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ENGR-43_Lec-14a_IDeal_Op_Amps.pptx 1 Bruce Mayer, PE Engineering-43: Engineering Circuit Analysis Bruce Mayer, PE Licensed Electrical.

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Presentation on theme: "ENGR-43_Lec-14a_IDeal_Op_Amps.pptx 1 Bruce Mayer, PE Engineering-43: Engineering Circuit Analysis Bruce Mayer, PE Licensed Electrical."— Presentation transcript:

1 ENGR-43_Lec-14a_IDeal_Op_Amps.pptx 1 Bruce Mayer, PE Engineering-43: Engineering Circuit Analysis Bruce Mayer, PE Licensed Electrical & Mechanical Engineer Engineering 43 Chp 14-1 Op Amp Circuits

2 ENGR-43_Lec-14a_IDeal_Op_Amps.pptx 2 Bruce Mayer, PE Engineering-43: Engineering Circuit Analysis Ckts W/ Operational Amplifiers  OpAmp Utility 1.OpAmps Are Very Useful Electronic Components 2.We Have Already Developed The Tools To Analyze Practical OpAmp Circuits 3.The Linear Models for OpAmps Include Dependent Sources –A PRACTICAL Application of Dependent Srcs

3 ENGR-43_Lec-14a_IDeal_Op_Amps.pptx 3 Bruce Mayer, PE Engineering-43: Engineering Circuit Analysis Real Op Amps  Physical Size Progression of OpAmps Over the Years Maxim (Sunnyvale, CA) Max4241 OpAmp LM324 DIP LMC6294 MAX4240

4 ENGR-43_Lec-14a_IDeal_Op_Amps.pptx 4 Bruce Mayer, PE Engineering-43: Engineering Circuit Analysis Apex PA03 HiPwr OpAmp  Notice OutPut Rating V  PwrOut → 30A75V → 2.25 kW!

5 ENGR-43_Lec-14a_IDeal_Op_Amps.pptx 5 Bruce Mayer, PE Engineering-43: Engineering Circuit Analysis OpAmp Symbol & Model  The Circuit Symbol Is a Version of the Amplifier TRIANGLE  The Linear Model Typical Values OUTPUT RESISTANCE INPUT RESISTANCE GAIN

6 ENGR-43_Lec-14a_IDeal_Op_Amps.pptx 6 Bruce Mayer, PE Engineering-43: Engineering Circuit Analysis OpAmp InPut Terminolgy  The Average of the two Input Voltages is called the Common-Mode Signal  The Difference between the Inputs is called the Differential-Signal, v id

7 ENGR-43_Lec-14a_IDeal_Op_Amps.pptx 7 Bruce Mayer, PE Engineering-43: Engineering Circuit Analysis OpAmp Power Connections  BiPolar Power Supplies  UniPolar Supply  For Signal I/O Analysis the Supplies Need NOT be shown explicitly But they MUST physically be there to actually Power the Operational Amplifier

8 ENGR-43_Lec-14a_IDeal_Op_Amps.pptx 8 Bruce Mayer, PE Engineering-43: Engineering Circuit Analysis OpAmp Circuit Model DRIVING CIRCUIT LOAD OP-AMP

9 ENGR-43_Lec-14a_IDeal_Op_Amps.pptx 9 Bruce Mayer, PE Engineering-43: Engineering Circuit Analysis v i →v o Transfer Characteristics Saturation  The OUTPUT Voltage Level can NOT exceed the SUPPLY the Level Linear Region v o /v i = Const

10 ENGR-43_Lec-14a_IDeal_Op_Amps.pptx 10 Bruce Mayer, PE Engineering-43: Engineering Circuit Analysis Unity Gain Buffer (FeedBack)  Controlling Variable =  Solve For Buffer Gain (I = V in /R i )  Thus The Amplification FeedBack Loop

11 ENGR-43_Lec-14a_IDeal_Op_Amps.pptx 11 Bruce Mayer, PE Engineering-43: Engineering Circuit Analysis UGB Algebra

12 ENGR-43_Lec-14a_IDeal_Op_Amps.pptx 12 Bruce Mayer, PE Engineering-43: Engineering Circuit Analysis The Ideal OpAmp  The IDEAL Characteristics R o = 0 R i =  A =  (open loop gain) BW =   The Consequences of Ideality

13 ENGR-43_Lec-14a_IDeal_Op_Amps.pptx 13 Bruce Mayer, PE Engineering-43: Engineering Circuit Analysis Summing Point Constraint  The MOST important aspects of Ideality: R i = ∞ → i + = i − = 0 –The OpAmp INput looks like an OPEN Circuit A = ∞ → v + = v − –The OpAmp Input looks like a SHORT Circuit  This simultaneous OPEN & SHORT Characteristic is called the →  SUMMING POINT CONSTRAINT Looks Like an OPEN to Current Looks Like a SHORT to Voltage

