Chapter 15: Operational Amplifiers Objectives After studying the material in this this chapter, you you should be able able to: 1. Desc Descri ribe be the the operational amplifier, or op-amp. op-amp. 2. State State the the purp purpose ose served served by a differential amplifier. 3. Describe Describe open-loo open-loop p voltage gain gain and state its typical typical range range of values. values. 4. Describe Describe the operati operation on of a discrete discrete differentia differentiall amplifier. amplifier. 5. Describe Describe the the various various voltage voltage and current current ratings ratings for an op-amp op-amp.. 6. Discuss Discuss the effects effects of common-mo common-mode de rejection rejection ratio ratio on op-amp operatio operation. n. 7. Discuss the relationship relationship between slew-rate and op-amp op-amp operating operating frequency. frequency. 8. Discuss slew-rate distortion distortion and the the means by by which it can be reduced. reduced. 9. Describe Describe and and analyze analyze the operation operation of the inverti inverting ng amplifier amplifier.. 10.Describe and analyze the operation of the noninverting amplifier. 11.Compare and contrast the operating characteristics characteristics of the inverting and noninverting amplifiers. 12.List the common op-amp faults and the symptoms of each. 13.Define gain-bandwidth product and explain its significance. 14.Describe the various types of feedback. 15.Describe the effects of negative feedback on inverting amplifier gain and bandwidth. 16.Calculate the attenuation factor and factor and feedback factor for factor for a given feedback amplifier. 17.Calculate the input and output impedance values for inverting and noninverting amplifiers.
Introduction The active devices devices discussed discussed in previous chapters chapters are all discrete components, components , meaning that each physical package contains a single component. In contrast, an integrated circuit contains circuit contains any number of active and/or passive components constructed on a single piece of semiconductor material. This chapter focuses on an an integrated circuit circuit called an operational amplifier . The operational amplifier (or op-amp) op-amp) is a high-gain dc amplifier that has extremely high input impedance and low output impedance. The topics discussed in this chapter include: Op-amp packages and component codes Op-amp operation and characteristics characteristics Differential amplifier operation Op-amp specifications specifications Inverting amplifier operation, analysis, and fault symptoms Noninverting amplifier operation, analysis, and fault symptoms Op-amp frequency response Negative feedback • • • • • • • •
The op-amp is a high-gain dc amplifier that has extremely high input impedance and low output impedance. The op-amp schematic symbol is shown in Figure 15.1. (Note that the component also has offset null input pins that are not shown in the figure.)
The signal inputs to the op-amp are labeled inverting and noninverting . In most cases, an input signal is applied to one of these inputs, while the other is used to control the operating characteristics of the device. The application determines which input is used as the signal input.
FIGURE 15.1 Op-amp schematic symbol. The power supply inputs, +V and –V , are normally connected as shown in Figure 15.2. As shown, the component can operate with dual-polarity or single-polarity supply voltages.
FIGURE 15.2 Supply voltage connections. Op-amps are available in a variety of packages, including metal cans, dual in-line packages (DIPs), and surface mount packages (SMPs). Two common packages are shown in Figure 15.3. An 8-pin DIP is illustrated in Figure 15.3.
FIGURE 15.3 Op-amp packages. The component contained in a given package is identified by a code printed on the package.
