Electronic – MOSFET drain-source on-state resistance as a function of temperature and drain current

Reading into the authors explanation of the transconductance value (Kn) it was discovered that this value is not the same transconductance value PSpice uses (KP). The author wastes a paragraph of ink explaining that the value Kn used in the book is commonly known as the transconduction parameter, however the reader should refer to the value as the conduction parameter. The author defines the conduction parameter as:

1: Kn = (W*un*Cox)/(2L) and Cox = eox/tox

THEN at the bottom of the page it is written that "we can rewrite the conduction parameter in the form":

2: Kn = (k'n/2)(W/L)

The following page defines k'n as the process conduction parameter:

3: k'n = un*Cox

By default Pspice defaults the width and length to .1uM. Therefor equation two becomes:

4: Kn = k'n/2

Based on the evidence that the PSpice output was off by a factor of 2, k'n represents the value PSpice considers to be the transconductance parameter. The author of the book considers this value to be the process conduction parameter. This result was confirmed with other examples from the book.

I think I am more confused now than before. How do I know what value to use when I look at a spec sheet!?!?

A MOSFET does not have resistance in the same sense that R1 and R2 do. There is no single number which characterizes the behavior of the drain-source path. Instead, the equivalent resistance (drain-source voltage divided by drain-source current) will depend on 3 things: gate-source voltage, drain-source voltage or current (take your pick) and temperature. For data sheet switching use, gate-source voltage is generally held quite high, like 10 volts, while drain-source current is specified at some high level, where "high" depends on the transistor rating. Than the drain-source voltage is measured and the ratio of voltage to current is calculated to produce a resistance figure, referred to as Rds(on).

So it's perfectly possible to measure the effective resistance of the MOSFET in your drawing if you replace the motor with a resistor or other element which produces the same current as the motor would draw. But it is not (reasonably) possible to accurately determine the effective resistance without actually drawing current. Among other things, it's necessary to take into account of whatever heatsink has been attached to the MOSFET.