Lecture Notes on Operational Amplifiers - Microelectronic Circuits | ECE 3040, Study notes of Electrical and Electronics Engineering

Download Lecture Notes on Operational Amplifiers - Microelectronic Circuits | ECE 3040 and more Study notes Electrical and Electronics Engineering in PDF only on Docsity! ECE 3040 - Dr. Alan DoolittleGeorgia Tech Lecture 28 Operational Amplifiers Reading: Jaeger 11.1-11.5 and Notes ECE 3040 - Dr. Alan DoolittleGeorgia Tech + Vout - + Vin - Model Operational Amplifier •Operational Amplifier or “Op-Amp” is a multistage amplifier that is used for general electrical signal manipulation. •The numbers of applications possible with Op-amps are two numerous to list. •Most everyone agrees: “Op-Amp analysis is significantly easier than transistor analysis.” •Though they are often internally complex, their use in circuits most often simplifies the overall design. •The circuit is modeled by an ideal voltage amplifier. + Vout - + Vin - Circuit Symbol ECE 3040 - Dr. Alan DoolittleGeorgia Tech vin vout iin i2 i- i+ iout v- v+ Inverting Amplifier •Finite voltage gain results from an infinite voltage gain amplifier with “negative feedback” (feedback that takes a fraction of the output voltage and mixes it back into the negative summation node). 1 2 in 2 1 in 1 1 in 1 in in - 1 -in in 22 221 v 0 R v R v 3, and 2 1, Combining R v i)3 ground virtual the todue 0but v R v-v i resistanceinput infinite todue )2 0)1 R Rv vRRv iiii vRiRiv o oin in oinin −= =−−− = = = =+= =−−− − Overall circuit gain is finite, negative (for this feedback configuration) and set by the feedback resistor network. ECE 3040 - Dr. Alan DoolittleGeorgia Tech vin vout iin i2 i- i+ iout v- v+ •Input Resistance: 1Ri v R in in in == Inverting Amplifier ECE 3040 - Dr. Alan DoolittleGeorgia Tech vt i2 it v- v+ •Output Resistance: i1 0 i v 00v , ii and 0 vsince 0i but, RiRiv t t t 21 -1 1231t == += = == += outR thus Inverting Amplifier ECE 3040 - Dr. Alan DoolittleGeorgia Tech Summing Amplifier vin,a vout iin,a v- v+ vin,b vin,c iin,b iin,c i2       ++−= −−−= ++=− ++= cR Rv bR Rv aR Rvv cR Rv bR Rv aR Rvv cR v bR v aR v R v iiii cinbinainout cinbinainout cinbinainout cinbinain 1 2 1 2 1 2 1 2 1 2 1 2 1112 ,,, ,,, ,,, ,,,2 •Output is a scaled sum of inputs. •Scaling can be controlled by ratios of resistors ECE 3040 - Dr. Alan DoolittleGeorgia Tech Difference Amplifier vin,a vout v- v+ vin,b v- v+ vout vth vin,b 21 21 2 , || RRRandRR R vv thainth =+ = Using Superposition we can combine the results of the Inverting and Non-inverting solutions: 1 2 , 1 2 21 2 , 1 2 1 1 R R vv R R RR R vv R R vv ainout ainout thout =       + + =       += 1 2 bin,v R R vout −= ( ) 1 2 bin,ain, 1 2 bin, 1 2 ain, vv vv R Rv R R R Rv out out −= −= vin,a=0vin,b=0 This circuit amplifies the difference of two signals ECE 3040 - Dr. Alan DoolittleGeorgia Tech vin vout v- v+ Non-Ideal (Real World) Operational Amplifiers Finite Open-Loop Gain •Real op-amps do not have “infinite” “open loop (without feedback)” gain. •Voltage gains are typically large but finite: ~104-106 V/V •Finite gain causes a deviation from ideal amplifier behavior ( ) ( ) result gain infinite theapproaches R R11A 1A A, A1 A v v A so, βvvAvvAv factorfeedback theasknown is RR R βv RR Rvv 1 2 loop closed v, openloop openloop openloop openloopout loop closed v, outopenloopopenloopout 21 1 out 21 1 out ⇒+== >> + == −=−= + = = + = +−+ − β β β β β If gainlooptheiswhere where in ECE 3040 - Dr. Alan DoolittleGeorgia Tech Non-Ideal (Real World) Operational Amplifiers Finite Output Impedance ( ) ( ) ( ) ( ) ( ) ( ) ( )21 , 21 ,1 21 1 21 2212 , 2 1 11 RR A R R RRR A v i R vv RR R v RR v iRRiv R vvAv i iii i v R openloopv o out o openloopv x x out xx x x o openloopvx o ox x x out +        + = + + + == = + = + =⇒+= −− = += = − − −+ β β β Ro is very small so this term is EXTREMELY small! ECE 3040 - Dr. Alan DoolittleGeorgia Tech Non-Ideal (Real World) Operational Amplifiers Finite Input Impedance: Non-Inverting Case •Real Op-Amps have a large but finite input resistance, RID ( ) ( ) ( ) IDopenloopvin IDopenloopv x ID x openloopv openloopv x x x openloopv openloopv xopenloopvoutout ID x x RAR RA v R v A A v i v A A v vvAvv RR R v RiRiv R vv i β β β β β β ββ , , , , , , , 21 1 1211 21ID21x 1 1 1 1 )Ror R R to(due i and i tocompared icurrent theNeglecting += + =         + − = + = −== + = ≈= >> − = − −− − − RID is very large so Rin is EXTREMELY large! ECE 3040 - Dr. Alan DoolittleGeorgia Tech Non-Ideal (Real World) Operational Amplifiers Finite Input Impedance: Inverting Case •Real Op-Amps have a large but finite input resistance, RID •Rin=R1 +R’in •Find R’in by forming a new test circuit Rin R’in R’in ( ) ( ) ( )        + +=         + = + +== + += − +=+= − − openloopv IDin openloopv IDin openloopv ID in openloopv ID out ID A R RRR Thus A R RR R A Rv i R R vAv R v R vv R v iii , 2 1 , 2 2 , 1 11 2 1,11 2 11 21 1 , 1 ' 11' Since RID>>R2/(1+Av,openloop) and Av,openloop is very large, ( ) 1 , 2 1 , 2 1 11 R A RRR A RRRR openloopv in openloopv IDin ≈        + +=⇒        + +=