# What is the maximum power an inductor can transfer in a SMPS?

I'm trying to analyze a boost converter circuit. I have all the specs for the inductor used, including inductance (6.8uH) and saturation current (1A). This runs from a 3V supply. I'm wondering if there is a formula for the maximum power than an inductor with a certain inductance and saturation current can transfer when operated from a fixed supply voltage, regardless of at what frequency/duty cycle it is being driven? In other words, what is the theoretical maximum power of a boost converter using that particular inductor and running off of 3V?

The boost converter in this case is usually operating in discontinuous mode, but apparently may switch to continuous mode some of the time.

With a fixed supply voltage and a fixed inductance and a known saturation current, you not only have the maximum energy that the coil can store:

$$E = 0.5 I_{sat}^2 L$$

but also how long it takes to charge the coil with that amount of energy:

$$t_{charge} = \frac{I_{sat} L}{V_{supply}}$$

The power transferred is equal to the energy per cycle divided by the cycle period, $t_{charge} + t_{discharge}$.

The discharge time depends on the output voltage, with higher voltages giving shorter times, but in any case, the total period cannot be shorter than $t_{charge}$, so this puts an upper limit on the maximum power transfer.

Continuous conduction mode does not change this; while it allows higher switching frequencies, the energy transferred per cycle is proportionally less.

• Continuous conduction mode allows twice this amount as the current could be at the saturation level for the entire discharge time (at the limit assuming infinite frequency). – Kevin White Sep 1 '15 at 2:17

Each switching cycle, energy is stored in the choke, then discharged into the load. Your limit is the total energy that can be stored in the choke, multiplied by the frequency the converter runs at. In your case, the choke can store $\frac{1}{2}LI^2 = \frac{1}{2}(6.8x10^{-6})(1)^2=3.4\mu J$. Multiply that by your switching frequency and you get your maximum total power throughput, assuming borderline conduction or discontinuous mode. CCM is more complex, but I believe the math works out with the same limit.

Now, you asked "regardless of frequency". Unfortunately I don't think that's possible to figure; frequency is inherently a property of the power transfer, it's where the "seconds" in "Joules per second" comes from. Of course, the properties of the choke itself will give you some frequency limit beyond which skin effect or core losses will make it melt.

• I see, sorry, faulty assumption on my part. I think I meant to say "regardless of frequency, but at a fixed supply voltage" :) The choke may be able to store that much energy, but to do that every cycle may require higher voltages at higher frequencies, so a fixed supply voltage limits the energy even if the frequency can vary, right? – Alex I Sep 1 '15 at 1:48
• I think Dave Tweed answered the modified question already, thanks to both of you guys! – Alex I Sep 1 '15 at 1:49