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Schedule… Date Day Class No. Title Chapters 29 Oct Wed 17 Operational Amplifiers 8.1 – 8.2 30 Oct Thu 31 Oct Fri 1 Nov Sat 2 Nov Sun 3 Nov Mon Recitation 18 Operational Amplifiers HW Due date Lab Due date Exam HW 7 8.3 – 8.4 LAB 6 4 Nov Tue 5 Nov Wed ECEN 301 19 Binary Numbers 13.1 – 13.2 Discussion #17 – Operational Amplifiers 1 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. ECEN 301 Discussion #17 – Operational Amplifiers 2 Lecture 17 – Operational Amplifiers ECEN 301 Discussion #17 – Operational Amplifiers 3 Ideal Amplifiers Amplifier: a device for increasing the power of a signal. Power increase is called gain (A) RS + 0:21 vS(t) + Gain A – CD RL vL – Source Amplifier Load Source Amplifier Load vL (t ) AvS (t ) ECEN 301 Discussion #17 – Operational Amplifiers 4 Ideal Amplifiers Simplified Amplifier Model: The source “sees” and equivalent load (Rin) The load “sees” and equivalent source (Avin) RS Rout RS + vS(t) + Gain A – RL vL – Source NB: Thévenin equivalent ECEN 301 Amplifier + vS(t) + – vin – Avin Rin + + – RL vL – Load NB: equivalent resistance Discussion #17 – Operational Amplifiers 5 Ideal Amplifiers The gain is dependent on the source and load (i.e. is different for different sources and loads) Rout RS + vS(t) + – vin – Avin Rin + + – RL vL – Rin vin vS RS Rin RL vL Avin Rout RL Rin RL vS vL A RS Rin Rout RL NB: expression for vL depends on the source (RS) and the load (RL) ECEN 301 Discussion #17 – Operational Amplifiers 6 Ideal Amplifiers The gain can be made to be almost independent of the source (RS) and the load (RL) Let Rin → ∞ Let Rout → 0 Rout RS + vS(t) + – vin – Avin Rin + + – RL vL if R in : vin vS – Rin RS Rin vS if R out 0 vL Avin RL Rout RL Avin vL AvS NB: it is desirable for an amplifier to have: • a very large input impedance • a very small output impedance ECEN 301 Discussion #17 – Operational Amplifiers 7 Op-Amps Operational Amplifier: originally designed (late 1960’s) to perform mathematical operations (analog computer) Addition Subtraction Integration differentiation Positive power supply (usually +15V) VS+ Inverting Input – Output Noninverting Input + NB: the power supplies (VS+ and VS–) are often omitted in drawings – they are implicit VS– Negative power supply (usually –15V) ECEN 301 Discussion #17 – Operational Amplifiers 8 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) i1 i1 + vin + + v– v+ – – – – + i2 v– io – – Rin + Rout vin + vo AOLvin– + – + v+ + vo – i2 NB: op-amps have near-infinite input resistance (Rin) and very small output resistance (Rout) vo AOLvin AOL (v v ) ECEN 301 AOL – open-loop voltage gain Discussion #17 – Operational Amplifiers 9 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) i1 – – + vin + + v– + i2 v+ – io + Ideally i1 = i2 = 0 (since Rin → ∞) vo – – i1 i2 0 ECEN 301 Discussion #17 – Operational Amplifiers 10 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) i1 i2 0 ECEN 301 What? No input current?? In reality there is a small current Discussion #17 – Operational Amplifiers 11 Op-Amps – Closed-Loop Mode The Inverting Amplifier: the signal to be amplified is connected to the inverting terminal RF iF RS iS vS(t) + – v– – i1 v+ i2 + + vo – ECEN 301 Discussion #17 – Operational Amplifiers 