[SOLVED] Why Vc is equal to (Vs + Vd)/2?

[NewbV]

while I have been studying MOSFET with CMOS VLSI Design A Circuits and Systems Perspective (NEIL H.E. WESTE)
I have thought about this for many hours, but I could not get it.

In the part where I boxed, Vc = (Vs + Vd)/2.
why Average of Vs and Vd?
I personally think Vc = Vd - Vs.

Is there anyone who can help me with this matter?

Sorry for my poor English. English is not my mother language.
Thx you for your help!

 

[erikl]

I understand Vc = (Vs + Vd)/2 is the local channel voltage at a special point between source and drain (about half way between source and channel depletion end at the drain side of the channel).

Your definition, however, Vc = Vd - Vs = Vds , the drain-to-source voltage of the FET. You could call it the channel's voltage drop.

 

[NewbV]

Hi erikl.
First of all, thank you for your advice. really appreciated!

Can you tell me a bit more about the difference between Vc and Vds?
I thought Vc = Vds. but they seem like a bit different when I see your comment.

And! Does the special point mean a random dot on the channel?
Last! The voltage level of Vc is based on GND? or Vs?

Anyway, again, thx for your help! for real!

 

[erikl]

Can you tell me a bit more about the difference between Vc and Vds?
I thought Vc = Vds. but they seem like a bit different when I see your comment.

Vds - as the abbreviation tells - is the voltage between drain and source.
Vc is a voltage at some point in the channel. At the source ("begin" of the channel) Vc=Vs,
at the drain ("end" of the channel) Vc=Vd , i.e. in a 1-dimensional representation Vc in x-direction changes from Vs to Vd.

Note that in saturation region operation, the channel doesn't reach to the drain, it ends in between,
it "pinches" off:

And! Does the special point mean a random dot on the channel?

Not a random point, but the point in x-direction, where the channel ends in saturation,
s. the triangular drain-side channel end in the 2-dimensional representation above.

Last! The voltage level of Vc is based on GND? or Vs?

Vc is referred to Vs, very often Vs = GND .