# small and large signal difference

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#### jimito13

Hello all,

I have a very theoritical question...Where the terms "small signal" & "large signal"
came from,that is why ac signals are called small and dc signals are called large?For example if we have a sinusoidal signal (ac) with amplitude 20Volts,why it is called small signal since it's amplitude is quite big/large?I would appreciate any helpful answer to my question.

#### LvW

jimeece13 said:
Hello all,

I have a very theoritical question...Where the terms "small signal" & "large signal"
came from,that is why ac signals are called small and dc signals are called large?For example if we have a sinusoidal signal (ac) with amplitude 20Volts,why it is called small signal since it's amplitude is quite big/large?I would appreciate any helpful answer to my question.

Who calls a 20 volts sinusoidal signal "small" and a dc signal "large"?
I hope - nobody.

Answer: Assume that the ac signal is processed in a circuit (passiv or active, like an amplifier or a filter). This ac signal is a "small" signal when any non-linearities of that circuit have no or only a negligible influence. That means, there is no absolute boundary which separates a small from a large signal. It depends on the linearity of the system.
Example: A signal to be amplified by a transistor is called "small signal" when the excursions along the voltage-current characteristic are small enough, so that this characcteristic can be assumed to be linear (with a small error which seems to be acceptable).

### jimito13

Points: 2

#### jimito13

I said that for the 20Volts sinusoidal signal as an example since everywhere i see that ac signals are called "small".Ofcourse it is wrong and i knew that (it would be crazy to mean that since it has such a big amplitude!) but i wanted some confirmation.

So the conclusion is that the distinguish between small and large signals is relevant to the linearity or non linearity that they cause in a circuit right?Is there any other parameter that makes these two terms different (for example,the amplitude or the frequency of a signal)?I do not care about their exact boundary but for their situations that make them different as terms.

LvW,can you show me a graph for the example you told above.I would be thankful.

Thanks again

#### hakeen

##### Full Member level 5
For more basic theoretical details you can refer to

https://en.wikipedia.org/wiki/Small-signal_model

For graphical representation you can consider the amplification of a BJT or simple I_V curve of a diode. If the signal is really small so that the respective region on I_V curve can be taken as linear, then it is a "small signal". Because you can model the diode as a linear component.

https://en.wikipedia.org/wiki/Diode_modelling
(under Title small signal modelling)

Hope it helps you imagine a graphical presentation.

Cheers

#### checkmate

I+i=K/2*W/L*(VGS+vgs-Vth)^2
Work out the small-signal transconductance i/vgs. You will find a linear term, and a non-linear one. You will find that the non-linear term will only be small when vgs<<VGS-Vth. There you have your small signal criterion.

#### FvM

##### Super Moderator
Staff member
I feel, that the basic electronic circuit design text books are full of respective examples. I would like to refer to a mathematical answer. You should know about taylor series approximation. If the first order taylor polynomial represents the circuit characteristic with sufficient accuracy, it's small signal.

#### LvW

jimeece13 said:
I said that for the 20Volts sinusoidal signal as an example since everywhere i see that ac signals are called "small".
...................
Thanks again

Here is another reasoning:

To calculate the frequency response of a circuit there is a very well known tool called
"ac analysis" (sorry - I don't know if it is the correct english term; in german it is "Wechselstrom-Rechnung"; perhaps somebody else can help).
This classical method also is used for ac analysis in simulation programs.
The key point: This analysis always assumes that all signal excursions are extremly small and a sinusoidal signal remains undistorted. Therefore, in simulation programs (ac analysis) you can use for example 1000 volts as an input signal for an opamp.
The output will be 20000 volts (if the gain is 20). That means, 1000 volts are handled as if there would be 1 mikrovolt.

#### DZC

##### Full Member level 3
To my understanding, large signal is kind of transfer function when you apply a slow enough signal
small signal is around some specific point such large signal transfer function

#### LvW

DZC said:
To my understanding, large signal is kind of transfer function when you apply a slow enough signal
small signal is around some specific point such large signal transfer function

No, that is not correct.
Small/large has nothing to do with the "speed" of a signal (frequency).
More than that, a "large signal" is a signal (voltage or current) and no "transfer function".

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