Feedback – a brief introduction in the context of electronics

Let me share with you a very short summary which may aid  some of you as a brief introduction in feedback topic. So here it is, enjoy it.

What does feedback mean?

Feedback is a concept related to systems. It is a phenomenon in which the system output is transmitted to the system input with either regenerative or degenerative manner.  If it is regenerative it is called “positive feedback”, or if it is degenerative it is called “negative feedback”. But for our purposes, i.e. for amplifier design negative feedback is used almost exclusively for the following reasons:

a)Desensitize the gain: Make the gain of the circuit less sensitive to exterior effects (e.g. temperature)

b)Reduce the nonlinear distortion: Make the output proportional to the input, i.e. make the amp. have a constant gain.

c)Control the input and output impedances: Increase or decrease the output and input impedances according to the feedback topology.

d)Extend the bandwidth of the amplifier.

e)Increase the noise immunity of the system. That is, we wish to eliminate the contribution of unwanted signals to the output.

All of the above desirable properties are obtained in expense of gain reduction:

If the basic amp. has a gain A, with feedback we have a gain

which is approximately equal to 1/β. So we may conclude that the gain of the amplifier with feedback entirely depends on the feedback network, and this is consistent with the desirable property (a) listed above: With feedback, the gain is nearly independent of the basic amplifier structure. And note that this relation holds for all four feedback topologies.

We can see the effect of feedback on frequency response by analyzing the effect of feedback on the transfer function.  We can analytically see it from the following expression:

By inspection we can see that the new upper and lower 3dB frequencies are:

Hence, we can conclude that the midband (where we have constant gain and linear phase response) is widened.

Here is the basic structure of a feedback amplifier:

We’ll finalize this  discussion with introducing basic feedback topologies:

Note: Feedback-type notation first indicates the connection at the input then at the output. (i.e. respectively: mixing and sampling)

1)Series-Shunt Feedback:
This topology is used for voltage amplifiers. At output we sample voltage (so shunt connect it), and we connect it in series with the voltage source at input. Here is the block diagram:

Input resistance with feedback is given by:

Output resistance with feedback is given by:

where R’_o and R’_of are resistances with load resistances included.

2)Series-series feedback:
This topology is used for transconductance amplifiers. At output we sample current (so we connect it in series), and we connect it in series with the voltage source at input. Here is the block diagram:

The input resistance with feedback is given by:

The output resistance with feedback is given by:

3) Shunt-Series Feedback:

This topology is used for current amplifiers. At output, we sample current (so we connect it in series), and we connect it in parallel with the current source at input. Here is the block diagram:

The input resistance with feedback is given by:

The output resistance with feedback is given by:

4)Shunt-Shunt Feedback:

This topology is used for transresistance amplifiers. At output, we sample voltage (so we shunt connect it), and we connect it in parallel with the current source at input. Here is the block diagram:

The input resistance with feedback is given by:

The output resistance with feedback is given by:

In order to conclude we may say that, shunt sampling decreases the output resistance, whereas series sampling increases it. In the same manner, shunt feeding(mixing) decreases the input resistance and series feeding increases it.

References:

1 – Sedra & Smith, Microelectronic Circuits, Oxford 5/e
2 – Morgül, Kahya & Çiçekoğlu, Basic Electronic Experiments, Boğaziçi University Press