Chapter 8 Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

2 Ideal Amplifier Characteristics A voltage amplifier Simple voltage amplifier model

3 If the input resistance of the amplifier Rin were very large, the source voltage vS and the input voltage vin would be approximately equal:

4 By an analogous argument, it can also be seen that the desired output resistance for the amplifier Rout should be very small, since for an amplifier with Rout = 0, the load voltage would be

5 We can see that as Rin approaches infinity and Rout approaches zero, the ideal amplifier magnifies the source voltage by a factor A vL = AvS Thus, two desirable characteristics for a general-purpose voltage amplifier are a very large input impedance and a very small output impedance.

6 The Open-Loop Model The ideal operational amplifier behaves very much as an ideal difference amplifier, that is, a device that amplifies the difference between two input voltages. Operational amplifiers are characterized by near-infinite input resistance and very small output resistance. As shown in Figure 8.4, the output of the op-amp is an amplified version of the difference between the voltages present at the two inputs.

7 The input denoted by a plus sign is called the noninverting input (or terminal), while that represented with a minus sign is termed the inverting input (or terminal). The current flowing into the input circuit of the amplifier is zero, or:

8 The Inverting Amplifier The input signal to be amplified is connected to the inverting terminal, while the non-inverting terminal is grounded. Inverting amplifier

9 The voltage at the noninverting input v + is easily identified as zero, since it is directly connected to ground: v + = 0. The effect of the feedback connection from output to inverting input is to force the voltage at the inverting input to be equal to that at the non-inverting input.

10 Example 8.1 Inverting Amplifier Circuit Determine the voltage gain and output voltage for the inverting ampilfier circuit of figure 8.5. What will the uncertainty in the gain be if 5 and 10 percent tolerance resistors are used, respectively? Figure 8.5

11 Figure 8.6 Figure 8.5

12 Check your understand Calculate the uncertainty in the gain if 1 percent “precision” resistors are used.

13 The Summing Amplifier Summing amplifier Noninverting amplifier

14 Example 8.2 Voltage Follower

15 Check your understand Derive an expression for the closed-loop gain of the voltage follower that includes the value of the open-loop voltage gain as a parameter. How large should the open-loop gain be if we desire to achieve the intended closed-loop gain with less than 0.1 percent error?

16 The Differential amplifier

17 The analysis of the differential amplifier may be approached by various methods; the one we select to use at this stage consists of 1. Computing the noninverting- and inverting- terminal voltages v+ and v−. 2. Equating the inverting and noninverting input voltages: v− = v+. 3. Applying KCL at the inverting node, where i2 = −i1.

18 The differential amplifier provides the ability to reject common-mode signal components (such as noise or undesired DC offsets) while amplifying the differential-mode components. To provide impedance isolation between bridge transducers and the differential amplifier stage, the signals v1 and v2 are amplified separately.

19

20 Check your understand Derive the result given above for the differential amplifier, using the principle of superposition. Think of the differntial amplifier as the combination of an inverting amplifier with input equal to ύ 1 and a non- inverting amplifier with input equal to ύ 1.

21

22 Example 8.3 Electrocardigram (EKG) Amplifier Figure 8.11 Two-lead electrocardiogram Figure8.12 EKG waveform

23 Figure 8.13 EKG amplifier

24 Instrumentation Amplifier Instrumentation amplifier

25 Example 8.14 Instrumentation Amplifier Determine the closed-loop voltage gain of the instrumentation amplifier circuit of figure 8.14.

26 Figure 8.15 Input (a) and output (b) stages of instrumentation amplifier

27

28 Example 8.5 Level Shifter The level shifter of figure 8.16 has the ability to add or subtract a DC offset to or from a signal. Analyze the circuit and design it so that it can remove a 1.8-V DC offset from a sensor output signal.

29 Figure 8.17 Figure 8.16 level shifter

30 Check your understand With reference to Example 8.5, find ∆R if the supply voltages are symmetric at +or- 15V and a 10-kΏ resistors. With reference to Example 8.5, find the range of value of V ref if the supply voltages are symmetric at +or- 15V and a 1-kΏ potentiometer id tied to the two 10-k Ώ resistors.

