# It's not a straight line: Computing the Correct Drain to Source Resistance from V-I curves

Performing an efficiency calculation for a power converter will certainly require knowledge of the Drain to Source ON-resistance (hereby called R_{DSON}) of the switch. In doing so we may refer to the V-I characteristics of the said MOSFET. We will probably be thinking that all we need do is to find the slope - "V/I" - to get the R_{DSON}.

But hold on just a minute! Is the V-I curve really a straight line as we imagined? If not, the R_{DSON} is clearly a function of the current through the MOSFET. So what is the R_{DSON} we need to take for our calculation? We can do a "worst-case analysis" based on the highest R_{DSON} (slope) along the V-I curve: which would always be found to occur at the highest instantaneous value of current, i.e. the peak switching current. But is that value really "worst case", or is it even *worse* than "worst-case"?!

The current through the MOSFET is actually varying every cycle between two values, the peak and the trough. It is certainly not fixed at the peak value (at which we may be finding the "worst-case" slope). We are not interested in finding the worst-case *instantaneous* value of the R_{DSON}, what we want is the worst-case value over the *entire switching cycle*. In a switching converter, the R_{DSON} is actually varying smoothly between two values, just as the current is.

By a rather painful analysis, it can be shown that a very close fit to the exact integration-based calculation is obtained simply by (a) finding the R_{DSON} at the extreme current values: the peak and trough, and (b) averaging these two values to get the effective R_{DSON} over the entire cycle. Simple enough!

But hold on a minute longer. Look at the published V-I curve (the black part of the attached Figure ...this represents a typical integrated switcher device rated for 1.5A). The device is therefore supposed to function up to 100 degrees-C at 1.5A. But does the curve extend all the way? No at all! The 100 degrees-C is mysteriously truncated! No other information is available in the Datasheet. The only way out for us as designers is to try to extrapolate the V-I curve .see gray part.

**Click to Enlarge**

We now see that the curve intersects at a whopping drop of 17V at 1.5A at 100 degrees-C! Maybe that is what the vendor didn't want to circle out for us. But at least we can now find the effective R_{DSON}.

However, we could *erroneously* take the average over the *entire* range to get

This estimate is way too optimistic. As mentioned previously, a more correct estimate is the RDS averaged over the RDS at the extreme values. At peak value

We also know that the R_{DSON- MIN} is 10Ω from the datasheet since the R_{DSON} is rather typically stated at only 1/10^{th} the maximum current i.e. 10Ω at 150mA in this case.

So the correct effective R_{DSON} is the average of the two

Now that we know the RDS is 50 percent higher than what was indicated to us, we also have a better idea of the conduction loss in the MOSFET.

Please drop me a note at sanjaya.maniktala@nsc.com and copy sohr@cmp.com. One year of this column is now completemany thanks to you all.