14 ENGR-43_Lec-14a_IDeal_Op_Amps.pptx 14 Bruce Mayer, PE Engineering-43: Engineering Circuit Analysis Analyzing Ideal OpAmp Ckts 1.Verify the presence of NEGATIVE FeedBack 2.Assume the Summing Point Constraint Applies in this fashion: i + = i − = 0 (based on R i = ∞) v + − v − = 0 (based on A O = ∞) 3.Use KVL, KCL, Ohm’s Law, and other linear ckt analysis techniques to determine quantities of interest

15 ENGR-43_Lec-14a_IDeal_Op_Amps.pptx 15 Bruce Mayer, PE Engineering-43: Engineering Circuit Analysis Voltage Follower  The Voltage Follower Also Called Unity Gain Buffer (UGB) from Before Connection w/o BufferBuffered Connection  The SOURCE Supplies The Power  The Source Supplies NO Power (the OpAmp does it)  Usefulness of UGB

16 ENGR-43_Lec-14a_IDeal_Op_Amps.pptx 16 Bruce Mayer, PE Engineering-43: Engineering Circuit Analysis Inverting OpAmp Ckt  Determine Voltage Gain, G = V out /V in  Start with A o  Now From Input R  Apply KCL at v −  Finally The Gain  Next: Examine Ckt w/o Ideality Assumption

17 ENGR-43_Lec-14a_IDeal_Op_Amps.pptx 17 Bruce Mayer, PE Engineering-43: Engineering Circuit Analysis Replace OpAmp w/ Linear Model  Consider Again the Inverting OpAmp Circuit  Draw the Linear Model 1.Identify the Op Amp Nodes

18 ENGR-43_Lec-14a_IDeal_Op_Amps.pptx 18 Bruce Mayer, PE Engineering-43: Engineering Circuit Analysis Drawing the OpAmp Linear Model 2.Redraw the circuit cutting out the Op Amp 3.Draw components of linear OpAmp (on the circuit of step-2) i R

19 ENGR-43_Lec-14a_IDeal_Op_Amps.pptx 19 Bruce Mayer, PE Engineering-43: Engineering Circuit Analysis Drawing the OpAmp Linear Model 4.UNTANGLE as Needed  The BEFORE & AFTER

20 ENGR-43_Lec-14a_IDeal_Op_Amps.pptx 20 Bruce Mayer, PE Engineering-43: Engineering Circuit Analysis NonIdeal Inverting Amp  Replace the OpAmp with the LINEAR Model Label Nodes for Tracking  Draw The Linear Equivalent For Op-amp  Note the External Component Branches b - ab - d

21 ENGR-43_Lec-14a_IDeal_Op_Amps.pptx 21 Bruce Mayer, PE Engineering-43: Engineering Circuit Analysis NonIdeal Inverting Amp cont.  On The LINEAR Model Connect The External Components  ReDraw Ckt for Increased Clarity  Now Must Sweat the Details

22 ENGR-43_Lec-14a_IDeal_Op_Amps.pptx 22 Bruce Mayer, PE Engineering-43: Engineering Circuit Analysis NonIdeal Inverting Amp cont.  Node Analysis Note GND Node  Controlling Variable In Terms Of Node Voltages  The 2 Eqns in Matrix Form 2

23 ENGR-43_Lec-14a_IDeal_Op_Amps.pptx 23 Bruce Mayer, PE Engineering-43: Engineering Circuit Analysis Inverting Amp – Invert Matrix  Use Matrix Inversion to Solve 2 Eqns in 2 Unknowns Very Useful for 3 Eqn/Unknwn Systems as well –e.g.,  The Matrix Determinant   Solve for v o

24 ENGR-43_Lec-14a_IDeal_Op_Amps.pptx 24 Bruce Mayer, PE Engineering-43: Engineering Circuit Analysis Inverting Amp – Invert Matrix cont  Then the System Gain  Typical Practical Values for the Resistances R 1 = 1 kΩR 2 = 5 kΩ  Then the Real-World Gain  Recall The Ideal Case for A→  ; Then The Eqn at top

25 ENGR-43_Lec-14a_IDeal_Op_Amps.pptx 25 Bruce Mayer, PE Engineering-43: Engineering Circuit Analysis Compare Ideal vs. NonIdeal  Ideal Assumptions  Gain for Real Case Replace Op-amp By Linear Model, Solve The Resulting Circuit With Dep. Sources

