1.8.0: Ideal Oeratioal Amlifiers Revisio: Jue 10, 2010 215 E Mai Suite D Pullma, WA 99163 (509) 334 6306 Voice ad Fax Overview Oeratioal amlifiers (commoly abbreviated as o-ams) are extremely useful electroic devices. Some argue, i fact, that oeratioal amlifiers are the sigle most useful itegrated circuit i aalog circuit desig. Oeratioal amlifier-based circuits are commoly used for sigal coditioig, erformig mathematical oeratios, ad bufferig. These toics are discussed briefly below. Sigal coditioig is the rocess of maiulatig a give sigal (such as a voltage) to imrove its roerties or usefuless. Examles of commo sigal coditioig rocesses are: Level adjustmet: the overall level of a sigal may be too small to be usable. For examle, the voltage outut from a thermocoule (a electrical comoet used to measure temerature) may be oly a few thousadths of a volt. It is ofte desirable to amlify the sigal to icrease the outut voltage this is ofte doe usig circuits cotaiig oeratioal amlifiers. Noise reductio: electrical sigals are suscetible to oise; a udesirable comoet of a sigal. (For examle, static o a radio sigal.) Oeratioal amlifier circuits ca be used to remove udesirable comoets of a voltage sigal. Sigal maiulatio: Electrical sigals are ofte used to trasmit iformatio. For examle, the voltage outut of a thermocoule chages as the temerature of the thermocoule chages. The sesitivity of the thermocoule outut to temerature chages may be chaged by a oeratioal amlifier circuit to rovide a more readily usable outut voltage-totemerature relatioshi. A commo use of electrical circuits is to erform mathematical oeratios. So far, we have focused o develoig mathematical models of existig circuits we have bee erformig aalysis tasks. The desig rocess, coversely, ca be cosidered to cosist of imlemetig a electrical circuit that will erform a desired mathematical oeratio. (Of course, a large art of the desig rocess cosists of determiig what mathematical oeratio is to be erformed by the circuit.) Oeratioal amlifier circuits are readily develoed to erform a wide rage of mathematical oeratios, icludig additio, subtractio, multilicatio, differetiatio, ad itegratio. It is ofte desirable to electrically isolate oe sectio of a electrical circuit from aother. For examle, usig a electrical circuit to suly ower to a secod electrical circuit may result i udesirable loadig effects, i which the ower requiremets of the secod circuit exceed the ower that the first circuit ca rovide. I this case, a buffer ca be used to isolate the two circuits ad thus simlifyig desig roblems associated with itegratig the two circuits. Oeratioal amlifier circuits are commoly used for this urose. Doc: XXX-YYY age 1 of 7 Coyright Digilet, Ic. All rights reserved. Other roduct ad comay ames metioed may be trademarks of their resective owers.
1.8.0: Ideal Oeratioal Amlifiers Before begiig this chater, you should be able to: Aly Kirchoff s voltage ad curret laws to electrical circuits (Chater 1.4) Use odal aalysis ad mesh aalysis to aalyze electrical circuits (Chater 1.6.1, Chater 1.6.2) Rereset systems as block diagrams (Chater 1.7.0) After comletig this chater, you should be able to: State ideal oeratioal amlifier modelig rules State costraits o oeratioal amlifier outut voltage Rereset oeratioal amlifiers as deedet voltage sources Be able to idetify 741-tye oeratioal amlifier i coectios This chater requires: N/A Oeratioal amlifiers (or o-ams) are active devices. This differs from assive devices, such as resistors, i that a exteral ower source must be rovided to the oeratioal amlifier i order to make it fuctio roerly. O-ams are rather comlex devices, cosistig of a umber of itercoected trasistors ad resistors. We will ot be iterested here i a detailed descritio of the iteral oeratio of oeratioal amlifiers istead, we will use a o-am model which rovides us with relatively simle iut-outut relatios for the overall circuit. This simlified model will be adequate for may aalysis ad desig uroses. The oeratioal amlifier symbol which we will most ofte use is show i Figure 1. Oeratioal amlifiers are essetially three-termial devices, havig two iut termials ad oe outut termial. The iuts are called the ivertig termial (idicated by the sig) ad the o-ivertig termial (idicated by the sig). We will use v ad i to deote the voltage ad curret at the ivertig termial, ad v ad i to deote the voltage ad curret at the o-ivertig termial. The voltage ad curret at the outut termial are deoted as v OUT ad i OUT. It is assumed that v, v, ad v OUT are all relative to some commo referece voltage level, such as groud. Figure 1. Oeratioal amlifier symbol. Basic Ideal Oeratioal Amlifier Model: We will begi by summarizig the rules goverig ideal oeratioal amlifiers. Subsequetly, we will rovide some backgroud material relative to these rules ad some additioal criteria which the www.digiletic.com age 2 of 7 Coyright Digilet, Ic. All rights reserved. Other roduct ad comay ames metioed may be trademarks of their resective owers.
