Chapter 5-4 Operational amplifier Department of Mechanical Engineering

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1 MEMS08 Chaper 5-4 Operaional amplifier Deparmen of Mechanical Engineering

2 Insrumenaion amplifier Very high inpu impedance Large common mode rejecion raio (CMRR) Capabiliy o amplify low leel signals Consisen bandwidh Deparmen of Mechanical Engineering

3 Inegraor Lossless capacior V O = RC o in d y RC ( ) = x( ) d = k x( )d o o Deparmen of Mechanical Engineering

4 Differeniaion and inegraion V O = RC o in d Deparmen of Mechanical Engineering

5 Improed Inegraor Lossy capacior Rs is shun resisor Rs=0R The use of shun resisor is o limi he low frequency gain of he circui. Oherwise, a small DC offse a he inpu would be inegraed oer ime, eenually sauraing he op amp. DC offse due o he inpu bias curren can be minimized by R. Choose: R RR s = R R s Deparmen of Mechanical Engineering

6 Inegraor Deparmen of Mechanical Engineering

7 Example s =5e u( )V o ( 0 ) = 0V Find o () for >0 Deparmen of Mechanical Engineering

8 Deparmen of Mechanical Engineering Summing Inegraor ( ) ( ) ( ) ( ) ( ) ( ) ( ) R x R x R R i i i c = = = ( ) ( )d i C c o c = ( ) ( ) ( ) d R R C c = 0 ( ) ( ) ( ) d R C x R C x y = 0 ( ) ( ) ( ) [ ] d x k x k y = 0

9 Differeniaor Deparmen of Mechanical Engineering

10 Differeniaor The inpu signal o he differeniaor is applied o he capacior. The capacior blocks any DC conen so here is no curren flow o he amplifier summing poin, resuling in zero oupu olage. The capacior only allows AC ype inpu olage changes o pass hrough and whose frequency is dependan on he rae of change of he inpu signal. A low frequencies he reacance of he capacior is "High" resuling in a low gain (Rf/Xc) and low oupu olage from he op-amp. A higher frequencies he reacance of he capacior is much lower resuling in a higher gain and higher oupu olage from he differeniaor amplifier. Deparmen of Mechanical Engineering

11 Differeniaor Deparmen of Mechanical Engineering

12 Improed Differeniaor Amplifier Deparmen of Mechanical Engineering

13 Example: Inegraor and Swich An inegraor and a olage-conrolled swich 0 An inegraor is a circui ha can perform he mahemaical operaion of inegraion. The oupu olage, o (), is relaed he inpu of he inegraor, s (). ( ) K ( ) d ( ) = s o Inegraors hae many applicaions. One is o measure a ime ineral -. ( ) = K ( ) V ( ) 0 s o Deparmen of Mechanical Engineering

14 Example: Inegraor and Swich Volage conrolled swich - Swich can be conrolled elecronically. The node olage, c (), is called he conrol olage. Deparmen of Mechanical Engineering

15 Example: Inegraor and Swich To design an inegraor circui ( ) = K ( ) V ( ) s o o o ( ) = ( ) 0V 00ms 0V K V s = 00ms K =0 s Deparmen of Mechanical Engineering

16 Example o = RC = K RC C = µ F R = 0 ( V s) s d µ F = 00kΩ o ( ) = ( ) 50 Deparmen of Mechanical Engineering

17 Op-Amp Open Loop Gain In Op-amp, pracically, he gain is so high ha he oupu will be drien o V cc or V cc for any appreciable difference beween V and V. This is useful in he comparaor. For pracical applicaions oher han he comparaor, negaie feedback is used o conrol he deice gain. Deparmen of Mechanical Engineering

18 Comparaor The exremely large openloop gain of an op-amp makes i an exremely sensiie deice for comparing is inpu wih zero. For pracical purposes, if V >V, he oupu is drien o he posiie supply olage; If V <V i is drien o he negaie supply olage. The swiching ime for - o is limied by he slew rae of he op-amp. Deparmen of Mechanical Engineering

19 Comparaor The basic comparaor will swing is oupu o a he slighes difference beween is inpus. Bu here are many ariaions where he oupu is designed o swich beween wo oher olage alues V H and V L. Also, he inpu may be ailored o make a comparison o an inpu olage V T oher han zero. Deparmen of Mechanical Engineering

20 Comparaor: applicaion Ofen i is desirable ha swiching occurs a prescribed olage. Comparaor can be used for his purpose. o ( ) = V V H L if if > < V H and V L are he only wo alues ha o () can hae. Deparmen of Mechanical Engineering

21 Comparaor: Example For he following circui, suppose V A >V T > c (0), V T is a hreshold olage; and he inpu olages for he comparaor are = c = V T ( ) V H if c ( ) o ( ) = The oupu olage V L if c ( ) The capacior olage ( ) = V ( 0) c A > V < V ( RC ) [ V ] e A, he comparaor olage swiches from V L o V H T A ( RC ) [ ( 0) V ] e V = V c A c = RC ln V ( 0) T V V A c A T A T Deparmen of Mechanical Engineering

22 Comparaor: Example For he shown circui, he iniial alue of he capacior olage is c (0) =.667V. Wha alue of he resisance, R, is required if he comparaor is o swich from V L o V H a ime =ms? Deparmen of Mechanical Engineering

23 Deparmen of Mechanical Engineering Comparaor: Example For he shown circui, he comparaor is used o compare he resisor olage R () wih a hreshold olage V T. Suppose V A >V T > Ri L (0). A ime, he comparaor oupu olage swiches from V L o V H ( ) ( ) L R A L A L e R V i R V i = 0 ( ) ( ) [ ] 0 L R A L A L T e V Ri V Ri V = = ( ) = A T A L V V V Ri R L 0 ln

24 Comparaor: Example For he shown circui, he iniial alue of he inducor is i L (0) =ma. Wha alue of he inducance, L, is required if he comparaor is o swich from V L o V H a ime =0ms? Deparmen of Mechanical Engineering

25 The Sample and Hold circui When The Sample and Hold circui uses wo buffers o keep a olage leel sored in a capacior. Pressing S sample will charge he capacior o he presen signal leel, while he inpu buffer ensures he signal won' be changed by he charging process. From here, he oupu buffer will make sure ha he olage leel across he sorage cap won' decrease oer ime. Pressing S clear will shor ou he sorage cap, discharging i and seing he oupu o 0V. We can build he Sample and Hold circui wih mechanical pushbuon swiches o see i in acion. In acual pracice, he swiches used are arious forms of ransisor swich, which proides cleaner swiching and also allows anoher circui o conrol he sample and clearing operaions. Deparmen of Mechanical Engineering

26 Uses of Linear Op-Amp Circuis Amplifiers Making signals bigger! Summing Amp Mixing (e.g. audio applicaions) Analogue arihmeic Inegraor Analogue compuing Acie filer design Difference Amp Balanced line receiers Deparmen of Mechanical Engineering

27 Ideal Op-Amp Linear Circui Analysis.. 3. I V V OUT = 0 and = V I = 0 = anyhing! When negaie feedback is applied, he use of hese assumpions makes design/analysis much easier (alhough no necessarily simple!). Of course, hey aren really rue Deparmen of Mechanical Engineering

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