Designing your own HV Transformer

In Transformer Corner Part 2, I looked at the power supply used in my early Prototype, and showed how to determine the key requirements for the HV transformer.

Now, let’s see how I could choose the materials and design the transformer – without any pesky mathematical formulae!

Picking a core

The first challenge was to find a suitable core from my junk box. First off, recall from Part 1 that this couldn’t be iron (too ‘slow’ for 151 kHz), and it couldn’t be air (too ‘weak’ for 25mA). I suppose I could have tried plastic, milk, or even beer – but I knew better. I knew about a substance called Ferrite.

Ferrite is a beautiful, fascinating substance – lightweight yet capable of hosting intense magnetic fields at high frequencies. But there are many different types and grades of the material, with different characteristics. The choice must not be taken lightly! I looked at each of my transformers carefully, and evaluated them strictly on which one looked the coolest. Very scientific…

Well, to cut a long story short, this junk core did work in the Prototype. But only barely. The transformer doesn’t have much power, so the image on the screen is a little dim. And it gets very, very hot. Thank goodness for my Auto Power-off feature!

Picking a BETTER core

Later, long after the Prototype was complete, I learned a far smarter way to choose materials. I discovered that transformer cores and bobbins with published technical specifications are actually available in hobbyist quantities (like one), from large houses like RS Components, and from numerous mom-and-pop shops around the globe.

Inside the specifications, there is a characteristic called “A_L-value“, which tells you how much inductance you get per square-of-turns around the core. This is really helpful, because we know what primary inductance we want (we calculated this in Part 2).

But, this A_L-value by itself won’t help us in choosing a core. You could choose a low-inductance core and have many turns, or a high-inductance core and have only a couple turns, and theoretically get the same total inductance!

… Here is where losses come in. For a small current output, using a massive core with just a couple primary turns will work – but it’ll be pretty inefficient. Think of my ‘inertia’ analogy – it makes the thing just too dang lunky, and to keep up the induction the switcher will have to pass some pretty heavy current through the primary winding. And you’d have to use thicker wire. And the core itself would heat up. All so very wasteful.

But at the other extreme, if you choose a small core and have lots of primary turns, you end up with a different set of problems:

• Since the wire itself has some resistance, with many turns, power will be lost in the winding, generating heat. Lovely.
• Why not use thicker wire for the primary to lower the resistance? Sure! But… how many turns of thick wire can you fit around the tiny bobbin? Not many.
• Let’s say you manage to squeeze 50 turns of thick wire on the primary. Congratulations! But uh-oh. You forgot you have to wind the secondary, with 14 times more turns. That’s a whopping 700 turns! You could use super-thin wire to fit it on the bobbin, but then you face the resistance and heat problem again – there just wouldn’t be much power for the poor old Oscilloclock.

So, therein lies the compromise, and it’s an important choice.

For my proposed circuit, I would choose something like the TDK PC44-EPC19 core. It nestles nicely in the hand, is not too heavy, and has the most luscious fragrance to it. OK, ignore the last part – but generally it just feels ‘right’.

How many turns?

The primary inductance of my transformer needs to be around 80 µH. The specification above tells me that the PC44-EPC19 core will give me 940 nH (or 0.94 µH) inductance per square of turns. Arghh.. there is a little bit of maths involved! 80 divided by 0.94 gives around 85 square-of-turns. The number of turns is the square-root of that, which is 9.2 turns.

But wait!! Look closer at the A_L-value in the spec. It says 940 nH plus or minus 25%. This means that, depending on the core’s manufacturing lot and also on how it’s mounted physically, the square-of-turns could be anywhere from 68 to 113, and hence the turns required could be anywhere from 8.25 to 10.6. What if we wound 9 turns, but our core was on the ‘light’ side? We’d end up with a fair bit less than 80 µH. Would it matter so much?

Nope. These switching regulator ICs are pretty smart. They can adjust switching speed and duty cycles to work with your transformer’s inductance, to a certain extent. So for now, let’s just assume we’ll wind 9½ turns, and move on.

Picking the wire

Copper wire for transfomers, or magnet wire, comes in all kinds of gauges (diameters). We need to pick a wire gauge for both the primary, and the secondary.

The key factor for choosing this is going to be the resistance per unit length. My antique but trustworthy ARRL Handbook shows this as “Ohms per 1000 ft”, as shown below. (Ugh. Feet!! Normally, I boycott non-metric measurements, but I love this book so much that I’m going to use this chart anyway.)

1. Primary Winding

The main concern here is the primary resistance, which we know from Part 2 should total around 0.08 ohms. We need to pick a wire that, with 9½ turns around the bobbin, will match that value. If we look at the specs for the BEPC19-1111 bobbin that goes with my core, the l_W measure tells us that the length of wire for each turn around the core is 34.4 mm.

At 9½ turns, the length of wire is 326.8mm, about 1.07 feet. Now let’s go back to the wire gauge chart, and look at a few choices:

• #28 gauge: 0.06617 ohms/ft x 1.07 ft = 0.0708 ohms
• #29 gauge: 0.08344 x 1.07 = 0.0893 ohms
• #30 gauge: 0.1052 x 1.07 = 0.1126 ohms

To get 0.08 ohms, we should choose something between #28 (dia. 0.3211 mm) and #29 (dia. 0.2859 mm). But you know what? I have a nice big spool of 0.25 mm coil wire that I bought 25 years ago that I really want to use up. This is a tad thinner than #30 – the resistance will end up close to 0.12 ohms. But I DON’T CARE! I’m going to use this wire. We’ll see soon whether it works okay or not.

2. Secondary Winding

We know from Part 2 that the secondary turns ratio is 1:14. If we have 9½ turns on the primary, then we’ll have 133 turns on the secondary.

The first thing to worry about when choosing wire for the secondary is whether it will handle the required current, without too much power loss in the form of heat. Let’s see how it turns out:

If I use the same 0.25 mm diameter wire, then the total resistance for 133 turns calculates to about 1.6 ohms. But in practice, it’ll be closer to 2 ohms, because we’re going to have to overlap turns (133 turns at this diameter simply won’t fit on the bobbin in a straight line), and that will cause increased resistance.

Now, if I fully load down my output to 25 mA, then I have .025 squared x 2 ohms = 1.25 mW of power loss in my winding. Compared to the total power output, 150V x 25mA = 3.75 W, this is miniscule. And also, .025 x 2 = 0.05V voltage loss is tiny compared to 150V. Great!

What if I used super-thin, super-cheap #40 gauge wire? Ha – still only 9.75 mW and 0.4V loss! All this just proves an Oscilloclock theorem:

In the case of low current HV outputs, secondary wire gauge doesn’t really matter! Just use whatever you have handy.

There is just ONE possible problem left. Will the required number of turns fit around the bobbin? Well, manufacturers have charts showing the maximum number of turns for each bobbin and given wire size. See below. It says maximum 1,600 turns of 0.25 mm wire will fit around the bobbin – so my 133 turns is well within the limits.

If we look at it the other way around, the maximum diameter I could use to fit 133 turns would be around 0.48 mm, or about #25 gauge.

So… Design complete!

We’ve decided on the following:

• Core (TDK PC44-EPC19)
• Bobbin (TDK BEPC19-1111)
• Primary and Secondary wire (0.25 mm)
• Primary turns (9½)
• Secondary turns (133)

In the last post in the series, I examine the hand-winding process, and you can see just how well (or poorly?!) my transformer works!