##### 1.5 OPERATIONAL AMPLIFIERS

An operational amplifier (op-amp) is a high-gain direct-coupled amplifier and, as shown in Fig. 1.41, has three basic building blocks—a differential amplifier as an input stage, dc-level shifter or level translator and an output power stage.

The differential amplifier gives an output proportional to the difference between the two inputs. As the op-amp is a direct-coupled amplifier, the output is referenced to a dc voltage. If there is a need to ensure that the output is referenced to the zero level, there arises the need for a level translator or a dc level shifter, which translates the dc voltage at the output to zero. An operational amplifier, unless otherwise warranted, needs to be balanced before it is used for an application. When the two inputs are grounded, if there is a dc voltage at the output, it is adjusted to zero. This is called balancing an op-amp. An op-amp is schematically represented as in Fig. 1.42. It has two inputs, an inverting input and a non-inverting input.

**FIGURE 1.41** The basic building blocks of an operational amplifier

An op-amp, being a high-gain amplifier, may oscillate at high frequencies. To overcome this problem, frequency compensation is provided in the amplifier which reduces the gain at those frequencies. However, the most popular commercially available 741 op-amp is internally compensated. To balance 741, between pins 1 and 5, a 10-kΩ potentiometer is connected and its centre tap is returned to – *V _{EE}* source (|

*V*| = |

_{CC}*V*|), as shown in Fig. 1.43.

_{EE}The op-amp can be used in many applications. Consider the inverting amplifier shown in Fig. 1.44. Ideally an op-amp has *R _{i}* = ∞,

*R*= 0,

_{o}*A*= ∞. Since

_{V}*A*=

_{V}*v*, as

_{o}/v_{i}*A*→ ∞,

_{V}*v*→ 0. This implies that there exists a short circuit at the input. If really there exists a short circuit at the input, the entire current

_{i}*I*should flow through this short circuit. However, we also have

*R*= ∞, which means that there exists an open circuit between the input terminals, in which case the entire input current

_{i}*I*now should flow through

*R*

^{′}. These are two contradictory conditions. However, as

*A*is very large,

_{v}*v*is very small. Hence, for all practical purposes, the two input nodes are at the same potential. Thus, we can say there exists a virtual ground at the input and as

_{i}*R*is very large, the input current

_{i}*I*flows through

*R*

^{′}. Hence, the equivalent circuit of inverting amplifier in Fig. 1.44 is drawn as shown in Fig. 1.45.

From the equivalent circuit in Fig. 1.45

*v _{o}* = −

*IR*

^{′}and

*v*=

_{s}*IR*

**FIGURE 1.42** Schematic representation of an op-amp

**FIGURE 1.43** Balancing of the 741 op-amp

**FIGURE 1.44** An op-amp as an inverting amplifier

**FIGURE 1.45** Simplified equivalent of Fig. 1.44

An op-amp can be used as an non-inverting amplifier, differential amplifier, subtracting amplifier, logarithmic and antilog amplifier, in active filters and in many more analogue applications. We are going to consider some of the applications later.

When an op-amp is used as a differential amplifier, the signal at the output is required to be proportional to the difference of the two input signals, *v*_{1} and *v*_{2}, called the difference signal, *v _{d}*. However, there appears a common mode signal,

*v*which is due to the average of the two input signals,

_{c}*v*

_{1}and

*v*

_{2}which gives rise to an error term in the output. Therefore,

Where *A _{d}* is the differential gain and

*A*is the common mode gain. The second term in Eq. (1.49) in the output is due to an unwanted error signal which should ideally be zero.

_{c}The goodness of an operational amplifier—how effectively the op-amp is able to reject the unwanted common mode signal and deliver only the differential signal at the output—is given by the common mode rejection ratio (CMRR), also known as *ρ*. It is the figure of merit of a differential amplifier.

Substituting Eq. (1.50) in Eq. (1.49):

If the signal in the output due to the common mode component is to be zero, ideally, *ρ* → ∞, then *v _{o}* =

*A*. In practice,

_{d}v_{d}*ρ*should be very large. However, the main limitation in an op-amp is its slew rate, defined as the maximum time rate-of-change of the output voltage

*v*under large signal conditions.

_{o}The slew rate *S* limits the maximum frequency and amplitude to which the op-amp can respond. If *v _{o}* =

*V*, then

_{m}sin ωt*dv*=

_{o}/dt*ωV*cos

_{m}*ωt*. Now, (

*dv*) is maximum when cos

_{o}/dt*ωt*= 1. Therefore, the slew rate

*S*is given by the relation:

The maximum amplitude at the output is:

If the op-amp has *S* = 10 V*/μs* and if *f* = 1 MHz, then the maximum possible output voltage is:

If *f* = 0.1 MHz:

Thus, to derive a larger output voltage we have to sacrifice bandwidth. Else, to derive larger bandwidth we have to be content with smaller output.