Operation Overview The input stage of the op-amp is a differential amplifier —a circuit that amplifies the difference between two input voltages, as shown in Figure 15.4. The op-amp output for a given pair of inputs depends on several factors: The gain of the amplifier The polarity relationship between V 1 and V 2 The values of the supply voltages The load resistance • • • •
FIGURE 15.4 Op-amp differential input voltage. Op-amp gain. The open-loop voltage gain ( AOL) of an op-amp is its maximum possible value of voltage gain. The value of AOL is typically 10,000 or greater, with values in the range of 200,000 being common. Values of Av in this range are virtually impossible for a single BJT or FET. The term open-loop means that there is no feedback path between the output and the input terminals. In practical applications, a feedback path is generally added to limit the voltage gain of the circuit to a desired value. (This is discussed later in the chapter.) Input/output polarity . When the voltage at the noninverting input ( V 2) is the more positive of the two input voltages, the output swings toward + V . When the voltage
at the inverting input (V 1) is the more positive of the two input voltages, the output swings toward –V . Relating these statements to the op-amp schematic symbol: When the noninverting (+) input is the more positive of the two, the output swings toward +V . When the inverting (–) input is the more positive of the two, the output swings toward –V . Equation 15.1 can also be used to determine the polarity of the op-amp output voltage for a given set of input voltages. Supply voltages. The supply voltages determine the absolute limits on the output voltage swing. The output from an op-amp can never exceed some value that is slightly less than the supply voltages. Load resistance. The peak-to-peak output from an op-amp is also affected by the value of the load resistance. When the curves for an op-amp are not available, you can estimate the maximum possible output from the component using the following guidelines: When RL > 10 k , the output from the op-amp is limited to approximately (– V + 1 V) and (+V – 1 V). When 2 k RL 10k , the output from the op-amp is limited to approximately (–V + 2 V) and (+V – 2 V). When RL < 2 k , you must use the load resistance versus output voltage curve to determine the limits on the op-amp output. The Basic Differential Amplifier A differential amplifier produces an output voltage that is proportional to the difference between two input voltages. A basic differential amplifier is shown in Figure 15.5. Note that conventional emitter current is in the direction shown in the figure. (Electron flow is in the opposite direction.) The base of Q1 is the inverting input (I). The base of Q2 is the noninverting input (NI). The output voltage (V out) is measured at the collector of Q1 with respect to the collector of Q2. The two transistors share a common emitter resistor. Assuming that the transistors are perfectly matched and the base currents are equal: IE1 = IE2 and IC1 = IC2 Assuming that RC1 = RC2, the transistor collector voltages are equal, and V out = 0 V. Note that V out 0 V whenever the inputs to Q1 and Q2 are equal. •
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FIGURE 15.5 A basic differential amplifier. When the inputs to Q1 and Q2 are equal (as described above), the differential amplifier is said to be in common-mode operation. There are two other operating modes for a differential amplifier: Single-ended mode. In this mode, an active input signal is applied to one input of the differential amplifier. The other input is usually returned to ground (directly or via a resistor). Differential mode. In this mode, active input signals are applied to both inputs. The output amplitude and polarity depends on the relationship between those inputs. The most common op-amp circuits use single-ended mode operation. When the active input signal is applied to the inverting input, the input and output voltages are 180° out of phase. When operated in this fashion, the circuit is referred to as an inverting amplifier . When the active input signal is applied to the noninverting input, the input and output voltages are in phase. When operated in this fashion, the circuit is referred to as a noninverting amplifier . Op-Amp Specifications Here are some of the ratings that are commonly included on the spec sheet for a given op-amp: Output offset voltage. This is a voltage that may appear at the output of an opamp. It is caused by an imbalance in the differential amplifier ( V BE1 V BE2). This imbalance results in one transistor conducting harder than the other. Input offset voltage. This is the difference between the values of V BE for the transistors in the differential amplifier that produces an output offset voltage when the signal inputs are grounded. •
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Input offset current. This is the slight difference between the values of IB1 and IB2 that can be caused by differences in the transistor beta ratings. The effects of input offset current are minimized using a compensating resistor . Input bias current. This is the average value of quiescent dc biasing current drawn by the signal inputs of an op-amp. Since both inputs require a biasing current, an op-amp will not work if either of its inputs is open . Common-mode rejection ratio (CMRR). This is a measure of the ability of an opamp to “ignore” common-mode signals, equal to the ratio of differential gain to common-mode gain. Common-mode signals are identical signals that are applied simultaneously to the two inputs of an op-amp, as shown in Figure 15.6.
FIGURE 15.6 Common-mode input signals. Ideally, the output from an op-amp is 0 V when common-mode signals are applied. Therefore, the ideal CMRR ratio is found as
The practical CMRR of an op-amp (or op-amp based circuit) is always lower than this value. Power supply rejection ratio. This is the ratio of a change in op-amp output voltage to a change in supply voltage, generally in the V/V range. For example, a 5 V/V rejection ratio means that the output voltage will change by 5 V for each 1 V change in supply voltage. Output short-circuit current. This is the maximum output current for an op-amp, measured under shorted load conditions. Slew rate. This is the maximum rate at which the output voltage from an op-amp can change. The slew rate of an op-amp determines its maximum operating frequency (along with the amplitude of the amplifier output). Input and output resistance. These ratings typically fall within the following ranges: Rin 1 M and Rout 100 . These ranges are consistent with our definition of an op-amp as a device with extremely high input resistance and low output resistance. Some other op-amp characteristics are listed below. Input voltage range. This is the maximum allowable differential input to an opamp. Large signal voltage gain. This is the open-loop voltage gain of an op-amp. Supply current. This is the current that an op-amp draws from its power supply when in its quiescent (inactive) state.
