# Linear & time invariant

#### sharanbr

Joined Apr 13, 2009
82
Hello All,

I would like to know if negative feedback amplifiers are considered as linear systems?

I have another question but that is more related to linear systems ...

For a system to be linear, is it necessary that all the components of the systems themselves need to be linear by nature?
For example, an amplifier has feedback gain path, error detection and then integrator.
If an amplifier is linear then does it mean that all of the above necessarily need to be linear in nature?

#### Alec_t

Joined Sep 17, 2013
14,313
An amplifier with purely resistive negative feedback would generally be linear, but over a limited input amplitude and frequency range only.
In principle it should be possible IMO to make an amplifier with a linear response, under a limited set of conditions (e.g. for a specific frequency), even if one or more system components were non-linear. This would require compensating non-linearity elsewhere in the system and might be far from easy.

#### WBahn

Joined Mar 31, 2012
30,048
First, we need to decide what it means to be linear. Aside from the mathematical definition, we have to acknowledge that virtually nothing in the real world is perfectly linear, so it's really a question of whether a system can be "linear enough" for a given application.

It certainly helps if all of the components are linear, but if they aren't then the nonlinearities have to be compensated for with other nonlinearities. This is not easy without using feedback. However, with feedback, many nonlinearities can be made to go away, at least enough for the overall system to be acceptably linear.

#### sharanbr

Joined Apr 13, 2009
82
An amplifier with purely resistive negative feedback would generally be linear, but over a limited input amplitude and frequency range only.
In principle it should be possible IMO to make an amplifier with a linear response, under a limited set of conditions (e.g. for a specific frequency), even if one or more system components were non-linear. This would require compensating non-linearity elsewhere in the system and might be far from easy.
thanks ...

#### sharanbr

Joined Apr 13, 2009
82
First, we need to decide what it means to be linear. Aside from the mathematical definition, we have to acknowledge that virtually nothing in the real world is perfectly linear, so it's really a question of whether a system can be "linear enough" for a given application.

It certainly helps if all of the components are linear, but if they aren't then the nonlinearities have to be compensated for with other nonlinearities. This is not easy without using feedback. However, with feedback, many nonlinearities can be made to go away, at least enough for the overall system to be acceptably linear.
Dear Bahn,

My question arises due to the fact that fundamental analysis of negative feedback amplifier involves step and sinusoidal input and then analysis the output with the basic assumption that such a system is linear and time invariant ...

#### #12

Joined Nov 30, 2010
18,224
Dear Bahn,
My question arises due to the fact that fundamental analysis of negative feedback amplifier involves step and sinusoidal input and then analysis the output with the basic assumption that such a system is linear and time invariant ...
That's a good starting assumption, the first step, the first model in your mind and your math. In the real world, we assume correct results first, then examine how close to perfect they are. (I think) An analog amplifier always has non-linear components, but the ratio of maximum available voltage gain to the voltage gain actually used, results in a number which describes the worst case error. Using operational amplifiers with gain numbers in the millions of volts per volt results in distortion rates that are best described as tens of decibels below the voltage of the signal output.

Last edited:

#### WBahn

Joined Mar 31, 2012
30,048
Dear Bahn,

My question arises due to the fact that fundamental analysis of negative feedback amplifier involves step and sinusoidal input and then analysis the output with the basic assumption that such a system is linear and time invariant ...
You are mixing question and a premise -- or perhaps more accurately you are asking about both general and specific concepts without recognizing that they are not the same thing. You first asked if negative feedback amplifiers are linear systems. In general the answer is no. A negative feedback amplifier does not HAVE to be linear. You then stated that it is a "fact" that .... What do you base that "fact" on? You only assume that a system is linear and time invariant if it is supposed/expected to be linear and time invariant. If the system is NOT supposed to be linear and time invariant, why would you make such an assumption when analyzing it since all you have done is guaranteed that your results will be meaningless?