26 ENGR-43_Lec-14a_IDeal_Op_Amps.pptx 26 Bruce Mayer, PE Engineering-43: Engineering Circuit Analysis Compare Ideal vs. NonIdeal cont.  Ideal Case at Inverting Terminal  Gain for NonIdeal Case  The Ideal Op- amp Assumption Provides an Excellent Real-World Approximation.  Unless Forced to do Otherwise We Will Always Use the IDEAL Model

27 ENGR-43_Lec-14a_IDeal_Op_Amps.pptx 27 Bruce Mayer, PE Engineering-43: Engineering Circuit Analysis Example  Differential Amp  KCL At Inverting Term  KCL at NONinverting Terminal  Assume Ideal OpAmp  By The KCLs A simple Voltage Divider

28 ENGR-43_Lec-14a_IDeal_Op_Amps.pptx 28 Bruce Mayer, PE Engineering-43: Engineering Circuit Analysis Example  Differential Amp cont  Then in The Ideal Case  Now Set External R’s R 4 = R 2 R 3 = R 1  Subbing the R’s Into the v o Eqn

29 ENGR-43_Lec-14a_IDeal_Op_Amps.pptx 29 Bruce Mayer, PE Engineering-43: Engineering Circuit Analysis Ex. Precision Diff V-Gain Ckt  Find v o  Assume Ideal OpAmps Which Voltages are Set? What Voltages Are Also Known Due To Infinite Gain Assumption? Now Use The Infinite Resistance Assumption  CAUTION: There could be currents flowing INto or OUTof the OpAmps

30 ENGR-43_Lec-14a_IDeal_Op_Amps.pptx 30 Bruce Mayer, PE Engineering-43: Engineering Circuit Analysis Ex. Precision Diff V-Gain Ckt cont  The Ckt Reduces To Fig. at Right  KCL at v 1  KCL at v 2  Eliminate v a Using The above Eqns and Solve for v o in terms of v 1 & v 2 Note the increased Gain over Diff Amp OpAmp Current

31 ENGR-43_Lec-14a_IDeal_Op_Amps.pptx 31 Bruce Mayer, PE Engineering-43: Engineering Circuit Analysis NONinverting Amp - Ideal  Ideal Assumptions Infinite Gain  Since i − = 0 Arrive at “Inverse Voltage Divider” Infinite R i with v + = v 1

32 ENGR-43_Lec-14a_IDeal_Op_Amps.pptx 32 Bruce Mayer, PE Engineering-43: Engineering Circuit Analysis Example  Find I o for Ideal OpAmp  Ideal Assumptions  KCL at v −

33 ENGR-43_Lec-14a_IDeal_Op_Amps.pptx 33 Bruce Mayer, PE Engineering-43: Engineering Circuit Analysis Example: TransResistance Ckt  The trans-resistance Amp circuit below performs Current to Voltage Conversion Find v o /i S  Use the Summing Point Constraint → v − = 0V Now by KCL at v − Node with i − = 0 –Notice that i S flows thru the 1Ω resistor –Thus by Ohm’s Law

34 ENGR-43_Lec-14a_IDeal_Op_Amps.pptx 34 Bruce Mayer, PE Engineering-43: Engineering Circuit Analysis Key to OpAmp Ckt Analysis  I OA  Remember that the “Nose” of the OpAmp “Triangle” can SOURCE or SINK “Infinite” amounts of Current I OA = ± ∞ | I OA,max | = I sat

35 ENGR-43_Lec-14a_IDeal_Op_Amps.pptx 35 Bruce Mayer, PE Engineering-43: Engineering Circuit Analysis Example: TransResistance Ckt  Notice that the OpAmp Absorbs ALL of the Source Current  The (Ideal) OpAmp will Source or Sink Current Out-Of or In-To its “nose” to maintain the V-Constraint: v + = v −

36 ENGR-43_Lec-14a_IDeal_Op_Amps.pptx 36 Bruce Mayer, PE Engineering-43: Engineering Circuit Analysis Example: TransConductance Ckt  The transonductance Amp circuit below performs Voltage to Current Conversion Find i o /v 1  Use the Summing Point Constraint → v − = v + → i − = i + = 0  Thus v − = v 1  Then by KCL & Ohm Notice the Output is Insensitive to Load Resistance 0 0

37 ENGR-43_Lec-14a_IDeal_Op_Amps.pptx 37 Bruce Mayer, PE Engineering-43: Engineering Circuit Analysis Example: Summing Amp Circuit  Label Important Quantities  By Virtual Short (v + =v − ) Across OpAmp Inputs  Also by Summing Point Contstraint (i + = i − =0) KCL at v f node

