# MOS temperature dependence of Vds, Vgs

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#### whoopie

##### Newbie level 1
Hello there!

If I have a NMOS which is diode-connected and operating in the saturation region we can derive the equation for Vgs based from the well-known equation for drain current (ignoring the effects of channel length modulation)

Vgs = Vth + √[(2*Id*L)/(kn*W)]

and if we take its derivative with respect to temperature, we can get the rate of change of Vgs with respect to temperature. Also, since it is diode connected then Vgs=Vds which means that they both have the same rate of change with respect to temperature.

Now the question is: What if it is not diode-connected? Assuming it is still in saturation region, we can still get the rate of change of Vgs with respect to temperature but I can't find a way to determine the rate of change of Vds with respect to temperature. Please help guys.

#### ZekeR

##### Full Member level 5
When you find dVgs/dT, you are making some assumption about the current Id through the transistor (probably constant?). dVds/dT is going to reflect the temperature coefficient of whatever Id is being drawn out of... a voltage source, perhaps? (in this case, dVds/dT = 0). Or perhaps it is a diode-connected PMOS? In either case, once you detach the drain from the gate, dVds/dT no longer depends on the NMOS but rather the tempco of whatever it is drawing current from (and the tempco of the current).

-Edit-

Note that above, I'm assuming constant drain current and constant source voltage.

whoopie

### whoopie

Points: 2

#### erikl

##### Super Moderator
Staff member
... I can't find a way to determine the rate of change of Vds with respect to temperature.

If you know the Vgs vs. temp. dependency for constant drain current Id, it's just a question of the drain load and its possible temperature dependence.

whoopie

### whoopie

Points: 2
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