PHYSICS 536 Experiment 12: Applications of the Golden Rules for Negative Feedback

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1 PHYSICS 536 Experment : Applcatns f the Glden Rules fr Negatve Feedback The purpse f ths experment s t llustrate the glden rules f negatve feedback fr a varety f crcuts. These cncepts permt yu t create and understand a vast number f practcal crcuts usng nly tw smple rules. The pamps used n ths experment are fully cmpensated,.e. the penlp phase shft s less than 35 t reduce the danger f scllatn. Hwever, fr future applcatns yu shuld remember that a cmpensated pamp can scllate f addtnal phase shft s ntrduced accdentally n the feedback lp. V R R 3 V V R V 0 Opamp Rule I. In the frequency range where the pen lp gan f the pamp, A, s much greater than the gan wth feedback,.e. A >>, G O the vltage at the nvertng nput wll be equal t the vltage at the nnnvertng nput. That s t say, the nputs f the pamp becme a vrtual grund, V = V. Opamp Rule II. In the frequency range where A >> G, the O feedback current wll be equal t the nput sgnal current. That s t say,.ths f means that the pamp effectvely draws n current. V R R 3 V R f V 0 The maxmum utput sgnal vltage (peaktpeak) s lmted by the slew rate V / t( V / µ s) Vpp (.) π f ( MHz) The slew rate s n vlts / µ sec and the frequency I n MHz. The gan f a nnnvertng amplfer s

2 G G R R = jf / f R jf / f O = (.) where the break frequency s f = ft / GO. The rate f vltage change caused by current (I) flwng nt a capactr s V Ι = Τ C (.3) The gate t surce vltage f a FET s ( / ) V = V I I (.4) gs T d dss A. OpAmp Cmparsn at Hgher Frequency. In ths sectn yu wll cmpare the perfrmance f a general purpse 4 pamp t a relatvely hgh speed LM38 pamp n the nnnvertng amplfer crcut shwn belw. Always use bypass capactrs (refer t GIL sectn 3.), and turn ff the pwer supples befre cmpnents are changed. 0K K V V 0 Tp 5V K Fgure 3 4. Calculate the mdfrequency clsedlp gan. Fr bth pamps, calculate the clsed lp break frequency and the maxmum ampltude sgnal that can be btaned at f wthut slew rate dstrtn. Use the fllwng typcal specfcatns fr these pamps. Include these calculatns n yur labratry reprt. OpAmp Slew Rate f T 38 0V / µ sec 5MHz 4 0.5V / µ sec.mhz

3 .) Use the slew rate t calculate the rse and fall tme f an utput pulse whse ampltude s 0V. Draw a sketch f fr a 0kHz nput square wave. Include these calculatns n yur labratry reprt. v D the fllwng checks t ensure that the crcut s wrkng befre yu begn the measurements n steps 3 and 4. When there s n nput sgnal, V shuld be less than ± 0.V. Measure the gan usng a khz sne wave. 3.) Use a 4 pamp. It s gd practce t bserve the nput and utput sgnals smultaneusly (GIL 4.3). Measure f (GIL 5.6A). Be sure that the sgnal ampltude des nt exceed the slewlmt n the frequency range yu are usng. After yu measure f, ncrease the sze f the sgnal and bserve the ampltude at whch slewrate dstrtn becmes evdent. Next, use a 0k Hz square wave and adjust the sgnal ampltude s that V p p) s apprxmately 0V. Measure the pstve and negatve slew rate frm the scpe ( face. Yu d n need t sketch v fr the sne r square wave. 4.) Repeat step 3 fr the 38. Yu shuld bserve a large ncrease n the gan at the clsedlp breakfrequency f, whch ndcates that the phase shft f the 38 exceeds 90 degrees n ths frequency range. Yu als see that the 38 has better hgh frequency gan than the 4. The slew rate f the 38 s s large that yu prbably cannt bserve slewrate dstrtn n ths crcut. The utput rse and fall fr a square wave are much faster fr the 38 than fr the 4. Observe ths fact, but t s nt necessary t measure the slew rate r sketch. Yu shuld als ntce a damped versht n the utput pulse, whch s caused v by the excess phase shft. B. A Smple Ramp Vltage Generatr Opamp rule II s appled n the fllwng crcut. The nput sgnal s a square wave appled at pnt A. Pnt B s a vrtual grund (GR II). ± 5V pwer supples are used fr all crcuts. V A R K D I C f 00pf R I B 5K 3 4 K D 6 LM38 V 0

4 f When v s negatve, the electrns that flw thrugh R are pulled nt the feedback capactr C by the pamp. Dde prevents current frm flwng thrugh R durng ths part f the cycle. v rses at a cnstant rate as s charged. C f When v ges pstve, a larger current flws thrugh R t dscharge C f rapd ly. When v reaches0.6v, dde s frward based, whch causes I t flw thrugh D rather than nt C f. Snce n current s flwng nt the capactr at ths tme, v stays at 0.6V untl v ges negatve agan. Then the cycle s repeated. V V 5V 0V 5V 0.6V 5.) Gven that the nput sgnal v s a 50kHz, 0V square wave (.e. v swtches between 5V and 5V). Calculate the slpe and sze f the ramp. 6.) Observe and sketch the wavefrms descrbed n step5. Change the slpe f the ramp by adjustng the ampltude f v. Change the length f the ramp by adjustng the perd f v. Ntce that f yu make the v t large, the pamp saturates,.e. v s cnstant. Observe that des nt g belw 0.6V. v C. Summng Crcut Snce pnt B n the fllwng crcut s a vrtual grund (GRII), and are prprtnal t the tw nput sgnals v and v. GRII requres that the ttal nput current ( ) must be pulled thrugh R f. Sgnal Generatr V ut V T V External Scpe Trgger R R K K B R f 3 4 K K f 6 V LM38

