Operational Amplifiers
Ideal Op Amp Circuits
The operational amplifier, or op amp as it is commonly called, is a fundamental active element of analog circuit design. It is most commonly used in amplifier 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 first 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 uppercase subscripts, e.g. vI , iO , rIN . Small-signal quantities are indicated by lower-case letters with lower-case subscripts, e.g. vi , io , rout . Transfer function variables and phasors are indicated by upper case letters and lower-case subscripts, e.g. Vi , Io , Zin .
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 difference 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 vO = 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
The operational amplifier, or op amp as it is commonly called, is a fundamental active element of analog circuit design. It is most commonly used in amplifier 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 first 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 uppercase subscripts, e.g. vI , iO , rIN . Small-signal quantities are indicated by lower-case letters with lower-case subscripts, e.g. vi , io , rout . Transfer function variables and phasors are indicated by upper case letters and lower-case subscripts, e.g. Vi , Io , Zin .
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 difference 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 vO = 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