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Simple Diff Pair Nonlinearity

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I have a simple MOS diff pair with MOS loads and self biased output common mode in a 28nm process.
For example: input pair NMOS, loads: PMOS (gates connected to drain via high resistance for setting the common mode).

Linearity is important for my application.
However, all linearity analysis and discussion I find is related to the drain current nonlinearity (ids/VGS). If I ac ground the outputs (i.e., there is no swing and hence no gain) these expressions match pretty closely with my simulations. However, gain is also very important and without AC ground the linearity is orders of magnitude lower than expected (e.g. -40 dB!).

I suspect that the "traditional" ID/VGS nonlinearity is completely swamped by the ID/VDS nonlinearity (i.e., the dependence of ID on VDS).
I am wondering why I seem to be the one person in the world carying about this ... or why there is no single word in literature discussing this.

The problem is that I do not have an analytical expression and the linearity seems to be completely "arbitrary". There is no obvious dependency on GM/ID, ID, VDS etc. It is probably a complicated function of all the parameters.

But how would you design such a simple diff pair if linearity is a concern and the VDS nonlinearity is so dominant?

As a reference, with ac ground, the drain current nonlinearity follows a nice relationship with GM/ID which becomes better with low GM/ID and worse with high GM/ID (IIP3=+12 dBm for GM/ID=5 and IIP3=-5 dBm for GM/ID=24).
With the loads, I cannot get below IIP3=-13 dBm and IIP3 shows no clear relationship between GM/ID, VDS, ID etc.

Thanks!
 

I suspect that the "traditional" ID/VGS nonlinearity is completely swamped by the ID/VDS nonlinearity (i.e., the dependence of ID on VDS).
I am wondering why I seem to be the one person in the world carying about this
Every one know such thing except for you.

Assume amplifier.
"ID/VGS" dominates input nonllinearity.
"ID/VDS" dominates output nonllinearity.

... or why there is no single word in literature discussing this.
Simply you do know nothing.

The problem is that I do not have an analytical expression and the linearity seems to be completely "arbitrary".
There is no obvious dependency on GM/ID, ID, VDS etc.
It is probably a complicated function of all the parameters.
You can easily build behavioral model, if you don't include frequency characteristics.
Then you can study relations between GM/ID, ID, VDS etc. by using it.

BTW, most text book refer only input nonlinearity.
For example, chapter-2 of the following refers only input nonlinearity.
https://www.amazon.com/Microelectro...=sr_1_4?s=books&ie=UTF8&qid=1486125508&sr=1-4

Very simple example.
Code:
V1=Vgs*[1+beta2*(Vds0-Vds)]
Ids=(A0+A1*V1+A2*V2^2+A3*V1^3) * tanh(gamma*Vds)

But how would you design such a simple diff pair if linearity is a concern and the VDS nonlinearity is so dominant?
If VDS is low, output nonlinearity is large.
This is true for case where load is high or output amplitude is large.

Can you understand what is imcomplete or lacking in the following ?
https://www.edaboard.com/threads/360302/
 
Last edited:

Hi,

Assume amplifier.
"ID/VGS" dominates input nonllinearity.
"ID/VDS" dominates output nonllinearity.

This is the first time I hear the term input and output nonlinearity (I have taken many advanced circuits and RF courses which all covered nonlinearity).
Can you elaborate what you mean by that? IIP vs OIP?

Assuming an amplifier, I input an input signal, the amplifier distorts it (due to VGS and VDS dependency) and I get distorted output waveform. I can measure the distortion with HD, IIP, .... I do not see input/output difference.

For example, chapter-2 of the following refers only input nonlinearity.
**broken link removed**

I have this book - and read chapter 2. I do not see where in the chapter even 2D Taylor series would be described.
Example 2.4 only covers "ID/VGS" nonlinearity as everywhere else.
Can you give a more specific pointer?

Very simple example.

Thanks, I'll play with this but I'm not sure yet how I'll fit the actual transistor into it.


But how would you design such a simple diff pair if linearity is a concern and the VDS nonlinearity is so dominant?
If VDS is low, output nonlinearity is large.
This is true for case where load is high or output amplitude is large.

You mean large signal VDS (bias point) - right?

Yes, I would think so.

But this wouldn't this imply that lower GM/ID (=higher VDsat) has better linearity?
I also set the CM to change the output common mode of the diffpair and sweeping IIP3 vs VOC for different GM/ID (or other parameters) has completely "arbitrary" shapes.

Can you understand what is imcomplete or lacking in the following ?

Yes. In the differential version the voltage swing is just half and hence the third order coefficient is 1/4 smaller.
 

This is the first time I hear the term input and output nonlinearity (I have taken many advanced circuits and RF courses which all covered nonlinearity).
It seems all courses you take are too low level...

Consider a load line.
Output load line is drawn on ID/VDS which characterize output nonlinearity.
These are very common all for Vacume Tube, BJT and FET.

On the other hand, VGS is an input for common source amplifier.

Can you elaborate what you mean by that? IIP vs OIP?
No, none of them.
----------------------

Basically both IIP and OIP are nonlinear characteristics for small signal.
If output nonlinearity is very small, OIP=Gain*IIP.
If output nonlinearity is not small, this relation is not satisfied.

I have this book - and read chapter 2.
I do not see where in the chapter even 2D Taylor series would be described.
Surely read my appends.
BTW, most text book refer only input nonlinearity.
For example, chapter-2 of the following refers only input nonlinearity.

https://www.amazon.com/Microelectro...=sr_1_4?s=books&ie=UTF8&qid=1486125508&sr=1-4

Very simple example.
Code:
V1=Vgs*[1+beta2*(Vds0-Vds)]
Ids=(A0+A1*V1+A2*V2^2+A3*V1^3) * tanh(gamma*Vds)
Thanks, I'll play with this but I'm not sure yet how I'll fit the actual transistor into it.
This is "W.R.Curtice and M.Ettenberg Model"

If you truely understand "Saleh Model, etc.", you have to know more related issues.
https://www.edaboard.com/threads/348252/

But this wouldn't this imply that lower GM/ID (=higher VDsat) has better linearity?
No.
ID/VDS is never straight line even for enough saturation region.
What do you mean by higher VDsat ?
Dynamic range is small for higher VDsat.

Yes.
In the differential version the voltage swing is just half and hence the third order coefficient is 1/4 smaller.

Before going to next.
Answer my quetions in your....
https://www.edaboard.com/threads/351341/#9
https://www.edaboard.com/threads/355656/#13
https://www.edaboard.com/threads/363583/#2
 
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