12 Op-Amps – Closed-Loop Mode The Inverting Amplifier: the signal to be amplified is connected to the inverting terminal RF Feedback current: current from the output is fed back into the input of the op-amp Node a iF RS iS vS(t) + – v– – i1 v+ + + vo – vS v iS RS vo v iF RF i1 0 KCL at Node a : iS iF i1 0 iS iF ECEN 301 Discussion #17 – Operational Amplifiers 13 Op-Amps – Closed-Loop Mode The Inverting Amplifier: the signal to be amplified is connected to the inverting terminal RF From Open - Loop Model : iF RS iS vS(t) + – vo AOL (v v ) v– – AOL (0 v ) i1 v+ + vo – ECEN 301 AOLv + vo v AOL Discussion #17 – Operational Amplifiers 14 Op-Amps – Closed-Loop Mode The Inverting Amplifier: the signal to be amplified is connected to the inverting terminal RF iS iF vS v vo v RS RF iF RS iS vS(t) + – v– – i1 v+ + + vo – ECEN 301 vS vo / AOL vo vo / AOL RS RS R R F F vS v v v S o o RS RS AOL RF AOL RS 1 1 1 vS vo RF / RS AOL RF / RS AOL Discussion #17 – Operational Amplifiers 15 Op-Amps – Closed-Loop Mode The Inverting Amplifier: the signal to be amplified is connected to the inverting terminal RF 1 1 1 vS vo RF / RS AOL RF / RS AOL iF RS iS vS(t) + – v– – NB: if AOL is very large these terms → 0 i1 v+ + + vo – Closed - Loop Gain : A CL vo vS ECEN 301 Discussion #17 – Operational Amplifiers RF RS 16 Op-Amps – Closed-Loop Mode The Inverting Amplifier: the signal to be amplified is connected to the inverting terminal RF From Open - Loop Model : v v out AOL iF RS iS vS(t) + – v– – i1 v+ + + vo – NB: as AOL → ∞ v– → 0 As AOL v v ECEN 301 Discussion #17 – Operational Amplifiers 17 Op-Amps – Closed-Loop Mode The Inverting Amplifier: the signal to be amplified is connected to the inverting terminal RF NB: two important results for an ideal op-amp with negative feedback iF v– RS iS vS(t) + – – i1 v+ i2 + + vo – ECEN 301 i1 i2 0 v v Discussion #17 – Operational Amplifiers 18 Op-Amps – Closed-Loop Mode Example1: determine AOL and vo RS = 1kΩ, RF = 10kΩ, vs(t) = Acos(ωt), A=0.015, ω = 50 rads/s RF iF RS iS vS(t) + – v– – i1 v+ + + vo – ECEN 301 Discussion #17 – Operational Amplifiers 19 Op-Amps – Closed-Loop Mode Example1: determine AOL and vo RS = 1kΩ, RF = 10kΩ, vs(t) = Acos(ωt), A=0.015, ω = 50 rads/s RF A CL iF RS iS vS(t) + – v– vo – i1 v+ + R vo F vS RS + vo RF vS RS 10 4 3 0.015 cos(t ) 10 0.15 cos(t ) – A CL RF RS 10 ECEN 301 Discussion #17 – Operational Amplifiers 20 Op-Amps – Closed-Loop Mode Example1: determine AOL and vo RS = 1kΩ, RF = 10kΩ, vs(t) = Acos(ωt), A=0.015, ω = 50 rads/s RF iF iS vS(t) + – 0.10 – i1 v+ + + vo – Voltage (V) RS 0.15 v– 0.05 vs(t) 0.00 vo(t) -0.05 -0.10 -0.15 0.0 0.2 0.4 0.6 0.8 1.0 time (s) ECEN 301 Discussion #17 – Operational Amplifiers 21 Op-Amps – Closed-Loop Mode Example2: What is the min/max gain, and gain uncertainty if 5% tolerance resistors are used? RS = 1kΩ, RF = 10kΩ, vs(t) = Acos(ωt), A=0.015, ω = 50 rads/s RF A CL nom 10 iF RS iS vS(t) + – v– – i1 v+ + + vo A CL min RF min RS max A CL max RF max RS min 9500 1050 9.05 10500 950 11.05 Discussion #17 – Operational Amplifiers 22 – ECEN 301 NB: nominal gain Op-Amps – Closed-Loop Mode Example2: What is the min/max gain, and gain uncertainty if 5% tolerance resistors are used? RS = 1kΩ, RF = 10kΩ, vs(t) = Acos(ωt), A=0.015, ω = 50 rads/s RF iF