1. Basic Electric Circuits Introduction To Operational Amplifiers Lesson 8

2. Basic Electric Circuits Operational Amplifiers One might ask, why are operational amplifiers included in Basic Electric Circuits? The operational amplifier has become so cheap in price (often less than $1.00 per unit) and it can be used in so many applications, we present an introductory study early-on in electric circuits. 1

3. Basic Electric Circuits Operational Amplifiers What is an operational amplifier? This particular form of amplifier had the name “Operational” attached to it many years ago. As early as 1952, Philbrick Operational Amplifiers (marketed by George A. Philbrick) were constructed with vacuum tubes and were used in analog computers. * Even as late as 1965, vacuum tube operational amplifiers were still in use and cost in the range of $75. * Some reports say that Loebe Julie actually developed the operational amplifier circuitry. 2

4. Basic Electric Circuits Operational Amplifiers The Philbrick Operational Amplifier. From “Operational Amplifier”, by Tony van Roon: http://www.uoguelph.ca/~antoon/gadgets/741/741.html

5. Basic Electric Circuits Operational Amplifiers My belief is that “operational” was used as a descriptor early-on because this form of amplifier can perform operations of adding signals subtracting signals integrating signals, The applications of operational amplifiers ( shortened to op amp ) have grown beyond those listed above. 3

6. Basic Electric Circuits Operational Amplifiers At this level of study we will be concerned with how to use the op amp as a device. The internal configuration (design) is beyond basic circuit theory and will be studied in later electronic courses. The complexity is illustrated in the following circuit. 4

7. Basic Electric Circuits Operational Amplifiers The op amp is built using VLSI techniques. The circuit diagram of an LM 741 from National Semiconductor is shown below. 5 V+ V- VoVo V in (-) V in (+) Figure 8.1: Internal circuitry of LM741. Taken from National Semiconductor data sheet as shown on the web.

8. Basic Electric Circuits Operational Amplifiers Fortunately, we do not have to sweat a circuit with 22 transistors and twelve resistors in order to use the op amp The circuit in the previous slide is usually encapsulated into a dual in-line pack (DIP). For a single LM741, the pin connections for the chip are shown below. Taken from National Semiconductor data sheet as shown on the web. 6 Figure 8.2: Pin connection, LM741.

9. Basic Electric Circuits Operational Amplifiers The basic op amp with supply voltage included is shown in the diagram below. 7 Figure 8.3: Basic op am diagram with supply voltage.

10. Basic Electric Circuits Operational Amplifiers In most cases only the two inputs and the output are shown for the op amp. However, one should keep in mind that supply voltage is required, and a ground. The basic op am without a ground is shown below. 8 Figure 8.4: Outer op am diagram.

11. Basic Electric Circuits Operational Amplifiers A model of the op amp, with respect to the symbol, is shown below. Figure 8.5: Op Amp Model. 9

12. Basic Electric Circuits Operational Amplifiers The previous model is usually shown as follows: Figure 8.6: Working circuit diagram of op amp. 10

13. Basic Electric Circuits Operational Amplifiers Application: As an application of the previous model, consider the following configuration. Find V o as a function of V in and the resistors R 1 and R 2. 11Figure 8.7: Op amp functional circuit.

14. Basic Electric Circuits Operational Amplifiers In terms of the circuit model we have the following: Figure 8.8: Total op amp schematic for voltage gain configuration. 12

15. Basic Electric Circuits Operational Amplifiers Circuit values are: R 1 = 10 k  R 2 = 40 k  A = 100,000 R i = 1 meg  13

16. Basic Electric Circuits Operational Amplifiers We can write the following equations for nodes a and b. Eq 8.1 Eq 8.2 14

17. Basic Electric Circuits Operational Amplifiers Equation 8.1 simplifies to; Eq 8.3 Equation 8.2 simplifies to; Eq 8.4 15

18. Basic Electric Circuits Operational Amplifiers From Equations 8.3 and 8.4 we find; This is an expected answer. Fortunately, we are not required to do elaborate circuit analysis, as above, to find the relationship between the output and input of an op amp. Simplifying the analysis is our next consideration. 16 Eq 8.5

