1. INTRODUCTION With this chapter, we begin the discussion of the basic op-amp that forms the cornerstone for linear applications; that is, the signal is directly proportional to the input signal. Chapter 2 Basic Linear Amplifier Circuits

2. OBJECTIVES At the completion of this chapter, you will be able to do the following Design, compare, and predict the performance of the following op-amp circuits: non-inverting amplifier inverting amplifier voltage follower summing amplifier difference amplifier Chapter 2 Basic Linear Amplifier Circuits

3. OBJECTIVES cont. Minimize the output-offset voltage due to the input bias current, input offset current, and input offset voltage. Recognize the input and feedback elements of linear op-amp circuits. Determine the effects of feedback upon circuit performance. Chapter 2 Basic Linear Amplifier Circuits

4. Non-lnverting Amplifiers As shown in Fig. 2-1, the op-amp is connected as a non-inverting amplifier. This is because the input signal is applied to the op-amp’s Chapter 2 Basic Linear Amplifier Circuits

5. Non-lnverting Amplifiers Non-inverting (+) input. Resistor R1 is called the input element, and resistor R2 is called the feedback element, since it diverts, or “feeds back” part of the output voltage to one of the op-amp’s inputs. In this case, part of the output is returned to the inverting (-) input. Chapter 2 Basic Linear Amplifier Circuits

6. Non-lnverting Amplifiers For this non-inverting amplifier, the output voltage is given by: (Eq. 2-1) Chapter 2 Basic Linear Amplifier Circuits

7. Non-lnverting Amplifiers The voltage gain, or the ratio of the output voltage to the input voltage, is: Voltage gain = = Chapter 2 Basic Linear Amplifier Circuits

8. Non-lnverting Amplifiers Consequently, the voltage gain of a non-inverting amplifier will always be greater than unity (1.0), no matter how large we make R1. Chapter 2 Basic Linear Amplifier Circuits

9. Non-lnverting Amplifiers Since the input signal is applied to the op-amp’s non-inverting input, the output voltage will always be in phase with the input. Chapter 2 Basic Linear Amplifier Circuits

10. Non-lnverting Amplifiers More simply, when the input voltage goes positive, the output does the same. The only difference between the input and output voltages is that the output voltage will be I + R2/R1 times larger than the input. Chapter 2 Basic Linear Amplifier Circuits

11. Non-lnverting Amplifiers As pointed out in the previous chapter, the open-loop gain AOL is an intrinsic characteristic of the op-amp when there is no feedback. Chapter 2 Basic Linear Amplifier Circuits

12. Non-lnverting Amplifiers When feed­back is used, we then refer to the closed-loop gain A CL, Which is simply the voltage gain of the op-amp configuration (Equation 2-2), or Chapter 2 Basic Linear Amplifier Circuits for the non-inverting amplifier

13. Non-lnverting Amplifiers The loop gain, A L is the reduction of the open-loop gain by the closed-loop gain, so that by definition, Chapter 2 Basic Linear Amplifier Circuits or

14. Non-lnverting Amplifiers For all practical purposes, the input impedance of the non-inverting amplifier is the intrinsic input impedance of the op-amp itself, which is high enough to minimize loading of the input circuitry. Chapter 2 Basic Linear Amplifier Circuits

15. Non-lnverting Amplifiers On the other hand, the output impedance of the circuit of Fig. 2-1 is determined from the formula: Chapter 2 Basic Linear Amplifier Circuits or where Z oi is the intrinsic output impedance of the op-amp, as determined from the manufacturer’s data sheet.

16. Chapter 2 Basic Linear Amplifier Circuits Non-lnverting Amplifiers Example To see how these concepts just discussed fit into place, assume that a type 741 op-amp is used in the circuit of Fig. 2-1 with R1 = 1 KOhm and R2= 100 KOhm From Equation 2-3, the voltage, or closed-loop gain (A CL ) is: A L = 200 000 101 = 2000 From a given manufacturer’s data sheet, the open loop gain for the 741 op-amp is typically 200,000. From Equation 2-4, the circuit’s loop gain (A L ) is then:

17. Chapter 2 Basic Linear Amplifier Circuits Non-lnverting Amplifiers Example Using a typical value of 75 Ohm for the 741’s intrinsic output impedance (Zoi), the output impedance of the completed non-inverting amplifier is then: Zo = Z oi /A OL = 75 Ohm 2000 = 0.04 Ohm From this example it should now be evident that the result of adding feedback increases the loop gain, which in turn decreases the output impedance of the amplifier circuit! We can then connect almost any load to the output, as long as the maximum output current rating of the op-amp is not exceeded.

18. Chapter 2 Basic Linear Amplifier Circuits Non-lnverting Amplifiers Usually, the calculation of the op-amp circuit’s output impedance can be ignored since it is such a small number. It was included here to demonstrate the effect of external feedback.