RS iS vS(t) + – – A CL nom 10 9.05 10 9.5% i1 + 100 A CL nom A CL min 100 v– v+ Max % Error : + vo – Min % Error : 100 A CL nom A CL max A CL nom 10 11.05 10 10.5% 100 ECEN 301 Discussion #17 – Operational Amplifiers 23 Op-Amps – Closed-Loop Mode The Summing Amplifier: sources are summed together independently of load and source impedances RF RS1 vS1(t) + – – – i1 RS2 vS2(t) + iF v– v+ + + vo i2 – RSN vSN(t) + – ECEN 301 iN Discussion #17 – Operational Amplifiers 24 Op-Amps – Closed-Loop Mode The Summing Amplifier: sources are summed together independently of load and source impedances RF Node a RS1 vS1(t) + – – KCL at Node a : – i1 RS2 vS2(t) + iF v– v+ + + i1 i2 iN iF vo i2 – NB: v– = v+ = 0 RSN vSN(t) + – ECEN 301 iN vSn in RSn n 1, 2, , N Discussion #17 – Operational Amplifiers vo iF RF 25 Op-Amps – Closed-Loop Mode The Summing Amplifier: sources are summed together independently of load and source impedances RF Node a RS1 vS1(t) + – – ECEN 301 N v+ + + vo i2 RSN vSN(t) + – i1 RS2 vS2(t) + – iF v– – vsn vo RF n 1 Rsn N RF vo vsn n 1 Rsn iN Discussion #17 – Operational Amplifiers 26 Op-Amps – Closed-Loop Mode The Noninverting Amplifier: the signal to be amplified is connected to the noninverting terminal RF iF RS iS vS(t) + – ECEN 301 R v– – i1 v+ + + i1 vo – Discussion #17 – Operational Amplifiers 27 Op-Amps – Closed-Loop Mode The Noninverting Amplifier: the signal to be amplified is connected to the noninverting terminal RF Node a iF RS iS vS(t) + – ECEN 301 R v iS S RS v– – vo v iF RF i1 0 i1 v+ + + i1 vo KCL at Node a : iS iF i1 0 – Discussion #17 – Operational Amplifiers iS iF 28 Op-Amps – Closed-Loop Mode The Noninverting Amplifier: the signal to be amplified is connected to the noninverting terminal RF Since i1 0 : Node a (i.e. no current th rough R no voltage drop) iF RS iS vS(t) + – R v vS v v– – i1 v+ + + i1 vo – i F iS vo v S v S RF RS RF vo 1 vS RS ECEN 301 Discussion #17 – Operational Amplifiers 29 Op-Amps – Closed-Loop Mode The Noninverting Amplifier: the signal to be amplified is connected to the noninverting terminal RF Node a Closed - Loop Gain : iF RS iS vS(t) + – R v– A CL – i1 v+ + + i1 vo – vo vS RF 1 RS NB: always positive and greater than or equal to 1 ECEN 301 Discussion #17 – Operational Amplifiers 30 Op-Amps – Closed-Loop Mode Voltage Follower: the voltage on the output of the op-amp is equal to the source voltage v– – i1 v+ + + i1 vS(t) + – ECEN 301 vo – Discussion #17 – Operational Amplifiers 31 Op-Amps – Closed-Loop Mode Voltage Follower: the voltage on the output of the op-amp is equal to the source voltage NB: an ideal op-amp with negative feedback has the property v– – v v i1 v+ + + i1 vS(t) + – ECEN 301 vo – v vs v vo vo vS Discussion #17 – Operational Amplifiers 32 Op-Amps – Closed-Loop Mode Voltage Follower: the voltage on the output of the op-amp is equal to the source voltage ib Circuit 1 + va – Circuit 1 + vb – Circuit 2 If va ≠ vb ib is the load current Loading: changing the behaviour of one circuit by connecting another circuit to it ECEN 301 Discussion #17 – Operational Amplifiers 33 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 (ib = 0) Loading: changing the behaviour of one circuit by connecting another circuit to it ECEN 301 Discussion #17 – Operational Amplifiers 34