1.8.0: Ideal Oeratioal Amlifiers oeratioal amlifier must satisfy. It should be emhasized that these rules gover ideal oeratioal amlifiers; modelig of o-ideal oeratioal amlifiers will most likely be erformed i later electroics courses. Ideal o-am modelig rules: 1. No curret flows flows ito the iut termials: i i = 0. = 2. The voltages at the iut termials are the same: v = v. No requiremets are laced o the outut voltage ad curret. Oe may ot coclude that i OUT = 0 simly because the iut currets are zero. It may aear, from the iut-outut relatios goverig the o-am, that the o-am violates Kirchoff s curret law this is because we are ot examiig the details of the iteral oeratio of the o-am. Sice the o-am is a active device with its ow ower suly, it ca rovide a outut curret with o iut curret. Oeratioal amlifiers, ulike assive devices, are caable of addig ower to a sigal. The resece of the exteral ower sulies raises some additioal costraits relative to o-am oeratio; we address these issues ext. A more comlete schematic symbol for a oeratioal amlifier, icludig the o-am s exteral ower sulies, is show i Figure 2. Figure 2 shows two additioal o-am termials. Oe is coected to a voltage source V ad the other is coected to a voltage source V -. These termials are sometimes called the ositive ad egative ower suly termials. We must set the exteral voltage sulies so that the ositive ower suly voltage is greater tha the egative ower suly voltage: V > V. I our discussios, it will be assumed that the ower suly voltages are relative to the same referece voltage as all other voltages o the schematic. Figure 2. Oeratioal amlifier schematic, icludig exteral ower sulies. The ower suly voltages rovide a costrait o the rage of allowable outut voltages, as rovided below: Outut Voltage Costrait: The outut voltage is costraied to be betwee the ositive ad egative ower suly www.digiletic.com voltages: age 3 of 7 V < vout < V. Coyright Digilet, Ic. All rights reserved. Other roduct ad comay ames metioed may be trademarks of their resective owers.
1.8.0: Ideal Oeratioal Amlifiers The above costrait is based o ure iequalities i geeral, the outut voltage rage will be somewhat less tha the rage secified by V- ad V. The margi betwee the outut ad the suly voltages will vary deedig o the secific o-am; oututs commoly remai a volt or so away from the suly voltages. Ay attemt to drive the outut voltage beyod the rage secified by the suly voltages will cause the outut to saturate at the aroriate suly voltage. Oeratioal Amlifier Model Backgroud: The above rules goverig our ideal oeratioal amlifier model ca be alied directly to oeratioal amlifier circuits, but some backgroud iformatio will allow more isight ito the basis for these rules. We will still, however, treat the oeratioal amlifier as a sigle circuit elemet with some iutoutut relatioshi. A oeratioal amlifier oerates as a differetial amlifier with a very high gai. That is, the outut of the amlifier is the differece betwee the iut voltages, multilied by a large gai factor, K. Figure 3 shows the oeratio of the o-am, from a systems-level stadoit: Figure 3. Block diagram of o-am oeratio Thus, the iut-outut relatio for a oeratioal amlifier is v OUT = K( v v ) = K v (1) P i where v is the differece betwee the voltages at the iut termials ad K is a very large umber. i (Values of K for tyical commercially available oeratioal amlifiers are o the order of 10 6 or higher.) Sice the outut voltage is costraied to be less tha the suly voltages, V K vi < < V so V K V < vi < (2) K If the voltage sulies are fiite ad K is very large, the differece i the iut voltages must be very small. Thus, i v 0. ad v v. www.digiletic.com age 4 of 7 Coyright Digilet, Ic. All rights reserved. Other roduct ad comay ames metioed may be trademarks of their resective owers.
