Lecture 5: Operational Amplifiers and Op Amp Circuits

Transcription

1 Lecture 5: peratonal mplers and p mp Crcuts Gu-Yeon We Dson o Engneerng and ppled Scences Harard Unersty guyeon@eecs.harard.edu We

2 erew eadng S&S: Chapter Supplemental eadng Background rmed wth our crcut analyss tools, we begn the real meat o the materal or ths course by lookng at op amps. p amps were ntally constructed out o acuum tubes, then dscrete transstor components. Wth the adent o the ntegrated crcut, op amp ICs came out n the 60 s. They are extremely useul because they are ersatle and one can do almost anythng wth op amps. To start, we wll look at an deal erson o the op amp and see how they are useul. Then, we wll nestgate arous non-dealtes o real ampler desgn and how they aect op amp crcuts. We ES54 - Lecture 5

3 p-mp Termnals op amp symbol (we wll use most oten) - op amp symbol wth power supply connectons t a mnmum, op amps hae termnals: nput and output. n op amp also requres dc power to operate. ten, the op amp requres both poste and negate oltage supples. We ES54 - Lecture 5

4 Ideal p mp 0 0 ( - ) The op amp s desgned to sense the derence between the oltage sgnals appled to the two nput termnals and then multply t by some gan actor such that the oltage at the output termnal s ( - ). ne o the nput termnals () s called an nertng nput termnal denoted by - The other nput termnal () s called a non-nertng nput termnal denoted by The gan s oten reerred to as the derental gan or open-loop gan Notce that we can model the ampler as a oltage-controlled oltage source We ES54 - Lecture 5 4

5 Ideal p mps Characterstcs Ideal op amp characterstcs: Does not draw nput current so that the nput mpedance s nnte ( 0 and 0) The output termnal can supply an arbtrary amount o current and the output mpedance s zero The op amp only responds to the oltage derence between the sgnals at the two nput termnals and gnores any oltages common to both nputs. In other words, an deal op amp has nnte common-mode rejecton. The requency response o an deal op amp s lat or all requency. In other words, t amples sgnals o any and all requences by the same amount. Lastly, s or can be treated as beng nnte. Useul b/c we can easly specy a closed-loop gan as wll see later. We wll see later that real op amps do not hae the characterstcs aboe, but we stre to make them behae as close to an deal op amp as possble. We ES54 - Lecture 5 5

6 p mps n the Inertng Conguraton I 0 Let s look at an op amp n an nertng closed-loop conguraton. There are two resstors and s called the (negate) eedback resstor and also closes the loop. resstor between termnals and would be a poste eedback resstor. Closed-Loop Gan G Dened, G I ssume s nnte and the amp s tryng to produce a oltage on termnal. Then, the oltage derence between termnals and should be ery small, - 0 and n. By denton 0 So, we say there s a rtual short between the two termnals and that termnal s a rtual ground snce termnal s grounded. We ES54 - Lecture 5 6

7 Use KCL to sole or the close-loop gan. I 0 I 0 0 G We can adjust the closed-loop gan by changng the rato o and. I the nput s a sne wae, then the output s a sgn wae phase-shted by 80 degrees. The closed-loop gan s (deally) ndependent o op amp open-loop gan and we can make t arbtrarly large or small and o desred accuracy dependng on the accuracy o the resstors. Ths s a classc example o what negate eedback does. It takes an ampler wth ery large gan and through negate eedback, obtan a gan that s smaller, stable, and predctable. In eect, we hae traded gan or accuracy. Ths knd o trade o s common n electronc crcut desgn as we wll see. We ES54 - Lecture 5 7

8 Fnte pen-loop Gan Snce nnte s not physcally possble, what happens when s nte? Instead o a rtual ground, assume nput termnal has potental / I - 0 G ( ) ( ) s nnty, G - / and the oltage at termnal goes to 0 the rtual ground assumpton we made earler To mnmze the eects o open-loop gan on G, we want << We ES54 - Lecture 5 8

9 Input and utput esstance ssumng an deal op amp wth nnte open-loop gan, n the closed-loop nertng conguraton, the nput resstance s. I I n I To make n hgh, need to make hgh whch s not practcal See Example. n S&S or a possble soluton to ths problem The output resstance s 0 snce t s the output o a oltage source We can model the closed-loop nertng ampler wth the ollowng equalent crcut usng a oltage-controlled oltage source I n -( / ) I 0 We ES54 - Lecture 5 9

10 Inertng Conguraton wth General Impedances Z Z o Let s replace and n the nertng conguraton wth mpedances Z (s) and Z (s). We can wrte the closed-loop transer uncton as o Z Z By placng derent crcut elements nto Z and Z, we can get nterestng operatons. Some examples Integrator Derentator Summer Unty Gan Buer We ES54 - Lecture 5 0

