# Channel resistance in MOSFET

When there is no channel length modulation there is infinite channel resistance according to relation :
rds = 1/lamda * Id..So does this mean that drain current is zero ?

• Yes, but do not forget you are talking of differential, small signal variations around bias point.So $\underbrace{i_\text{D}}_\text{total} = \underbrace{I_\text{D}}_\text{bias}+ \underbrace{i_\text{d}}_\text{variation}=I_\text{D}$ BTW: rds usually designates resistance when in triode region and MOS is used as a switch. Differential output resistance when in saturation region (your case) is better named ro. Dec 8, 2016 at 8:14
• That means ac current is zero, right ?
– ajk
Dec 9, 2016 at 15:56

Have a look at the picture below. The green lines show the drain current of a transistor without channel length modulation (resistance is inifinite) and the black lines are for a transistor with channel length modulation.

The current is obviously not zero, but the change of current (and therefore the slope of the curve) in the saturation region is zero, if no channel length modulation is present.

• So that means ac current is zero right ?
– ajk
Dec 9, 2016 at 15:56
• The ac current caused by rds is zero. Right. Dec 9, 2016 at 16:13

Just to clarify, I think saying that the slope of an I/V curve is zero and therefore resistance is infinite is both confusing and incorrect. Resistance is not infinite, or we would not have current flow!

Keep in mind that the overall current is made up of the DC and AC components (AC = small signal component "riding" atop the DC bias point).

For the curves of a transistor in saturation and no channel length modulation, the overall resistance is not infinite when simply dividing bias point voltage and current. But since the differential at that point in the curve is 0, there is an infinite AC impedance.