1.8.0: Ideal Oeratioal Amlifiers The secod oeratioal amlifier modelig rule is a result of the high iut resistace of oeratioal amlifiers. We assume that ay differece i the iut termial voltages is due to the oeratioal amlifier s iut resistace, R i, times the curret at the iut termials (see Figures 1 or 2 for sig covetios ad variable defiitios): v v = R i i We will also assume that KCL alies across the iut termials, so i = i The above equatios ca be combied to give i v v = i = (3) R i Sice the iut resistace of oeratioal amlifiers is very large ad the voltage differece across the iut termials is very small, i i 0. = The above results suggest that a oeratioal amlifier oerates as a voltage-cotrolled-voltage source as show i Figure 4. Tyically, commercially available oeratioal amlifiers have very high gais, K, very high iut resistaces, R i, ad very low outut resistaces, R out. Figure 4. Equivalet circuit for oeratioal amlifier model. Combiig the criteria rovided by equatios (1) ad (2) results i the iut-outut relatioshi show grahically i Figure 5 below. The circuit oerates liearly oly whe the outut is betwee the suly voltages. Whe the outut attemts to go outside this rage, the circuit saturates ad the outut remais at the aroriate suly voltage. Notice that the egative suly voltage i Figure 5 is idicated as a egative umber; this is fairly tyical, though ot a requiremet. www.digiletic.com age 5 of 7 Coyright Digilet, Ic. All rights reserved. Other roduct ad comay ames metioed may be trademarks of their resective owers.
1.8.0: Ideal Oeratioal Amlifiers Figure 5. O-am iut-outut relatioshi. Our ideal oeratioal amlifier model rules are based o the above, more geeral, oeratioal amlifier relatioshis. The assumtios relative to ideal oeratioal amlifier oeratio, alog with their associated coclusios, are rovided below: The outut voltage is bouded by the ower suly voltages: < v < V V OUT K. This, i cojuctio with equatio (2) imlies that v = 0 ad v = v. i = i R i. This, i cojuctio with equatio (3) imlies that i = 0. R OUT = 0. Commercially Available Oeratioal Amlifiers: Oeratioal amlifiers are available commercially as itegrated circuits (ICs). They are geerally imlemeted as dual i-lie ackages (DIPs), so called because the termials (is) o the ackage are i airs ad lie-u with oe aother. A tyical DIP is show i Figure 5. The is o DIPs are umbered; i order to correctly coect the DIP, i 1 must be correctly orieted. Pi 1 is commoly located by lookig for a otch at oe ed of the IC i 1 will be to the immediate left of this otch, if you are lookig at the IC from the to. Alterate methods of idicatig i 1 are also used: sometimes the corer of the IC earest i 1 is shaved off or a small idetatio or dot is located at the corer of the IC earest i 1. Figure 5. Dual i-lie trasistor ackage. www.digiletic.com age 6 of 7 Coyright Digilet, Ic. All rights reserved. Other roduct ad comay ames metioed may be trademarks of their resective owers.
1.8.0: Ideal Oeratioal Amlifiers Oe commo o-am device is the 741 o-am. The 741 is a eight-lead DIP; a to view of the ackage, with the leads labeled, is show i Figure 6. Key features of the ackage are as follows: Orietatio of the is is determied by the locatio of a semicircular otch o the ackage, as show i Figure 6. (Recall that Figure 6 is a to view of the device.) Alterately, some ackages lace a circular idetatio ear i 1 i order to rovide the orietatio of the is. Ivertig ad o-ivertig iuts are labeled as IN ad IN i Figure 2. They are is 2 ad 3, resectively. The outut is labeled OUT o Figure 6. This termial is i 6 o the ackage. The ositive ad egative ower sulies are labeled as V ad V- o Figure 6. They are is 7 ad 4, resectively. V should be less tha 15 volts ad V- should be more tha -15 volts. A larger rage of ower suly voltages may destroy the device. The is labeled -OFFSET NULL, OFFSET NULL, ad NC (is 1, 5, ad 8) will ot be used for this class. The offset ull is are used to imrove the o-am s erformace. The NC i is ever used. (NC stads for ot coected ). Figure 6. 741-tye oeratioal amlifier i coectios. www.digiletic.com age 7 of 7 Coyright Digilet, Ic. All rights reserved. Other roduct ad comay ames metioed may be trademarks of their resective owers.