How to calculate inductance of transformer primary coil - magnetization

[szzuk]

I want to put 40V and 200mA at 100Khz on the primary coil of a transformer I plan on making. How do I calculate the minimum inductance required for the primary? I would prefer the calculator than someone to do the sums for me, I might change the current or frequency. Regards, Szzuk.

 

[dr pepper]

This is an inetersting page, it looks like it for mains trannys but switchers are mentioned further down, your use of the term magnetization might not be what you meant, have a look anyways,

https://ludens.cl/Electron/Magnet.html

You can lower the inductance by introducing an air gap, that involves other complications however.

 

[szzuk]

There are many electronicians, both hobby and professional, who are at war with electromagnetism. Whenever they need to design a coil or a transformer, an abyss of desperation opens in front of these poor people. The worst thing is that usually these poor victims are not really at fault, since the authors of electronic textbooks seem to have struck a plot to explain these things in such a messy way that nobody can really understand them! Or maybe these authors themselves didn't have a clue about the matter?

This quote from the start of that website is exactly were I'm at. I have all the kit to make transformers and in the past i've made a dozen or more. But none of them worked properly, or at all...

I mentioned magnetisation because I have a transformer I made some time ago which has the 1:5 turns ratio I currently need, however when I tried it I found I was only getting a small voltage on the primary. I guessed I'd reached the saturation point of the current and hadn't magnetised the transformer properly. Has my terminology got really ugly now?

Regards,

Szzuk.

 

[MrAl]

Hi,


Are you trying to get some level of magnetization for some reason or do you just need to design a transformer for step up or down use?

I ask because the "transformer equation" takes into account the inductance so you dont have to explicitly calculate that. You just have to know the input voltage and frequency, and of course facts about the transformer construction.

 

[szzuk]

I just need a step up of the voltage that works. So 40Vpp at 100Khz.

I built one a few months ago that has a turns ratio of 1:5 with 18uH and 400uH but it doesn't do much in my circuit.

Regards, szzuk

 

[MrAl]

Hi again,

Well i think you can ignore the primary inductance for now and start with the transformer equation for square waves:

B=E*10^8/(4*F*A*N)
where
B is the flux density in Gauss,
E is the square wave peak voltage in volts,,
F is the frequency in Hertz,
A is the cross sectional area of the core in square centimeters,
N is the number of primary turns.

What you do is select the core area and number of turns that give you a reasonable B value that the core material can handle.
For ferrite this can be quite low like 1000, but for steel laminations as high as 20000. Usually you'd want to be on the ramped part of the BH curve somewhat lower than Bsat for that material so that if you get a larger input (sometimes a surge) the construction can still deal with it.

 

[dr pepper]

Are you making a switch mode supply, or are you making a high freq transformer supply, such as a car stereo voltage booster?

Your original design problem probably was due to core saturation its one of the tricky parts of trannys, voltage and time need to be considered and the maximum flux density the core will take.

I have a little test jig which tells you the al value and gives an idea as to what flux density the core will take of a particular core, I re-use trannys from scrap tv's anything like that as inductors and transformers.

Dont expect to get a high efficiency supply straight away, theres a lot to consider in a switcher, however you can get a working supply with a little care.

A bulb in series with the incomming power to limit current has saved me a few fets and controller chips.

 

[szzuk]

Hi,

Ok so i'll assume it is a ferrite core and set B=1000. Then E=40Vpp. F=100000 Hz. A=2cm (perhaps a little small).

Now I'll try to calculate N by rearranging.

=> N = E*10^8/(4*F*A*B) = 5

Hmmm. Thing is I have another transformer here that i built ages ago, its about 8 turns on the primary and 25 on the secondary, about 2cm area. And it doesn't work.

I just did some measurements on the load without any transformer and it looks like I need 6Amps. I think any trafo this size has got to be too small?

 

[szzuk]

Are you making a switch mode supply, or are you making a high freq transformer supply, such as a car stereo voltage booster?

Your original design problem probably was due to core saturation its one of the tricky parts of trannys, voltage and time need to be considered and the maximum flux density the core will take.

I have a little test jig which tells you the al value and gives an idea as to what flux density the core will take of a particular core, I re-use trannys from scrap tv's anything like that as inductors and transformers.

Dont expect to get a high efficiency supply straight away, theres a lot to consider in a switcher, however you can get a working supply with a little care.

A bulb in series with the incomming power to limit current has saved me a few fets and controller chips.

Its a piezo driver test rig. It allows me to change frequency and voltages on my piezos. The rig works fine for my typical piezos with a bought transformer allowing 600V at any frequency up to ~150Khz. However I have new piezos with higher current requirements and needing up to 200V. So I need to swop my bought 1:12 trafo for another of around 1:5, the bought one doesn't work with these new piezos. The piezo has a capacitance of around 170nF so much of the current will just be getting stored rather than used (I think).

 

[MrAl]

Hi,

Ok so i'll assume it is a ferrite core and set B=1000. Then E=40Vpp. F=100000 Hz. A=2cm (perhaps a little small).

Now I'll try to calculate N by rearranging.

=> N = E*10^8/(4*F*A*B) = 5

Hmmm. Thing is I have another transformer here that i built ages ago, its about 8 turns on the primary and 25 on the secondary, about 2cm area. And it doesn't work.

I just did some measurements on the load without any transformer and it looks like I need 6Amps. I think any trafo this size has got to be too small?

Hi,


Well the B might be lower for that core material (what material is it) or there may be a net DC current in the primary which could quickly saturate the core and render the whole thing useless. Try it again with a sizable cap in series with the primary just to see if it works better.
If not, then you'll have to look into the core material type and see if it requires a lower B value.
You have to at least know that the core material is made for transformers of that high frequency and not lower like 400Hz.

