# switch mode power supply frequency change

I am relatively new in the field of Switch Mode Power Supplies but I was looking at the Flyback converter with an input voltage of between 30V to 88V DC and an output that would charge a 24V lead acid battery bank. The main reason for deciding on this topology was the power requirements of 720W.

The best transformer that I could find off the shelf is a 250 Watt Wurth Elektronik with part number 760895741 that is designed for 220Vac mains use where the input voltage to the transformer is between 320Vdc and 350Vdc. It has a turns ratio of 27:3:3:2.

My question is this: if I change the input frequency, will this effect the output voltage as higher frequencies in SMPS results in smaller inductors?

## 2 Answers

I was looking at the Flyback converter with an input voltage of between 30V to 88V DC and an output that would charge a 24V lead acid battery bank.

For charging a battery a fly back design is not needed. Use a buck converter. This is a much simpler approach having just one off-the-shelf inductor (normally).

If you did choose a fly back design (why would you?) then the frequency will directly affect the output level because energy is transferred more often per second and this can mean an over-charge situation unless you have a feedback system that compensates by altering the mark-space ratio.

Choosing a transformer that is intended for mains frequencies (50 or 60 Hz) will not work adequately when used in a fly back scenario because fly back converters usually operate at significantly higher frequencies.

OK the wurth transformer is of for 100kHz but we cannot possibly know if this device is adequate without understanding the power requirements for your charging battery - do yourself a favour and use a buck converter.

• The power requirements are 720W, I am hoping to use three 20A off the shelf inductors in parallel... not sure if it will work. – Matt Jul 17 '15 at 8:40

Before talking about power electronics, I want to first talk about battery charging. Lead acid batteries can be dangerous if too much voltage is placed on the terminals. See this website for the "gassing voltage" of cells at which point hydrolysis of water occurs and hydrogen gas is generated, which is flammable. Make sure whatever implementation you design does not exceed this gassing voltage. Explosions of lead acid batteries are rather nasty.

There are several methods of battery charging. The link above provides several methods and these links has some more explanation. Constant current followed by a topping off with constant voltage is the most expedient as constant current ensures a steady flow of electrons to continue charging at the maximum rate, while in a constant voltage charger, the charging current decreases as the battery charges and thus it is slower. However, constant voltage chargers are much easier to make as you don't need to sense the current.

So let's talk about power electronics. We know that our output voltage is somewhere around 24 V. Do more research on this value to determine a safe value for battery charging. Nevertheless, this is lower than your input voltage of 30 V. This suggests we should use a voltage converter than produces an output voltage lower than the input voltage. This is known as a buck or down converter. Note that DC to DC converters convert voltage and current, the input and output current remain the same. As a toy example, suppose we have an input voltage of 10 V and input voltage of 1 A. If the output voltage is 5 V, the output current will be 2 A. Overall power (P=IV) is conserved.

Moving on to your question. Switching frequency and component size is one of those great trade-offs in power electronics. I would first read up on buck converters and their derivation if you are not already familiar. If you stay within certain constraints, the average output voltage will not change with respect to frequency. A buck converter produces output voltage $$V_{out} = D \cdot V_{in}$$

where D is the duty cycle of of gate control. This equation is only valid if we are in continuous conduction mode. The wiki page has information on this. Essentially, the inductor current is never allowed to reach zero. The inductor current can be modeled as two signals, the average current and the ripple current. ripple current is a function of frequency.

$$\Delta I_L = \frac{V_{in} D (1-D) T}{2L}$$

This is the equation for inductor ripple current. Study it a bit and look at T, the switching period, and L the inductor value. T is directly proportional to the ripple current while L is inversely proportional. This is why we can trade frequency for component size to keep the same ripple current. By going up in frequency by a factor of 2, we can reduce our inductor value by a factor of 2 and keep the same ripple current.

Now you may say, "why is this important?" Ripple current and ripple voltage are important because if the buck converter is not keeping a constant output, it is failing at it's job as a regulation device. Furthermore, loads may expect specific voltages. This is very true in your battery charging application. Ripple may cause the output voltage to swing above the nominal output voltage and then again back below. This is dangerous to the lead acid batteries as too high of a voltage can cause hydrolysis and the generation of hydrogen gas.

Lastly, in terms of inductors, I've often custom made inductors for my power circuits, but you might be able to find some fixed inductors pre-made. There are many calculations that go into sizing these components. Here's a TI application note that goes into good detail about it. Be aware of the current rating, core saturation current, temperature rating, and derating curves. The TI app note does a good job of touching on these points.

Make sure that other components are rated properly. Your power rating of 720 W seems a bit high. Drawing 30 A @ 24 V is a lot of current. I would do more research on the expected current draw. In any case, make sure the wires and switches can all handle the expected peak current plus some extra margin.

In summary: 1) Be very careful of how you design this charger, do not exceed the gassing voltage.

2) Use a down converter since the charging voltage is lower than your input voltage.

3) Changing the switching frequency will not affect the average output voltage if you remain in continuous conduction mode.

4) Change the switching frequency will affect the ripple of the output voltage. Pay careful attention to the peak ripple as you do not want to go over the gassing voltage.

5) Look at your power rating again, it seems large.