# Small Signals and Large Signals Terminology: Models and Amplifiers

I am studying microelectronics. I recently got confused about about the small signal models and large signal models. After reading an extensive list of sources, I have come up with some pointers which I want to verify that I have got right.

The term "small signal" can refer two things:

Small signal amplifier and small signal model/analysis. The same thing can be said about the term "large signal". Both small and large signals are AC signals, and they are large or small with respect to the quiescent or operating point established by the DC bias circuit obtained using DC modelling in both large and small signal amplifier analysis.

Both large and small signal models can be used to model the non linear devices like diodes and transistors (which are operated as amplifiers in active region). The transistor amplifiers are used as voltage or current amplifiers when used as small signal amplifiers and the transistor amplifiers are used as power amplifiers when used as large signal amplifiers.

The small signal amplifier is an amplifier when the applied AC input is small with respect to the DC operating point on the DC load line. This type of amplifier uses small signal modelling for its AC analysis. Small signal modelling involved linearizing the non-linear circuit elements at the DC operating point.

1. DC load line which gives operating point.

The small signal amplifier analysis includes two steps:

1. DC analysis using DC modelling or Large Signal Modelling
2. AC analysis using Small Signal AC (or Incremental) Modelling

The large signal amplifier is used as a power amplifier.

The large signal amplifier analysis includes two steps:

1. DC analysis using DC modelling or Large Signal Modelling
2. AC analysis is done using graphical analysis and no specific model is used here to model the AC operation of large signal.

The DC analysis is done using large signal modelling in both small and large signal amplifiers so it is also called large signal analysis.
The AC analysis done in small signal amplifiers using small signal modelling is small signal analysis.

Please provide feedback if my points are accurate or need improvement.

(I tried searching large signal model of a transistor and also searching dc model of a transistor. The results obtained in images section of google search show the kinds of circuits for dc models and large signal models. That is also how I inferred large signal models and DC models are the same. Some references are also present to support this point).

(Please search through the references using the terms "small-signal" or "small signal" and "large-signal" or "large signal".)

I believe most of the books tend to refer the DC model as the large signal model. These books include:

1. Design of Analog CMOS Integrated Circuits by Behzad Razavi
2. Analysis and Design 8of Analog Integrated Circuits by Gray and Meyer
3. Electrical Engineering Principles and Applications by Allan R. Hambley
4. Microelectronic Circuits by Sedra/Smith
5. Electronic Devices and Circuits by Balbir Kumar
6. Microelectronics Circuit Analysis and Design by Donald A. Neamen

According to Microelectronics Circuit Analysis and Design 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.

Large signal amplifiers (or power amplifiers) involve large signal analysis or operation which should include non linearities and is more accurate in comparison to small signal modelling. But it means that large signal analysis or DC analysis of power amplifiers should be done. But what about the AC analysis? Also, we were doing DC analysis (large signal analysis) of all amplifiers already, so why small signal was needed in the first place?

• Unless I am wrong, I should explain more simply this terminology of "small" or "large" signals. If a device is "linear" with any signals, then it can be designed by a "small" model which is by definition a "linear" model. When it is "non linear", even with "small" signals, then it needs a "large" model to define its non-linearities (example of some low level tunnel diode). Under some "definitions", a "system" or "device" can be "modeled" also by a linear model (example of a switch). Commented Dec 10, 2021 at 8:34
• You should also see my answer at this post (explaining why a signal is considered as "small signal" and/or why "large model" must be used: electronics.stackexchange.com/questions/577088/… Commented Dec 11, 2021 at 10:39
• I have read your edit. Practically, at this point you don't need to overthink these details. DC operating point is established by spice like simulators as the first step. If the circuit strays from it another calculation is done. ABSTOL and RELTOL determine what's considered accurate. For instance in Razavi's book (pg 90-91) large signal analysis is only determining operating points and transistor operating regions as Vin is swept from Vin=VDD to Vin=0. Where the DC OP is, the appropriate transistor models are used.
– Syed
Commented Dec 11, 2021 at 10:56
• Yes. I read it (perhaps my power understanding of English, sorry). It is ok when there are no "non-linearities" that depend on the level of the signals unless I am wrong. I would only point, because of the "slew-rate" (non-linearity of limited current somewhere in an op-amp which happens at "some level"), small analysis can't be applied with "large signals". Commented Dec 11, 2021 at 11:19
• Ok for the edit. Please note that, for my thinking, I don't especially "like" the terminology of "large signals". I prefer the terminology used by simulators which is "transient analysis". It does mean that there is not one large model and one "quiet point" ... but there is ... successive quiet point determined by the equations of the device, unless I am wrong. Sorry for my poor English if some words are not the right ones. Commented Dec 11, 2021 at 17:36

.. and they are large or small with respect to the quiescent or operating point established by the dc bias circuit obtained using DC modeling in both large and small signal amplifier analysis

Correct: you are linearizing a non-linear component (say a diode). Its resistance ranges from that of an off-switch (M$$\\Omega\$$) to an on-switch (m$$\\Omega\$$). For analysis you need a number (not a range). So you linearize it around the Q-point established by DC biasing. With the non-linearity removed you can analyze the circuit and solve it. If the signal strays outside of that Q-zone you need to get a better estimate of the resistance value. The absolute value of small signal is arbitrary but usually if the effective resistance of the linearized component could change by more than 10% it is time to find a new estimate.

The term "small signal" can refer two things : small signal amplifier and small signal model

The "small-signal" prefix refers to the intended range concerning ac signals that are small enough so that the circuit keeps operating around the Q-point. DC analysis is necessary to arrive at the various parameters of such a small-signal model. In that context you can have a model, an amplifier or even analysis.

Large signal analysis can be done only by providing the most appropriate model for various devices in the circuit at the current signal level. Hence a point by point linearization of the entire circuit during simulation would be required as one size cannot fit all signal levels. That's why you will not find a convincing "image" of a large signal model anywhere.

Large-signal modeling and analysis is considered an advanced topic and not covered in most UG courses. It is best left to simulators for a good reason. Switching from one model to the other also results in discontinuities mid-simulation that must be handled in a simulator. Remember that a computer cannot do a visual analysis in the regular sense of the word. You have referred to this as "AC analysis is done using graphical analysis" for the large-signal case.

I hope it clarifies a few points.

My suggestion to you would be to ask a more focused question. Or, to load a picture each of a (1) DC model, (2) small-signal model and a (3) large-signal model, as you understand them currently and then to ask more focused questions around these. Referring respondents to review all the documents you have referenced is going to get you fewer replies in general.

The same dc equations can be used to describe the ac behavior with inclusion of parasitic and inductive effects of the device ...

No, and this is a totally wrong statement.

When I use the large signal or dc equations, just as they are, in the analysis of the device in the ac domain, the ac analysis is large signal ac analysis and is more accurate.

Not at all, where did you read this?

This kind of behavior is more general and can be used in all amplifiers (small signal amplifiers and large signal amplifiers) but more needed in large signal amplifiers.

Transistors don't have behavior. Their function is determined (completely) by their terminal characteristics.

When I linearize the dc equations and use the linearized equations to analyze the behavior of the device in the ac domain (including capacitive and inductive effects of the device and the circuit, of course), the ac analysis becomes small signal ac analysis. This is an approximated (and linear) model. It can be used for both large and small signal amplifiers but used mostly in small signal amplifiers who accuracy is not that important.

There are serious gaps in your understanding. I don't blame you for it but I must say that this is not a university or an online chat group. You can review your books and ask your instructor for clarifications. The accuracy of small signal analysis is quite important. Entire books are devoted to this analysis. One should, at the same time, be aware of its limitations.