[SOLVED] ıf some current is injected to drain of the MOSFET, why vds increases?

Hi everyone,
In the figure, according to the Mr.Baker's book, if we inject the current to drain, Id increases (I agree with that) so Vds increases since we keep Vgs constant. I agree with that too if we just look at the formula of Id= Idsat+Idsat*lambda*(Vds-Vdsat). However, if ı consider this situation in that way, Vd=Vdd-Id*R1, Vd must be going to decrease. According to the same book, Ro=1/(lambda*Idsat) so it does not change too. Please can somebody explain me this situation?
Thank you.

Note: It is a long-channel MOSFET.

When current Iinjected is injected to node D, a part of this current (say I1) will go into MOSFET, increasing its current, and remaining part of the injected current (say I2) will flow into R1 and into node VDD - going opposite to the original current in R, and hence decreasing voltage drop on R1 and increasing voltage Vds on a MOSFET.

If R0 is a differential resistance of MOSFET (R0 = dVds/dIds), andinjected current is small, we have:

R0*I1 = R1*I2.

I1+I2 = Iinjected.

Max
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Thank you for your answer Mr.Max. I need to ask one more question. I am a little bit confused about the resistances of MOSFET. As I know, Ro=dVDS/dID in both saturation and linear region, just the formula of ID changes. When we try to calculate AC gain, we are using small-signal model where the resistance equals the 1/gm. Another usage of MOSFET as a switch, Rn=VDS/ID . So does it make sense to distinguish the resistances like that? and as a switch, everybody talks about we need to guarentee that the mosfet is fully opened so VGS=10V typically. But if the VDS<VOV , the mosfet is in the linear region. So to use MOSFET as a switch, is it okey that we are in linear region or we need to have more Vds to be in the saturation?
Thank you.

Hi Derun93 -

1/gm = dVgs/dIds is inverse transconductance.
It always makes sense to distinguish between different resistances, such as differential resistance (Rd=dV/dI) vs "integral" (or total) resistance (R=V/I), as they have different significance, and often different values.

When a MOSFET operates as a switch, in most applications, ideally, it's resistance should be small when it is in ON state, i.e. its Vgs should be maximum, and it should operate in the linear region (i.e. small Vds).

Other than small total resistance (Rdson), power transistor should satisfy a number of other requirements - such as uniformity of current distribution over device area, current densities in interconnects (metal and via layers) within spec, etc.

Max