38 ENGR-43_Lec-14a_IDeal_Op_Amps.pptx 38 Bruce Mayer, PE Engineering-43: Engineering Circuit Analysis Example: Summing Amp Circuit  Use Ohm for i A & i B  Also by Ohm Thru R f

39 ENGR-43_Lec-14a_IDeal_Op_Amps.pptx 39 Bruce Mayer, PE Engineering-43: Engineering Circuit Analysis Example: Summing Amp Circuit  Recall i A & i B  Sub for i A & i B  But by Virtual Short v f =0; Thus after ReArranging

40 ENGR-43_Lec-14a_IDeal_Op_Amps.pptx 40 Bruce Mayer, PE Engineering-43: Engineering Circuit Analysis Example: Summing Amp Circuit  Input Resistances:  Similarly for R inB

41 ENGR-43_Lec-14a_IDeal_Op_Amps.pptx 41 Bruce Mayer, PE Engineering-43: Engineering Circuit Analysis Example: Summing Amp Circuit  For the OUTput Resistance as seen by the LOAD, put the Circuit in a “Black Box”  Thévenizing the Black Box  Recall v o

42 ENGR-43_Lec-14a_IDeal_Op_Amps.pptx 42 Bruce Mayer, PE Engineering-43: Engineering Circuit Analysis Example: Summing Amp Circuit  Thus Have  From the LOAD Perspective Expect  But the Previous analysis v o does NOT depend on R L at ALL  If v L = v o in all cases then have Since v o is Not affected by R L, then R o = 0

43 ENGR-43_Lec-14a_IDeal_Op_Amps.pptx 43 Bruce Mayer, PE Engineering-43: Engineering Circuit Analysis Example: Summing Summary

44 ENGR-43_Lec-14a_IDeal_Op_Amps.pptx 44 Bruce Mayer, PE Engineering-43: Engineering Circuit Analysis Example: I & V Inputs  Required Find the expression for v o. Indicate where and how Ideal OpAmp assumptions Are Used  Infinite Gain Assumption Fixes v −  Use Infinite Input Resistance Assumption  Apply KCL to Inverting Input  Then Solving  Set Voltages

45 ENGR-43_Lec-14a_IDeal_Op_Amps.pptx 45 Bruce Mayer, PE Engineering-43: Engineering Circuit Analysis Example – Find G and V o  Ideal Assumptions  Solving  Yields Inverse Divider

46 ENGR-43_Lec-14a_IDeal_Op_Amps.pptx 46 Bruce Mayer, PE Engineering-43: Engineering Circuit Analysis Example  OpAmp Based I-Mtr  Desired Transfer Characteristic = 10V/mA → Find R 2 NON-INVERTING AMPLIFIER

47 ENGR-43_Lec-14a_IDeal_Op_Amps.pptx 47 Bruce Mayer, PE Engineering-43: Engineering Circuit Analysis Offset & Saturation  A NonInverting Amp But How to Handle This???  Start w/ KCL at v − Assume Ideality Then at Node Between the 1k & 4k Resistors  Then the Output  Notes on Output Eqn Slope = 1+(R2/R1) as Before Intercept = − (0.5V)x(4kΩ/1kΩ)

48 ENGR-43_Lec-14a_IDeal_Op_Amps.pptx 48 Bruce Mayer, PE Engineering-43: Engineering Circuit Analysis Example – Offset & Saturation  Note how “Offset” Source Generates a NON-Zero Output When v 1 = 0  The Transfer Characteristic for This Circuit IN LINEAR RANGE − 2V Offset “Saturates” at “Rail” Potential

49 ENGR-43_Lec-14a_IDeal_Op_Amps.pptx 49 Bruce Mayer, PE Engineering-43: Engineering Circuit Analysis WhiteBoard Work LLet’s Work a Unity Gain Buffer Problem Vs = 60mV Rs = 29.4 kΩ R L = 600 Ω FFind Load Power WITH and withOUT OpAmp UGB

50 ENGR-43_Lec-14a_IDeal_Op_Amps.pptx 50 Bruce Mayer, PE Engineering-43: Engineering Circuit Analysis All Done for Today What’s an OpAmp?

