1. ECEN 301Discussion #17 – Operational Amplifiers1 DateDayClass No. TitleChaptersHW Due date Lab Due date Exam 29 OctWed17Operational Amplifiers8.1 – 8.2 30 OctThu 31 OctFri RecitationHW 7 1 NovSat 2 NovSun 3 NovMon18Operational Amplifiers8.3 – 8.4 LAB 6 4 NovTue 5 NovWed19Binary Numbers13.1 – 13.2 Schedule…

2. ECEN 301Discussion #17 – Operational Amplifiers2 Increase Helaman 12:2 2 Yea, and we may see at the very time when he doth prosper his people, yea, in the increase of their fields, their flocks and their herds, and in gold, and in silver, and in all manner of precious things of every kind and art; sparing their lives, and delivering them out of the hands of their enemies; softening the hearts of their enemies that they should not declare wars against them; yea, and in fine, doing all things for the welfare and happiness of his people; yea, then is the time that they do harden their hearts, and do forget the Lord their God, and do trample under their feet the Holy One—yea, and this because of their ease, and their exceedingly great prosperity.

3. ECEN 301Discussion #17 – Operational Amplifiers3 Lecture 17 – Operational Amplifiers

4. ECEN 301Discussion #17 – Operational Amplifiers4 Ideal Amplifiers Amplifier: a device for increasing the power of a signal. ÙPower increase is called gain (A) v S (t) +–+– RSRS Gain A +vL–+vL– RLRL Source Amplifier Load 0:21 CD SourceAmplifierLoad

5. ECEN 301Discussion #17 – Operational Amplifiers5 Ideal Amplifiers Simplified Amplifier Model: ÙThe source “sees” and equivalent load (R in ) ÙThe load “sees” and equivalent source (Av in ) v S (t) +–+– RSRS Gain A +vL–+vL– RLRL Source Amplifier Load NB: Thévenin equivalent NB: equivalent resistance v S (t) +–+– RSRS +vL–+vL– RLRL R in +–+– R out Av in + v in –

6. ECEN 301Discussion #17 – Operational Amplifiers6 Ideal Amplifiers The gain is dependent on the source and load (i.e. is different for different sources and loads) v S (t) +–+– RSRS +vL–+vL– RLRL R in +–+– R out Av in + v in – NB: expression for v L depends on the source (R S ) and the load (R L )

7. ECEN 301Discussion #17 – Operational Amplifiers7 Ideal Amplifiers The gain can be made to be almost independent of the source (R S ) and the load (R L ) ÙLet R in → ∞ ÙLet R out → 0 v S (t) +–+– RSRS +vL–+vL– RLRL R in +–+– R out Av in + v in – NB: it is desirable for an amplifier to have: a very large input impedance a very small output impedance

8. ECEN 301Discussion #17 – Operational Amplifiers8 Op-Amps Operational Amplifier: originally designed (late 1960’s) to perform mathematical operations (analog computer) ÙAddition ÙSubtraction ÙIntegration Ùdifferentiation – + Positive power supply (usually +15V) Negative power supply (usually –15V) Output Inverting Input Noninverting Input VS+VS+ VS–VS– NB: the power supplies (V S + and V S – ) are often omitted in drawings – they are implicit

9. ECEN 301Discussion #17 – Operational Amplifiers9 Op-Amps – Open-Loop Mode Open-Loop Model: an ideal op-amp acts like a difference amplifier (a device that amplifies the difference between two input voltages) – + +v+–+v+– +v––+v–– +vo–+vo– ioio i2i2 i1i1 – v in + – + +–+– R out R in i1i1 A OL v in +vo–+vo– – v in + v–v– v+v+ NB: op-amps have near-infinite input resistance (R in ) and very small output resistance (R out ) A OL – open-loop voltage gain i2i2

10. ECEN 301Discussion #17 – Operational Amplifiers10 Op-Amps – Open-Loop Mode Open-Loop Model: an ideal op-amp acts like a difference amplifier (a device that amplifies the difference between two input voltages) – + +v+–+v+– +v––+v–– +vo–+vo– ioio i2i2 i1i1 – v in + Ideally i 1 = i 2 = 0 (since R in → ∞)

