# Dynamic Resistance

#### mjm609

Joined Dec 1, 2007
3
Hey, I was having a little trouble with a homework problem.

It asks to calculate the dynamic resistance looking into the drain of an enhanced n channel mosfet. My book has not been helpful, for it only gives references to dynamic resistance for zener diodes. I've tried searching in google, but again, no luck. Can anyone help point me in the right direction?

thanks.

#### cheddy

Joined Oct 19, 2007
87
By dynamic resistance do you mean depletion and pinch off?

#### Ron H

Joined Apr 14, 2005
7,014
You need to derive (or find) the equation for Vds as a function of Ids for the diode-connected MOSFET (which is what your circuit is). Dynamic resistance is rate of change of voltage as a function of current (hint: use calculus).

#### mjm609

Joined Dec 1, 2007
3
I found a couple of E-Books and did some more research. In my current course we didn't go too in depth with some of the complex equations and channel length ect. I was, however, able to find a simplified model. Thanks Ron and Cheddy for the responses.

#### Ron H

Joined Apr 14, 2005
7,014
Since you seem to have solved your problem, I'll tell you that I found this. It has the equation you needed, but it still needs to be differentiated and evaluated at the operating point.

#### GS3

Joined Sep 21, 2007
408
You need to derive (or find) the equation for Vds as a function of Ids for the diode-connected MOSFET (which is what your circuit is). Dynamic resistance is rate of change of voltage as a function of current
Exactly. And it will not be constant but will change with voltage and current.

In other words at any give set of conditions (voltage and current) what variation in current does an very small variation in voltage cause (or viceversa). That is the dynamic resistance.

#### Ron H

Joined Apr 14, 2005
7,014
Exactly. And it will not be constant but will change with voltage and current.
Good point. That's why I added this in my last post.
Since you seem to have solved your problem, I'll tell you that I found this. It has the equation you needed, but it still needs to be differentiated and evaluated at the operating point.

In other words at any give set of conditions (voltage and current) what variation in current does an very small variation in voltage cause (or viceversa). That is the dynamic resistance.