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OpAmps01 - Ideal Op Amp Circuits The operational amplier or...

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Ideal Op Amp Circuits The operational ampli fi er, or op amp as it is commonly called, is a fundamental active element of analog circuit design. It is most commonly used in ampli fi er and analog signal processing circuits in the frequency band from 0 to 100 kHz . High-frequency op amps are used in applications that require a bandwidth into the MHz range. The fi rst op amps were vacuum-tube circuits which were developed for use in analog computers. Modern op amps are fabricated as integrated circuits that bare little resemblance to the early circuits. This chapter covers some of the basic applications of the op amp. It is treated as an ideal circuit element without regard to its internal circuitry. Some of the limitations imposed by non-ideal characteristics are covered in the following chapter. The notation used here is as follows: Total quantities are indicated by lower-case letters with upper- case subscripts, e.g. v I , i O , r IN . Small-signal quantities are indicated by lower-case letters with lower-case subscripts, e.g. v i , i o , r out . Transfer function variables and phasors are indicated by upper case letters and lower-case subscripts, e.g. V i , I o , Z in . 1.1 The Ideal Op Amp The ideal op amp is a three terminal circuit element that is modeled as a voltage-controlled voltage source. That is, its output voltage is a gain multiplied by its input voltage. The circuit symbol for the ideal op amp is given in Fig. 1.1(a). The input voltage is the di ff erence voltage between the two input terminals. The output voltage is measured with respect to the circuit ground node. The model equation for the output voltage is v O = A ( v + v ) (1.1) where A is the voltage gain, v + is the voltage at the non-inverting input, and v is the voltage at the inverting input. The controlled source model of the ideal op amp is shown in Fig. 1.1(b). Figure 1.1: (a) Op-amp symbol. (b) Controlled-source model. The terminal characteristics of the ideal op amp satisfy four conditions. These are as follows: 1. The current in each input lead is zero. 2. The output voltage is independent of the output current. i
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ii IDEAL OP AMP CIRCUITS 3. The voltage gain A is independent of frequency. 4. The voltage gain A is very large, approaching in fi nity in the limit. The fi rst condition implies that the resistance seen looking into both input terminals is in fi nite. The second implies that the voltage gain is independent of the output current. This is equivalent to the condition that the output resistance is zero. The third implies that the bandwidth is in fi nite. The fourth implies that the di ff erence voltage between the two input terminals must approach zero if the output voltage is fi nite. For it to act as an ampli fi er, the op amp must have feedback applied from its output to its inverting input. That is, part of the output voltage must be sampled by a network and fed back into the inverting input. This makes it possible to design an ampli fi er so that its gain is controlled by the feedback network.
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