Physics 310 Lecture 6a Op Amps

Transcription

1 Physcs 0 Fr. /7 Ch 9..5,.9, pp B: Operatonal mplers HW5: * ; Lab 5 Notebook Mon. /0 Wed. / Ch 9 (the rest): Operatonal mplers Quz Ch 9, Lab 6: Operatonal mplers HW 6: Ch9 Pr,*, 4*, 5, Equpment Electroncs porton o Chrs s Thess to demonstrate use o Opmps Lab #6 nnouncements Mdterm just ater break. Symbol & connectons Standlone Behavor comparator Feedback postve & negatve Schmtt trgger as example o postve eedback Golden ules or operaton wth negatve eedback. vertg and nonvertg puts are kept at the same voltage. no current lows to the puts pplcatons: Follower Invertg mp Nonvertg mp Currenttooltage Converter Summer / dder Derence mp Integrator & Derentator ctve Flters? Characterstcs o eal Op mps Input mpedance Input oset voltage Common mode rejecton rato Slew rate Frequency response I do NonInvertg mp They do Derental mp (we set up equvalent together) For Thursday: Input Impedance / put mpedance One example o reasong opamp operaton They then work group problem on at least one.

2 Introducton Physcs 0 Up to ths pot, we ve only dealt wth dscrete components dvdual resstors, capactors, dodes, transstors, ny terestg operaton we want perormed calls or some combaton o these. Now we ll meet our rst Integrated Crcut, an Operatonal mpler. To, momentarly, peak under ts hood, look at page D70. It s a whole crcut o resstors (~) and transstors (~4) and one capactor, all are already wred up or you and sealed a case. We are not gog to try to reason through ts detaled ner workgs, rather we ll adopt a ew rules o thumb and consder ts applcatons. There s a world o applcatons or ths handy crcutacase. The book pots that t was orgally desgned wth analog mathematcs (addg, subtractg, derentatg, tegratg, ) md. It certaly makes these operatons easy, but you can dream up all sorts o other uses. The Ideal Operatonal mpler Intally, let s not worry ab the detals o how t s acheved (or nearly acheved) yet, let s just thk ab how we d want t to behave. O course, the deal can t actually be met, but here s the wsh lst, and, many applcatons, real opamp behavor s essentally deal. Inte Input mpedance Z (so t doesn t eect the put sgnal or create other loadg problems) Zero put mpedance Z 0 (so t can mata ts put sgnal dependent o the load t bears) Inte mplcaton, (want an ampler go all the way!) Here s a symbol or the Opmp. Where = ( ). 99 Comparator Wth the undamental rule that = ( ), the most basc thg that an Opmp does s compare ts two puts: >, then the put s large and postve; <, then the put s large and negatve. So, perhaps the most natural use o an Op mp s as a Comparator one put may take a reerence voltage whle the other takes your sgnal; the comparator tells you, a bg way, the sgnal s greater or less than the reerence. For you to really get how comparators work, I should slghtly ree our pcture o an Op mp. In most crcutlogc dagrams, we don t bother showg t, but addton to havg two put and one put lead, an opamp has two power leads, just lke any other electrcal devce (thk the power cord or a stereo, toaster, vacuum cleaner, computer, ) When we do bother showg t, the drawg looks lke ths.

3 Physcs 0 These power les are oten on the order o / 5 olts. Under that smooth trangular hood o the Opmp s a mess o transstors (and a ew resstors), and these power rals act kd o lke the cc and EE o the whole mess. Wth that md you may not be surprsed when I say that there s a very practcal lmtaton on the relaton = ( ) where >>. The put can t exceed these rals. n Opmp plugged to a / 5 olt supply can t generate a sgnal sde that range: hgher than 5 or lower than 5. Now, sce s generally huge, t doesn t take a very bg derence between and to send to one ral or the other. In act, or most practcal purposes, I > then I < then Now, let s consder ths bt o crcutry. It s desgned so that an dcator lght turns on whenever the put sgnal,, exceeds a threshold reerence value, re. re LED On the let we have a voltage dvder that uses a varable resstor order to etune the desred reerence voltage, re. On the rght we have an LED whch, lke any dode, only passes current / lghts up, when ts head s lower voltage than ts tal. That means I < re then and the lght s OFF I > re then and the lght s ON To get a better eel or ths crcut, see what put a hypothetcal (and a bt messy) put sgnal prompts. LED o re LED on