5 The sgnal generatr s cnnected t the pamp as shwn n the sketch abve. s a square wave and s the vlt snce wave frm the generatr. The peak value f V s 0.V because v vlt s the RMS value and the utput resstance s K, whch causes a 50% attenuatn. The vlt sgnal ges t the external trgger nput f the scpe thrugh a Tcnnectr befre t ges t the crcut. Use the external scpe trgger..) Set the sgnal generatr fr 0kHz. D nt cnnect ntally. Observe v and v wth a scpe prbe (r a cable wth a clp lead). Yu shuld see that the crcut has a gan f. Mve the scpe prbe frm t. Start small and ncrease v untl ts ampltude s smlar t v, whle cntnung t bserve v. The utput shuld be the sum f the tw nput waves. Vary the ampltude f v v v as needed t understand the wavefrm at the utput. v v D. Reactance n the Feedback Lp. (Yu make skp sectn D f t wll cause the lab t exceed 3 hurs.) A capactr s ncluded n the feedback lp f the fllwng nvertng amplfer. The parallel 00K resstr s needed t set the quescent cndtns. It des nt affect the sgnal when X << R. c R f 00K V R K 3 0.0µf 4 6 V K LM38 Fgure The usual gan equatn apples except that the feedback path has reactance rather than a resstr. v xc jxc Xc = = = 90 (.5) v R R R

6 8.) Calculate v / v fr.6khz and 6kHz sne waves. What s the phase shft between v and? v 9.) Return t nternal trggerng. Measure the gan f the amplfer fr the tw frequences n step 8. Measure the phase shft at.6khz (GIL5.). Snce the amplfer nverts, cmpare the negatve peak f v t the precedng pstve peak f v. A square wave nput prduces a trangle wave at the utput. When v s pstve, v s a negatve ramp whse slpe s determned by I and the capactr. Snce 0V, the pstve and negatve slpes are the same, prducng a trangle wave. v s symmetrc arund 0.) Gven that v s a 0V(pp), 0kHz square wave, calculate the rate at whch v changes. Draw a sketch f v and v ncludng tme and vltage scales..) Observe the wavefrms descrbed n step 0. Yu can vary the perd f the square wave and ts ampltude t see the effect n the utput. The trangle wave may nt be symmetrc arund zer vlts. That s, the whle wave may be n the pstve (r negatve) sde f zer vlts. In that case, the peaks f the wave can be flattened by saturatn lmts f the pamp (apprxmately 3V). E. Feedback Dfference Amplfer R 5 must be adjusted t make R3/( R4 R5) exactly equal t R / R. In that case, v wll be zer when and v are equal because v s equal t v. On the ther hand when s zer, the v crcut s smply an nvertng amplfer wth a gan f dfference amplfer s:.) Cnnect pnts A and B tgether and apply a 0V(pp), khz sne wave t them. Adjust R untl s as small as 5 v pssble (typcally 0mV). In ths dfferental mde there s mnmal respnse at the utput, althugh a large sgnal s appled t bth nputs. v ( R / R ). Therefre the gan f ths v = ( R / R )( v v ) R 0K (.6) V V A B R R 3 K K R K LM 38 V 3) Cnnect pnt B t grund and apply a V sgnal t pnt A. Yu shuld see that the utput sgnal s amplfed by a factr f 0. Snce the dfferental gan s 0, and the 4 cmmnmde gan s 0.00, the cmmn mde rat s 0, r 80db. R 5 K

7 F. Feedback Cntrlled Cnstant Current Surce. The utput f the pamp adjusts the gate vltage t keep the surce f the FET at 0V, because the surce s cnnected t the nvertng nput. The electrns flwng thrugh R must flw thrugh the FET. The pamp wll adjust the gate vltage t let I g thrugh the FET even f there s a change n the dran vltage, hence ths s an excellent cnstant surce. 5V I Analg Meter 3 6 I MPF0 4 4 I =V n /R R 5V V n Fgure 3 4.) Calculate the value f the dran current fr R equal t 50K and 5K. Assume that s V and I dss s 5mA. Calculate the gate vltage fr the tw resstr values. 5.) The analg meter s nserted n the dran lead t bserve the FET current. Use the dgtal meter t measure the gate vltage relatve t cmmn. Measure Id, V g and V s fr the tw resstrs. Ntce that the gate vltage s changed by the pamp t let the current thrugh, whle keepng the surce at 0V. When the 5K resstr s n the crcut, vary the pstve supply vltage frm 5 t 0V t see that the pamp changes the gate vltage t let the same current flw thrugh FET at the lwer dran vltage. Ntce that the surce vltage stays at 0V, hence the current flwng thrugh R and the FET s cnstant. V T Opamp: 4 Capactrs: 0. µ f Resstrs: 4K,.K, 0K COMPONENTS Please get the fllwng cmpnents later f smene s watng.

8 Devces: 38 pamp, N94 ddes, MPF0 FET Capactrs: 00pf, 0.0 µ f Resstrs: K pt, 9.K, 5K, 5K, 50K