CHAPTER 5. The Operational Amplifier 1

Transcription

1 EECE22 NETWORK ANALYSIS I Dr. Charle J. Kim Cla Note 9: Oerational Amlifier (OP Am) CHAPTER. The Oerational Amlifier A. INTRODUCTION. The oerational amlifier or o am for hort, i a eratile circuit building block. 2. The o am i an electronic unit that behae like a oltage-controlled oltage ource. 3. The o am may alo be regarded a a oltage amlifier with ery high gain. 4. An o am can um ignal, amlify a ignal, integrate it, or differentiate it. The ability of the o am to erform thee mathematical oeration i the main reaon it i called an oerational amlifier.. The term oerational amlifier wa introduced by John Regazzini and hi colleague, in their work on analog comuter for the National Defene Reearch Council during World War II. The firt o am ued acuum tube rather tranitor. B. OP AMP PACKAGE. The o am i an electronic deice coniting of a comlex arrangement of reitor, tranitor, caacitor, and diode. 2. O am are commercially aailable in integrated circuit (IC) ackage in eeral form. A tyical one i the 8-in ingle or dual in-line ackage (DIP) hown below. 3. For a ingle DIP o am (tyically ua74), in or terminal 8 i unued (NC), and terminal and are of little concern to u. 4. For a dual DIP o am (tyically LM348), all 8 in are ued for two o am [left]. A tyical quad o am (LM324) i dilayed below right. The main goal of thi chater i to get tudent to be familiar with the node oltage method alication when actie element are reent in a circuit.

2 C. CIRCUIT SYMBOLS AND TERMINAL BEHAVIORS. The fie imortant terminal in an o am are: (a) Inerting inut (-) (b) Noninerting inut (+) (c) Outut (d) Poitie ower uly, V+ (e) Negatie ower uly, V- 2. The circuit ymbol for the o am i the triangle. 3. An inut alied to the noninerting terminal aear with the ame olarity at the outut. 4. An inut alied to the inerting terminal aear inerted at the outut.. The o am mut be owered by a oltage uly.. The equialent circuit model of an o am i hown below. The outut ection conit of a oltage-controlled deendent oltage ource in erie with the outut reitance R o. The outut reitance R o i the Theenin equialent reitance een at the outut terminal. The inut reitance R i i the Theenin equialent reitance een at the inut terminal. 7. Therefore, according to aboe equialent circuit of o am, it can be aid that the o am ene the difference between the two inut, multilie it by the gain A, and caue the reulting oltage to aear at the outut. 8. The outut oltage of the equialent circuit then i gien by, o = A( n) where i the oltage between the non inerting terminal and ground, and n i the oltage between the inerting terminal and ground. A i called the oen-loo oltage gain ince it i the gain of the o am without any external feedback from outut to inut. 9. Tyical alue of oltage gain A, inut reitance, outut reitance, and uly oltage: 2

3 Parameter Tyical Range Ideal Value Oen-loo gain, A - 8 Inut Reitance, R i - 3 Ω Ω Outut Reitance, R o - Ω Ω Suly ltage, V cc 24 V 9. Outut oltage limitation: The magnitude of the outut oltage cannot exceed V cc. Deending on the ower uly oltage and the differential inut oltage d = - n, o am can oerate in three mode: (a) Poitie aturation: o = Vcc (b) Linear region: Vcc o Vcc (c) Negatie aturation: o = Vcc. The oltage tranfer characteritic combine the three region of mode. Vcc if A( n ) < Vcc o = A( n ) if Vcc A( n ) + Vcc + Vcc if A( n ) > + Vcc D. IDEAL OP AMP MODEL. An o am i ideal if it ha the following characteritic: (a) Infinite oen-loo gain, i.e., A = (b) Infinite inut reitance, i.e., R i = Ω (c) Zero outut reitance, i.e., R o = Ω 2. Two imortant characteritic of the ideal o am for circuit analyi: (a) The current into both inut terminal are zero, i.e., i =i n =. Thi i due to infinite inut reitance: an oen circuit exit between two terminal and current cannot flow through. (b) The oltage acro the inut terminal i negligibly mall, i.e., = n.. Thi i due to infinite oen-loo gain. In the linear region, the magnitude of the outut oltage mut be le than the uly ower oltage, i.e., Vcc A( n ) Vcc. Een for a ractical o am, the gain A i about the, and the V cc i jut about 24V. Therefore, to atify the 24 3 inequality for the linear region mode, ( n ) =.24 =. 24 [mv]. 3

4 E. EXAMPLE of OP AMP CIRCUIT ANALYSIS (uing the ideal o am model and the non-ideal o am equialent circuit model) o Q: Calculate the cloed-loo gain (i.e., there i a feedback), and find i o when = [V]. (with R i =2MΩ, R = Ω, and oen-loo gain A=2x.) F. ANALYSIS A: uing the exact (i.e., non-ideal) OP Am model (a) The circuit diagram and it redrawn circuit are hown below: (b) Let aly the node-oltage method to the right circuit. node : + + = (Since V o =V 2 ). with V = Ri 4 ---> + + = ( ) ( V ) = 2 4 4

5 ( ---> ) V. V = () V2 V A( ) V2 V A( ) node 2: + + = + + = 4 2 Ro 4 2 It imlifie to: V V + V 2 + 4V 4A + 4AV = Again, 9V ( + 4A) + 4AV = 9V ( + 8 ) + 8 = ---> 8V + 9V = (2) 4V From () : V = By ubtitution to (2): V = and V = V Therefore, = V (e) For the current i o : alying KCL at node 2 yield: 3V io = + = = =.49 [A] F. ANALYSIS A: uing the Ideal OP Am model (a) By the contraint of ideal o am, = n and i =i n =, and node oltage method alication: (b) Contraint and hidden alue: by the ideal o am model, V =V and V o =V 2. node : + V V V o + = 4 ---> = 9V = 9V o Therefore the cloed-loo gain i: = 9 2 node 2: i = + = ---( with V =) (9V ) > = V i = =. [A] 4 4