dc model and parameters comparison with that of large signal

[anubhavsingh244]

I am studying microelectronics. I have studied about the DC analysis and the AC analysis. The DC analysis is just to find the operating point or the quiescent point and then the AC analysis is done. An AC analysis can be done in two ways for non-linear devices (like diodes and transistors): small signal AC analysis and large signal AC analysis. Small and large signal AC analysis are used in transistors amplifiers (transistors act as amplifiers in active region). I know that when we linearize the large signal model of non-linear devices, it becomes small signal signal model. But many books refer to the semiconductor device equations (like current equations or voltage equations), used to describe the behavior of the device at DC and to find the operating point, as large signal. These books refer to DC parameters such as VBE as large signal. Some sources say the term large-signal refers to the magnitude of the AC signal relative to the operating bias and in that case I think vbe (the ac signal) should be the large signal parameter.

This pdf is made by me and shows my effort in making sense of the large signal analysis and large signal parameters which are used interchangeably with dc analysis and dc parameters most of the time (I don't know why. Is it because both DC model and large signal AC model use the accurate non-linear equations for analysis and hence we have Large Signal DC Model and Large Signal AC Model?).

Based on my current understanding, I have come up with some points which are shown through the example of a diode in attached pdf file. Please provide your valuable feedback.

 

[frankrose]

... many books refer to the semiconductor device equations (like current equations or voltage equations), used to describe the behavior of the device at DC and to find the operating point, as large signal. These books refer to DC parameters such as VBE as large signal. Some sources say the term large-signal refers to the magnitude of the AC signal relative to the operating bias and in that case I think vbe (the ac signal) should be the large signal parameter...

A large signal is any signal having enough magnitude to reveal a circuit's nonlinear behavior. So all books you read can be be true regarding this. BTW first line of wikipedia article regarding differences between small and large signal section:

Small-signal model - Wikipedia

en.wikipedia.org

...large signal analysis and large signal parameters which are used interchangeably with dc analysis and dc parameters most of the time (I don't know why. Is it because both DC model and large signal AC model use the accurate non-linear equations for analysis and hence we have Large Signal DC Model and Large Signal AC Model?).

I think you are confused a bit, that is sure I am, because I don't understand what do you want to say with this sentence?
What is large signal AC model?
In simple SPICE analysis (AC,DC,Tran for example) we don't use AC large signal model, only small signal model for AC analysis and large signal model (=device equations) for DC analysis. Small signal models are derived from DC analysis results, so AC analysis use both models.

More complicated equations, mathematical descriptions are required to take into account non-linear behavior in AC analysis which could mean large signal AC modelling (browse for periodic steady state analysis + shooting Newton method, harmonic balance analysis, Volterra series).

And sorry about it, but actually I think you are doing a bit too much effort on this. Don't read too much books if you feel they confuse you, only which you see as easy to understand, have good examples, explanations and your teacher, consultant advised.

 

[anubhavsingh244]

Hi frankrose,

Thanks for your reply.

Based on the knowledge gained, I have made some pointers. Please verify if these are correct or not:

1. Large signal models do both ac and dc analysis.
2. Large signal models are also called dc models or large signal dc models.
3. Small signal models do only ac analysis after doing dc analysis separately (due to superposition due to linearity).
4. Large signals models are done mostly using simulation and referred to as transient analysis.
5. Small signal analysis is a specific case of large signal models at a specific operating point to assume linearity.
6. DC biasing circuits (done simulantaneosly with large signal models and done separtely with small signal ac models[due to superposion]) are obtained from large signal models at zero frequency (neglecting effcts of capacitors and inductors).
7. All DC parameters can be referred to as large signal parameters.

Please see a question I have below:

 

[frankrose]

Well...

1. yes.... large signal models are used for both, AC and DC analysis.
2. no, large signal models are large signal models, maybe device equations, but that is all.
"DC models" term is rather used when you are talking about the models applied in DC analysis, which are the large signal models.
And large signal dc models name sounds twisted, I have't seen or heard it before, or cannot remember.
3. kind of, yes.
4. every analysis with non-linear devices use the large signal models. And much easier in any case, even with linear components to use simulation, I don't see your point.
5. no, it is not specific "case" of it, but you have some feelings here.
In an operating point the non-linear device have a bias voltage, current which is set by the environment and its large signal model.
The small signal model is created with derivation of the large signal model in a single point (=linearization around operating point) and it helps to identify its AC behavior.
6. I have no idea, rephrase it please.
7. I guess yes, if you wanted.