19. Chapter 2 Basic Linear Amplifier Circuits Non-lnverting Amplifiers End of Non-Inverting Amplifiers

20. lnverting Amplifiers As shown in Fig. 2-2, the op-amp is connected as an inverting amplifier. This is because the input signal is applied to the op-amp’s inverting (-) input through R1, which is called the input element. Resistor R2 is the feedback element. For the inverting amplifier, the output voltage is given by the equation Chapter 2 Basic Linear Amplifier Circuits

21. lnverting Amplifiers The minus (-) sign in the above equation indicates that when the input signal voltage goes positive, the output voltage goes negative, and vice versa. In other words, the output signal is of opposite polarity with respect to the input, which is the same as saying that the output is 180 degrees out of phase with the input. Chapter 2 Basic Linear Amplifier Circuits

22. lnverting Amplifiers The voltage, or closed-loop gain, is then: Chapter 2 Basic Linear Amplifier Circuits

23. lnverting Amplifiers Consequently, the voltage gain of the inverting amplifier can be either less than, equal to, or greater than 1, depending on the relation of R2 to R1. Chapter 2 Basic Linear Amplifier Circuits

24. lnverting Amplifiers The loop gain is then: Chapter 2 Basic Linear Amplifier Circuits

25. lnverting Amplifiers Unlike the non-inverting amplifier, the input impedance of the in­verting amplifier circuit is simply the value of the input element, R1, and will be much less than that of the non-inverting circuit. The circuit’s output impedance, as before, is determined solely by the op­ amps intrinsic output impedance and the circuit’s loop gain, so that: Chapter 2 Basic Linear Amplifier Circuits

26. lnverting Amplifiers For the special case when R1 and R2 are equal, we then have a unity gain inverter, which is handy when we only want to invert the polarity of the input signal. Chapter 2 Basic Linear Amplifier Circuits

27. lnverting Amplifiers Switching in different feedback resistors, as shown in Fig.2-3, can control the closed loop gain of the basic inverting amplifier. Chapter 2 Basic Linear Amplifier Circuits

28. lnverting Amplifiers DC output offset In the ideal op-amp, the output voltage is zero when the input voltage is also zero. However, all commercial op-amps have a small, but finite, dc output voltage called the output offset voltage, even though the input may be grounded. Chapter 2 Basic Linear Amplifier Circuits

29. lnverting Amplifiers DC output offset The dc output offset voltage is a result of three sources: input offset current input bias current input offset voltage Chapter 2 Basic Linear Amplifier Circuits

30. lnverting Amplifiers DC output offset As stated in Chapter 1, the input bias current must be supplied to both inputs of the op-amp to assure that the op-amp behaves properly. For the inverting amplifier circuit of Fig. 2-5, the input bias current, with no input signal, flows through both the input and feedback re­sistors. Chapter 2 Basic Linear Amplifier Circuits

31. lnverting Amplifiers DC output offset Ohm’s law, when a current flows through a known resist­ance develops a voltage across this resistance (V = IR). Since the non-inverting input of the op- amp is grounded, the voltages developed across these resistors appear as a dc input voltage, which in turn is amplified by the op-amp. Chapter 2 Basic Linear Amplifier Circuits

32. lnverting Amplifiers DC output offset For the inverting amplifier circuit of Fig. 2-5, the output voltage (V0S) generated as a result of the input bias current (IB) is: V OS =I B R 2 Chapter 2 Basic Linear Amplifier Circuits

33. lnverting Amplifiers DC output offset The method commonly used to correct for the output voltage offset due to the input bias current is to place an additional resistor R3 be­tween the non- inverting (±) input and ground as shown in the figure below. Chapter 2 Basic Linear Amplifier Circuits

34. lnverting Amplifiers DC output offset The value of this additional resistor is equal to the parallel combination of R1 and R2, or: Chapter 2 Basic Linear Amplifier Circuits so that the voltage developed across R3 is equal and opposite to the voltage across the parallel combination of R1 and R2. Since the two voltages are equal and opposite, they cancel.

35. lnverting Amplifiers DC output offset However, the above discussion assumes that the bias currents flowing into both inputs are equal. Unfortunately, in a typical op-amp, both bias currents are not exactly equal, the value for I b (from the data sheet) being only an average of the two input bias currents. Chapter 2 Basic Linear Amplifier Circuits

36. lnverting Amplifiers DC output offset Since there will be a difference in the two bias currents, called the Input offset current, Ios, there will still exist a small but finite dc out­put offset voltage, equal to: Vos = IosR2 Chapter 2 Basic Linear Amplifier Circuits

37. lnverting Amplifiers DC output offset The remaining source of output offset is due to the op-amp’s input offset voltage, resulting from mismatches in the internal circuitry and fabrication of the op-amp. As shown for the inverting amplifier circuit of Fig. 2-7, the input offset voltage,Voi, can be represented as a small battery in series with the non-inverting input of an ideal op-amp. (as shown above) Chapter 2 Basic Linear Amplifier Circuits

38. lnverting Amplifiers DC output offset For the circuit in Fig. 2-7, the dc output offset voltage, as a result the input offset voltage, is calculated from: Chapter 2 Basic Linear Amplifier Circuits