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Calculating self-resonant frequency of HV Transformer?

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Ash Small

Wed Jan 30 2013, 08:22PM

Registered Member #3414 Joined: Sun Nov 14 2010, 05:05PM
Location: UK
Posts: 4245

Say I have a secondary consisting of four series pancake coils, each with ten layers of 50 turns of 0.2mm wire. Windings are eliptical, first layer circumferance ~200mm, with 1mm insulation between layers (see pic below).

Say these are around a core consisting of two sets of 9cm^2 'C' cores, total CSA 18cm^2.

Say these cores are most efficient @~25kHz, and I'm aiming for ~25 volts per turn. 50 turns per layer = 1.25kV per layer. 500 turns per pancake, four pancakes = 2000 turns total @ 25 volts per turn =50kV.

How do I go about calculating the self-resonant frequency of the transformer?

(Elliptical shape has been chosen to reduce capacitance between core and windings, apparently.)

Antonio

Wed Jan 30 2013, 11:11PM

Registered Member #834 Joined: Tue Jun 12 2007, 10:57PM
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This is very difficult, because is a function of distributed capacitances in the windings.

Ash Small

Wed Jan 30 2013, 11:17PM

Registered Member #3414 Joined: Sun Nov 14 2010, 05:05PM
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Posts: 4245

Antonio wrote ...

This is very difficult, because is a function of distributed capacitances in the windings.

Well, I've tried to leave a reasonable gap between layers.....to reduce inter-layer capacitance.

2Spoons

Thu Jan 31 2013, 03:28AM

Registered Member #2939 Joined: Fri Jun 25 2010, 04:25AM
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That doesn't really change the complexity of the problem. You'd still need to calculate all the distributed capacitances. I can't see any realistic way of predicting the resonant frequency with any degree of confidence.

Josh Campbell

Thu Jan 31 2013, 03:33AM

Registered Member #5258 Joined: Sun Jun 10 2012, 10:15PM
Location: Missouri - USA
Posts: 119

In practice measurement has been the only proven way to find the self resonant frequency of any inductor which is not fully understood. Even then it is extremely complex.
Keep in mind the frequency is generally very high since inductance typically outweighs capacitance many times.

Edit: I suppose I was a bit hasty, Steve has some good advice here. I would still very much like to see your calculations vs real measurements.

Steve Conner

Thu Jan 31 2013, 08:51AM

Registered Member #30 Joined: Fri Feb 03 2006, 10:52AM
Location: Glasgow, Scotland
Posts: 6706

That doesn't follow at all. Resonant frequency is determined by the product of L and C, not the ratio. If you have lots of inductance, even a tiny capacitance can ruin your day.

You can approximate the capacitance between adjacent layers using the parallel plate equation. Then use conservation of energy to turn all those little capacitances into a single capacitance referred to the whole winding. I think they more or less end up in series.

That is a very simple hand-waving analysis, but straight away you can see why old TV flybacks used a large disc secondary. Less "plate" area, more layers, means smaller capacitors and more of them in series, so the self-capacitance is reduced. The voltage between layers is also reduced. Generally, anything that reduces the voltage between layers helps with the self-capacitance.

IIRC the Radio Designer's Handbook (aka RDH4) has a procedure for estimating self-resonant frequency, aimed at tube amp output transformers.

Ash Small

Thu Jan 31 2013, 10:18AM

Registered Member #3414 Joined: Sun Nov 14 2010, 05:05PM
Location: UK
Posts: 4245

So if I was to wind one pancake, it would be a relatively straightforward process to calculate inter-winding capacitance four four in series?

What about calculating the inductance? would the easiest way be to again wind one pancake, and measure it, then work from there?

Steve Conner

Thu Jan 31 2013, 10:33AM

Registered Member #30 Joined: Fri Feb 03 2006, 10:52AM
Location: Glasgow, Scotland
Posts: 6706

When you have several pancakes in series, the capacitances are also in series, so to a first approximation the self-resonant frequency is the same as for a single pancake. But the capacitance from each pancake to ground (ie the tank and core) has to be treated separately, as does the load capacitance. The more pancakes you stack in series, the worse the effect of this extra capacitance gets.

The inductance you need for the calculation is the leakage inductance of the secondary mounted on the core, with the primary shorted. To a first approximation, it's the same as the inductance of the coil with an air core, and you can calculate this easily enough. In practice it's somewhat less, especially if you can get the primary close to the secondary. This is hard in HV transformers though, because of the clearance requirements.

Ash Small

Thu Jan 31 2013, 04:28PM

Registered Member #3414 Joined: Sun Nov 14 2010, 05:05PM
Location: UK
Posts: 4245

So I really just have to 'suck it, and see'...I'll wind a whole secondary, and measure it (~1/2 mile of 0.2mm wire).

At the moment, I can only manufacture bobbins ~40mm long, and I need ~96mm, so it may be another few weeks.

It will be difficult to get the primary under the secondary (~15 turns of ~20 amp cable), but I haven't completely ruled it out yet.

Steve Conner

Thu Jan 31 2013, 04:46PM

Registered Member #30 Joined: Fri Feb 03 2006, 10:52AM
Location: Glasgow, Scotland
Posts: 6706

You might want to consider using a copper foil primary to get the height down. A "20 amp" cable might well be under-utilised at 25kHz due to skin effect.

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