19. Basic Electric Circuits Operational Amplifiers For most all operational amplifiers, R i is 1 meg  or larger and R o is around 50  or less. The open-loop gain, A, is greater than 100,000. Ideal Op Amp: The following assumptions are made for the ideal op amp. 17

20. Basic Electric Circuits Ideal Op Amp: (a)i 1 = i 2 = 0: Due to infinite input resistance. (b) V i is negligibly small; V 1 = V 2. 18 Figure 8.9: Ideal op amp.

21. Basic Electric Circuits Ideal Op Amp: Find V o in terms of V in for the following configuration. 19Figure 8.10: Gain amplifier op amp set-up.

22. Basic Electric Circuits Ideal Op Amp: Writing a nodal equation at (a) gives; 20 Eq 8.6

23. Basic Electric Circuits Ideal Op Amp: With V i = 0 we have; With R 2 = 4 k  and R 1 = 1 k , we have Earlier we got 21 Eq 8.7

24. Basic Electric Circuits Ideal Op Amp: When V i = 0 in Eq 8.7 and we apply the Laplace Transform; Eq 8.8 In fact, we can replace R 2 with Z fb (s) and R 1 with Z 1 (s) and we have the important expression; Eq 8.9 22

25. Basic Electric Circuits Ideal Op Amp: At this point in circuits we are not able to appreciate the utility of Eq 8.9. We will revisit this at a later point in circuits but for now we point out that judicious selections of Z fb (s) and Z in (s) leads to important applications in Analog Filters Analog Compensators in Control Systems Application in Communications 23

26. Basic Electric Circuits Ideal Op Amp: Example 8.1: Consider the op amp configuration below. Figure 8.11: Circuit for Example 8.1. 24 Assume V in = 5 V

27. Basic Electric Circuits Operational Amplifiers At node “a” we can write; From which; V 0 = -51 V 25 Eq 8.10 Example 8.1 cont.

28. Basic Electric Circuits Operational Amplifiers Example 8.2: Summing Amplifier. Given the following: Figure 8.12: Circuit for Example 8.2. Eq 8.11 26

29. Basic Electric Circuits Operational Amplifiers Example 8.2: Summing Amplifier. continued Equation 8.11 can be expressed as; Eq 8.12 If R 1 = R 2 = R fb then, Eq. 8.13 Therefore, we can add signals with an op amp. 27

30. Basic Electric Circuits Operational Amplifiers Example 8.3: Isolation or Voltage Follower. Applications arise in which we wish to connect one circuit to another without the first circuit loading the second. This requires that we connect to a “block” that has infinite input impedance and zero output impedance. An operational amplifier does a good job of approximating this. Consider the following: Figure 8.13: Illustrating Isolation. 28

31. Basic Electric Circuits Operational Amplifiers Example 8.3: Isolation or Voltage Follower. continued Figure 8.14: Circuit isolation with an op amp. It is easy to see that: V 0 = V in 29

32. Basic Electric Circuits Operational Amplifiers Example 8.4: Isolation with gain. Figure 8.15: Circuit for Example 8.4: 30 Writing a nodal equation at point “a” and simplifying gives;

33. Basic Electric Circuits Operational Amplifiers Example 8.5: The noninverting op amp. Consider the following: Figure 8.16: Noninverting op am configuration. 31

34. Basic Electric Circuits Operational Amplifiers Example 8.5: The noninverting op amp. Continued Writing a node equation at “a” gives; Remember this 32

35. Basic Electric Circuits Operational Amplifiers Example 8.6: Noninverting Input. Find V 0 for the following op amp configuration. Figure 8.17: Op amp circuit for example 8.6. 33

36. Basic Electric Circuits Operational Amplifiers Example 8.6: Noninverting Input. The voltage at V x is found to be 3 V. Writing a node equation at “a” gives; or 34

37. End of Lesson 8 CIRCUITS Operational Amplifiers