51 ENGR-43_Lec-14a_IDeal_Op_Amps.pptx 51 Bruce Mayer, PE Engineering-43: Engineering Circuit Analysis Bruce Mayer, PE Registered Electrical & Mechanical Engineer Engineering 43 Appendix

52 ENGR-43_Lec-14a_IDeal_Op_Amps.pptx 52 Bruce Mayer, PE Engineering-43: Engineering Circuit Analysis

53 ENGR-43_Lec-14a_IDeal_Op_Amps.pptx 53 Bruce Mayer, PE Engineering-43: Engineering Circuit Analysis 29.4 k 29.4

54 ENGR-43_Lec-14a_IDeal_Op_Amps.pptx 54 Bruce Mayer, PE Engineering-43: Engineering Circuit Analysis  Unity Gain Buffer Source-Driven Circuit Vs = 60mV Rs = 29.4 kΩ R L = 600 Ω

55 ENGR-43_Lec-14a_IDeal_Op_Amps.pptx 55 Bruce Mayer, PE Engineering-43: Engineering Circuit Analysis Key to OpAmp Ckt Analysis  I OA  Remember that the “Nose” of the OpAmp “Triangle” can SOURCE or SINK “Infinite” amounts of Current I OA = ± ∞

56 ENGR-43_Lec-14a_IDeal_Op_Amps.pptx 56 Bruce Mayer, PE Engineering-43: Engineering Circuit Analysis Unity Gain Buffer  Controlling Variable =  Solve For Buffer Gain by KVL  Thus The Amplification

57 ENGR-43_Lec-14a_IDeal_Op_Amps.pptx 57 Bruce Mayer, PE Engineering-43: Engineering Circuit AnalysisComparator  Ideal Comparator and Transfer Characteristic  “Zero-Cross” Detector → Heart of Solid State Relay Cnrtl

58 ENGR-43_Lec-14a_IDeal_Op_Amps.pptx 58 Bruce Mayer, PE Engineering-43: Engineering Circuit Analysis Find G & R in for NonIdeal Case  Determine Equivalent Circuit Using Linear Model For Op-Amp  Add Input Source-V  The OpAmp Model

59 ENGR-43_Lec-14a_IDeal_Op_Amps.pptx 59 Bruce Mayer, PE Engineering-43: Engineering Circuit Analysis Example  Required Draw The Linear Equivalent Circuit Write The Loop Equations 1.Locate Nodes + - o v  v  v R i R O 2.Place the nodes in linear circuit model

60 ENGR-43_Lec-14a_IDeal_Op_Amps.pptx 60 Bruce Mayer, PE Engineering-43: Engineering Circuit Analysis Example cont 3.Add Remaining Components to Complete Linear Model  Examine Circuit Two Loops One Current Source  Use Meshes Mesh-1 Mesh-2 Controlling Variable  DONE But Could Sub for (v + -v - ) and solve for i 2

61 ENGR-43_Lec-14a_IDeal_Op_Amps.pptx 61 Bruce Mayer, PE Engineering-43: Engineering Circuit Analysis Find G & R in for NonIdeal Case  The Equivalent Circuit for Mesh Analysis  Add The External Components  Now Re-draw Circuit To Enhance Clarity Be Faithful to the NODES There Are Only Two Loops

62 ENGR-43_Lec-14a_IDeal_Op_Amps.pptx 62 Bruce Mayer, PE Engineering-43: Engineering Circuit Analysis Find G & R in for NonIdeal Case  Now The Mesh Eqns Mesh-1 Mesh  The Controlling Variable in Terms of Loop Currents  Eliminating v i  Continue Analysis on Next Slide

63 ENGR-43_Lec-14a_IDeal_Op_Amps.pptx 63 Bruce Mayer, PE Engineering-43: Engineering Circuit Analysis G & R in for NonIdeal Case cont  The Math Model From Mesh Analysis  The Input-R and Gain  Then the Model in Matrix Form →

64 ENGR-43_Lec-14a_IDeal_Op_Amps.pptx 64 Bruce Mayer, PE Engineering-43: Engineering Circuit Analysis G & R in for NonIdeal Case cont  The Matrix-Inversion Soln  Invert Matrix as Before Find Determinant,  Adjoint Matrix  Then the Solution  Solving for Mesh Currents

65 ENGR-43_Lec-14a_IDeal_Op_Amps.pptx 65 Bruce Mayer, PE Engineering-43: Engineering Circuit Analysis G & R in for NonIdeal Case cont  The (Long) Expression for The input Resistance  By Mesh Currents  This Looks Ugly How Can we Simplify? –Recall  A →   R i → 

66 ENGR-43_Lec-14a_IDeal_Op_Amps.pptx 66 Bruce Mayer, PE Engineering-43: Engineering Circuit Analysis G & R in for NonIdeal Case cont  Use A→  in Expression for   Now Since For Op-Amps R i →  Also, then v o  Finally then G:  And The Expression for R in :  Infinite Input Resistance is GOOD


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