Operational amplifiers, or op-amps, are perhaps the most common building blocks found in analogue circuits. They can be used to create amplification stages very easily, and many other types of circuit besides. There are very many ‘op-amp cookbooks’ around that give lots of these circuits, so we won’t add to them here. The main purpose of this chapter is to present you with a pair of tables to enable easy selection of resistor values for any desired gain.

We’ll take a moment, however, to state the two rules that govern an op-amp’s behaviour for the purpose of achieving a first-off analysis of their circuits:

1. The input terminals of op-amps draw no current.

2. The output of the op-amp does whatever it can to keep the voltage between the input terminals at zero.

These two statements are something of a generalization, but they are fine if you want to work out what an op-amp circuit is doing.

There are two common ways to use op-amps as amplifier stages. We look at them next.

Figure 11.1 shows a basic inverting op-amp circuit. This circuit can be used to give either attenuation or gain with two resistors. The output is in antiphase with the input. The gain is given by:

Values of *R*_{1} and *R*_{2} can be found from Table 11.1, where gain is given both as a ratio and in dBs. *R*_{1} and *R*_{2} may, of course, be scaled by factors of 10 without affecting the gain. The Table only shows values above unity gain (0 dB). If you need to select a pair of resistors to give attenuation, then the Table can still be used, but the positions of *R*_{1} and *R*_{2} should be switched. The dB column then reads attenuation directly, or the *A*_{V} column the reciprocal of gain expressed as a ratio.

The input resistance of the circuit is equal to the value of the input resistor, *R*_{1}*.*

The output resistance is, for practical purposes, negligible. (Limitations on its ability to drive a load will be dependent on maximum values of output current, voltage swing and slew rate, for which the manufacturer’s data on the chip used should be consulted.)

It is sometimes desirable to limit the frequency response of the circuit. The standard method is to add suitable value capacitors, as in Figure 11.2. *C*_{1}, in series with the input resistor, limits low frequency response, while *C*_{2}, in parallel with *R*_{2}*,* limits high frequency response. Each gives a 6 dB/octave slope, as for the first order LPF and HPF described in Chapter 9. The equations for the lower −3dB point, *f*_{t–}, and the upper−3 dB point, *f*_{t+}, are also similar:

Figure 11.3 shows a non-inverting op-amp circuit, in its most basic configuration. This circuit has a gain as follows:

This means that the circuit can only provide gain of greater than 1. Its input impedance is very large, and is not usually taken into account. As with the inverting op-amp, its output impedance is very low, with the same restrictions on output drive applying (Figure 11.4).

Where it is desired to restrict the bandwidth of the stage, capacitors *C*_{1} and *C*_{2} are added. The calculations are identical to those for the inverting stage. Note that with *C*_{1} in this position the input signal must have some defined DC level. If the input is connected using a DC block capacitor then *C*_{1} must be omitted so that the op-amp has a DC reference. If it is desired to limit the low frequency response of the stage it is sometimes better to connect the input via a suitable high-pass filter, as described in Chapter 9.

The main advantage of this stage (other than its being non-inverting) is that of its input impedance. It makes an ideal buffer stage, after circuits which are sensitive to load impedance (such as the reactive circuits described in Part Two).

Where it is desired to use this circuit without gain, purely as a buffer stage, it is customary to omit *R*_{1} and make *R*_{2} short circuit – i.e. to link the output terminal to the inverting input terminal, as in Figure 11.5. This is a ‘voltage follower’. The output is identical to the input, but comes from a very low source impedance.

Values for *R*_{1} and *R*_{2} for the non-inverting amplifier can be selected using Table 8.1, in the ‘Voltage dividers’ chapter. The dB column gives values of gain directly, and the A column values of the reciprocal of gain as a ratio. *R*_{1} from the table should be fitted as position *R*_{2} from Figure 11.3 and *R*_{2} as *R*_{1}*.* As usual, *R*_{1} and *R*_{2} can be scaled by factors of 10 if desired.

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