Schedule Date Day Class Title Chapters HW Lab Exam No. Due - PowerPoint PPT Presentation

Schedule… Date Day Class Title Chapters HW Lab Exam No. Due date Due date 8.1 – 8.2 29 Oct Wed 17 Operational Amplifiers 30 Oct Thu 31 Oct Fri Recitation HW 7 1 Nov Sat 2 Nov Sun 8.3 – 8.4 3 Nov Mon 18 Operational Amplifiers LAB 6 4 Nov Tue 13.1 – 13.2 5 Nov Wed 19 Binary Numbers Discussion #17 – Operational Amplifiers ECEN 301 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. Discussion #17 – Operational Amplifiers ECEN 301 2

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

Ideal Amplifiers Amplifier : a device for increasing the power of a signal.  Power increase is called gain ( A ) R S + + v S (t) v L Gain A R L – CD 0:21 – Source Amplifier Load Source Load Amplifier ( ) ( ) v t Av t L S Discussion #17 – Operational Amplifiers ECEN 301 4

Ideal Amplifiers Simplified Amplifier Model :  The source ―sees‖ and equivalent load ( R in )  The load ―sees‖ and equivalent source ( Av in ) R S R out R S + + + Av in + v S (t) + + v L Gain A R L v S (t) R L – v L v in R in – – – – – Source Load Amplifier NB : Thévenin NB : equivalent equivalent resistance Discussion #17 – Operational Amplifiers ECEN 301 5

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

Ideal Amplifiers The gain can be made to be almost independent of the source ( R S ) and the load ( R L )  Let R in → ∞  Let R out → 0 R out R S if R : if R 0 in out + + Av in R R in + + L v v v Av v S (t) R L v L v in in S L in R in R R R R – – out L S in – Av – v in S v Av L S NB : it is desirable for an amplifier to have: • a very large input impedance • a very small output impedance Discussion #17 – Operational Amplifiers ECEN 301 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) + V S – + NB : the power supplies ( V S Inverting Input – ) are often omitted in and V S Output drawings – they are implicit + Noninverting Input – V S Negative power supply (usually – 15V) Discussion #17 – Operational Amplifiers ECEN 301 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) i 1 i 1 v – – – – i o – + v in R in R out + + + v in + i 2 + v – + v o – A OL v in v + + + v o – v + – – – i 2 NB : op-amps have near-infinite input resistance ( R in ) and very small output resistance ( R out ) v A v o OL in A OL – open-loop voltage gain A ( v v ) OL Discussion #17 – Operational Amplifiers ECEN 301 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) i 1 – – i o + v in + Ideally i 1 = i 2 = 0 + + + (since R in → ∞) i 2 v – v o v + – – – 0 i i 1 2 Discussion #17 – Operational Amplifiers ECEN 301 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) What? No input current?? 0 i i In reality there is a small current 1 2 Discussion #17 – Operational Amplifiers ECEN 301 11

Op-Amps – Closed-Loop Mode The Inverting Amplifier : the signal to be amplified is connected to the inverting terminal R F i F v – R S – i 1 i S + + v + + v S (t) – i 2 v o – Discussion #17 – Operational Amplifiers ECEN 301 12

Op-Amps – Closed-Loop Mode The Inverting Amplifier : the signal to be amplified is connected to the inverting terminal R F Feedback current : current from the output Node a is fed back into the input of the op-amp i F v – R S – v v v v i 1 o S i i i 0 i S S F 1 R R + + S F v + + v S (t) – v o KCL at No de a : – i i i 0 S F 1 i i S F Discussion #17 – Operational Amplifiers ECEN 301 13

Op-Amps – Closed-Loop Mode The Inverting Amplifier : the signal to be amplified is connected to the inverting terminal R F From Open - Loop Model : i F v – ( ) v A v v R S OL o – ( 0 ) A v i 1 OL i S + + A v v + + OL v S (t) – v v o o v A – OL Discussion #17 – Operational Amplifiers ECEN 301 14

Op-Amps – Closed-Loop Mode The Inverting Amplifier : the signal to be amplified is connected to the inverting terminal R F i i S F i F v v v v S o v – R S R R – S F i 1 v v / A v v / A i S S o OL o o OL + + R R R R v + S S F F + v S (t) v v v v – v o S S o o R R A R A R S S OL F OL S – 1 1 1 v v S o R / R A R / R A F S OL F S OL Discussion #17 – Operational Amplifiers ECEN 301 15

