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J

jason

Jan 1, 1970
0
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
 
jason said:
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).

You bias the FET and find the biasing voltages/currents in order to
find the small signal model (which applies to the AC). Generally you
have DC biasing voltages well above what you expect for an AC signal
you want to use. This allows the AC not to affect biasing to a certain
degree. You generally want to do something to the AC only, i.e. amplify
or buffer.
When we are using equation
Id = 1/2.W/L.unCox.(Vgs-Vth)^2 ---------eq(1)

That is the DC biasing equation. It may work for AC, but since Vgs will
be changing, it wouldn't be worth much.
Actually we are calculating the Id in DC or ac?
In most of the time, we are interested in Id(dc) or Id(ac)?

Id DC determines the small signal model used to find Vout or Iout (AC).
For example, transconductance in small signal is determined by Id (DC)
but is used to determine 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?

DC, id is determined by the small signal model.
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?
Small signal models usually replace the transitor with a current source
and two resistors.
Also for transfer function, we are interested to find the Vout/Vin at
ac or dc value?
AC


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


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

These are lecture notes to a course at UCSD I took. The BJT and Mosfet
show how small signal models are derived. It may help.
http://ece-classweb.ucsd.edu:16080/winter05/ece102/
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?

They are small signal AC values.
 
A

Andrew Holme

Jan 1, 1970
0
jason said:
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?

It gives you the sum:

1/2.W/L.unCox.(Vgs-Vth)^2 = Id(dc) +id(ac)
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?

Use calculus to work out small-signal transconductance:
gm = d(Id) / d(Vgs)
Also for transfer function, we are interested to find the Vout/Vin at
ac or dc value?

Frequency is a variable in the transfer function e.g. the Laplace s, or jw
For DC, w=0 (w = omega)
You can write a trasnsfer function, in terms of s, or jw, valid for both AC
and DC.
Often, but not always, we are only interested in AC
And also the input and output impedance, will there be difference for
ac or dc analysis?

For small-signal analysis, input/output impedances may be calculated using
linear approximation i.e. taking the slope of the graph at that point and
assuming it approximates a striaght line.
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?

"Small signal analysis" means: small AC signal.
 
A

Active8

Jan 1, 1970
0
jason wrote:

"Small signal analysis" means: small AC signal.

I've seen capitalization used incorrectly in places, but here's the
way I learned to use it:

UC = upper case
LC = lower case

variable subscript qty represented example
UC UC steady dc component I_C, V_CE
UC UCUC DC power supply V_CC
LC UC total instantaneous i_B, v_BE
IOW, referred to 0V

LC LC instantaneous AC component i_b, v_ce
IOW referred to DC component I_B or V_CE -
the average value of the sine

UC LC RMS value of AC signal I_b, I_c, V_be

note that the last notation is used in sinusoidal stady-state
analysis, where we use vector values.

Also note that in F(s) = L f(t), F(s) suggests a steady state or rms
value and after solving and transforming back to the time domain,
you get f(t) which is used to solve instantaneous values. You can
see that in V(s) = L v(t).
 
J

jason

Jan 1, 1970
0
Hi Geo, Andrew and Mike,

Thanks so much for the time to explain. It is very helpful advice and
guide.

Tried the calculus solving gm = d(Id) / d(Vgs)
Find that Dc part which is a constant will vanish after the
differentiation
So left with the ac terms ->d id(ac)/dvgs (Note that dVgs is actually
dvgs)
AM I right Andrew?

Then for Mike, you have make it really a simplified way to understand
the notations. One last thing to check that is , what does IOW stand
for ?

Thanks a lot Geo , Andrew and Mike

rgds
Jason
 
A

Andrew Holme

Jan 1, 1970
0
jason said:
Tried the calculus solving gm = d(Id) / d(Vgs)
Find that Dc part which is a constant will vanish after the
differentiation
So left with the ac terms ->d id(ac)/dvgs (Note that dVgs is actually
dvgs)
AM I right Andrew?

Yes.

Using Mike's notation strictly, the total instantaneous variables would be:
i_D, v_GS;
instantaneous AC components: i_d, v_gs;
steady DC components: I_D, V_GS

So:
v_GS = V_GS + v_gs
d(v_GS) = d(v_gs)
 
A

Active8

Jan 1, 1970
0
Hi Geo, Andrew and Mike,

Thanks so much for the time to explain. It is very helpful advice and
guide.

Tried the calculus solving gm = d(Id) / d(Vgs)
Find that Dc part which is a constant will vanish after the
differentiation
So left with the ac terms ->d id(ac)/dvgs (Note that dVgs is actually
dvgs)
AM I right Andrew?

You shouldn't have snipped out the relevant equation:

Id = 1/2.W/L.unCox.(Vgs-Vth)^2 ---------eq(1)

and you didn't show your answer.

Yeah, constants drop out, but here's the prob. You're using the
model of the MOSFET in saturation. I think you want it in the
quadratic region:
2
W V_DS
Id = u.Cox - [ (V_GS - V_T)V_DS - ---- ]
L 2

The other prob is that dI/dV should really be the partial diff of
I_DS wrt V_GS with V_DS held constant. IOW:

D = round d

D I_D |
----- |
D V_GS | V_DS

Then you'll get:

W
gm = u.Cox - V_DS
L

In saturation, i.e., eq(1):

W
gm = u.Cox - (V_GS - V_T)
L

See how ugly it looks when I do V_GS rather than just Vgs.

Try the calc for an exercise.
Then for Mike, you have make it really a simplified way to understand
the notations. One last thing to check that is , what does IOW stand
for ?

"In other words." The Dialog news reader underlines it and gives the
definition in a tool tip pop up. I'm trying out the Pan reader and I
don't think it does that, but you can always pop abbrevs and
acronyms into google and see what happens. Sometimes adding "jargon"
or other key words helps.
Thanks a lot Geo , Andrew and Mike

You're welcome. Thanks for helping to reinforce my knowledge.
 
A

Active8

Jan 1, 1970
0
I read in sci.electronics.design that Andrew Holme <[email protected]>


Note the date. 'IOW' means 'Isle of Wight'.

LOL. Good observation, but I posted and jason queried on the 31st.
Andrew posted on the 1st and I hopefully straightened out the whole
subject (the gm thing) on the 1st.
 
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