Bruce Mayer, PE Licensed Electrical & Mechanical Engineer BMayer@ChabotCollege.edu

1. Engineering 43 Chp14-1Op Amp Circuits Bruce Mayer, PE Licensed Electrical & Mechanical EngineerBMayer@ChabotCollege.edu

2. Ckts W/ Operational Amplifiers • OpAmp Utility • OpAmps Are Very Useful Electronic Components • We Have Already Developed The Tools To Analyze Practical OpAmp Circuits • The Linear Models for OpAmpsInclude Dependent Sources • A PRACTICAL Application of Dependent Srcs

3. Physical Size Progression of OpAmps Over the Years Real Op Amps LM324 DIP LMC6294 MAX4240 Maxim (Sunnyvale, CA) Max4241 OpAmp

4. Apex PA03 HiPwr OpAmp • Notice OutPut Rating • 30A @75 V • PwrOut → 30A•75V→ 2.25 kW!

5. The Circuit Symbol Is a Version of the Amplifier TRIANGLE OUTPUT RESISTANCE INPUT RESISTANCE GAIN OpAmp Symbol & Model • The Linear Model • Typical Values

6. OpAmpInPutTerminolgy • The Average of the two InputVoltages is calledthe Common-ModeSignal • The Difference between the Inputs is called the Differential-Signal, vid

7. 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 actuallyPower the Operational Amplifier

8. LOAD OP-AMP DRIVING CIRCUIT OpAmp Circuit Model

9. vi→vo Transfer Characteristics LinearRegionvo/vi = Const Saturation • The OUTPUT Voltage Level can NOT exceed the SUPPLY the Level

10. Unity Gain Buffer (FeedBack) FeedBackLoop • Controlling Variable = • Solve For Buffer Gain (I = Vin/R) • Thus The Amplification

11. The IDEAL Characteristics Ro = 0 Ri =  A =  (open loop gain) BW =  The Consequences of Ideality The Ideal OpAmp

12. Summing Point Constraint • The MOST important aspects of Ideality: • Ri = ∞ → i+ = i− = 0 • The OpAmpINput 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

13. Analyzing Ideal OpAmpCkts • Verify the presence of NEGATIVE FeedBack • Assume the Summing Point Constraint Applies in this fashion: • i+ = i−= 0 (based on Ri =∞) • v+ − v− = 0 (based on AO= ∞) • Use KVL, KCL, Ohm’s Law, and other linear ckt analysis techniques to determine quantities of interest

14. The Voltage Follower Also Called Unity Gain Buffer (UGB) from Before Voltage Follower • Usefulness of UGB Connection w/o Buffer Buffered Connection • The SOURCE Supplies The Power • The Source Supplies NO Power (the OpAmp does it)

15. Determine Voltage Gain, G = Vout/Vin Start with Ao Inverting OpAmp Ckt • Finally The Gain • Now From Input R • Apply KCL at v− • Next: Examine Ckt w/o Ideality Assumption

16. Consider Again the Inverting OpAmp Circuit Replace OpAmp w/ Linear Model Identify the Op Amp Nodes • Draw the Linear Model

17. Redraw the circuit cutting out the Op Amp R i Drawing the OpAmp Linear Model Draw components of linear OpAmp (on the circuit of step-2)

18. UNTANGLE as Needed Drawing the OpAmp Linear Model Before • The BEFORE & AFTER After

19. Replace the OpAmp with the LINEAR Model Label Nodes for Tracking b - d b - a NonIdeal Inverting Amp • Draw The Linear Equivalent For Op-amp • Note the External Component Branches

20. On The LINEAR Model Connect The External Components NonIdeal Inverting Amp cont. • ReDraw Ckt for Increased Clarity • Now Must Sweat the Details

21. Node Analysis Note GND Node NonIdeal Inverting Amp cont. 2 • Controlling Variable In Terms Of Node Voltages • The 2 Eqns in Matrix Form

22. 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 Inverting Amp – Invert Matrix • The Matrix Determinant  • Solve for vo

23. Then the System Gain Inverting Amp – Invert Matrix cont • Typical Practical Values for the Resistances • R1 = 1 kΩR2 = 5 kΩ • Then the Real-World Gain • Recall The Ideal Case for A→; Then The Eqn at top

24. Compare Ideal vs. NonIdeal • Ideal Assumptions • Gain for Real Case • Replace Op-amp By Linear Model, Solve The Resulting Circuit With Dep. Sources

