# Where do the harmonics come from in OpAmps?

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#### Edward_2288

##### Member level 4
Harmonics

Hi all,

in op amps, where do the harmonics come from? what elements do contribute the harmonics?

Thx.

#### hrkhari

##### Full Member level 4
Re: Harmonics

Harmonics are mainly contributed by the nonlinearity of the transistor constructing the Op-Amp, by reviewing the drain current equation of the transistor it could be observed that the relation of the input -output are in a manner of quadratic hence contributing to weighted frequency component also known as harmonic component.

#### Edward_2288

##### Member level 4
Re: Harmonics

do you mean it is caused by the ac component of the drain current due to square law? then is it the only source?

#### Humungus

##### Full Member level 6
Re: Harmonics

Nonlinearity arises from the relation between Vg, Vd and Vb with the drain current. It affects linearity through output conductance and transistor transconductance.

Remember that Vg, Vd and Vb also contribute to change transistor mobility. So, you must use a quite general equation for Id=f(Vg, Vd, Vb).

#### drasta

##### Junior Member level 3
Re: Harmonics

Nonlinearity can develop from narrow bandwidth of amplifier and also unstability.

#### gunturikishore

##### Full Member level 2
Re: Harmonics

The linearity of the transistor has got a condition that the input signal is sufficiently small that the higher degree nonlinear components arising from the non linerity of the transistors can be safely neglected. Wherever this fails and you can not ignore the higher degree components you have to pay attention for the harmonics.

J

#### jiangwp

##### Guest
Re: Harmonics

From the frequency-amplitude curve, the OP can be seen as a low filter with gain weighted.

Because the nonlinearity and the natural noise of transistor, after the clean input signal passs the nonlinearity system(OP), the harmonics is appear. In the meanwhile, the power supply is varing as time change , and the transistor is not matched perfect, the electroincs is flowing nonsymmetry . All the reason above results in the harmonics.

#### lakeoffire

##### Member level 3
Harmonics

Nonlinearity is a large-signal concept. The linear AC analysis is just an approximation near a specific operation point. When the signal becomes larger, the deviation from the operating point will become larger too, and thus the linear ac approximation will cause larger error.
The basic reason of nonlinearity is due to the nonlinear characteristics of the active devices like the FETs. The core of an opam is generally a transisor or a diff-pair. You can refer to Gray & Meyer's book for the large signal derivation, and you will find that the relation between the input and output is nonliear.

#### crazyamd

##### Member level 1
Re: Harmonics

lakeoffire said:
Nonlinearity is a large-signal concept. The linear AC analysis is just an approximation near a specific operation point. When the signal becomes larger, the deviation from the operating point will become larger too, and thus the linear ac approximation will cause larger error.
The basic reason of nonlinearity is due to the nonlinear characteristics of the active devices like the FETs. The core of an opam is generally a transisor or a diff-pair. You can refer to Gray & Meyer's book for the large signal derivation, and you will find that the relation between the input and output is nonliear.

that is not quite true. nonlinearity exists for both small and large singal input to op amp.

#### terryssw

##### Full Member level 3
Re: Harmonics

Nonlinearity is surely a large-signal concept. In electronics when you talk about small signal, it is always referred to the input signal levels such that the circuit exhibit in linear time-invarient systems. Of course small signal equivalent circuit is only an approximation, and you must always look at large signal response (transient) at the final stage of the design.

#### crazyamd

##### Member level 1
Re: Harmonics

terryssw said:
Nonlinearity is surely a large-signal concept. In electronics when you talk about small signal, it is always referred to the input signal levels such that the circuit exhibit in linear time-invarient systems. Of course small signal equivalent circuit is only an approximation, and you must always look at large signal response (transient) at the final stage of the design.

again, that's not true. the nonlinearity of a circuit would be much worse under large signal operation, but it always exsits because no circuit is "linear" even for very small singal. this has nothing to do with the analysis/simulation type: small signal != AC analysis. of course you need run trans for pss to determine the distortion.

#### jason_class

##### Member level 5
Re: Harmonics

Then who is right and wrong for this topic? Seems confusing
Kindly elaborate more
Thank you

Jason

#### terryssw

##### Full Member level 3
Re: Harmonics

crazyamd said:
terryssw said:
Nonlinearity is surely a large-signal concept. In electronics when you talk about small signal, it is always referred to the input signal levels such that the circuit exhibit in linear time-invarient systems. Of course small signal equivalent circuit is only an approximation, and you must always look at large signal response (transient) at the final stage of the design.

again, that's not true. the nonlinearity of a circuit would be much worse under large signal operation, but it always exsits because no circuit is "linear" even for very small singal. this has nothing to do with the analysis/simulation type: small signal != AC analysis. of course you need run trans for pss to determine the distortion.