Regardnig your figure, I still feel you are confused a lot. Even your question is confused. You don't see that large signal means the non-linearity of the device is not negligible. Small signal means that the excitation is small enough to handle the device as linear component in its DC operating point.

Here is an example:
VBE = 0.7V DC operating voltage
vbe = 1mV amplitude AC voltage superimposed on VBE, it cannot change operating point

then vBE=VBE+vbe=0.701V, which is rather a large signal, compared to vbe

vbe is only 1mV, why would you call it "large signal ac voltage"? compared to 0.7V it is small!
DC voltage (=VBE) called large because it is much larger than vbe, x700 times bigger!

 

[dick_freebird]

Small signal is an idealization. Just as the "impulse
function" is useful analytically, but does not exist in
reality. A "zero width" operating point based linear
approximation is figured, and used for various
AC and DC sensitivities, gain, frequency response
that would be computationally impractical if a
fully detailed solution (like TRAN) were used and
post-processed.

 

[anubhavsingh244]

Well...

1. yes.... large signal models are used for both, AC and DC analysis.
2. no, large signal models are large signal models, maybe device equations, but that is all.
"DC models" term is rather used when you are talking about the models applied in DC analysis, which are the large signal models.
And large signal dc models name sounds twisted, I have't seen or heard it before, or cannot remember.
3. kind of, yes.
4. every analysis with non-linear devices use the large signal models. And much easier in any case, even with linear components to use simulation, I don't see your point.
5. no, it is not specific "case" of it, but you have some feelings here.
In an operating point the non-linear device have a bias voltage, current which is set by the environment and its large signal model.
The small signal model is created with derivation of the large signal model in a single point (=linearization around operating point) and it helps to identify its AC behavior.
6. I have no idea, rephrase it please.
7. I guess yes, if you wanted.

Regardnig your figure, I still feel you are confused a lot. Even your question is confused. You don't see that large signal means the non-linearity of the device is not negligible. Small signal means that the excitation is small enough to handle the device as linear component in its DC operating point.

Here is an example:
VBE = 0.7V DC operating voltage
vbe = 1mV amplitude AC voltage superimposed on VBE, it cannot change operating point

then vBE=VBE+vbe=0.701V, which is rather a large signal, compared to vbe

vbe is only 1mV, why would you call it "large signal ac voltage"? compared to 0.7V it is small!
DC voltage (=VBE) called large because it is much larger than vbe, x700 times bigger!

About my 2nd point: So all dc models are large signal models but not vice versa?

About my 6th point: I needed something to distinguish between DC models and Large Signal Models, as some books just claim them to be same. But I kind of knew they are different. So I said that when we consider large signal models for DC analysis, we obtain DC models. Isn't that right? (Just like we obtain small signal ac models by linearizing the large signal model for AC analysis at a particular operating point).

About the figure: I know vbe is instantaneous AC voltage. When we do small signal ac analysis, vbe is also referred to as small signal AC voltage (time instantaneous form). Now consider that the input signal applied is large so as to disturb the operating point of the device. Now the small signal model is no longer valid for AC analysis and we have to go for large signal model for AC analysis. This applied large input signal to cause operating point to change is vbe, right? (vBE=VBE+vbe) In that case, vbe becomes large signal ac voltage (time instantaneous form).

Clearly, large signal models and dc models cannot be used interchangeably. However why parameters of DC parameters then referred to as large signal parameters? Small and Large signal should be decided by vbe, the applied input ac voltage. So these ac parameters like vbe which should be large or small based on the applied input.

--- Updated Dec 14, 2021 ---

Clearly, large signal models and dc models cannot be used interchangeably. However why parameters of DC parameters then referred to as large signal parameters? Small and Large signal should be decided by vbe, the applied input ac voltage. So these ac parameters like vbe which should be large or small based on the applied input.

Better phrasing: Clearly, large signal models and dc models cannot be used interchangeably. However why parameters of DC model then referred to as large signal parameters? Small and Large signal should be decided by vbe, the applied input ac voltage. So the ac parameters like vbe are the ones that should be referred to as large or small based on the applied input signal level with respect to operating point.

