ) Z f f jω fc f jωτ = = = = V( jω ) Z jωc jωc jωτ ( ) If ω << τ r f << f wth f = πc, rut bemes dfferentatr If ω >> τ r f >> f, rut bemes nertng amplfer wth gan f Cutff frequeny r rner frequeny: f = πc Band-Pass Flter ( ) C f C f Seres mbnatn f lw-pass and hgh-pass flter Tw utff frequenes r rner frequenes: f = πc and f = πc wth f > f If f << f, rut bemes dfferentatr If f >> f, rut bemes ntegratr f f. Frequeny espnse ( ) Fr a real p amp, bandwdth s nt nfnte. Open-Lp Gan Op amp s mult-stage d dfferental amplfer wth hgh gan Stray r juntn apatanes n eah stage gan attenuatn ( slpe n lg-lg plt and 9 phase shft per stage) slpe hanges wth frequeny eal p amp has a lmted pen-lp bandwdth Pssble sllatn (gan greater than at 8 phase shft) - - BME, KHU

11 Cmpensatn ( ) Add a apatr (external r nternal) fxed slpe f and maxmal phase shft f 9, pen-lp utff frequeny f abut 4 Hz N sllatn Clsed-Lp Gan Clsed-lp gan s usually muh smaller than the maxmal pen-lp gan f p amp. Clsed-lp gan s determned by external elements frmng negate feedbak. Clsed-lp gan an neer exeed pen-lp gan. Lp Gan Lp gan = (pen-lp gan f p amp) (lsed-lp gan f p amp rut) At lw frequeny: hgh lp gan, external feedbak rut determnes the p amp rut At hgh frequeny: lw lp gan, the p amp rut fllws the p amp penlp gan Hgh lp gan hgh auray and stablty Measurement f lp gan Break feedbak lp at any pnt n the lp Injet a sgnal Measure the gan arund the lp Examples Unty gan fllwer: lp gan = pen-lp gan f Inertng amplfer wth gan f : lp gan = (pen-lp gan)/ Gan-Bandwdth Prdut Gan-bandwdth prdut = (gan at f) (bandwdth at f) Unty-gan-bandwdth prdut s gen n spefatn f p amp - - BME, KHU

12 Cmpensated p amp has gan slpe f Unty-gan-bandwdth prdut n Hz Bandwdth f p amp rut = Op amp rut gan Slew ate Fr an p amp, nternal urrent sure has ts I max. d Imax Change n ltage arss the mpensatn apatr: dt = C d dt lmted d Slew rate Sr = dt max Fr snusdal nput, full-pwer respnse r maxmal frequeny fr rated utput s Sr f p = where V r s the rated utput ltage. πv r Unmpensated p amp s faster useful fr mparatrs s. Offset Vltage Fr a real p amp, t prdue =. Offset ltage = must be nsdered fr small nput sgnals. Nullng Add an external nullng pt. Adjust the pt nrease I E at ne nput and derease at the ther = Drft Temperature hange (enrnment r self-heatng) hange n ffset ltage, ( ) Spefatn Maxmal ffset ltage hange per C suh as. µv/ C Maxmal ffset ltage er a gen temperature range suh as 5 t 85 C Nse ( ) Semndutr juntns nse ltage sures and nse urrent sures - - BME, KHU

13 Fr lw sure mpedane ( and small), n dmnates. Charatersts andm At lw frequeny ampltude f (flker nse) At mdfrequeny smaller ampltude expressed n rms unts f Sme p amps exhbt bursts f nse (pprn nse). V Hz n n d A d n 3. Bas Current Base r gate urrent t keep transstrs turned n bas urrent Bas urrent flws thrugh feedbak resstrs smaller resstrs are desrable (abut kω) Cautn: urrent flwng thrugh feedbak resstrs plus urrent flwng thrugh lads must be smaller than p amp utput urrent ratng t small resstrs annt be used Dfferental Bas Current Dfferene between tw nput bas urrents << eah bas urrent Cmpensatn resstr mnmzes the effet f bas urrents f ( ) f f BME, KHU