11 Inertng Integrator C o / (db) C -0db/dec We replace Z (the negate eedback mpedance) wth a capactor and Z s a resstor. o ω (log scale) /C sc sc o o ( j ω ) ( jω) jωc ωc ω ωc C How about n the tme doman? and C C C C t ( 0) ( τ ) dτ t ( t ) ( τ ) dτ ( 0) 0 I 0 C C We ES54 - Lecture 5

12 C o Whle the DC gan n the preous ntegrator crcut s nnte, the ampler tsel wll saturate. To lmt the low-requency gan to a known and relable alue, add a parallel resstor to the capactor. o Z Z C s C We ES54 - Lecture 5

13 Derentator db C 0dB/dec o /C ω (log scale) o Z Z sc sc ( jω ) ( jω) jωc ωc ω C o when db 0 We ES54 - Lecture 5

14 Weghted Summer n o n You can also buldng a summer.,,..., n n n 0 n n o We ES54 - Lecture 5 4

15 Non-Inertng Conguraton To aod the nerson, shown s a non-nertng conguraton 0 as I I I I o Now what happens as nnty and 0 I Unty-Gan mpler o I We ES54 - Lecture 5 5

16 ES54 - Lecture 5 We 6 Derence mpler Now, we can combne the non-nertng ampler and nertng ampler conguratons to be able to take a derence between two nputs. You can use superposton or brute orce t o - as 0 -

17 Fnte pen-loop Gan and BW So ar, we hae assumed nnte gan and nnte bandwdth (BW) or the ampler, but that s not realty. mplers hae nte gan and BW. Here s an example o the open-loop gan s. requency plot o an ampler. Notce that the gan can be hgh at low requency, but starts to roll o at a low requency also. They are also requency compensated to roll o at -0dB/dec (or a sngle pole) to guarantee that op amp crcuts wll be stable (more on ths later n the semester when we talk about the guts o buldng amplers and eedback). We ES54 - Lecture 5 7

18 We can represent requency response characterstcs o ths ampler as we dd or a sngletme constant low-pass lter. 0 s ω ( jω ) For requences much greater than ω b (ω >> ω b ) we can approxmate the gan as 0ω b ( jω ) jω 0ω b ( j0 ) ωt 0ω b ω ω t s called the unty-gan BW. So the gan can be represented as So gen ths equaton, we can nd the gan at any requency. b 0 jω ω ωt s b We ES54 - Lecture 5 8

19 ES54 - Lecture 5 We 9 Frequency esponse o Closed-Loop mplers Let s look at the closed-loop gan equaton we dered earler or or an ampler wth nte op-amp open-loop gan. 0 >> /, then we can approxmate the equaton as Thereore, the closed-loop gan has a response that rolls o at 0dB/dec at a requency, ω -db, that s a uncton o the gan set by the nput and eedback resstors. ( ) ( ) b s s ω 0 and ( ) ( ) ( ) t s s s ω 0 ( ) ( ) ( ) ( ) s s s s t db db t ω ω ω ω where

20 utput Saturaton So ar, we hae been lookng at the amplcaton that can be acheed or relately small (ampltude) sgnals. For a xed gan, as we ncrease the nput sgnal ampltude, there s a lmt to how large the output sgnal can be. The output saturates as t approaches the poste and negate power supply oltages. In other words, there s lmted range across whch the gan s lnear. We ES54 - Lecture 5 0

21 Slew ate (BW lmted) nother source o nonlnear dstorton comes rom the lmted slew rate o the ampler. emember, we modeled the ampler as a sngle tme constant crcut. Thus, an nput sgnal sees attenuaton beyond the BW o the op amp. Let s look at the tme doman response o the crcut by takng the nerse Laplace transorm o the ampler s transer uncton multpled by a step wth magntude n. K s ω db s n ( t ) L ω dbt { } K( e ) n The output does not change nstantaneously. ather, we see an exponental response that slews the output up. The maxmum output slew rate s dened as the derate o the output oltage at t0. d ( t ) S ωdbkn dt max We ES54 - Lecture 5

22 oltage sets The crcut mplementaton o amplers s subject to a arety o mperectons durng ts abrcaton. Ths mperecton can be due to physcal mbalances that occurs een at DC (or zero requency). To understand ths problem, assume the two nputs to the ampler are connected together. Instead o a zero output, n real crcuts, we get a poste or negate oltage at the output. out 0 ne can x the mbalance by addng a DC oltage oset between the two nputs untl the output goes to zero. Ths s an nput oset oltage ( S ) n the ampler whch can be compensated or wth a oltage o equal magntude and opposte polarty. out 0 S We ES54 - Lecture 5

23 Input Bas Crcuts In real amplers, the two nput termnals hae to be suppled wth dc currents called nput bas currents. They can be represented by two current sources I B and I B. Furthermore, there can be msmatch between these currents I S. I B 0 I B 0 I B I B I B I B We can reduce the output oltage eects rom the nput bas current by addng a resstor nto the poste termnal. Howeer, msmatches between I B and I B (I S I B - I B ) results n an oset oltage S I S. We ES54 - Lecture 5