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Small-signal and large-signal MOSFET channel resistance

When running SPICE DC simulations one could often see two types of MOSFET transistor operating point parameters for the channel resistance printed by the simulator. These often have different names depending on model versions spanning a range: ron, rout, rds, rd, 1/gds – these are at first sight ambiguous and could be a source of confusion. Usually one of them is much bigger than the other. Here is actually what each of them represents.

ron - this is the large-signal MOSFET channel resistance. This parameter is derived by the partial derivative of the current operating point versus a point where Vds = 0 and Ids = 0.

Even if trivial, worth noting here that we calculate ron by:

$$r_{on} = \left[ \frac{\partial v_{ds}}{\partial i_{ds}} \right]_{V_{gs} = \text{const}} $$

Thus, for convenience I provide here a plot where the red line shows the partial derivative of the chosen point at the I-V curve, with respect to a 0 volts 0 amps operating point – this is in fact what is referred as ron. It is sometimes called large-signal resistance and it is calculated through the slope of the line connecting (0,0) with (vds,ids).

rout - this is the small-signal MOSFET channel resistance. Usually when running fixed operating point simulations we are interested in the small-signal resistance for the specific operating point. It is computed through the tangent line at (vds,ids), here is an example plot:

Looked at it the other way rout is vds over ids for a single point.

$$r_{out} = \left[ \frac{v_{ds}}{i_{ds}} \right]_{V_{gs} = \text{const}} $$

The small-signal output resistance is usually the one needed for evaluating impedances of current sources etc... It is worth noting that $1/g_{ds}$ is effectively equivalent to $r_{out}$ and represents the small-signal conductance of the device.

Date:Fri Dec 25 12:11:32 CET 2018


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