ENGS2613 Intro Electrical Science Week 8 Dr. George Scheets Read 5.5 – 5.7 Problems 5.8, 9, 12, 14, 19, 23, 28, 30, & 31 Next Quiz Friday 24 March Chapter 5 OpAmps Will not have +Vcc & -Vcc defined So don't worry about hitting a power supply rail Quiz 4 Results Hi = 10, Low = 2, Ave = 5.71, Deviation = 1.95 No adjustments to scores required.

Quiz #5 Friday, 24 March Closed Book & Neighbor Up to 3 unattached sheets of notes OK Keep on your desk Have them on hand before you start Calculator OK Smart Phones NOT OK Reaching down for something in backpack? Get permission first All we're doing Friday

OpAmps High Gain Devices High Input Resistance Typically, Voltage Gain = Vout/Vin > 10,000 Vout(t) = [Vp(t) – Vn(t)]*Voltage Gain High Input Resistance Rin typically > 1 MΩ Ignore current into or exiting OpAmp input So long as external resistors < Rin/10

Op Amp Characteristics +Vcc vp(t) Av Rin + vout(t) = Av(vp(t)-vn(t)) vn(t) - -Vcc Rin? In M ohms Voltage gain Av? On order of 104 - 106

OpAmps High Gain Devices High Input Resistance Negative Feedback? Typically, Voltage Gain > 10,000 Vout(t) = [Vp(t) – Vn(t)]*Voltage Gain High Input Resistance Rin typically > 1 MΩ Ignore current entering OpAmp input So long as external resistors < Rin/10 Negative Feedback? Assume Vp(t) = Vn(t) a.k.a. Virtual Short

OpAmps On quizzes & tests, assume Ideal OpAmp… Voltage Gain = ∞ Input impedance = ∞ Absolutely no current enters/exits OpAmp input side Current will generally enter or exit OpAmp output Output can source or sink any value Vp = Vn if negative feedback Output doesn't hit Power Supply rails If +Vcc & -Vcc not shown … unless specifically stated otherwise

OpAmps (Analysis Assumptions) Is there negative feedback? Generally, must be "Yes" to be Linear Yes? Set Vp = Vn No? Output likely to hit power supply rail Assume no current thru OpAmp input Analyze Ohm's Law Kirchoff's Current Law Kirchoff's Voltage Law

Op Amps: No Feedback Av Output likely to hit rails Use: Comparator +Vcc Av + vout(t) = Av(vp(t)-vn(t)) vin(t) - -Vcc Output likely to hit rails Unless tiny voltage Use: Comparator Compares two voltages Yields binary output

Op Amps: Positive Feedback & No Negative Feedback Av vout(t) = Av[vp(t) - 0] + vin(t) 0 v - Output likely to hit rails May get stuck there Use: None Suppose |Vcc| = 15 v

Op Amps: Positive Feedback 10 v if feedback & input resistors = 5 v Av vout(t) = Av[vp(t) - 0] + vin(t) 15 v - Output likely to hit rails May get stuck there Suppose |Vcc| = 15 v

Op Amps: Positive Feedback 7.5 v if feedback & input resistors = 0 v Av vout(t) = Av[vp(t) - 0] + vin(t) 15 v - Output likely to hit rails May get stuck there Suppose |Vcc| = 15 v

Op Amps: Positive Feedback ≈ 0 v if feedback & input resistors = -15 v Av vout(t) = Av[vp(t) - 0] + vin(t) 15 v - Suppose |Vcc| = 15 v Vp slightly > 0? Vout can be stuck at 15 V Vp exactly = 0? Unstable. Vout will end up at -15 V Vp slightly < 0 Vout rockets to -15 V

Op Amps: Negative Feedback Av vout(t) = Av[vp(t)-vn(t)] - vin(t) + 0 v Safe to assume vp(t) = vn(t) Assume no current enters Op Amp If low R outside paths exist

Op Amps: Negative Feedback vout(t) = Av[v+(t) – v-(t)] 0 v 5 v Av - vin(t) 0 v + Stable System Linear so long as don't hit Power Supply Limits & get Clipped Output Suppose |Vcc| = 15 v

Op Amps: Negative Feedback (Ideal) Av vout(t) - vin(t) -5.0 v + Suppose… OpAmp Voltage Gain = ∞ External elements are Resistors of R Ω V+ = V-

Op Amps: Negative Feedback (Actual) vout(t) = 10,000[v+(t) – v-(t)] 5 v Av - vin(t) -4.999 v + Suppose… OpAmp Voltage Gain = 10,000 OpAmp Input Impedance = ∞ External elements are Resistors of R Ω

