1. BMayer@ChabotCollege.edu ENGR-43_Lec-04_Op-Amps.ppt 1 Bruce Mayer, PE Engineering-43: Engineering Circuit Analysis Bruce Mayer, PE Licensed Electrical & Mechanical Engineer BMayer@ChabotCollege.edu Engineering 43 Chp 4 Op Amp Circuits

2. BMayer@ChabotCollege.edu ENGR-43_Lec-04_Op-Amps.ppt 2 Bruce Mayer, PE Engineering-43: Engineering Circuit Analysis Ckts W/ Operational Amplifiers  Why Study OpAmps At This Point? 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. BMayer@ChabotCollege.edu ENGR-43_Lec-04_Op-Amps.ppt 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. BMayer@ChabotCollege.edu ENGR-43_Lec-04_Op-Amps.ppt 4 Bruce Mayer, PE Engineering-43: Engineering Circuit Analysis Apex PA03 HiPwr OpAmp  Notice OutPut Rating 30A @75 V  PwrOut → 30A75V → 2.25 kW!

5. BMayer@ChabotCollege.edu ENGR-43_Lec-04_Op-Amps.ppt 5 Bruce Mayer, PE Engineering-43: Engineering Circuit Analysis XX  xx  X  xx

6. BMayer@ChabotCollege.edu ENGR-43_Lec-04_Op-Amps.ppt 6 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

7. BMayer@ChabotCollege.edu ENGR-43_Lec-04_Op-Amps.ppt 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 be there to actually Power the Operational Amplifier

8. BMayer@ChabotCollege.edu ENGR-43_Lec-04_Op-Amps.ppt 8 Bruce Mayer, PE Engineering-43: Engineering Circuit Analysis OpAmp Circuit Model DRIVING CIRCUIT LOAD OP-AMP

9. BMayer@ChabotCollege.edu ENGR-43_Lec-04_Op-Amps.ppt 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. BMayer@ChabotCollege.edu ENGR-43_Lec-04_Op-Amps.ppt 10 Bruce Mayer, PE Engineering-43: Engineering Circuit Analysis Unity Gain Buffer  Controlling Variable =  Solve For Buffer Gain  Thus The Amplification

11. BMayer@ChabotCollege.edu ENGR-43_Lec-04_Op-Amps.ppt 11 Bruce Mayer, PE Engineering-43: Engineering Circuit Analysis The Ideal OpAmp  The IDEAL Characteristics R o = 0 R i =  A =   The Consequences of Ideality

12. BMayer@ChabotCollege.edu ENGR-43_Lec-04_Op-Amps.ppt 12 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

13. BMayer@ChabotCollege.edu ENGR-43_Lec-04_Op-Amps.ppt 13 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

14. BMayer@ChabotCollege.edu ENGR-43_Lec-04_Op-Amps.ppt 14 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

15. BMayer@ChabotCollege.edu ENGR-43_Lec-04_Op-Amps.ppt 15 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

16. BMayer@ChabotCollege.edu ENGR-43_Lec-04_Op-Amps.ppt 16 Bruce Mayer, PE Engineering-43: Engineering Circuit Analysis Drawing the OpAmp Linear Model 4.UNTANGLE as Needed  The BEFORE & AFTER

17. BMayer@ChabotCollege.edu ENGR-43_Lec-04_Op-Amps.ppt 17 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

18. BMayer@ChabotCollege.edu ENGR-43_Lec-04_Op-Amps.ppt 18 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

19. BMayer@ChabotCollege.edu ENGR-43_Lec-04_Op-Amps.ppt 19 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

20. BMayer@ChabotCollege.edu ENGR-43_Lec-04_Op-Amps.ppt 20 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., http://www.wikipedia.org/wiki/Matrix_inversion  The Matrix Determinant   Solve for v o

21. BMayer@ChabotCollege.edu ENGR-43_Lec-04_Op-Amps.ppt 21 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

22. BMayer@ChabotCollege.edu ENGR-43_Lec-04_Op-Amps.ppt 22 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

23. BMayer@ChabotCollege.edu ENGR-43_Lec-04_Op-Amps.ppt 23 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

24. BMayer@ChabotCollege.edu ENGR-43_Lec-04_Op-Amps.ppt 24 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

25. BMayer@ChabotCollege.edu ENGR-43_Lec-04_Op-Amps.ppt 25 Bruce Mayer, PE Engineering-43: Engineering Circuit Analysis Example  Differential Amp cont  Then in The Ideal Case  Now Set External Rs R 4 = R 2 R 3 = R 1  Subbing the Rs Into the v o Eqn