So why you call AC analysis a small-signal analysis? Do it means that when you run small-signal analysis, you can only apply very small signal, and also you will expect some level (even it is very small) of distortion in AC analysis?

What do you mean by large signal and small signal? (how small it should be? 1mV? 1uV? 1nV? they all exhibits nonlinearity!) In basic electronics circuits context, small signal does not mean that your input signal is really small. The actual meaning of small signal is "The input signal level such that the systems exhibits as a linear system".

When someone say some kind of small signal analysis or small signal equivalent circuit, linearity is automatically assure. If you really consider the non-linearity or harmonics, then you are talking about "large signal behavior" even if your input signal is at the level of 1uV.

Furthermore, the small signal analysis (ie AC analysis) used in all simulators all simulate the circuit linearly. Even if you have the input of 10000V in AC analysis, you will not see even just a little harmonics in the simulator output, i.e. all harmonics component must be mathematically zero in AC analysis.

So nonlinearity must be a "large-signal pheonomena". When you consider "small signal", you will not consider nonlinearity. The main point of large or small signal is not in the signal level, but in the sense that you do or do not consider the non-linear distortion. But of course, this is also why small-signal analysis is only an approximation to true circuit behavior.

#### alchen77

##### Junior Member level 2
Re: Harmonics

hi terryssw
so every time when we do the AC simulation and need to do the TRAN to verify again?
and we check the AC simulation data for what kind of purpose?? now I only use the gain and phase margin can you teach me what else?? thank you very much.

#### crazyamd

##### Member level 1
Re: Harmonics

terryssw said:
crazyamd said:
terryssw said:
Nonlinearity is surely a large-signal concept. In electronics when you talk about small signal, it is always referred to the input signal levels such that the circuit exhibit in linear time-invarient systems. Of course small signal equivalent circuit is only an approximation, and you must always look at large signal response (transient) at the final stage of the design.

again, that's not true. the nonlinearity of a circuit would be much worse under large signal operation, but it always exsits because no circuit is "linear" even for very small singal. this has nothing to do with the analysis/simulation type: small signal != AC analysis. of course you need run trans for pss to determine the distortion.

So why you call AC analysis a small-signal analysis? Do it means that when you run small-signal analysis, you can only apply very small signal, and also you will expect some level (even it is very small) of distortion in AC analysis?

What do you mean by large signal and small signal? (how small it should be? 1mV? 1uV? 1nV? they all exhibits nonlinearity!) In basic electronics circuits context, small signal does not mean that your input signal is really small. The actual meaning of small signal is "The input signal level such that the systems exhibits as a linear system".

When someone say some kind of small signal analysis or small signal equivalent circuit, linearity is automatically assure. If you really consider the non-linearity or harmonics, then you are talking about "large signal behavior" even if your input signal is at the level of 1uV.

Furthermore, the small signal analysis (ie AC analysis) used in all simulators all simulate the circuit linearly. Even if you have the input of 10000V in AC analysis, you will not see even just a little harmonics in the simulator output, i.e. all harmonics component must be mathematically zero in AC analysis.

So nonlinearity must be a "large-signal pheonomena". When you consider "small signal", you will not consider nonlinearity. The main point of large or small signal is not in the signal level, but in the sense that you do or do not consider the non-linear distortion. But of course, this is also why small-signal analysis is only an approximation to true circuit behavior.

basically i agree what you said, but you are mixing two different things together.

first of all, as for the concept of small/large signal, to be exact, the "small or large" is determined in reference to circuit operating point. it makes little sense to use absolute value to represent the signal level.

and of course, you won't see distortion in ac analysis or so called small signal analysis, because the simulator linearizes the circuit around the operating point for ac simulation. but as i've said, harmonic distortion always exists regardless the actual input signal level. in other words, in trans simulation, even if your input level is smaller than the operating point, you still have HARMONICS! that's why you can't say it's must "large signal pheonomena".

#### terryssw

##### Full Member level 3
Re: Harmonics

alchen77 said:
hi terryssw
so every time when we do the AC simulation and need to do the TRAN to verify again?
and we check the AC simulation data for what kind of purpose?? now I only use the gain and phase margin can you teach me what else?? thank you very much.