OpAmps (Analysis Assumptions) No Current enters or exits inputs Effectively, the OpAmp input isn't there But Negative Feedback make Vp = Vn - + vout 1 Ω 5 Ω 10 Ω vin |Vcc| = 25v Av = 10,000 - + vout 1 Ω 5 Ω 10 Ω vin |Vcc| = 25v Av = 10,000

OpAmps (Analysis Assumptions) Look for Negative Feedback If yes, set Vp(t) = Vn(t) If no, Vp(t) ≠ Vn(t) Vout(t) = [Vp(t) – Vn(t)]*Voltage Gain Output will probably hit a power supply rail - + vout 1 Ω 5 Ω 10 Ω vin |Vcc| = 25v Av = 10,000 I Have Negative Feedback Here → V- = V+ = Vout(1/11) [Vin – V-]/5 = I = [V- – Vout]/1 [Vin – Vout/11]/5 = [Vout/11 – Vout] → Vout/Vin = -11/49

Max output current = 35 – 40 ma 5v in? I2R = 1.040 W 1.020a |Vcc| = 25v Av = 10,000 -.1020v 1 Ω 1.020a - 5v 5 Ω + -11/49*5v = -1.122v -.1020v Opamp Output must sink 1.122 amps 10 Ω 1 Ω .1020a .1020a LM741 can't do it. Max output current = 35 – 40 ma

OpAmps: External Resistors |Vcc| = 25v Av = 10,000 Rin = 1 MΩ -.1020v 1 Ω 1.020a - 5v 5 Ω + -11/49*5v = -1.122v -.1020v Generally not too small: X or XX Ohms. Current flows too large. 10 Ω 1 Ω .1020a .1020a

Max output current = 35 – 40 ma 5v in? I2R = 10.4 mW 1.020 ma |Vcc| = 25v Av = 10,000 Rin = 1 MΩ -.1020v 10K Ω 1.020 ma - 5v 5K Ω + -11/49*5v = -1.122v -.1020v Opamp Output must sink 1.122 m amps 10K Ω 1K Ω 102.0 μa 102.0 μa LM741 can do it. Max output current = 35 – 40 ma

OpAmps? External Resistors 1.020 ma |Vcc| = 25v Av = 10,000 Rin = 1 MΩ -.1020v 10K Ω 1.020 ma - 5v 5K Ω + -11/49*5v = -1.122v -.1020v Just Right if in X or XX K Ohm range 10K Ω 1K Ω 102.0 μa 102.0 μa

OpAmps: External Resistors |Vcc| = 25v Av = 10,000 Rin = 1 MΩ 1 MΩ 10 μa - 5 MΩ + Generally too large: X or XX M Ohms. Current flows in/out OpAmp inputs cannot be ignored. 10 MΩ 1 MΩ

Op Amps: Output Load Av Ideally, load does not effect characteristics - vout(t) vin(t) + Rload Ideally, load does not effect characteristics Practically, load may effect characteristics If Op Amp output can't source or sink enough current

Voltage gain is independent of load if 25v in? |Vcc| = 25v Av = 10,000 5.102 ma -.5102 v LM741 can sink 35 – 40 ma 10K Ω 5.102 ma - 25v -11/49*25v = -5.612 v 5K Ω + LM741 can sink additional 29.80 – 34.80 ma -.5102 v RL 10K Ω 1K Ω 102.0 μa Voltage gain is independent of load if load > 5.612/.0298 = 188.3 Ω 510.2 μa

Current & Voltage Values are Incorrect 5v in & 10 Ω Load? |Vcc| = 25v Av = 10,000 1.020 ma -.1020v LM741 can sink 35 – 40 ma 10K Ω 1.020 ma - 5v -11/49*5v = -1.122v 5K Ω + I_load I_load = 1.122/10 = 112 mA LM741 can't sink this!! 10 Ω -.1020v 10K Ω 1K Ω 102.0 μa 102.0 μa Current & Voltage Values are Incorrect

5v in? Operating outside OpAmp's Comfort Zone? Voltages & Currents may not be as expected. Here sunk current maxes out at 40 mA. 269.8 μA 3.651 V 10K Ω 269.8 μA - 5v -0.3960 V vout 1 Ω 5 Ω 10 Ω 5v 40 mA 5K Ω + 0.03960 A 10 Ω -.03600 V 10K Ω 1K Ω 36.00 μA 36.00 μA

OpAmp with Positive & Negative Feedback Do see Real World Use In Reality: May have some instability issues Ideally: Tend to be stable On Quiz or Test Analyze as if stable Vp = Vn Circuit gain Vout/Vin super high? Indication system is possibly unstable - + vout 1 Ω 5 Ω 10 Ω vin |Vcc| = 25v Av = 10,000