# What PWM frequency to use on SMPS

Just to give a little back ground on the project - I am currently building a buck converter linked up to 2 * 250W solar panels in parallel, then use an MPPT algorithum to track the max power. I will be using a TI Stellaris microcontroller to control the PWM, and will be using a synchronous buck topology with possibly a multiphase design to reduce the current through each mosfet (as well as lower output ripple).

The question relates to which is the best frequency to use for a buck converter? How to determine the best frequency?

I have experimented with 15-24kHz on a synchronous buck circuit already, and am aware most smps designs use 50kHz and upwards. My aim is to make the system as efficient as possible, and I seem to remember reading somewhere that lower PWM frequencies are more efficient, but cannot seem to find any literature on this after extensive searches online.

Any input would be appreciated, and if there is source information you can point me to even better.

There are many sources of loss in a SMPS. Here are just two:

### switching losses

Each time the "switch" (usually a MOSFET) changes from on to off, it spends some time in a state between. During this time, there is simultaneously significant current in the device, and significant voltage across it. As $P=IE$, this means the MOSFET is wasting input electrical energy to warm itself.

To minimize these losses, you want to switch as little as possible. The lower the frequency, the less often you switch, and the lower the switching losses.

### resistive losses in the inductor

A real inductor has resistance, and will experience losses according to Joule's law: $P=I^2 R$. The current in this inductor is not constant: it grows when it is storing input energy, and it decreases as it is releasing that stored energy to the output.

Clearly, the point of the SMPS is to deliver current to the load, so we can not eliminate this current. However, we do have a choice of the shape of that current. The output filter (often as simple as a capacitor) means we can have high current ripple in the inductor and still get a steady output voltage. However, if there is high current ripple, there must necessarily be times where the inductor current is much more than the current required by the load. Since losses are proportional to the square of current, this means our losses are higher when there is current ripple, compared to the case when there is no current ripple.

To minimize these losses, you want the switching frequency as high as possible, as this will minimize the current ripple.

### conclusion:

If the "best" frequency is one that has minimal losses, then the best switching frequency is the optimal balance between multiple kinds of loss. These are not the only kinds of loss. To determine the best frequency, you will have to perform a careful analysis of all the potential losses in your specific SMPS, determine how those losses change as frequency, then solve that system of equations for a minimum loss.

• Phil thanks for the answer, this helps me understand what I have read before and put it into perspective, also gives me a direction to follow. Quick question, using a multiphase buck design should reduce current ripple, therefore allowing a lower frequency to be used? – Ant Jan 26 '14 at 15:54
• @Ant that's a little beyond what I can confidently answer, but I'm sure if you ask it as a new question, you will get a good response. – Phil Frost Jan 26 '14 at 16:48

This is somewhat of a aside to what you asked, but if you are worried about every last bit of efficiency, don't connect the two solar panels together, especially if that leads to a multi-phase switcher. There will be differences between the two panels, and of course the insolation can vary too as shadows cross the two panels differently. 250 W is certainly doable, but quite a lot already, so it should be more efficient and probably easier to design a 250 single phase switcher and make two of them, then to design a 500 W multi-phase switcher.

• Olin thanks, this is one idea as well and looking at this as an option. I ideally want to make the system modular, so one alternative is micro MPPT per panel, just producing a DC output at this stage though not full inverters. – Ant Jan 26 '14 at 15:56