That's great Steve! Thanks for the explanation. I have a few questions though.
I think there's a number missing from your equations - the gate voltage at which the MOSFET saturates. AFAIK, Vgs(th) is the gate voltage at which the MOSFET starts to conduct, but there is also another voltage, higher than Vgs(th), where the MOSFET is conducting so hard that the linear part of the switching action has finished and the conduction loss becomes the only factor.
If you look at the charging of the gate of a mosfet you'll find that the gate voltage reaches a threshold voltage where it stays relatively constant while charge flows into the gate. The same is true of the discharging of the gate of a mosfet (this is for the FQP50N06 -- see below for a link to the datasheet).
You say that when the driver output goes high, the MOSFET gate voltage jumps quickly up to Vgs(th) then sits at that voltage until the gate capacitance has been charged, and the time for this is determined by Qg / Ig. But during this time, surely the gate voltage is increasing steadily towards the other threshold I mentioned? And during that time, the drain circuit is transitioning between no current flow into the MOSFET, through the linear region, to minimum voltage across the MOSFET? And the same in the other direction?
See page 18 of
this guide to datasheet parameters.
The first sloped portion of the graph is where the mosfet is in a constant voltage mode, and where the increase in gate voltage results in the opening of the channel. The horizontal portion of the graph is the point at which the mosfet is in a constant current condition as the channel opens still further to lower Vds. The gate voltage again starts to rise after the mosfet has essentially reached the minimum Vds. This is a reasonably adequate method of determining the gate current when the gate is driven by a voltage source via a fixed resistor. However, you can quite rightly point out that is *is* an underestimate. However, I am also overestimating the power dissipation by assuming that the full current into the inductor is being switched. In reality, unless the SMPS is operating in continuous mode, it will be zero. Even in continuous mode, the current should be less that the calculated current which is based on an almost 100% duty cycle.
Oh, it's important that you use total Gate charge for these calculations. (I just went back and checked -- I did say that -- phew)
This voltage is naturally going to vary with Id. Here is an example for a 2N7000

So the actual voltage is going to depend on a number of factors. Since turning off the mosfet is going to be the issue, rather than overcomplicating it, I decided to use a lower voltage. Note that with a gate driver capable of a given current, all of this goes away.
The question is, what voltage is this plateau at. I've suggested using Vgs(th). For that same mosfet (in this case an
FQP50N06 -- picked entirely at random), Vgs(th) is given as:
And I normally suggest you use the worst case, in this case 4V is the worst case, and it is an approximation for the plateau voltage seen above. Sure, it may be better to read the value off the graph, but the graph is not always available, and reading it off the datasheet is non-trivial anyway.
Have you just approximated those two voltages to be the same thing? If so, wouldn't it be better to use a voltage somewhat higher than Vgs(th)? Or I may be missing something.
Yes. On both counts.
However when we're switching the inductive load off we have a few complicating factors.
Firstly Vds is likely to rise, increasing dissipation faster than the simple linear model predicts, and secondly any method of switching the gate to whatever voltage levels we have may not switch completely to these levels or may be current limited as it approaches them. The chosen voltage gives a bias to the "difficulty" in switching the mosfet off.
Second, the actual power dissipation calculation is going to be a lot more complicated than that formula because it depends on the actual nature of the progression of the drain-source resistance or drain-source current. Towards one end of the linear region, the drain-source circuit will approximate a current sink, and towards the other end, it will approximate a resistance, right? The shape of the power dissipation waveform will be pretty complicated and hard to estimate, I think. And the interaction with the inductor will be complicated too. Or will it actually be simplified by the fact that in the short term (and switching is short term), the inductor is actually just a constant current source?
Sure, there is a lot more variation, but we hope to include that in the slack we give by using the maximum values for gate charge, Rds(on), etc. What we want is a ballpark estimate (perhaps somewhere in the diamond rather than the entire ballpark) not to pinpoint the position of the batter. And we try to aim for closer to worst-case (so we don't hit a foul ball as it were). Enough of the baseball analogies!
Third, I think your use of duty cycle may be misleading. The 555 oscillator is running at a 60% duty cycle and that is the operating duty cycle of the MOSFET, but that's irrelevant to the power dissipation. The duty cycle you're talking about is the proportion of the time that the MOSFET is being switched, vs. the proportion of the time when it's either permanently ON or permanently OFF (probably permanently OFF), right? That doesn't happen in a boost converter except when the output voltage reaches the regulation target, right? And it's just a separate factor that can be easily bolted onto the equation if it's relevant, right?
That is correct. I tried to make that clear, but I probably failed.
Note that I also did not include Rds(on) * Id * Mosfet Duty Cycle * System duty cycle.
Also note that there are graphs which give a far better estimate of how much the fudge factor should be. Whilst not exactly discussing this, the graph of the thermal response gives you a good idea of the thermal lag in the device.

Everything converges at around t = 1 sec, so that's where I get my 1 second max from. Note that this will change for different packages, and also if a heatsink is connected. However it is not wise to push it.
Finally I don't understand how the switching loss can be expressed as an amount of power if the switching frequency isn't known.
Aaaagh! MASSIVE ERROR. Thanks, and corrected.
Each transition through the linear region should cause a defined amount of energy loss, not power loss. That can be converted to a power figure if the number of transitions per second is known, but that figure isn't in the formula, as far as I can see.
You are exactly correct. When formulated correctly you calculate the energy lost in a second which corresponds (as if by magic) to the rate of power loss
Thanks again and please enlighten me further
I hope I have corrected my errors sufficiently and explained some of the fudge factors.[/quote][/quote]