11. ECEN 301Discussion #17 – Operational Amplifiers11 Op-Amps – Open-Loop Mode Open-Loop Model: an ideal op-amp acts like a difference amplifier (a device that amplifies the difference between two input voltages) What? No input current?? In reality there is a small current

12. ECEN 301Discussion #17 – Operational Amplifiers12 Op-Amps – Closed-Loop Mode The Inverting Amplifier: the signal to be amplified is connected to the inverting terminal – + +vo–+vo– i1i1 RFRF RSRS v S (t) +–+– v+v+ v–v– iFiF iSiS i2i2

13. ECEN 301Discussion #17 – Operational Amplifiers13 Op-Amps – Closed-Loop Mode The Inverting Amplifier: the signal to be amplified is connected to the inverting terminal – + +vo–+vo– i1i1 Feedback current: current from the output is fed back into the input of the op-amp RFRF RSRS v S (t) +–+– v+v+ v–v– iFiF iSiS Node a

14. ECEN 301Discussion #17 – Operational Amplifiers14 Op-Amps – Closed-Loop Mode The Inverting Amplifier: the signal to be amplified is connected to the inverting terminal – + +vo–+vo– i1i1 RFRF RSRS v S (t) +–+– v+v+ v–v– iFiF iSiS

15. ECEN 301Discussion #17 – Operational Amplifiers15 Op-Amps – Closed-Loop Mode The Inverting Amplifier: the signal to be amplified is connected to the inverting terminal RFRF – + +vo–+vo– i1i1 RSRS v S (t) +–+– v+v+ v–v– iFiF iSiS

16. ECEN 301Discussion #17 – Operational Amplifiers16 Op-Amps – Closed-Loop Mode The Inverting Amplifier: the signal to be amplified is connected to the inverting terminal RFRF – + +vo–+vo– i1i1 RSRS v S (t) +–+– v+v+ v–v– iFiF iSiS NB: if A OL is very large these terms → 0

17. ECEN 301Discussion #17 – Operational Amplifiers17 Op-Amps – Closed-Loop Mode The Inverting Amplifier: the signal to be amplified is connected to the inverting terminal RFRF – + +vo–+vo– i1i1 RSRS v S (t) +–+– v+v+ v–v– iFiF iSiS NB: as A OL → ∞ v – → 0

18. ECEN 301Discussion #17 – Operational Amplifiers18 Op-Amps – Closed-Loop Mode The Inverting Amplifier: the signal to be amplified is connected to the inverting terminal RFRF – + +vo–+vo– i1i1 RSRS v S (t) +–+– v+v+ v–v– iFiF iSiS NB: two important results for an ideal op-amp with negative feedback i2i2

19. ECEN 301Discussion #17 – Operational Amplifiers19 Op-Amps – Closed-Loop Mode Example1: determine A OL and v o R S = 1kΩ, R F = 10kΩ, v s (t) = Acos(ωt), A=0.015, ω = 50 rads/s RFRF – + +vo–+vo– i1i1 RSRS v S (t) +–+– v+v+ v–v– iFiF iSiS

20. ECEN 301Discussion #17 – Operational Amplifiers20 Op-Amps – Closed-Loop Mode Example1: determine A OL and v o R S = 1kΩ, R F = 10kΩ, v s (t) = Acos(ωt), A=0.015, ω = 50 rads/s RFRF – + +vo–+vo– i1i1 RSRS v S (t) +–+– v+v+ v–v– iFiF iSiS

21. ECEN 301Discussion #17 – Operational Amplifiers21 Op-Amps – Closed-Loop Mode Example1: determine A OL and v o R S = 1kΩ, R F = 10kΩ, v s (t) = Acos(ωt), A=0.015, ω = 50 rads/s RFRF – + +vo–+vo– i1i1 RSRS v S (t) +–+– v+v+ v–v– iFiF iSiS

22. ECEN 301Discussion #17 – Operational Amplifiers22 Op-Amps – Closed-Loop Mode Example2: What is the min/max gain, and gain uncertainty if 5% tolerance resistors are used? R S = 1kΩ, R F = 10kΩ, v s (t) = Acos(ωt), A=0.015, ω = 50 rads/s RFRF – + +vo–+vo– i1i1 RSRS v S (t) +–+– v+v+ v–v– iFiF iSiS NB: nominal gain

