The operational amplifier

This particular integrated circuit has come to have wide applications because of its very high gain, its ability to carry out simple mathematical functions such as addition and subtraction, multiplication, differentiation and integration, and its use as a voltage comparator circuit or oscillator.
It is particularly useful because of its following properties:
(a) very high open loop voltage gain (A_o) - up to 10⁵ (100 000) for d.c. - although this does decrease with frequency (see later)
(b) a very high input resistance so that it draws virtually no current from the input signal;
(c) a very low output resistance
(d) it is a differential amplifier, giving an amplified output signal proportional to the difference between the two input signals providing that this difference is not too large (see later).

A common form of op amp used in schools is the type 741. This is made in what is called an 'eight-pin dual in line form' and is shown diagrammatically in Figure 1 together with the symbol for an operational amplifier (shortened to the words op amp.)

Of the eight pins on the op amp we are interested in only five:
(a) the inverting input (P) - inputs here will be changed in sign (pin 2)
(b) the non-inverting input (Q) - inputs here will not be changed in sign (pin 3)
(c) the output (F) (pin 6)
(d) the positive supply (+V_S) (pin 7)
(e) the negative supply (-V_S) (pin 4)

We will call the voltage at the inverting input V₁ and that at the non-inverting input V₂.
The positive and negative supply connections are shown on the above diagram but they will be assumed and omitted from the following circuits.

The internal circuitry of an op amp is complex and outside the scope of this section of work (the 741 contains twenty transistors, eleven resistors and one capacitor). We shall treat it as a 'black box' that will perform certain functions if connected into a circuit correctly.

The circuit symbol represents an 'open loop' amplifier with an 'open loop gain' A_o.
The output potential (V_o) is proportional to the DIFFERENCE in the potential between P and Q (i.e. to [V₂ - V₁]). Where V₁ is the input at the inverting input (P) and V₂ is the input at the non-inverting input (Q).

In fact it is given by the equation:

This is true providing the output potential is less than that of the supply voltage V_S. When V_o reaches V_S the op amp is said to be SATURATED. This can be seen from Figure 2 which is known as the transfer characteristic for the op amp.

Te output voltage lies between + V_S and – V_S. The supply voltage used in most examples in this book is 15 V and so V_o must be between +15V and -15V.
You can see that there is a small region between A and B where the graph rises linearly and it is in this region that the op amp is operated as an amplifier.



Since A_o is about 100 000 the op amp will saturate for a difference of potential between P and Q of more than 150 μV. (100 000 x 150x10^-6 = 15 V)

If the difference is more than 150 μV the output will be +15 V if V₁ < V₂ and -15V if V₁ > V₂.

Variation of gain with frequency

The open loop gain varies with frequency and this is shown in Figure 3. As the frequency of the input signal increases so the open loop gain falls. This can be explained by the decreased mobility of the charge carriers through the semiconductor material.

Feedback

An important property in various areas of Physics, particularly in electronics is that of feedback.

Feedback is the term used to describe the situation where a certain fraction of the output of a device is fed back to the input.
There are two types of feedback:
(a) negative feedback - this tends to reduce the output. A simple example of this is the flow of silty water through a hole. The slower the flow the more silt settles and the quicker the hole fills up and the slower the rate becomes and so on;
(b) positive feedback - this tends to increase the output. This is shown by a snowball rolling down a hill, the bigger it is the more snow it picks up and the bigger it becomes, and so on.

Voltage comparator

A voltage comparator circuit, as its name suggests is used to compare one voltage with another.
The op amp can do this.

If both inputs of the op amp are used at the same time the output voltage V_o is given by:

where V₁ is the inverting input and V₂ is the non- inverting input (Figure 4). The voltage difference between the two inputs is therefore amplified and appears at the output.

Alternatively, we can regard the circuit as one in which voltage 1 is amplified, voltage 2 is inverted and then amplified, and the difference between these final voltages is found.