Bobbin Design and Winding Radius

[7824c5a4]

Hi all,

I'm working through a flyback design using the semi-mysterious UF86A U-shaped ferrites from Hondark HK. My plan is to have my transformer in vacuumed mineral oil. Currently I have two bobbins drawn up in Solidworks, one for the primary and one for the secondary. I feel that this is going to be the best method to have the transformer be re-windable should I choose to change the ratio or wire gauge later while still holding the windings in the right place (i.e. not gluing or taping them down)

The problem I'm worried Im going to run into is reduced coupling on the primary as a result of having a bobbin between it and the core. I haven't been able to find definitive answers or a formula online about proximity of the windings to the core. If the center hole in this bobbin is the cross section of the core, will having the windings that far out kill the primary coupling?



Thanks!
Nate

[davekni]

semi-mysterious UF86A U-shaped ferrites

Probably PC40 ferrite material.

The problem I'm worried Im going to run into is reduced coupling on the primary as a result of having a bobbin between it and the core. I haven't been able to find definitive answers or a formula online about proximity of the windings to the core. If the center hole in this bobbin is the cross section of the core, will having the windings that far out kill the primary coupling?

Do you know what coupling factor you want?  For actual flyback drive as in old CRT supplies, coupling should be as high as possible.  CRT flyback transformers have primary winding under secondary for highest coupling.  Primary on opposite core leg will be much lower even if wound tightly against core.  If driving with a ZVS oscillator and feeding variable load such as arcs on secondary, then coupling needs to be 0.86 or under to avoid killing oscillation at certain loads.
FEMM is a free 2D/2.5D magnetics simulation program that I learned about from another forum post.  Not trivial to learn, but quite useful.  2D approximation is likely to underestimate inductance a bit, but close enough to be useful.

[7824c5a4]

Thanks for the reply and software rec, Dave! To be honest, I dont know what coupling factor Im looking for. Ultimately, this is going to be driving a 5 stage (10x) CW multiplier for a pretty low power X-Ray tube, but its also my first foray into ferrites and flybacks. Though its mostly just an experiment, Id like to see how ideal I can get this thing for the application.

If driving with a ZVS oscillator and feeding variable load such as arcs on secondary, then coupling needs to be 0.86 or under to avoid killing oscillation at certain loads.

The load will vary quite a bit at different tube output powers- Im assuming that qualifies. My rough estimate is between 50-100W. Is the oscillation more at risk of dying at a high load, or a low load? Also, if Im shooting for a coupling factor of .86 or less, presumably its acceptable to not have the primary as close as possible to the core. Am I understanding that correctly?

Edit: Im finding in LTSpice at least, that oscillation dies at very low load on the secondary side. Im also finding that resonant frequency changes quite drastically with load on the secondary. Are both of those results pretty accurate?

[davekni]

Edit: Im finding in LTSpice at least, that oscillation dies at very low load on the secondary side. Im also finding that resonant frequency changes quite drastically with load on the secondary. Are both of those results pretty accurate?

Glad you are simulating!  Can you share your schematic?  I'm guessing ZVS, but still don't know.
If ZVS, mid range between short circuit and open is the worst case.  If frequency is changing by more than 1.96:1, then coupling is too high.  What coupling factor are you using in LTSpice?  In your case, short-circuit load would be when power is first applied, when multiplier capacitors are at 0V.  Will pass through mid-load as capacitors charge.  Frequency is high with shorted secondary (primary inductance is low, just leakage inductance) and low with open secondary.
Both winding geometry and gap between ferrite core halves affect coupling and inductance.
With LTSpice results, you can see primary voltage and frequency, so calculate volts/turn and resulting magnetic flux, to verify you are not close to saturating the core.
I'm guessing this is for low duty cycle use, so core heating isn't too important.

[7824c5a4]

Super insightful! Thank you.

Here is the schematic I'm working with currently. Ive got coupling at 80%, and I'm currently just representing the 10x voltage multiplier as 500K (Don't ask how I got there, Ive just been experimenting. I don't know how to represent the multiplier or tube load quite yet but I'm assuming the tube will be operating around 75kV max at ~1mA).



