# How important is self-resonant frequency for an inductor when used in a fast (~3MHz) buck SMPS?

I'm using the LM2734Z, a 3 MHz buck regulator. It's really fast which means it has a small inductor.

One of the things I'm wondering is how important is the self-resonant frequency of the inductor? I'm using it to step 4.8V to 20V down to 3.3V ±5%.

I found a 3.3µH 2A inductor (as recommended by the datasheet for 3.3V @ 1A, I'm rating the output to 400mA maximum) "SDR0604-3R3ML." Its self-resonant frequency is 60 MHz, which seems to be well clear of 3 MHz, but it is a multiple and I'm wondering if harmonics come into it?

Even if this case is okay, is there a rule of thumb for avoiding certain resonant frequencies (i.e. if they match?)

I wouldn't worry about it for 2 reasons.

First it is a multiple but, 60Mhz is an even harmonic of 3Mhz. The output of the regulator should be basically a square wave and square waves have content at their fundamental and only odd harmonics. So 3, 9, 15, 21, 27, 33, 39, 45, 51, 57, 63. Of course a non-perfect wave will have some even harmonic content but it should be well below any odd harmonics, if its a good square wave, it'll be in the noise floor. If in question set up your scope to do an FFT on the regulator output and see what its output looks like at 60Mhz.

Second, as the list above shows, you're at a very high harmonic at 60mhz. The switching supply would have to be outputing a square wave with really fast rise/fall times to have much if any content up that high. Usually only the first 3-6 odd harmonics are what you need to worry about with a square wave, depending on rise/fall times. That would work out to a theoretical rule of thumb that as long as the SRF is 5-10 times your switching speed you should be fine.

EDIT: Decided to model this so some degree...

Test Circuit, I used the parameters from the inductor you linked for the inductance, stray capacitance, ESR and shunt resistance. Shunt resistance changes based on frequency and is defined in Eqn. I modeled a generic 10uF ceramic cap for the output filter cap including ESR and ESL and arbitrarily chose 1k for the load. Doing an AC sweep with a 1V source from 0 to 250Mhz then later to 1Ghz to peek at the frequency response. The output resistance of the switcher is a shot in the dark but probably about right.

Here we are doing a sweep without the output filter cap attached to see the SRF of the inductor model, as expected at 60Mhz.

Here we sweep with the cap in place:

This one is actually interesting. Whats happening is that even though the inductor loses its filtering properties at SRF there is still an RC filter formed by Rout,the inductors resistance and the output cap. This filter is capable of blocking the high frequencies somewhat, which is why we don't see as sharp a change is we saw with the inductor only. However at these frequencies the ESL of the cap is really starting to come into play so we see a rising output level as frequency increases.

Finally lets see how it increases:

At 1 ghz the inductor is completely dominated by the stray capacitance and the filter cap in dominated by the ESL, at 10Ghz (not shown) it levels right off.

Of course there are a bunch of stray inductances,capacitances and variations (especially at the really high frequencies) not included in this simple model but maybe it will aid as a pictorial representation of whats happening.

The most interesting thing that came out of this for me is that SRF isn't a brick wall. The inherent RC filter can mitigate some of the effect of hitting the SRF.

EDIT2: One more edit, mostly because i'm using this as an opportunity to play with Qucs circuit sim for the first time. Cool program.

This shows 2 things. First its displaying the frequency response of the circuit in magnitude (in dB, Blue) and phase (red) this shows more clearly where the component's parasitic capacitance / inductance takes over. It also shows a secondary sweep of the ESL of the output capacitor showing how important it is to minimize this through component selection and PCB layout. Its sweep from 1nH to 101nH in steps of 10nH. You can see if the total inductance on the PCB gets very high you lose almost all of your filtering capability. This will result in EMI issues and/or noise problems.

• Okay, so would a rule of thumb be to avoid resonant frequencies within 3-6 odd harmonics (so 6-12x frequency?) What about resonant frequencies below the operational frequency? What happens at the resonant frequency? Thanks. – Thomas O Oct 19 '10 at 18:38
• I usually use 5-10 as i include the fundamental as one of the first 3. In the example above a perfect square wave would have 1/29 (29th harmonic) or 3.45% of the magnitude at 63Mhz that it has at its fundamental, 3Mhz. That is for a perfect square wave, with rise/fall times of 0. In reality this harmonic is probably a lot smaller because the slew rate of the switcher can't move that fast, it can't produce content at frequencies that high. – Mark Oct 19 '10 at 18:46
• As to SRF less than your switching frequencies. When you cross the SRF the inductor's impedance drops back to what your would expect in magnitude but takes on a negative phase shift. It acts kinda like a capacitor that passes DC. Weird mode of operation and I think it would probably screw with the filter response although i've never actually worked out the math on that. – Mark Oct 19 '10 at 18:55
• Thanks for your edits explaining this. Much appreciated. – Thomas O Oct 19 '10 at 22:09
• The real buck convertor has extra capacitance in the high side mosfet and the freewheel diode .If you have big die area low Rds on mosfet and schottky diode and a low inductance , then the extra capacitance is much greater than the inherent capacitance of the coil.In other words the resonant frequency in your circuit will be much lower than 60 MHz.If you run the buck in DCM you will see this in the form of damped oscillations.You can use this to advantage with the accepted valley switch or the newer S TRAP switching regimes .This self resonance doesnt have to be a bad thing. – Autistic Oct 26 '15 at 20:05