25. Compare Ideal vs. NonIdeal cont. • The Ideal Op-amp Assumption Provides an Excellent Real-World Approximation. • Unless Forced to do Otherwise We Will Always Use the IDEAL Model • Ideal Case at Inverting Terminal • Gain for NonIdeal Case

26. KCL At Inverting Term Example  Differential Amp • KCL at NONinvertingTerminal • Assume Ideal OpAmp • By The KCLs A simple Voltage Divider

27. Then in The Ideal Case Example  Differential Amp cont • Now Set External R’s • R4 = R2 • R3 = R1 • Subbing the R’s Into the voEqn

28. Find vo Assume Ideal OpAmps Which Voltages are Set? Ex. Precision Diff V-Gain Ckt • 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

29. The Ckt Reduces To Fig. at Right KCL at v1 Ex. Precision Diff V-Gain Ckt cont • KCL at v2 • Eliminate va Using The above Eqns and Solve for vo in terms of v1 & v2 • Note the increased Gain over Diff Amp OpAmpCurrent

30. NONinverting Amp - Ideal • Ideal Assumptions • Infinite Gain • Since i− = 0 Arrive at “Inverse Voltage Divider” • Infinite Ri with v+ = v1

31. Example  Find Io for Ideal OpAmp • Ideal Assumptions • KCL at v−

32. Example: TransResistanceCkt • The trans-resistance Amp circuit below performs Current to Voltage Conversion • Find vo/iS • Use the Summing Point Constraint • → v− = 0V • Now by KCL at v− Node with i− = 0 • Notice that iS flows thru the 1Ω resistor • Thus by Ohm’s Law

33. Key to OpAmp Ckt Analysis  IOA • Remember that the “Nose” of the OpAmp “Triangle” can SOURCE or SINK “Infinite” amounts of Current IOA= ±∞ |IOA,max|= Isat

34. Example: TransResistanceCkt • Notice that theOpAmpAbsorbsALL of theSourceCurrent • The (Ideal) OpAmp will Source or Sink Current Out-Of or In-To its “nose” to maintain the V-Constraint: v+ = v−

35. Example: TransConductanceCkt • The transonductanceAmp circuit below performs Voltage to Current Conversion • Find io/v1 • Use the Summing Point Constraint • → v− = v+ • → i− = i+ = 0 • Thus v− = v1 • Then by KCL& Ohm • Notice the Output is Insensitive to Load Resistance 0 0

36. 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 vf node

37. Example: Summing Amp Circuit • Use Ohm for iA & iB • Also by Ohm Thru Rf

38. Example: Summing Amp Circuit • Recall iA & iB • Sub for iA & iB • But by Virtual Shortvf=0; Thus after ReArranging

39. Example: Summing Amp Circuit • Input Resistances: • Similarly for RinB

40. 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 vo

41. Example: Summing Amp Circuit • Thus Have • From the LOAD Perspective Expect • But the Previous analysis vo does NOT depend on RL at ALL • If vL = vo in all cases then have • Since vo is Not affected by RL, then Ro = 0

42. Example: Summing Summary

43. Required Find the expression for vo. Indicate where and how Ideal OpAmp assumptions Are Used Example: I & V Inputs • Set Voltages • Infinite Gain Assumption Fixes v− • Use Infinite Input Resistance Assumption • Apply KCL to Inverting Input • Then Solving

44. Example – Find G and Vo • Solving • Ideal Assumptions • Yields Inverse Divider

45. Desired Transfer Characteristic = 10V/mA → Find R2 NON-INVERTING AMPLIFIER Example  OpAmp Based I-Mtr

46. A NonInverting Amp But How to Handle This??? Offset & Saturation • Start w/ KCL at v− • Assume Ideality • Then at Node Between the 1k & 4k Resistors • Notes on Output Eqn • Slope = 1+(R2/R1) as Before • Intercept = −(0.5V)x(4kΩ/1kΩ) • Then the Output

47. Note how “Offset” Source Generates a NON-Zero Output When v1 = 0 The Transfer Characteristic for This Circuit “Saturates” at “Rail” Potential IN LINEAR RANGE −2V Offset Example – Offset & Saturation

48. WhiteBoard Work • Let’s Work a Unity Gain Buffer Problem • Vs = 60mV • Rs = 29.4 kΩ • RL = 600 Ω • Find Load Power WITH and withOUT OpAmp UGB

49. All Done for Today What’sanOpAmp?

50. Engineering 43 Appendix Bruce Mayer, PE Registered Electrical & Mechanical EngineerBMayer@ChabotCollege.edu