In the above image, it's operating at around 110kHz and ~15A on the primary, which is about the frequency and primary current I'm after since that's what Ive been basing most of the design on. (again no real reason- just experimenting for the sake of learning)

I got the inductance values for the primary halves and the secondary assuming:

• Ill have the core gapped at l_g of 1.0 mm (figured that was a good starting point)
• A_e of the core is 392mm²
• Path length l_e is 286mm
• Effective permeability μ_e of the gapped core will be 266.75nH/n² based on the ungapped permeability in the datasheet of 3962nH/n² and a gapped permeability of μ_e = (μ_i)/(μ_i * (1.0mm/286mm)+1)
• 3+3 Turns of Primary and 300 turns secondary

Plugging all that into the gapped inductance formula L= (μ₀*μ_e*n²*A_e)/(l_e*l_g) gives me 4.12μH for each half of the primary, and 41,205μH for the secondary. That gets me pretty neatly from 150V out of the ZVS fed with 48V up to 7500 to feed into the 10x CW multiplier. The multiplier is built from 1nF caps.

Edit: I should also mention that I got a max flux density of 92.8mT from B = (V_p)/(N_p*ω*A_e) where V_p is 150V (pi*DC input of the ZVS), N_p is 6 turns, ω is 2*pi*110kHz

[davekni]

In the above image, it's operating at around 110kHz and ~15A on the primary, which is about the frequency and primary current I'm after since that's what Ive been basing most of the design on. (again no real reason- just experimenting for the sake of learning)

110kHz may be OK, but that is rather high for HV transformers.  Intra-winding capacitance of secondary (and capacitance of lead wires and multiplier diodes) causes an unwanted secondary resonance, which becomes more problematic as operating frequency approaches that resonant frequency.

Effective permeability μe of the gapped core will be 266.75nH/n2 based on the ungapped permeability in the datasheet of 3962nH/n2 and a gapped permeability of μe = (μi)/(μi * (1.0mm/286mm)+1)

Magnetic calculations can be confusing.  3962nH/N^2 is not permeability.  It is inductance per turn squared.  Air (vacuum) has 4*PI*10^-7 H/m/N^2 = 1257nH/m/N^2.  If ferrite core halves are spaced 1mm apart, there are two 1mm x 12.5mm x 28mm gaps.  Area is 350mm^2 and length 2mm, so A/L is 175mm or 0.175m.  Inductance for just the gaps (presuming infinite ferrite permeability) is 1257 * 0.175 = 220nH/N^2.  (This ignores fringing fields around gap.)  Total inductance is same formula as parallel resistors: 3962 * 220 / (3962 + 220) = 208nH/N^2.

Plugging all that into the gapped inductance formula L= (μ0*μe*n2*Ae)/(le*lg) gives me 4.12μH for each half of the primary consisting of 3 turns each, and 42,205μH for the secondary at 300 turns.

With above 208nH/N^2, inductance is easy.  3 turns (N = 3) had 9 * 208 = 1872nH.

That gets me pretty neatly from 150V out of the ZVS fed with 48V up to 7500 to feed into the 10x CW multiplier. The multiplier is built from 1nF caps.

Open circuit with no losses, primary 6 turns should see +-PI * 48V = +-150V.  Secondary should be K * Nsec / Npri * Vpri = 0.8 * 300 / 6 * 150 = +-6000V.

For K of 0.8, frequency ratio should be 0.6:1 (sqrt(1-K^2)) between open and shorted output.  Are you seeing more change than that?

What conditions are causing oscillation to drop out?  I could be an issue of too much current for IRFP250N rather than a fundamental issue with Q getting too low for ZVS to oscillate.

BTW, if you have some reasonable way to form a single gap, a primary-only air gap has advantages.  I'm currently designing a somewhat similar ZVS-driven HV toy (weed zapper) using a somewhat similar large ferrite core.  I may buy a ferrite plate to insert into gap in HV side of core.  Thinking that is easier than cutting a gap in the other side.  Ferrite cutting generally requires a diamond wheel and lots of patience.  Also ideal to have windings not immediately adjacent gap(s).  Can either be radial space as in your bobbin example, or an axial gap between the two 3-turn primary winding halves (my plan).  Otherwise the high local magnetic fringing field from the gap causes large proximity-effect (eddy current) losses in copper near the gap.

[7824c5a4]

Magnetic calculations can be confusing.

lol I'm finding that out very quickly. Assuming I can gap just the primary side then, and that the actual core dimensions are 14.6x27.5=401.5mm² (my drawing has some errors) does the following seem plausible?

• A/L = .4015m
• Inductance for just the gaps is 1257 * 0.4015 = 504.69nH/N²
• Combined would be 447.1nH/N²
• Primary would be 4024nH, Secondary 40230uH

For K of 0.8, frequency ratio should be 0.6:1 (sqrt(1-K^2)) between open and shorted output.  Are you seeing more change than that?

