# Calculation of switching transformer at 100kHz

I am not able to desgin transformer for switching frequency 100kHz. It´s easy to desgin usual transformer for 50 Hz. But I´m totaly out when comes to switching transformers. What material should I use? Im not sure if Ferrite core E55 is enough.

My desired parameters is: approx. 315 V primary (after 230V rectifying), 12V secondary and 1000 VA of power. and full-bridge switching mode.

• E55 is a geometry - you also need to decide on a core material available in that form factor from the manufacturer you choose (3C90? N87?) based on your peak primary current and the core Bmax. – Adam Lawrence Jun 4 '20 at 13:53
• So what you suggesting? Because I want to learn how desgin properly switching transformer... But when I browsing internet am totaly out of equations without meaning for me :D – Sahasrar Jun 4 '20 at 14:00
• You need to learn how to design a forward-converter style transformer (energy transfer from primary to secondary during the on-time). Check any number of power supply IC controller websites or refer to any of the good power supply design books out there. You will not be able to design this without a good understanding of the maths... – Adam Lawrence Jun 4 '20 at 14:02
• There are several good books on this and transformer design takes up at least one chapter. If you can’t afford to purchase the books, I’m sure there are pirate copies floating around, but I like the feel of paper myself (and the small amount of money that accrues to the authors). – Spehro Pefhany Jun 4 '20 at 14:07
• Out of equations? I'll give you the two most important ones: Vt=NAB and L=N^2*Al – winny Jun 4 '20 at 15:07

I´m totaly out when comes to switching transformers. What material should I use? Im not sure if Ferrite core E55 is enough

In the example below I used an E55/28/25 core set and 3C90 core material just to take a stab at the viability of the design. I'm not really focusing on the numbers; rather I'm taking you through a form of procedure that gets you somewhere close to being able to wind the primary winding. My figures below are just as they come out of my calculator and I'm not vouching for them being correct when I first post this answer. They need double checking and any errors pointed out to me will result in this answer being corrected.

Regular AC power transformers (50 or 60 Hz) have a primary inductance. After all, the primary is just a coil of wire wrapped around a magnetic core and, you don't want the current taken by that inductance (secondary unloaded) to be "tens of amps". So, you wind the primary with enough inductance so that the residual current taken (called magnetization current) is not excessive.

If it is excessive then the core will saturate and you end up in a mess.

It's the same for any transformer operating at any frequency - you have to avoid core saturation and it's the magnetization current that causes core saturation. It's got nothing to do with load current because load current magnetic fields produced by primary and secondary cancel out.

In effect, the magnetic field in the core is ONLY due to magnetization inductance and the current that is taken by that inductance due to the applied primary voltage.

This is what you design first and subsequently, the secondary winding has the right number of turns to give you the right output voltage based on the number of turns on the primary.

So say you chose this core set: -

And let's say you chose an un-gapped core. It has an $$\A_L\$$ value of 8000 nH/turn. This means that 1 turn of wire would have an inductance of 8 μH. If you applied two turns it doesn't change to 16 μH but it rises as the square of the turns i.e. with 2 turns you get 32 μH.

But how much inductance do you need?

This sometimes takes a little bit of trial and error. Going back to a regular 230 volts 50 Hz transformer, it might have a primary magnetization inductance of (say) 10 henry. That's at 50 Hz so, for 100 kHz we should be ball-parking around 10 henries * 50/100,000 = 5 mH.

That would need about 25 turns i.e. 25 squared x 8 μH = 5 mH. This is just a ball-park estimate to see how things shape up. The next thing to calculate is how much peak magnetization current we get voltage is applied over 5 μs. I say 5 μs because that is what half a cycle at 100 kHz is.

We can also say that because the circuit uses a full-bridge driver, the current will start at -Ipk and rise to +Ipk over 5 μs. This means that for 2.5 μs the current changes from 0 to +Ipk. We know the applied voltage (315 volts DC) and we know the ball-park inductance (5 mH) and we know Faraday's law of induction: -

$$V = L\cdot\dfrac{di}{dt}$$

So, $$\\frac{di}{dt}\$$ = 315 volt / 5 mH = 63,000 amps per second. We know time (2.5 μs) hence the peak current will be 157.5 mA. It will alternate as a triangle waveform shape between -157.5 mA and +157.5 mA.

So now we know peak current (157.5 mA) and we know the number of turns (25). That gives us the MMF (magneto motive force) of 3.9375 At. We also know the mean length of the core (specified in the picture above in purple). So, MMF / core length tells us the H-field. With a core length ($$\\ell_e\$$) of 123 mm, H = 32 At/m.

Will this saturate the core?

This can be found by looking at the BH curve for the 3C90 material I chose: -

I reckon the peak flux density will be about 250 mT and that's OK in this application.

However, the secondary winding is only going to be about 1 turn i.e. 315/25 = 12.6 volts and, after rectification, this produces circa 12 volts. But this is just at an input voltage of 315 volts (~230 volts AC). If you need this to work at lower voltages the secondary turns need to be higher and you need to control the transformer primary with PWM to make the average voltage smaller at the higher supply voltages (requires a secondary inductance to average the voltage out).

Anyway, that's how I'd start to design the transformer then, I'd look at the range of supply voltages that the output is meant to stay regulated over. Then I'd look at what PWM chip to use to control it and what output inductor is required.

Will you get 1000 VA through an E55/28/25 core set like the one above - my gut feeling is more closer to 300 VA.