Most physical systems incorporate forms of feedback. A daily life example is when you keep your car on the road you look to see if you are too close to one side or the other and turn the steering wheel to correct the position (Visual feedback). Here we will explore the concept of feedback in the context of operational ampliﬁers.
Feedback can either be negative (degenerative) or positive (regenerative):
Negative feedback: As the output is increased, the input signal is decreased and vice versa. Negative feedback stabilizes the output to the desired level. Linear systems employ negative feedback.
Positive feedback: As the output is increased, the input signal is increased and vice versa. Positive feedback leads to instability, but it has its uses.
Negative feedback is applied to an OPAMP by connecting a passive component between its output terminal and its inverting (negative) input terminal. Negative feedback causes the voltage between the two input terminals to become very small and ideally zero. Correspondingly, a virtual short circuit is said to exist between the two input terminals. If the positive input terminal is connected to ground, a virtual ground appears on the negative input terminal.
Vs Vi Vo
Fig. 1 Negative Feedback Loop
The open-loop amplifier has a gain A; its output Vo is related linearly to the input signal Vi by Vo = AVi. The output Vo is fed to the load via the feedback network, which introduces a sample of the output back to the input again. This sample Vf is related to Vo by the feedback factor β, Vf = βVo. The feedback signal Vf is subtracted from the source signal Vs, generating the signal Vi, which is essentially the input of the feedback amplifier: Vi = Vs - Vf . When subtracting the feedback signal to generate the input signal, it results in a negative feedback operation mode, which reduces the signal that appears at the input of the basic amplifier. Ideally, the open-loop gain A is independent from all other circuit factors. The forward signal transmission occurs entirely through the basic open-loop amplifier and the reverse (feedback) transmission occurs entirely through the feedback network.
The gain of the feedback amplifier can be obtained by combining equations Vo = AVi and Vi = Vs – Vf to give Vf = Vo/Vs = AVi/ (Vi + AβVi) = AVi/[Vi(1+Aβ)] = A/(1+Aβ)
The quantity Aβ is called the loop gain. For the feedback to be negative, the loop gain Aβ should be positive; i.e. the feedback signal Vf should have the same sign as Vs. The quantity 1+Aβ is called the amount of feedback.
In many circuits the loop gain Aβ is very large (Aβ>>1), therefore Af ≈ 1/Aβ. This is a very interesting result; the gain of the feedback amplifier is almost entirely determined by the feedback network values. Since feedback networks generally consist of passive components, the advantage of including negative feedback in electronic circuits result in a stable, predictable and accurate feedback gain. The overall gain has very little dependence on the open-loop amplifier gain A. This is a desirable characteristic because the gain A is usually a function of many parameters, some of which have wide tolerances. The closed-loop gain (i.e. feedback gain) is almost entirely determined by the feedback elements.
Equations Vo = AVi and Vi = Vs – Vf can be used again to obtain the following expression for the feedback signal Vf: Vo = A/ (1+Aβ)Vs, Vf = βVo = Aβ/ (1+Aβ) Vs, for Aβ>>1 Vf ≈Vs, this implies that the input signal Vi is reduced to almost zero. If a large amount of negative feedback is employed (as it is often the case), the feedback signal Vf becomes an almost identical replica of the source signal Vs. From the above feedback network an immediate…