14 Drft Change f bas urrents due t temperature Cmpensatn resstr als mnmzes the effet f bas urrent drft Nse Nse urrents flw thrugh external equalent resstrs. { 4 4 } Ttal rms nse ltage s ( ) ( ) and : equalent sure resstanes t n n n kt kt BW n : mean alue f rms nse ltage n V Hz er a frequeny range n : mean alue f rms nse ltage n A Hz er a frequeny range k: Bltzmann s nstant T: temperature, K BW: nse bandwdth, Hz Types f p amp Small ( kω) sure resstanes BJT nput p amp prdues smaller nse Large sure resstane FET nput p amp prdues smaller nse due t smaller nse urrent Lw nse a amplfer desgn (nnnertng amplfer) by mpedane mathng Charaterst nse resstane s n = n n Set n = usng a transfrmer wth turns rat :N where N = ( ) n :N f s BME, KHU

15 4. Input and Output esstane Input esstane ( ) Op amp dfferental nput resstane, d : TΩ fr FET, MΩ fr BJT Amplfer-rut nput resstane, a A = d = = A d = = = d d ( A ) d a = = ( A ) d Ad, a uld be > TΩ Unty-gan fllwer: A A( ) Nnnertng amplfers: ( lp gan) leakage urrent Inertng amplfer: a = =, usually small a =, ery hgh, lmted by surfae d d d A d L C L Output esstane ( ) Op amp utput resstane, 4 Ω Amplfer-rut utput resstane, a fr unty-gan fllwer wth resste lad esste lad, L hange n utput urrent, d A d A = = = ( ) A = BME, KHU

16 a a = = A A, a uld be < -3 Ω All nnnertng and nertng amplfers: ( lp gan) a =, ery small, lad resstane s lmted by maxmal utput urrent f p amp (t small lad resstane p amp saturates nternally) fr unty-gan fllwer wth apate lad Capate lad, C L amp and slew rate L d C dt d = L, lmted by maxmal utput urrent f p C lwpass flter addtnal phase shft arund the lp pssble sllatn T preent sllatn, add a small resstr between and C L. Current bster fr large utput urrent: p amp hgh-pwer transstrs 6. Phase-Senste Demdulatrs Cnsder the ampltude-mdulated (AM) sgnal, ( t) = x( t)sω t Sgnal: x() t wth maxmal frequeny muh less than f = ω π Carrer: sω t wth ω = π f Detetn (r demdulatn) f the sgn Enelpe detetn ( ) etfatn and lwpass flterng Nse at arus frequenes annt be rejeted Tuned amplfer r bandpass flter an reme sme nse. Phase-senste demdulatn r synhrnus detetn ( ) Multplatn r swthng and lwpass flterng Exellent nse rejetn Phase-senste demdulatn fr x( t) = sωst Assume the fllwng, AM BME, KHU

17 () t = sω ts( ω t θ) AM s () t Lwpass Flter ( ω < ω < ω ) s rner yt () yt () = s θxt () If ( n ) () t = sω t () t = ()s t ω t AM ( ) = xt ()sω t θ sω t = xt ( ) s s { ( ωt θ) θ} π θ wth n =,,, and θ s nstant, then we an detet x() t frm ( t) = x( t)sω t. AM Nse nt synhrnzed wth ( t) = sω t s rejeted. Cruts: analg multpler, balaned mdulatr/demdulatr, rng demdulatr (a) (b) BME, KHU

18 () 4 - Example (a) xt ( πt) () = s 3 (d) (b) ( π ) { } ( π ) AM () t = s t 3s 3t () ( π ) { } ( π ) () t = s t 3s 3t (e) yt () = { s( π t) 3} BME, KHU

19 6. Mrmputers n Medal Instrumentatn Sensrs Analg Sgnal Pressng ADC Mrpressr System DAC I/O - User Interfae - DSP - Cntrl - Strage - Cmmunatn - Et BME, KHU