23. ECEN 301Discussion #17 – Operational Amplifiers23 Op-Amps – Closed-Loop Mode Example2: What is the min/max gain, and gain uncertainty if 5% tolerance resistors are used? R S = 1kΩ, R F = 10kΩ, v s (t) = Acos(ωt), A=0.015, ω = 50 rads/s RFRF – + +vo–+vo– i1i1 RSRS v S (t) +–+– v+v+ v–v– iFiF iSiS

24. ECEN 301Discussion #17 – Operational Amplifiers24 Op-Amps – Closed-Loop Mode The Summing Amplifier: sources are summed together independently of load and source impedances – + +vo–+vo– RFRF R S1 v S1 (t) +–+– v+v+ v–v– iFiF i1i1 R S2 v S2 (t) +–+– i2i2 R SN v SN (t) +–+– iNiN

25. ECEN 301Discussion #17 – Operational Amplifiers25 Op-Amps – Closed-Loop Mode The Summing Amplifier: sources are summed together independently of load and source impedances – + +vo–+vo– RFRF R S1 v S1 (t) +–+– v+v+ v–v– iFiF i1i1 R S2 v S2 (t) +–+– i2i2 R SN v SN (t) +–+– iNiN Node a NB: v – = v + = 0

26. ECEN 301Discussion #17 – Operational Amplifiers26 Op-Amps – Closed-Loop Mode The Summing Amplifier: sources are summed together independently of load and source impedances – + +vo–+vo– RFRF R S1 v S1 (t) +–+– v+v+ v–v– iFiF i1i1 R S2 v S2 (t) +–+– i2i2 R SN v SN (t) +–+– iNiN Node a

27. ECEN 301Discussion #17 – Operational Amplifiers27 Op-Amps – Closed-Loop Mode The Noninverting Amplifier: the signal to be amplified is connected to the noninverting terminal – + +vo–+vo– i1i1 RFRF R v S (t) +–+– v+v+ v–v– iFiF RSRS iSiS i1i1

28. ECEN 301Discussion #17 – Operational Amplifiers28 Op-Amps – Closed-Loop Mode The Noninverting Amplifier: the signal to be amplified is connected to the noninverting terminal – + +vo–+vo– i1i1 RFRF R v S (t) +–+– v+v+ v–v– iFiF RSRS iSiS i1i1 Node a

29. ECEN 301Discussion #17 – Operational Amplifiers29 Op-Amps – Closed-Loop Mode The Noninverting Amplifier: the signal to be amplified is connected to the noninverting terminal – + +vo–+vo– i1i1 RFRF R v S (t) +–+– v+v+ v–v– iFiF RSRS iSiS i1i1 Node a

30. ECEN 301Discussion #17 – Operational Amplifiers30 Op-Amps – Closed-Loop Mode The Noninverting Amplifier: the signal to be amplified is connected to the noninverting terminal – + +vo–+vo– i1i1 RFRF R v S (t) +–+– v+v+ v–v– iFiF RSRS iSiS i1i1 Node a NB: always positive and greater than or equal to 1

31. ECEN 301Discussion #17 – Operational Amplifiers31 Op-Amps – Closed-Loop Mode Voltage Follower: the voltage on the output of the op-amp is equal to the source voltage – + +vo–+vo– i1i1 v S (t) +–+– v+v+ v–v– i1i1

32. ECEN 301Discussion #17 – Operational Amplifiers32 Op-Amps – Closed-Loop Mode Voltage Follower: the voltage on the output of the op-amp is equal to the source voltage – + +vo–+vo– i1i1 v S (t) +–+– v+v+ v–v– i1i1 NB: an ideal op-amp with negative feedback has the property

33. ECEN 301Discussion #17 – Operational Amplifiers33 Op-Amps – Closed-Loop Mode Voltage Follower: the voltage on the output of the op-amp is equal to the source voltage Circuit 1 Loading: changing the behaviour of one circuit by connecting another circuit to it +va–+va– If v a ≠ v b i b is the load current Circuit 1 Circuit 2 +vb–+vb– ibib

34. ECEN 301Discussion #17 – Operational Amplifiers34 Op-Amps – Closed-Loop Mode Voltage Follower: the voltage on the output of the op-amp is equal to the source voltage – + Circuit 1 Circuit 2 Voltage follower can be used to prevent loading (i b = 0) Loading: changing the behaviour of one circuit by connecting another circuit to it