**Chapter 11: Op-Amp Applications**

One of the most common op-amp circuits is the inverting constant-gain multiplier, which provides a precise gain or amplification. Figure 11.1 shows a standard circuit connection, with the resulting gain being given by

**(11.1)** **FIG. 11.1**

*Fixed-gain amplifier.* **EXAMPLE 11.1 **Determine the output voltage for the circuit of Fig. 11.2 with a sinusoidal input of 2.5 mV.

**FIG. 11.2**

*Circuit for Example 11.2. * *Solution: *The circuit of Fig. 11.2 uses a 741 op-amp to provide a constant or fixed gain, calculated from Eq. (11.1) to be

The output voltage is then

A noninverting constant-gain multiplier is provided by the circuit of Fig. 11.3, with the gain given by

**(11.2) ** **FIG. 11.3**

*Noninverting fixed-gain amplifier.* **EXAMPLE 11.2 **Calculate the output voltage from the circuit of Fig. 11.4 for an input of 120

V.

*Solution: *The gain of the op-amp circuit is calculated using Eq. (11.2) to be

The output voltage is then

**FIG. 11.4**

*Circuit for Example 11.2.* **Multiple-Stage Gains **
When a number of stages are connected in series, the overall gain is the product of the individual stage gains. Figure 11.5 shows a connection of three stages. The first stage is connected to provide noninverting gain as given by Eq. (11.1). The next two stages provide an inverting gain given by Eq. (11.1). The overall circuit gain is then noninverting and is calculated by

where

**FIG. 11.5**

*Constant-gain connection with multiple stages. * **EXAMPLE 11.3 **Calculate the output voltage using the circuit of Fig. 11.5 for resistor components of value

*Rf* = 470 k

,

*R*1 = 4.3 k

,

*R*2 = 33 k

, and

*R*3 = 33 k

for an input of 80

V.

*Solution: *The amplifier gain is calculated to be

so that

**EXAMPLE 11.4 **Show the connection of an LM124 quad op-amp as a three-stage amplifier with gains of +10, –18, and –27. Use a 270-k

feedback resistor for all three circuits. What output voltage will result for an input of 150

V?

*Solution: *For the gain of +10,

For the gain of –18,

For the gain of –27,

The circuit showing the pin connections and all components used is given in Fig. 11.6. For an input of V1 = 150

V, the output voltage is

*Vo* =

*A*1

*A*2

*A*3

*V*1 = (10)(–18)(–27)(150

V) = 4860 (150

V) =

**0.729 V** **FIG. 11.6**

*Circuit for Example 11.4 (using LM124). *
A number of op-amp stages could also be used to provide separate gains, as demonstrated in the next example.

**EXAMPLE 11.5 **Show the connection of three op-amp stages using an LM348 IC to provide outputs that are 10, 20, and 50 times larger than the input. Use a feedback resistor of

*Rf* = 500 k

in all stages.

*Solution: *The resistor component for each stage is calculated to be

The resulting circuit is drawn in Fig. 11.7.

**FIG. 11.7**

*Circuit for Example 11.5 (using LM348).*