MOSFET Small-Signal Amplification

[igh]

Hi everyone,

I am trying to learn about circuits from some slides I obtained and I am stuck on a slide.

Here is a screenshot of it (it is in German): http://i.imgur.com/HCtWF.png

It says: Example: Illustration of maximum achievable amplification of a MOSFET with the use of the parameters g_m (transconductance) and g_DS (output conductance).

On the left is the circuit configuration. On the right is the effect of an input voltage change with x-axis drain voltage and y-axis drain current. It also has the derivation for the amplification.

What confuses me is how they obtained:

g_m * ΔU_GS + g_DS * ΔU_DS = 0

as a result of I₀ being constant. Perhaps I am not understanding the graph completely. Can someone point me in the correct direction?

For reference:
g_m = dI_D / dU_G with U_D const.
g_DS = dI_D / dU_D with U_G const.

Many thanks.

 

[es1]

It looks like they might be doing KCL at the drain to me.
Id(due to ∆Vg) + Id(due to ∆Vds) = 0.
But it is hard to follow. This is the usual way to derive the pi-model.
http://whites.sdsmt.edu/classes/ee320/notes/320Lecture28.pdf

 

[Kholdstare]

The change in I0 is represented by the sum of ( gm * change in Vg + gd * change in Vd ). You know this already if you understand the definition of gm and gd. Now they assumed the current to be constant. Thus they had to equate this to zero.