4 Physcs 0 comparator wth put lke ths can be an awully handy thg. Maybe, t s got an LED whch acts as an dcator lght. Perhaps the comes rom a thermocouple and represents a temperature, then the lght turns on to alert you when the temperature gets too low. Or maybe, rather than puttg to an LED, the comparator s put would then be used to tell a heater to turn on. That s useul! 99. Schmtt Trgger Sometmes though, such a comparator s a lttle too senstve. Thk o that heater stuaton, the heater turned on every tme the sgnal dropped below the reerence and turned o every tme t crossed above the reerence, then the darn thg would be cessantly turng on /o/on/o The way my thermostat works s the heater s turned on the room drops below, say 70 F and keeps gog untl the temperature clmbs above 7 F. That derence buys some tme ater the heater turns o, t ll take a whle beore the temperature drops all the way to 70 F aga, and the heater s turned on aga. ll ths, no doubt, s controlled by a comparator that has two reerence pots, stead o just one. When the put sgnal (trackg the temperature) drops below the lower reerence value, then the put goes low (and the heater s turned on). s the put sgnal (temperature) clmbs, the put stays low untl the upper reerence value s crossed, at whch pot the put goes hgh (and the heater s turned o). Smlarly, as the put sgnal (temperature) alls aga, the put stays hgh untl the lower reerence s crossed aga. You mght mage that some new angled component s needed to acheve ths, or at least a pecular combaton o multple Opmps. In act, t just takes one Opmp smply, though cleverly, wred up. LED re We ve smply added a eedback resstor,, connectg the put to the postve put. In general, ths kd o conguraton (put connected to put) s known as postve eedback. Qualtatvely, t s easy to see that the reerence voltage, re, now sn t determed by just the voltage dvder; t also depends on the put,. Seeg how t depends on the put takes only a lttle bt o work. I we mata that there are essentally only two possble put values, = or =, then we have only two cases to consder ( prcple, can assume any value between the two, but that would requre and re beg so close to exactly equal that you ll never see t). 4

5 When < re then = re Physcs 0 Ths looks lke a voltage dvder but wth replaced by & parallel,.e.,. Then re s set at re When > re then = re Ths s a lttle more complcated, but the analyss s stll qute straghtorward. I I I re re re re re Example. To make t a lttle more concrete, let s say we have =0 =k =k re =0 =0 =0 = k LED =k Then, the put s at the 0 ral ( < re ), the reerence voltage s k 0 re k k k 6 k k 0 k 0k I the put s at the 0 ral ( > re ), the reerence voltage s re k k k k k So, here s how put and put sgnals would be related: 5

6 Physcs 0 rehgh relow 0 6 LED o LED o re re 0, 0, re re 6 0 LED on Wth ths partcularly messy put, you can see a second eect o the Schmtt Trgger crcut not only does the Schmtt trgger gve a marg between swgg the put hgh and low, but that means that nosy oscllatons wth that marg have no eect on the put. 9 oltage Follower Negatve Feedback & the Golden ule. Whle there are uses or opamps postve eedback conguratons, the ar more common s a negatve eedback conguraton. That s one whch the put s connected back to the negatve put (oten va a resstor or a capactor.) How an opamp behaves negatve eedback can easly be summed up what s known as the Golden ule o negatve eedback: becomes whatever t needs to be to make =. Let s see why that s and what use we can make o t the smplest magable negatve eedback crcut: the Follower. Now, = ( ) and =, then = ( ), or. Ideally, at any rate >>, so. Why bother?, couldn t we get = by just removg the Opmp all together? Sure. The vrtue o the ollower s that t acts lke a buer: whatever source s generatg the sgnal sees te mpedance up the le, so t has no problem matag the desred value; 6

7 Physcs 0 meanwhle whatever s gog to go on and use sees zero put mpedance, so no matter how small a load t provdes, t wll not eect the value t s gettg ed. Puttg a ollower to use should drve home ts worth. Say you ve got a smple voltage dvder: s = 0 5. k v = 5 5. k Then you wre t up to some other bt o crcutry that has an put mpedance o 0 k. s = 0 5. k v = k 0 k But, you really want that 5s across your load, then sert a ollower. s = 0 5. k 5. k v = 5 0 k 9 Invertg mpler More requently, you don t just want the put = put, you want the opamp to, well, amply the voltage, and not tely, but by some nce, reasonable actor. qurk o the opamp s desgn s that t s qute easy to do that, but only you re wllg to vert the sgnal whle you re 7

8 Physcs 0 at t. We ll rst analyze the vertg ampler wth assumg the golden rule, and then we ll see the golden rule o opamps short cut. v ga, what specal ab an Opmp s that = ( ). nd ts put mpedance s nearly te (so t draws no current) and ts put mpedance s nearly zero. Let s analyze ths crcut makg only the approxmaton that the opamp draws no current / has te put mpedance. Then But sce = ( ), or, and here, 0, so Now,, then the denomator s approxmately just.,.e., How good an approxmaton s ths? Well, the book gves a table that shows, 0, then can be as small as 0 and the approxmaton wll stll be 99% rght. I 00, then has to be at least 0 4 to make ths approxmaton 99% good. That s pretty good. Now, you re concerned ab the eect o our tal approxmaton, that s approxmatg that t, I won t go through all the work here (you could you lke), but not makg that approxmaton gves whch, or large and large ternal approxmates to the same thg. t ( ) t t, t t 8

