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Op Amp Circuits

Op Amp Circuits. Objective of Lecture. Apply the ‘almost ideal’ op amp model in the following circuits: Inverting Amplifier Noninverting Amplifier Voltage Follower Summing Amplifier Difference Amplifier Cascaded Amplifiers Chapter 5.4-5.8 Fundamentals of Electric Circuits.

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Op Amp Circuits

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  1. Op Amp Circuits

  2. Objective of Lecture • Apply the ‘almost ideal’ op amp model in the following circuits: • Inverting Amplifier • Noninverting Amplifier • Voltage Follower • Summing Amplifier • Difference Amplifier • Cascaded Amplifiers • Chapter 5.4-5.8 Fundamentals of Electric Circuits

  3. Almost Ideal Op Amp Model Ri = ∞ W andRo = 0 W i2 = 0 Linear Region: When V+< vo< V- , vo is determined from the closed loop gain Av times v2 as v1 = v2 (vd = 0 V). i1 = 0 Saturation: When Av v2 ≥ V+, vo = V+. When Av v2 ≤ V-, vo = V-.

  4. Example #1: Inverting Amplifier if i1 = 0 is i V+ = 15V V- = -10V i2 = 0

  5. Example #1 (con’t) if i1 = 0 is i i2 = 0 V+ = 15V V- = -10V

  6. Example #1 • Closed loop gains are dependent on the values of R1 and Rf. • Therefore, you have to calculate the closed loop gain for each new problem.

  7. Example #1 (con’t) if i1 = 0 is i i2 = 0 vo

  8. Example #1 (con’t) • Since AV = -10 • If Vs = 0V, V0 = -10(0V) = 0V • If Vs = 0.5V, Vo = -10(0.5V) = -5V • If Vs = 1V, Vo = -10(1V) = -10V • If Vs = 1.1V, Vo = -10(1.1V) < V-, Vo = -10V • If Vs = -1.2V, V0 = -10(-1.2V) = +12V • If Vs = -1.51V, Vo = -10(-1.51V) > V+, Vo = +15V

  9. Example #1 (con’t) • Voltage transfer characteristic Slope of the voltage transfer characteristic in the linear region is equal to AV.

  10. Example #2: Noninverting Amplifier

  11. Example #2 (con’t)

  12. Example #2 (con’t)

  13. Example #2 (con’t)

  14. Example #2: Noninverting Amplifier

  15. Example #2 (con’t) • AV = +11 • If Vs = 0V, V0 = 11(0V) = 0V • If Vs = 0.5V, Vo = 11(0.5V) = +5.5V • If Vs = 1.6V, Vo = 11(1.6V) > V+, Vo = +15V • If Vs = -0.9V, V0 = 11(-0.9V) = -9.9V • If Vs = -1.01V, Vo = 11(-1.01V) < V- Vo = -10V

  16. Example #2 (con’t) • Voltage transfer characteristic Slope of the voltage transfer characteristic in the linear region is equal to AV.

  17. Example #3: Voltage Follower A voltage follower is a noninverting amplifier where Rf = 0W and R1 = ∞W. Vo /Vs = 1 +Rf/R1 = 1 + 0 = 1

  18. Example #4: Summing Amplifier V+ = 30V V-=-30V A summing amplifier is an inverting amplifier with multiple inputs.

  19. Example #4 (con’t) if i1 = 0 iA v1 iB i2 = 0 v2 iC We apply superposition to obtain a relationship between Vo and the input voltages.

  20. Example #4 (con’t) A virtual ground

  21. Example #4 (con’t)

  22. Example #4 (con’t) Note that the voltages at both nodes of RC are 0V.

  23. Example #4 (con’t)

  24. Example #4 (con’t)

  25. Example #4 (con’t)

  26. Example #4 (con’t)

  27. Example #4 (con’t) • Do not apply the limits on vo (V+≥ vo ≥ V-) until after adding the results from the three circuits together.

  28. Example #5: Difference Amplifier

  29. Example #5 (con’t) if iA i1 = 0 v1 i2 = 0 iB iC v2

  30. Example #5 (con’t) if iA i1 = 0 v1 i2 = 0 iB iC v2

  31. Example #5 (con’t) if iA i1 = 0 v1 i2 = 0 iB iC v2

  32. Example #5 (con’t) if iA

  33. Example #5 (con’t)

  34. Example #5 (con’t) • If RA/Rf = RB/RC • And if RA = Rf

  35. Example #6: Cascading Op Amps

  36. Example #6 (con’t) • Treat as two separate amplifier circuits

  37. Example #6 (con’t) First Circuit Second Circuit

  38. Example #6 (con’t) • It is a noninverting amplifier.

  39. Example #6 (con’t) • It is a inverting amplifier.

  40. Example #6 (con’t) • The gain of the cascaded amplifiers is the multiplication of the two individial amplifiers

  41. Summary • The ‘almost ideal’ op amp model: • Ri = ∞W. • i1 = i2 = 0A; v1 = v2 • Ro = 0W. • No power/voltage loss between the dependent voltage source and vo. • The output voltage is limited by the voltages applied to the positive and negative rails. • V+ ≥ vo ≥ V- • This model can be used to determine the closed loop voltage gain for any op amp circuit. • Superposition can be used to solve for the output of a summing amplifier. • Cascaded op amp circuits can be separated into individual amplifiers and the overall gain is the multiplication of the gain of each amplifier.

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