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High Voltage Planar Ferrite transformers. ( Intial Experiments )

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Uspring

Sun Sept 21 2014, 07:44AM

Registered Member #3988 Joined: Thu Jul 07 2011, 03:25PM
Location:
Posts: 711

Im needing others to review my math:

Faradays law states, that the voltage per turn is equal to the rate of change of the magnetic flux going through the turn. The flux is B*A, so for a sinusoidal time dependence you get:

Vmax = 2*pi*f*Bmax*A

This is equivalent to the first equation in Tony Matts list. The factor of 4.4 there is different from 2*pi. That is due to the Vrms, that is used there instead of Vmax.
For the A, f and Bmax quoted that works out to be about 100V per turn. You should use units of mÂ² for A and Tesla (V*s/mÂ²) for B.

Usage of Tesla instead of Gauss is much more pc in this forum and note that 1 Tesla is equal to 10000 Gauss.

Inductance of a 1.5 turn primary will be low even considering the large effect of the ferrite, so primary reactive currents might be larger than the mosfets or the primary winding like even for an unloaded secondary.

Sulaiman

Sun Sept 21 2014, 07:47AM

Registered Member #162 Joined: Mon Feb 13 2006, 10:25AM
Location: United Kingdom
Posts: 3140

Here are a few sums; (I have to think in metric)
1) Volume of one ferrite piece = 2.5 cm3, one pair = 5 cm3
2) Surface area of one pair = 15.8 cm2
3) In air, a 50C rise in temperature would allow 1.73W core dissipation (dT=(mW/cm2)^,833)
4) 1730mW/5cm3 = 345 mW/cm3
5) at 100kHz 345mW/cm3 = 200 gauss from your data sheet = 20mT
6) cross-sectional core area = 1.1 cm2
7) flux = 0.02 x 0.00011 = 2.1875 uWb
8) volts/turn = 2 x pi x 100E3 x 2.1875E-6 = 1.3744 Vpk
So if my calculations are correct, in air you could have 1.37 Volts peak per turn at 100 kHz with a 50C temperature rise if the copper losses are small.

Notice saturation flux density is not used at all, it's core loss vs. flux density and frequency.
Since copper losses will not be negligible, I guess that for each core set (pair) you can have about 1 Vpeak per turn in air at 100 kHz.

So my guess is for three core pairs.... 3 V peak (2.1 Vrms) per turn in air at 100 kHz
I don't know how to calculate for oil, but I guess 5 Vrms/turn continuous duty.
Please report on what you can actually achieve in continuous duty.

EDIT: D-oh .. see next post ... 2000 gauss = 200mT so 30 Vpeak for three core pairs in air.

Uspring

Sun Sept 21 2014, 08:26AM

Registered Member #3988 Joined: Thu Jul 07 2011, 03:25PM
Location:
Posts: 711

Good point. All your calculations seem valid. But did you get the core loss right? In

the field for 345mW/cmÂ³ at 100kHz looks like 2000 Gauss.

Dr. Slack

Sun Sept 21 2014, 08:29AM

Registered Member #72 Joined: Thu Feb 09 2006, 08:29AM
Location: UK St. Albans
Posts: 1659

I'm always nervous when people speak about fractions of a turn, like 1.5. It's topologically impossible to have exactly that, though it is possible to synthesise the effect with multiple windings and legged cores. It is certainly not possible to put 'half a turn' on with a single winding without getting something very undesirable.

How are your 1.5 turns arranged / intended to be arranged?

Uspring

Sun Sept 21 2014, 09:17AM

Registered Member #3988 Joined: Thu Jul 07 2011, 03:25PM
Location:
Posts: 711

Yeah, makes me queasy, too. In a sense half turns are impossible, since currents always flow in complete loops. It is possible to dump charges in e.g. a big aluminium ball, but that doesn't work for any length of time.

The term "self inductance" is motivated by the effect of current in one part of the wire on other parts of it. That is the cause of the inductance of a solenoid, where wires are closely spaced, to be proportional to nÂ². The inductance of a single straight wire on the other hand is proportional to its length.

What constitutes a half turn depends on its spacing relative to the wires leading to it and also e.g. ferrites, which guide the magnetic field.

Ash Small

Sun Sept 21 2014, 11:28AM

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

Sulaiman wrote ...

EDIT: D-oh .. see next post ... 2000 gauss = 200mT so 30 Vpeak for three core pairs in air.

This was my 'gut feeling' when I first looked at this, based on what I remember of calculations for my own project. From the 'pulse generator' research I did for my electronic ignition project, higher VPT is possible, but only at much higher frequencies, but I'm very interested in how this project turns out.

I also have reservations about the 'half turn' thing.

EDIT: I've not got into too much detail with the maths here yet, partly because I think oil cooling is the way to go here.

Conundrum

Sun Sept 21 2014, 02:28PM

Registered Member #96 Joined: Thu Feb 09 2006, 05:37PM
Location: CI, Earth
Posts: 4061

Glycol?

Also there are many cheap solvents with low envirowhiner potential (ie ethanol) and despite being flammable when mixed with other materials are reasonable insulators and easy to use.

Hazmatt_(The Underdog)

Sun Sept 21 2014, 03:51PM

Registered Member #135 Joined: Sat Feb 11 2006, 12:06AM
Location: Anywhere is fine
Posts: 1735

If it were me, I would stay away from anything soluable in water, because if it's soluable in water, it's also potentially capable of having dissolved salts in the water, increasing that conductivity to a failure point.

You're going for very high potentials, and it doesn't take much for corona to start, and then the end is near.

I'd go with oil or paraffin wax, but that's just me.

Sulaiman

Sun Sept 21 2014, 04:58PM

Registered Member #162 Joined: Mon Feb 13 2006, 10:25AM
Location: United Kingdom
Posts: 3140

Since power/weight and power/volume ratios seem important for this project
I'd consider potting the windings and clamping the core to a heat conductor/sink.
e.g. part of aircraft fuselage etc.

Patrick

Sun Sept 21 2014, 05:05PM

Registered Member #2431 Joined: Tue Oct 13 2009, 09:47PM
Location: Chico, CA. USA
Posts: 5639

OKmm I guess I'll look a 1 turn. I'll definitely use oil.

I fail to see why I can't use 3500 to 3800 guass?

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