 

[frankrose]

About my 2nd point: So all dc models are large signal models but not vice versa?

you can use it vice versa, no one gonna hurt. But the point, which is already written down, that large signal models exist, which you can call DC models, because DC analysis uses these models, or you can call them Transient models too, because transient analysis also use the large signal models.
Depends on context. That is all.

About my 6th point: I needed something to distinguish between DC models and Large Signal Models, as some books just claim them to be same. But I kind of knew they are different. So I said that when we consider large signal models for DC analysis, we obtain DC models. Isn't that right? (Just like we obtain small signal ac models by linearizing the large signal model for AC analysis at a particular operating point).

They are not different, it is just naming, somebody would like to call it differently. Forget DC models term, there are large and small signal models, that is all, really.

About the figure: I know vbe is instantaneous AC voltage. When we do small signal ac analysis, vbe is also referred to as small signal AC voltage (time instantaneous form). Now consider that the input signal applied is large so as to disturb the operating point of the device. Now the small signal model is no longer valid for AC analysis and we have to go for large signal model for AC analysis. This applied large input signal to cause operating point to change is vbe, right? (vBE=VBE+vbe) In that case, vbe becomes large signal ac voltage (time instantaneous form).

You cannot simply go to AC analysis if the small signal model is invalid because you use a large AC signal.
AC analysis always suppose small AC signal, so valid small signal model, even if you set/get high magnitudes in the simulator.

Try it, in simulator if you set 1000V magnitude AC input source for a 12V transistor amplifier you will get the same gain like when you set 1mV. You have to see how absurd it is, simply it is not possible in reality. AC analysis don't care about magnitudes, it just handle those as numbers. Magnitude setting in AC analysis is an aid for the designer to see the expected node/terminal amplitudes if the circuit operates linearly.

Better phrasing: Clearly, large signal models and dc models cannot be used interchangeably. However why parameters of DC model then referred to as large signal parameters? Small and Large signal should be decided by vbe, the applied input ac voltage. So the ac parameters like vbe are the ones that should be referred to as large or small based on the applied input signal level with respect to operating point.

No.

 

[anubhavsingh244]

you can use it vice versa, no one gonna hurt. But the point, which is already written down, that large signal models exist, which you can call DC models, because DC analysis uses these models, or you can call them Transient models too, because transient analysis also use the large signal models.
Depends on context. That is all.

They are not different, it is just naming, somebody would like to call it differently. Forget DC models term, there are large and small signal models, that is all, really.

You cannot simply go to AC analysis if the small signal model is invalid because you use a large AC signal.
AC analysis always suppose small AC signal, so valid small signal model, even if you set/get high magnitudes in the simulator.

Try it, in simulator if you set 1000V magnitude AC input source for a 12V transistor amplifier you will get the same gain like when you set 1mV. You have to see how absurd it is, simply it is not possible in reality. AC analysis don't care about magnitudes, it just handle those as numbers. Magnitude setting in AC analysis is an aid for the designer to see the expected node/terminal amplitudes if the circuit operates linearly.

No.

Thank you very much frankrose. Thanks to you, I have been able to understand most of these things. Most of the books just give definition of large signal analysis and then just move on to small signal analysis. I have been confused about dc models and large signal models for so long. To just give you an example, see this passage from a book on Microelectronics circuits by Donald A. Neamen:​

For the linear amplifier, then, the DC analysis can be performed with the AC source set to zero. This analysis, called a large signal analysis, establishes the Q-point of the transistors in the amplifier. This analysis and design was the primary objective of the previous chapter. The AC analysis, called a small-signal analysis, can be performed with the dc source set to zero. The total response of the amplifier circuit is the sum of the two individual responses.

These kinds of things were getting me really confused. But now I think most of the things are clear to me.

Although I would like to get a few things clarified before we close this discussion:
1) vbe (time instantaneous ac voltage) will remain small signal ac voltage irrespective the applied ac input voltage is small or large. Applied ac input voltage is small, consider small signal analysis and applied ac input is large, go for large signal analysis.
2) vBE= vbe + VBE is applicable whether large or small signal analysis.
3) DC parameters (like VBE) are large signal parameters because their values are way larger than applied ac voltage (vbe, which will always remain small signal).