Explaining the differences between DC and AC

Hello All,

I have been studying electronics for some time but my understanding on ac and dc analysis is still not too clear.

I wish you all can put some time to explain a little about the following;

Say for a mosfet(or cmos inverter) which has a DC biasing and ac signal applied to it).

When we are using equation
Id = 1/2.W/L.unCox.(Vgs-Vth)^2 ---------eq(1)

Actually we are calculating the Id in DC or ac?
In most of the time, we are interested in Id(dc) or Id(ac)?

I see there is book that put
Drain current = Id(dc) +id(ac)

So I just wondering if equation 1 will give us dc value or ac value?

Or the equation (1) is true for both ac and dc where we need to use it at a ac small signal circuit or dc small signal circuit?

Also for transfer function, we are interested to find the Vout/Vin at ac or dc value?

And also the input and output impedance, will there be difference for ac or dc analysis?

Anyone who has any document to explain about this, kindly share with me.

In books, it seems like when it use small signal circuit to analyse id, gmvgs and so on. All are written in small letter. Are they all ac value to be taken into consideration?

Kindly shed some lights on these topic.
Please help

Thank you so much


rgds and thanks
Jason

dc conbine to ac how is it

Actually, the equation Id = 1/2.W/L.unCox.(Vgs-Vth)^2 reflects the physical facts of the MOSFET, and is both correct for AC and DC.

for simple DC analysis, you put in the DC VGS to calculate the biasing DC current, while for AC analysis, you put in the combine gate-to-source voltage VGS+Vgs to calculate.

However, in engineering analysis, we assume that the AC signal is so small compared to the DC signal that the AC signal will not influence the biasing point (actually it will, and that is one of the source of non-linearity), so we usually use the equation to calculate the DC biasing current and use the derived transconductance in the small signal model to calculate the AC gain.

That is typical engineering method: so simplify by a reasonable approximation.

Enjoy it!

cmos ac & dc analysis

Dear SgPerzoid

That's a cool explanation.
Thank you

From your words, I can sya that
1) We can use dc to approximate the biasing point
2) Whenever we make small signal model using the dependent current sources gmvgs, it MUST be a ac analysis.
Am I right?
Please correct if I am wrong

Then if all is right, then we know that
gm= d (Id) /dVgs

So the Vgs here is ac Vgs or dc+ac Vgs?
Then Id =Id +id (ac and dc value) or?

The term gmVgs in small signal model seems to mean gm is the transconductance value we found from DC biasing(as approximation).
Then the term Vgs in gmVgs, I would like to know if it is pure ac or Dc value or ac+dc value

Kindly enligthen

Thank you

Jason

compare dc values with ac values

For Id = 1/2.W/L.unCox.(Vgs-Vth)^2
Id=Id(DC)+id(AC)
Usually, AC value<<DC value, so we can use Id=Id(DC).

For gm= d (Id) /dVgs
coz no change of DC value, dVgs=dvgs(AC)

That is what I understand.

calculate vgs

jason_class said:

Dear SgPerzoid

That's a cool explanation.
Thank you

From your words, I can sya that
1) We can use dc to approximate the biasing point
2) Whenever we make small signal model using the dependent current sources gmvgs, it MUST be a ac analysis.
Am I right?
Please correct if I am wrong

Then if all is right, then we know that
gm= d (Id) /dVgs

So the Vgs here is ac Vgs or dc+ac Vgs?
Then Id =Id +id (ac and dc value) or?

The term gmVgs in small signal model seems to mean gm is the transconductance value we found from DC biasing(as approximation).
Then the term Vgs in gmVgs, I would like to know if it is pure ac or Dc value or ac+dc value

Kindly enligthen

Thank you

Jason

Click to expand...

Yes, I think you got the point. Actually from the point of an Engineer, the biasing point just refers to the DC biasing condition, we never think it is an approximation of dc+ac (though it really is). DC and AC are isolation from the engineering's view, except when non-linear analysis is needed.

And I agree with you that when the VCCS gmVgs is used in the analysis, the analysis must be a small sugnal analysis.

gm= d (Id) /dVgs, here the Id and Vgs refers to small signal current/voltage, gm dipicts how efficiently the swing of a small signal voltage can be converted to the swing of a small signal current.

and plz be further noted that the dc biasing current ID, DC biasing voltage VGS and other DC parameters are constant values.

Added after 3 minutes:

Pipeline said:

For Id = 1/2.W/L.unCox.(Vgs-Vth)^2
Id=Id(DC)+id(AC)
Usually, AC value<<DC value, so we can use Id=Id(DC).

For gm= d (Id) /dVgs
coz no change of DC value, dVgs=dvgs(AC)

That is what I understand.

Click to expand...

Yes, I think you are right with the first anwer, while for the second one, mathematically you are right. However, gm is the small signal voltage-to-current conversion ratio, so the Id Vgs should be ac values conceptually.