Chapter 2ElectronicsSection 4 Operational Amplifiersn Textn New Words and Expressionsn Exercisesn Endn Translation of Long SentencesSection 4 Operational AmplifiersIntroductionOperational amplifiers are high-gain difference amplifiers, which were perfected during World War II. They became the foundation of analog computers, at one time analog computers were called “differential analyzers“ because they are used to solve differential equations. Operational amplifiers are also the basis of many important instruments. Section 4 Operational AmplifiersThe analog amplifier consists of a basic difference amplifier, implemented by feedback and other compensating amplifying circuits to give linear response, stability, freedom from drift, and other desirable properties. The complexity is required because operational amplifiers amplify dc as well as ac signals, capacitive coupling between amplifying stages is not permitted. Thus it is more difficult to isolate the long-term changes that arise from variations in temperature and power-supply voltage and from other effects that cause the output voltage to drift. Section 4 Operational AmplifiersAfter the invention of the transistor, solid-state operational amplifiers were introduced as integrated circuits. Now operational amplifiers are used to make high-quality, low-power analog amplifier, and it is possible to avoid designing individual transistor amplifier stages for many application. For most amplifying purposes and for many measuring and control applications, simple arrangements of operational amplifiers with feedback circuits will meet the designers needs. The availability of operational amplifiers as integrated circuits in theSection 4 Operational Amplifiersform of dual in-line packages (DIPs) or in other compact forms makes the solution of analog signal problems analogous in many respects to the solution of digital logic problems, that is, through the interconnection of integrated circuits. Operational AmplifierFig.2-5 shows the symbol for an operational amplifier. There are two inputs: the one marked with a plus sign is the noninverting input, and the one marked with a minus sign is the inverting input. The voltage amplified by the operational amplifier is the voltage difference between the two inputs. Section 4 Operational AmplifiersThe open-circuit gain is so large, l05 to l06, that a voltage difference of only a few microvolts will give an appreciable output. Because the operational amplifier is a difference amplifier, connections must always be made to both input terminals for proper operation. Fig.2-5 A symbol for an operational amplifier Section 4 Operational AmplifiersIf two different positive voltages are applied separately to the two inputs, the output of the operational amplifier will be at the maximum (saturated) value if the voltage at the noninverting input is larger than the voltage at the inverting input. If the voltages exchange their relative values that is, if the inverting input exceeds the noninverting inputthe operational amplifier will switch to a minimum output, which is the saturated negative voltage. The switching occurs very quickly whenever the relative values of the voltages change. Section 4 Operational AmplifiersWe will see that an operational amplifier is an excellent voltage comparator because it produces a large voltage swing at the instant of crossing, when an earlier relation in voltage magnitudes is reversed by only a few microvolts. If the operational amplifier is to operate in its linear range, a very small voltage difference must exist between the inverting and the noninverting inputs. In analyzing operational amplifying circuits, we assume, because of the large open-circuit gain, Section 4 Operational Amplifiersthat the voltage difference across the inputs is negligible. In some cases we will set the voltage to zero. When a portion of the output signal is returned to the input as negative feedback, the voltage difference cannot grow large because the output changes to minimize the voltage difference between the inputs.Two additional properties are present in operational amplifiers. They are a very high input impedance, approximately l06, and a low output impedance, approximately l00. These propertiesSection 4 Operational Amplifierscontribute to the usefulness of operational amplifiers by allowing signal sources with small current capabilities to drive operational amplifiers directly. In turn, operational amplifiers may drive devices that have severe signal requirements.To summarize, a good operational amplifier is characterized by a very large open-circuit gain of a million or so, an extremely small difference voltage between the inverting and the noninverting input terminals, a very high input impedance, and a small output impedance. An ideal operational amplifier, Section 4 Operational Amplifiershowever, would