So with the above dimensional adjustments made (4024nH for Primary and still 40230uHfor Secondary) I'm now getting 110kHz open and 208kHz shorted, so that cones close to 0.6 to 1 (.533:1). And with those changes, its no longer dropping out at either low or high load. With that, I should be able to choose my LC tank components and tune the frequency somewhere more acceptable.

Is 75kHz still too high in your opinion? My only 'real' reason for the high frequency was to reduce voltage drop in the multiplier as much as possible. Im not sure how to go about picking many of my target values yet (frequency, coupling factor, etc) other than getting too close to the saturation point.

BTW, if you have some reasonable way to form a single gap, a primary-only air gap has advantages.

Yeah Ive been considering this. I do want to find a way to gap it only on one side, and I hadn't considered the ferrite plate. I've been contemplating just sanding one of the faces very slowly with a high grit sandpaper to gain a millimeter. Redesigning the bobbin around the gap is easy enough, at least.

[davekni]

Is 75kHz still too high in your opinion? My only 'real' reason for the high frequency was to reduce voltage drop in the multiplier as much as possible. Im not sure how to go about picking many of my target values yet (frequency, coupling factor, etc)

Simulation is probably best way to decide.  Presuming PC40 material and that you want it to work even if core gets hot, 380mT is saturation flux density at 100C.  That limits you to 30kHz and up to avoid saturation with 3 + 3 turn primary.
Secondary intra-winding capacitance will be hard to estimate.  Do you have spec's on multiplier diodes, capacitance in particular?  10 diodes in parallel as far as AC capacitance seen by xformer secondary.  Add a bit more for capacitance between the two capacitor strings, perhaps 40pF per meter of length (depending on capacitor size and separation distance) in air, or 80pF per meter in oil.  Add total capacitance across secondary (diodes plus cap string-to-string plus a bit more for winding).  I'd also suggest simulating at least a voltage doubler on secondary rather than resistive load.  Could simulate entire 10x multiplier.  Either way, add resistor for DC load rather than across transformer.

I've been contemplating just sanding one of the faces very slowly with a high grit sandpaper to gain a millimeter.

In my experience, ferrite materials are too hard, as hard as sand paper grit, so sand paper is not effective.  Perhaps there is something harder that will work without going all the way to diamond.  My only success is with diamond-grit cutting wheels.

Redesigning the bobbin around the gap is easy enough, at least.

Your radial distance may already be sufficient without adding axial separation.  Though there is some advantage in axial separation of primary if using a single primary-side air gap.  That way it is possible to keep core flux within secondary close to that of primary, so increase volts/turn of secondary without saturation.  On the other hand, if you stay well above 30kHz, this becomes less important.  (I'm planning to run close to saturation, so this makes a difference for me.  Planning 30-40kHz for unloaded frequency.)

[7824c5a4]

Do you have spec's on multiplier diodes, capacitance in particular?

Yup, they're 2CL2FMs from eBay, which claim to be 1.9pF

I'd also suggest simulating at least a voltage doubler on secondary rather than resistive load.  Could simulate entire 10x multiplier.

LTSpice loses its mind when I do this and sees multi megavolt spikes Thats why Ive been simulating the two separately up to this point.

On the other hand, if you stay well above 30kHz, this becomes less important.

Perfect, that at least gives me a starting point for choosing my ZVS caps. Ill simulate the rest.

Thanks a ton for all your replies Dave, I've learned a lot. Ill follow up here when I end up actually getting the transformer wound and measured so hopefully someone can learn from my process!

[Twospoons]

I've gapped a ferrite core using an ordinary alumina grinding wheel. Its a bit tricky since the outer skin seems to be much harder than the inside - meaning its easy to abruptly grind off too much once the outer layer is gone.

If you want precise control, maybe a diamond hone would be ideal. They're pretty cheap.

[davekni]

LTSpice loses its mind when I do this and sees multi megavolt spikes Thats why Ive been simulating the two separately up to this point.

Yes, sometimes simulations fail to converge or converge to ridiculous values.  Two suggestions:
First, add some initial conditions, initial node voltages and currents (.ic statements).  For example, set L1 current to 1A and LP1 current to 1A.  Perhaps set initial FET drain voltages as well, one to 0V and the other to something higher, 48V or 150V (peak it normally gets to).
Second, if initial conditions aren't sufficient, look for LTSpice version 4.23 from 2016.  Older versions (that one and before) are actually better than later ones.  Perhaps has something to do with Analog Devices purchasing Linear Technology.
Getting simulation to work with more realistic rectified load is worth the trouble.