26. BMayer@ChabotCollege.edu ENGR-43_Lec-04_Op-Amps.ppt 26 Bruce Mayer, PE Engineering-43: Engineering Circuit Analysis Ex. Precision Diff V-Gain Ckt  Find v o  Assume Ideal OpAmp 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 OUT of the OpAmps

27. BMayer@ChabotCollege.edu ENGR-43_Lec-04_Op-Amps.ppt 27 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

28. BMayer@ChabotCollege.edu ENGR-43_Lec-04_Op-Amps.ppt 28 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

29. BMayer@ChabotCollege.edu ENGR-43_Lec-04_Op-Amps.ppt 29 Bruce Mayer, PE Engineering-43: Engineering Circuit Analysis Example  Find I o for Ideal OpAmp  Ideal Assumptions  KCL at v -

30. BMayer@ChabotCollege.edu ENGR-43_Lec-04_Op-Amps.ppt 30 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

31. BMayer@ChabotCollege.edu ENGR-43_Lec-04_Op-Amps.ppt 31 Bruce Mayer, PE Engineering-43: Engineering Circuit Analysis Find G & R in for NonIdeal Case cont  The Equivalent Circuit for Mesh Analysis  Add The External Components  Now Re-draw Circuit To Enhance Clarity There Are Only Two Loops

32. BMayer@ChabotCollege.edu ENGR-43_Lec-04_Op-Amps.ppt 32 Bruce Mayer, PE Engineering-43: Engineering Circuit Analysis Find G & R in for NonIdeal Case cont  Now The Mesh Eqns Mesh-1 Mesh-2 1 2  The Controlling Variable in Terms of Loop Currents  Eliminating v i  Continue Analysis on Next Slide

33. BMayer@ChabotCollege.edu ENGR-43_Lec-04_Op-Amps.ppt 33 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 →

34. BMayer@ChabotCollege.edu ENGR-43_Lec-04_Op-Amps.ppt 34 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

35. BMayer@ChabotCollege.edu ENGR-43_Lec-04_Op-Amps.ppt 35 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 → 

36. BMayer@ChabotCollege.edu ENGR-43_Lec-04_Op-Amps.ppt 36 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

37. BMayer@ChabotCollege.edu ENGR-43_Lec-04_Op-Amps.ppt 37 Bruce Mayer, PE Engineering-43: Engineering Circuit Analysis Example  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

38. BMayer@ChabotCollege.edu ENGR-43_Lec-04_Op-Amps.ppt 38 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

39. BMayer@ChabotCollege.edu ENGR-43_Lec-04_Op-Amps.ppt 39 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

40. BMayer@ChabotCollege.edu ENGR-43_Lec-04_Op-Amps.ppt 40 Bruce Mayer, PE Engineering-43: Engineering Circuit Analysis Example – Find G and V o  Ideal Assumptions  Solving  Yields Inverse Divider

41. BMayer@ChabotCollege.edu ENGR-43_Lec-04_Op-Amps.ppt 41 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

42. BMayer@ChabotCollege.edu ENGR-43_Lec-04_Op-Amps.ppt 42 Bruce Mayer, PE Engineering-43: Engineering Circuit AnalysisComparator  Ideal Comparator and Transfer Characteristic  “Zero-Cross” Detector → Heart of Solid State Relay Cnrtl

43. BMayer@ChabotCollege.edu ENGR-43_Lec-04_Op-Amps.ppt 43 Bruce Mayer, PE Engineering-43: Engineering Circuit Analysis Example  OpAmp Based I-Mtr  Desired Transfer Characteristic = 10V/mA → Find R 2 NON-INVERTING AMPLIFIER

44. BMayer@ChabotCollege.edu ENGR-43_Lec-04_Op-Amps.ppt 44 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)

45. BMayer@ChabotCollege.edu ENGR-43_Lec-04_Op-Amps.ppt 45 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

46. BMayer@ChabotCollege.edu ENGR-43_Lec-04_Op-Amps.ppt 46 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 Find Load Power WITH and withOUT OpAmp UGB

47. BMayer@ChabotCollege.edu ENGR-43_Lec-04_Op-Amps.ppt 47 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 = ± ∞

48. BMayer@ChabotCollege.edu ENGR-43_Lec-04_Op-Amps.ppt 48 Bruce Mayer, PE Engineering-43: Engineering Circuit Analysis Unity Gain Buffer  Controlling Variable =  Solve For Buffer Gain by KVL  Thus The Amplification