Power consumption. This is the power that an op-amp dissipates when in its quiescent state. Inverting Amplifiers The inverting amplifier is the op-amp counterpart of the common-emitter and common-source amplifiers. The circuit produces a 180° signal voltage phase shift from input to output. An inverting amplifier is shown in Figure 15.7. For the circuit shown:
Z in
Rin
Note the following: Z out is lower than the op-amp output impedance. Many references represent ACL as being negative to indicate the 180° phase shift of the circuit. ACM (in the CMRR equation) is the common-mode gain of the op-amp. • •
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FIGURE 15.7 The inverting amplifier. Noninverting Amplifiers The noninverting amplifier has most of the characteristics of the inverting amplifier. However: 1. It has much higher circuit input impedance. 2. It does not produce a 180° voltage phase shift from input to output; i.e., the input and output voltages are in phase. A noninverting amplifier is shown in Figure 15.8. For the circuit shown:
Note that the amplifier values of Z in and Z out are determined primarily by the op-amp input and output impedance ratings.
FIGURE 15.8 A noninverting amplifier. Figure 15.9 shows a special-case noninverting amplifier called a voltage follower . This circuit, which has a value of ACL = 1, is the op-amp counterpart of the emitter follower and source follower circuits.
FIGURE 15.9 The voltage follower. Op-Amp Frequency Response The op-amp is a dc amplifier ; meaning that it exhibits midband gain when operated at 0 Hz. Op-amp gain remains relatively constant at frequencies below some upper cutoff frequency (f C). When operated above f C, the voltage gain of the op-amp decreases at a rate of 20 dB per decade, as shown in Figure 15.10.
FIGURE 15.10 Op-amp frequency response. When the operating frequency of an op-amp continually increases, a frequency is reached where the gain of the component drops to 0 dB (unity). The frequency at which this occurs is called the unity-gain frequency . The unity gain frequency of an op-amp equals its gain-bandwidth product , as follows: ACLf C = f unity This relationship can be used to determine: The maximum value of ACL at a given value of f C The value of f C for a given value of ACL • •
The gain-bandwidth relationship also provides a means of measuring the unity-gain frequency of an op-amp, as follows: 1. Set up an inverting amplifier with a gain of 100 (an easy value to design for). 2. Apply an input signal, and increase the frequency until the peak-to-peak output voltage drops to 0.707 times the midband value. 3. Using the measured value of f C, solve the following equation: f unity = 100f C Negative Feedback Negative feedback provides a feedback signal that is 180° out of phase with the circuit input signal. An amplifier with negative feedback can be represented as shown in Figure 15.11a. Negative feedback is generally used to control the operating characteristics of an amplifier.
FIGURE 15.11 Negative feedback. Inverting and Noninverting Amplifier Operation The feedback path in the inverting amplifier (Figure 15.11b) is a negative feedback path. Connecting this negative feedback path to the op-amp: Reduces the amplifier voltage gain. Reduces the amplifier input and output impedance. Increases the amplifier bandwidth The feedback path in a noninverting amplifier is also a negative feedback path. In terms of circuit voltage gain and bandwidth, the feedback path has the same effect as it does in the inverting amplifier. • • •
Mathematical Analysis
A noninverting amplifier can be represented as shown in Figure 15.12. The ratio of feedback voltage to output voltage (shown in the figure) is the attenuation factor ( ) of the feedback network. Because v f < v out, the value of
is always less than 1.
FIGURE 15.12 Alternate representation of a noninverting amplifier. The overall voltage gain of a feedback amplifier such as the one in Figure 15.12 can be found as: or The Avf equation is important because it establishes the feedback factor of a negative feedback amplifier. The feedback factor (1 + Av ) in the denominator of the fraction appears (in one form or another) in most of the amplifier relationships. In most cases,
. As a result, the ACL equation can be simplified as follows:
or The relationship above is important because it is used to determine the feedback factor for a noninverting (or inverting) amplifier. The effects that the feedback factor has on the values of Z in and Z out for the inverting and noninverting amplifiers are illustrated in Figure 15.13.
FIGURE 15.13 Impedance relationships.