Thanks a ton for all your replies Dave, I've learned a lot. Ill follow up here when I end up actually getting the transformer wound and measured so hopefully someone can learn from my process!

You are certainly welcome!  I enjoy magnetics design.  And I will be learning from your results too.  There are always nuances that I haven't learned yet, sometimes critically important ones.

[7824c5a4]

Whew, a lot of simulating has happened in the last day!

I think I have some acceptable values chosen for components that keep my frequency around 50kHz under load, my primary current below 20A, and keep my ferrite from saturating (turns out that's the perk of having a beefy gapped core at low frequency!).

First things first: the LTSpice Sim. I was able to get LTSpice to simulate the CW Multiplier and ZVS in the same simulation on version 17.1.8 by just leaving the values of the CW's diodes blank. Specifying a particular model seems to be what was freaking it out. I ran some stepped tests at various loads with the tube represented by a resistor drawing ~.8 to 1.8mA and neither the voltage nor the frequency ever sagged. The current through the primary remained pretty constant around 14A as well.



Next up, I took Dave's advice and modeled the core and primary in FEMM (simultaneously horrible and amazing software, btw) to see what kind of flux and inductance I was going to get. I followed this gentleman's tutorial on iterative simulation in FEMM 

https://www.youtube.com/watch?v=JPMAo8OHVAA

and got some pretty interesting results! Below is an image of one of the iteration's results around 15A in the primary. You can see the flux density where my mouse is around 183mT. Below that is the graph showing inductance vs primary current from 10 to 50A. Pretty neat to be able to see the saturation point visualized.




Some things I think I still need to work on are modeling the additional capacitance from the diode, windings, etc in the CW multiplier, but I think LTSpice is already prepared to kill me in my sleep if I push it any harder. Also, I'd like to see if I can get FEMM to model the induced current in the secondary coil, but I haven't been able to figure that out quite yet. Being able to determine the coupling factor that results from my bobbin design would be quite handy since I've been assuming 80% thus far.

Let me know what you think or if you have any suggestions!

Hilarious Edit: I went looking for how to calculate coupling factor in Femm and stumbled across this reply from a very familiar name https://groups.io/g/femm/message/7095

[davekni]

First things first: the LTSpice Sim. I was able to get LTSpice to simulate the CW Multiplier and ZVS in the same simulation on version 17.1.8 by just leaving the values of the CW's diodes blank. Specifying a particular model seems to be what was freaking it out.

Interesting.  I usually have the opposite problem.  LTSpice fails to converge (gets hung) at some early time step when using default diode parameters.  Picking a diode from the built-in library usually fixes the issue.  (Many parts don't have breakdown voltage modeled, so low voltage parts can be used for high voltage circuits.)

Whew, a lot of simulating has happened in the last day!

Next up, I took Dave's advice and modeled the core and primary in FEMM (simultaneously horrible and amazing software, btw) to see what kind of flux and inductance I was going to get. I followed this gentleman's tutorial on iterative simulation in FEMM

Very impressive that you managed to learn FEMM enough to get useful results in one day!  Your parenthetical description of FEMM is a perfect summary.  Amazing tool with a terrible user interface that does not follow common GUI methods.

and got some pretty interesting results! Below is an image of one of the iteration's results around 15A in the primary. You can see the flux density where my mouse is around 183mT. Below that is the graph showing inductance vs primary current from 10 to 50A. Pretty neat to be able to see the saturation point visualized.

Looks like core has narrower width of vertical sections than height of horizontal legs.  Is that accurate for your core pieces?

Amazing progress!

[7824c5a4]

Looks like core has narrower width of vertical sections than height of horizontal legs.

Indeed it does:



Its a strange core, to be sure. Theres not many other experiments with it out there online- thats why Im so excited to simulate and use it. I originally saw it in this thread of oneKone's

https://highvoltageforum.net/index.php?topic=2089.0

[7824c5a4]

Mind the gap, some more sanding needed yet for a flush fit. Ive got the secondary bobbin nearly ready to go. In my experience 3d printing HV, oil-submerged parts, PLA has been just fine and has proven to be a fairly good insulator.



A friend is loaning me a vacuum pump to pump the oil-filled housing to get all the trapped and dissolved air out. The oil-filled housing will be one of PolyCase's ZQ060604 Boxes. https://www.polycase.com/zq-060604

I have yet to attempt to grind/sand in my 1mm air gap, but the coil formers will be ready when the gap is done!

[Patrick]

Beautiful work.

I'm reviving my conventional E core and Planar core experiments last seen on 4HV.org now that I have a career and (some ) money going...