31

32 Example 8.6 Temperature Control Using Op- Amps

33

34 Check your understand How much steady-state power, in Watts, will be input to the thermal system of Example 8.6 to maintain its temperature in the face of a 10ºC ambient temperature drop for values of K p of 1, 5, and 10.

35 Active Filters The class of filters one can obtain by means of op-amp designs is called active filters. Figure 8.19 op-amp circuit employing complex impedances

36 Active low-pass filter Normalized response of active low-pass filter

37 Normalized response of active high-pass filter Active high-pass filter

38 Normalized amplitude response of active bandpass filter Active bandpass filter

39 Example 8.7 Second- Order Low-Pass Fiter Determine the closed-loop voltage gain as a function of frequency for the op-amp circuit of Figure 8.27.

40

41 Check your understand

42 The Ideal Integrator Op-amp integrator

43 Example 8.8 Integrator a square Wave Determine the output voltage for the integrator circuit of Figure 8.30 if the input is a square wave of amplifier +or- A and period T.

44

45 Check your understand Plot the frequency response of the ideal integrator in the form of a Bode Plot. Determine the slope of the straight-line segments in decibels per decade. You may assume R s C F = 10.

46 The Ideal Differentiator Op-amp differentiator

47 Voltage Supply Limits The effect of limiting supply voltages is that amplifiers are capable of amplifying signals only within the range of their supply voltages.

48 Example 8.9 Voltage Supply Limits in an Inverting Amplifier Compute and sketch the output voltage of the inverting amplifier of Figure 8.33.

49 Figure 8.34 Op-amp output with voltage supply limit

50 Example 8.10 Voltage Supply Limits in an Op-Amp Integrator Compute and sketch the voltage of the integrator of Figure 8.35.

51 Figure 8.36 Effect of DC offset on integrator

52 Check your understand How long will it take for the integrator of Example 8.10 to saturate if the input signal has a 0.1-V DC bias [that is, ύ s (t) = cos(10t)]?

53 Frequency Response Limit Another property of all amplifiers that may pose severe limitations to the op-amp is their finite bandwidth.

54 Open-loop gain of practical op-amp The finite bandwidth of the practical op-amp results in a fixed gain-bandwidth product for any given amplifier.

55 Another limitation of practical op-amps results because even in the absence of any external inputs, it is possible that an offset voltage will be present at the input of an op-amp.

56 Example 8.11 Gain-Bandwidth Product Limit in an Op-Amp Determine the maximum allowable closed- loop voltage gain of an op-amp if the amplifier is required to have an audio-range bandwidth of 20 kHz.

57

58 Check your understand What is the maximum gain that could be achieved by the op-amp of Example 8.11 if the desired bandwidth is 100kHz?

59 Example 8.12 Increasing the Gain-Bandwidth Product Means of Amplifier in Cascade Determine the overall 3-dB bandwidth of the cascade amplifier of Figure 8.39.

60

61 Check your understand What is the actual gain in decidals at the cutoff frequency ω 0 for the cascade amplifier? What is the 3-dB bandwidth of the cascade amplifier of Example 8.12?

62

63 Example 8.13 Effect of input Offset Voltage on an Amplifier Determine the effect of the input offset voltage V os on the output of the amplifier of Figure 8.40.

64

65 Check your understand What is the maximum gain that can be accepted in the op-amp circuit of Example 8.13 if the offset is not to exceed 50 mV?

66 Input Bias Current Another nonideal characteristic of op-amps results from the presence of small input bias currents at the inverting and noninverting terminals. Figure 8.14

67 Example 8.15 Effect of slew Rate Limit on an Amplifier Determine the effect of the slew rate limit S 0 on the output of an inverting amplifier for a sinusoidal input voltage of known amplifier and frequency.

68 Figure 8.46 Distortion introduced by slew rate limit

69 Check your understand Given the desired peak output amplifier(10V), What is the maximum frequency that will not result in violating the slew rate limit for the op-amp of Example 8.15?

70 Example 8.16 Effect of Short Circuit Current Limit on an Amplifier Determine the effect of short circuit limit I sc on the output of an inverting amplifier for a sinusoidal input voltage of known amplitude.

71 Figure 8.48 Distortion introduced by short-circuit current limit