Having outlined the problems we can now examine the application of feedback and see how this may help us reduce their magnitude.
Figure 4·3 shows the amplifier in two situations. 4·3a shows the amplifier with no applied feedback. 4·3b shows a modified circuit where a pair of resistors applies feedback to the non-inverting input of the amplifier. This feedback is subtracted from the actual input and tends to reduce the signal levels, hence it is conventionally called Negative Feedback.
The feedback applied to the amplifier in 4·3b means that the voltage applied to the inverting input of the amplifier will be
we can now define a value we can call the Feedback Factor
to simplify the following expressions.
From the explanations given earlier, we can expect the effective gain 
to depend to some extent upon the signal level and the frequency. When the apply feedback the output will become
We can now rearrange this to define the overall voltage gain, 
, of the system with feedback applied as
It is usual to call 
the amplifier’s Open Loop Gain as it is the gain we obtain if we were to ‘break’ the feedback connection. In a similar way, it is usual to call 
the system’s Closed Loop Gain. In practice we can usually arrange for 
. Hence can say that for a suitably small 
we can approximate the above to
This result is an important one for two reasons. Firstly it tells us that the gain of the system with feedback applied is largely determined by the choice of the feedback factor, 
, not the inherent amplifier gain, 
. This is because it follows from the above that 
when 
.
The second reason can be seen to follow from the first. When 
the gain when feedback is applied only has a weak dependence up 
. This implies that changes in 
will have little effect. To see the effect of the feedback upon distortion let us assume that a change in signal level or frequency has caused the open loop gain to change from 
, where we can assume that 
is a small fractional Error in the expected gain. This means that the output level is in error by a fraction, 
, so we can use this as a simple measure of the amount of signal distortion/alteration produced by the unwanted change in gain.
The change in open loop gain will, in the feedback system, cause a related change, 
, in the closed loop gain such that
Combining expressions 4.10 and 4.11 we obtain
which since we can expect 
is similar to
i.e. the fractional magnitude of the amount of error (and hence the degree of distortion) is reduced by the factor 
. Now it is quite common for operational amplifier ICs to have low-frequency open loop gain values of the order of 106. Used with a feedback factor of 10, the result is a system whose voltage gain is almost exactly 10 where any distortions due to variations in gain with signal level or frequency are reduced by a factor of 105. The result is an amplifier system whose behaviour is largely determined by the choice of the resistors used for the feedback loop. Given its simplicity and the dramatic effect it can have, it is perhaps no surprise that Negative Feedback is often regarded as a ‘cure all’ for correcting amplifier imperfections. In reality, though, feedback can itself lead to problems...