Op-Amps – Closed-Loop Mode The Inverting Amplifier : the signal to be amplified is connected to the inverting terminal R F 1 1 1 v v S o R / R A R / R A i F F S OL F S OL v – R S – NB : if A OL is very large these terms → 0 i 1 i S + + Closed - Loop Gain : v + + v S (t) – v v o o A CL v – S R F R S Discussion #17 – Operational Amplifiers ECEN 301 16

Op-Amps – Closed-Loop Mode The Inverting Amplifier : the signal to be amplified is connected to the inverting terminal R F From Open - Loop Model : v i F out v v – R S A – OL i 1 i S NB : as A OL → ∞ v – → 0 + + v + + v S (t) – v o As A OL – v v Discussion #17 – Operational Amplifiers ECEN 301 17

Op-Amps – Closed-Loop Mode The Inverting Amplifier : the signal to be amplified is connected to the inverting terminal R F NB : two important results for an ideal i F op-amp with negative feedback v – R S – i 1 i S + 0 + i i v + + v S (t) 1 2 – i 2 v o v v – Discussion #17 – Operational Amplifiers ECEN 301 18

Op-Amps – Closed-Loop Mode Example1 : determine A OL and v o R S = 1k Ω , R F = 10k Ω , v s (t) = Acos( ω t), A=0.015, ω = 50 rads/s R F i F v – R S – i 1 i S + + v + + v S (t) – v o – Discussion #17 – Operational Amplifiers ECEN 301 19

Op-Amps – Closed-Loop Mode Example1 : determine A OL and v o R S = 1k Ω , R F = 10k Ω , v s (t) = Acos( ω t), A=0.015, ω = 50 rads/s R F R v o F A CL v R S S i F v – R R S F v v – o S R S i 1 i S 4 10 + + 0 . 015 cos( ) t v + + 3 10 v S (t) – v o 0 . 15 cos( t ) – R F A CL R S 10 Discussion #17 – Operational Amplifiers ECEN 301 20

Op-Amps – Closed-Loop Mode Example1 : determine A OL and v o R S = 1k Ω , R F = 10k Ω , v s (t) = Acos( ω t), A=0.015, ω = 50 rads/s R F i F 0.15 v – R S 0.10 – Voltage (V) 0.05 i 1 i S vs(t) 0.00 + vo(t) + v + -0.05 + v S (t) – -0.10 v o -0.15 0.0 0.2 0.4 0.6 0.8 1.0 – time (s) Discussion #17 – Operational Amplifiers ECEN 301 21

Op-Amps – Closed-Loop Mode Example2 : What is the min/max gain, and gain uncertainty if 5% tolerance resistors are used? R S = 1k Ω , R F = 10k Ω , v s (t) = Acos( ω t), A=0.015, ω = 50 rads/s R F A 10 NB : nominal gain CL nom i F v – R S – R R i 1 i S F max F min A A CL max + + CL min R R v + + S min S max v S (t) – v o 10500 9500 – 950 1050 11 . 05 9 . 05 Discussion #17 – Operational Amplifiers ECEN 301 22

Op-Amps – Closed-Loop Mode Example2 : What is the min/max gain, and gain uncertainty if 5% tolerance resistors are used? R S = 1k Ω , R F = 10k Ω , v s (t) = Acos( ω t), Max % Error : A=0.015, ω = 50 rads/s A A R F CL nom CL min 100 A CL nom i F 10 9.05 v – 100 R S 10 – 9 . 5 % i 1 i S + + Min % Error : v + + v S (t) A A – v o CL nom CL max 100 A CL nom – 10 11.05 100 10 10 . 5 % Discussion #17 – Operational Amplifiers ECEN 301 23

Op-Amps – Closed-Loop Mode The Summing Amplifier : sources are summed together independently of load and source impedances R F i F v – R S1 – + v S1 (t) i 1 – + + v + R S2 v o + v S2 (t) i 2 – – R SN v SN (t) + i N – Discussion #17 – Operational Amplifiers ECEN 301 24