When ever you do final stage simulation before you do the fabrication, you must always trust your transient simulation results. However, transient simuation is always longer, and if you don't do some AC simulation to determine some parameters first (e.g. GBW, phase margin, transfer function), then it would be only trial and errors in doing transient since transient is more abstract.

Also, when your signal of interest is really small-signal (remember the definition of small-signal), you would need AC analysis to help you determine various performance. The important simulations of such kinds include the following:

1. When you want to simulate noise performance (such as noise figure)
2. When you want to simulate small-signal transfer function (approximate)
3. When you want to simulate PSRR and CMRR
4. When you want to determine DC gain, GBW, phase margin etc
5. When you detemine the pole and zero.......

crazyamd said:
basically i agree what you said, but you are mixing two different things together.

first of all, as for the concept of small/large signal, to be exact, the "small or large" is determined in reference to circuit operating point. it makes little sense to use absolute value to represent the signal level.

Sure, of course this is the correct point, and my previous explanation clearly explain this issue. Small signal mean the signal level is small compared to the operating point (to be more exact, if should be compared to the curvature of the DC transfer curve at the operating point) such that nonlinearity is not a concern, right?

and of course, you won't see distortion in ac analysis or so called small signal analysis, because the simulator linearizes the circuit around the operating point for ac simulation. but as i've said, harmonic distortion always exists regardless the actual input signal level. in other words, in trans simulation, even if your input level is smaller than the operating point, you still have HARMONICS! that's why you can't say it's must "large signal pheonomena".

Bascially what you said is correct, but I just disagree your final conclusion. I must say that "nonlinearty is a large-signal pheonomena". Since again if you talk small signal, in definition, you do not consider the nonlinearity. You will ONLY talk large-signal when you consider non-linearity. Remember, you do not consider distortion temporary in small-signal anlaysis only, not completely ignored in your design. You can have a look on most common Analog IC design books, such as by Razavi, Grey, John Martins, and even some basics applied electronics textbook, they all say that "Non-Linearity is a large-signal pheonomena".

May be some comments can be provided by others?

#### crazyamd

##### Member level 1
Re: Harmonics

don't wanna quote the previous post again. it's a bit long. ;-)

small signal != small signal analysis.
by large signal, we usually mean the signal level is comparable to op point.

there's no distortioin in small signal analysis doesn't mean you can only see harmonic distortion when the signal level reaches the so called "large signal".

all the people you mentioned are real gurus in analog design. but quotaing their words is not the best way to prove your point. what they said is under certain context. in practice, if there's a stringent linearity requirement, you have to simulate/test your circuit even if the signal level is very small, comparing to the op point. after all, no circuit is really linear.

#### terryssw

##### Full Member level 3
Re: Harmonics

Dear Crazyamd:
Actually I am not saying your point is wrong. But in the sense of what large signal is in the electronic engineering, it is really true that nonlinearity is a large-signal pheonomena. Of course this does not mean that there is a circuit which is perferctly linear. This is just referred to what the pheonomena you are currently INTERESTED to (If you talk "large signal", you are interested to distortion, but if you talk "small signal", you are NOT interested to (NOT interested, but not totally ignored) nonlinearity, at least at the time you are talking "small-signal". The word phase "small-signal" automatically ASSUME linearity by definition.

This kind of theory is discussed thoroughly in the chapter, e.g., about the frequency response (ie small-signal analysis) of the amplifier. You are talking frequency response (which is related to GBW, phase margin, etc.) which is clearly the characteristic of linear time-invariant system, so people define the definition of "small-signal" such that you are not interested in non-linearity, and then only after that the concept of frequency response can be applied. That's why it call small-signal analysis.

So my main point is that, you cannot say the sentence "Non-linearity is a large-signal concept" by Mr. lakeoffire is not true in the previous few posts. I just support his conclusion. Again, I am not saying your thinking is wrong, but I just think Mr. lakeoffire is correct.

#### lastdance

Re: Harmonics

Some interesting posts...

Here's my view:

Distortion can occur due to transient (output unable to catch up with input), output clipping, input signal purity, noise...

It's therefore not required that a high level signal drives the input to cause distortion.

What crazyamd mentioned should not be small signal, but rather low-level signal to avoid confusion with the classical literature definition.

#### terryssw

##### Full Member level 3
Re: Harmonics

Yes, I also agree low-level signal and small-signal is completely different concept. You must consider low-level signal as large-signal if you are interested in distortion.

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