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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.)
Registered Member #2939
Joined: Fri Jun 25 2010, 04:25AM
Location:
Posts: 615
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.
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.
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.
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.
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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