9 Physcs 0 Makg these substtutons and solvg or gves t Golden ule or negatve eedback It s enlghteng to plug ths expresson back to = ( ). That gves s rather large, then 0,.e.,. That s the golden rule or opamps negatve eedback (that s, where the put s connected back to the negatve put): the put wll do what t s got to do to make the two puts equal. Here, we ve shown that that s a good approxmaton (sce s supposed to be wopp bg). For uture crcut analyss, as long as there s negatve eedback, we can assume ths to be the case. That makes our analyss much qucker. Just to show ts use, I ll reanalyze the vertg ampler, takg as a gven. Now, sce the ampler draws neglgble current, and the two put termals are (essentally) at the same voltage, the analyss goes v useul way to look at such crcuts s to thk o ther opampless equvalents. The sole uncton o the opamp here s to nal at ground wth dvertg any current to ground. So, the equvalent crcut s 0 0 where 0 so, and we re done! v The dashed le s to remd us that the mdpot happens to have =0, but no current s drawn down there. In general, opamps are oten used to do ths, to orce a pot a crcut to have zero voltage (because we all love zeros our mathematcal equatons) wth havg to dvert any current. 9

10 Physcs 0 Input mpedance. Whle the deal opamp may have te put mpedance, ths chunk o crcutry that volves two resstors and an opamp deally has an put mpedance equal to. So one typcally wants ths to be arly large so t doesn t draw too much current rom whatever s upstream o t your larger crcut. Note: later we ll look a lttle closer at the eects o real opamps not havg te put mpedance and te ga. For the moment, I ll borrowg a result rom that later work to show how good an approxmaton s:. I both ternal and are t qute large, then ths whole second term s neglgble. ( ) Makg these substtutons (wth an termedate step o solatg ) yelds t t t t so t v t 94 NonInvertg mpler We ve used the specc occason o analyzg the Invertg mpler crcut to learn some general thgs ab analyzg Opmp crcuts. Now we re gog to make use o some o those lessons. You ll see that analyzg these crcuts can actually be rather smple. Oten, you denty the equvalent nonopamp crcut and use our oldashoned, ohm slaw kd o reasong to analyze t. v 0

11 Physcs 0 The put s connected to the negatve put, so we re negatve eedback and we can assume that. ddtonally, the opamp draws vrtually no current rom ts puts. That gves us an equvalent crcut o v 0 95 Derental mpler Now you try. What s the equvalent noopamp crcut o ths? v ga, we ve got negatve eed back, so we can take or granted that current s drawn by the ampler. So, the equvalent crcut s, and, o course, no v o What can you say ab the currents through and? So you apply Ohm s law, what do you get? o How ab the currents through and? o

12 Physcs 0 and o 0 o Solvg both or o and settg them equal through that gves o So, The book notes that you buld ths crcut wth perectly balanced the resstors, = and =, then the put s smply. 95. Instrumentaton mpler It s a hassle to perectly balance resstors, but a sgle on chp crcut can do that better. Whle we re at t, we can slap some ollowers on the puts so we don t need to worry ab the crcut s put mpedances aectg the put sgnal. The resultg chp (roughly two ollowers and a derental ampler, all on one chp) s called an strumentaton ampler. I ll run through the logc o a smple Instrumentaton mpler crcut, t should make sense, but don t eel lke you need to be able to master t or the most part, t suces to merely apprecate how t works and know how to make t work or you. B I v Ths s the exact same crcut as shown the book s Fg 9.0; however, I ve bent the wres and named the resstors to emphasze t s smlarty to the crcut we ve just seen (that the book s Fg. 9.8). It s essentally the crcut we d just analyzed ( the blue box, wth a couple o Op mps tacked on to the puts. Quotg the result we d just gotten, () So now we just need to relate and to and. Here we go.

13 Physcs 0 Wth the top let Opmp negatve eedback, t s two puts must have equal voltage, so So But Ohm s law across the top says I (B) I Smlarly, lookg at the bottom let Opmp, I (C) (the current s the same sce the Opmps themselves dra o neglgble current.) Lookg at, Ohm s Law says I (D) Puttg these three equatons together, BC, and D elmatg I, I There s our relatonshp between, and,. Pluggg that to tells us how the put depends on the two puts. Ths s the book s Eq n 90, but tded a lttle and usg my names or the resstors. I we desgn our crcut so that,.e.,, then ths has the very smple orm o Tght equrements. Ths relatonshp s just as smple as the one or the smpler crcut, that wth just one Opmp, but the two ollowers gve t more desrable, hgh put mpedance. Unortunately, ths relatonshp s only as true as are and that the two resstors actually have the same resstance, and dtto or the two resstors. That s not easy to get realty, sde o a sgle chp. So chp manuacturers make Instrumentaton mpler chps that are essentally three (or more) Opmps some resstors all made on one chp.