 

[szzuk]

Hi,


Well the B might be lower for that core material (what material is it) or there may be a net DC current in the primary which could quickly saturate the core and render the whole thing useless. Try it again with a sizable cap in series with the primary just to see if it works better.
If not, then you'll have to look into the core material type and see if it requires a lower B value.
You have to at least know that the core material is made for transformers of that high frequency and not lower like 400Hz.

I tried some caps in series and it didn't make much difference. I will have to look up the core data, i'm fairly sure I would have bought something designed for high frequency but couldn't hazard a guess at the B or remember clearly, it was months ago now. Thanks, szzuk.

 

[Bob Scott]

Hi,

Ok so i'll assume it is a ferrite core and set B=1000. Then E=40Vpp. F=100000 Hz. A=2cm (perhaps a little small).

Now I'll try to calculate N by rearranging.

=> N = E*10^8/(4*F*A*B) = 5

I also ran into a mental roadblock when it comes to electromagnetics. I learned a few things:

Be aware that 5 turns is the minimum. Any less and the B goes up.

This equation comes in handy for calculating inductance:

L = 0.4 * pi * n^2 * mu * Ae/Le * 10^-8

L is in Henries. Ae is in square cm. Le is in cm. You can verify the Al values given for different cores with this equation. It works for all cored transformers with no gap.

There are also urban myths about transformers out there in the ether, like "Spread out the winding neatly all around the toroidal core for good coupling." Actually, It doesn't really matter how the windings are dressed around a high-mu core, so long as they go through the hole in the core, they count as one turn. Toroids for power transformers use high mu cores. If the core has a mu of 2000, it means that there is 2000 times more magnetic flux in the core as there would be if it were an air core, so the magnetic flux "leakage" that exists outside the core is so small that it can be ignored. And, you might consider an E core instead. They are easier to wind.

Once you calculate the inductance, you can find Xl:

Xl = 2 * pi * f * L

and you can plug the result into Ohms law:

I = V / Xl

to find your primary magnetising current.

 

[dr pepper]

If you want to go from 0 to 150kc or even 10kc to 150kc then you'll need something special transformer wise.

 

[szzuk]

Well I went through my order history to check which cores and bobbins I'd bought. I'm using an EPCOS EFD20 with 2 half cores, the ones linked to below.

https://uk.farnell.com/jsp/search/productdetail.jsp?SKU=1422729&MER=baynote-1422729-pr
https://uk.farnell.com/epcos/b66414w1008d1/bobbin-efd15-8pin/dp/1190583

So the Al is 1250nH, I'm going to guess this correlates to the B mentioned above...

I can do a few calcs based upon Bobs message from the trafo I tested last night and doesn't work.

Xl = 2 * Pi * 100000 * 18 *10^-6 = 11 ohms

I = V/Xl = 40/11 = 3.6A

I'm not getting anything like 3A or any voltage step up.

So, I'm thinking get the gapped core below? I'll be winding more but it might work...?

https://uk.farnell.com/epcos/b66417u0160k187/ferrite-core-half-gapped-efd20/dp/1781886

Regards,

Szzuk

 

[szzuk]

If you want to go from 0 to 150kc or even 10kc to 150kc then you'll need something special transformer wise.

I was wondering about that, I couldn't tell you why the bought trafo I use works from 0-150KHz with my other piezos! I guess I could make a few trafos when I can get one working... what range would you suggest?

Hi,

You have to at least know that the core material is made for transformers of that high frequency and not lower like 400Hz.

How do I check this?

 

[dr pepper]

start fromt the beginning
core saturation is largely caused by having voltage present accross the windings for too long, which means frequency is important. you can design a transfo to operate at your lowest frequency and it'll probably work at higher frequencies too, there is however a limit where the losses in the core become significant at higher freq's.
I'm still not sure if your design is a flyback psu or a step up transformer setup, I'm guessing the latter from what you've said.
If you read through harry ludens site on trannys you'll be able to plug in the values ffrom the etd20 datasheet and work out your primary turns, the important ones are max flux density, and al factor.
If your design is a stepup transformer rather than a flyback device then current in the primary is largely dependant on current in the secondary, if you've put one together and tested it without a load on the secondary and the primary current is small then thats a good sign, the core isnt saturating.
tip, if your operating at 100kc or higher then you might want to use either litz wire or 5 or 6 smallers wires to make up the csa to reduce skin effect which becomes significant at these freq's, I know this as a rule of thumb rather than understanding.
I now wait to be corrected, I'm not an expert on magnetics I know what I've had to so I could get by.

 

[szzuk]

Hi, it is a step up trafo i'm building, not a flyback. I've decided to buy some of the gapped cores for the EFD20 so I can reduce B and add more turns. The material I've been using for the core is N87 or N97, both are supposed to be fine for over 400KHz frequencies. I might need some bigger cores too, I'll look at them when I get a chance to use the Ludens website to do some calcs.

I don't know what litz wire is? Or 5 or 6 smaller wires? The terminology isn't familar with me, however I can probably order some easily with the gapped cores.

At a guess the core is saturating, so I'm trying to get around that.

 

[chemelec]

N87 Should be OK.

For your Expermintation, You should not use PRE-Gapped cores.
I find it is usually better to wind on Un-Gapped cores.
Than you can Add a Gap by applying a Thin piece of tape to the legs of the core.
Or if you need a Bigger gap, Two or three Layers of tape.

Litz Wire is Multiple Strands of Parallel Wires and it is Better for Higher Frequencies.

Considering 40 Volts input and 200mA, you need a reasonable amount of Inductance.
I would say defiinately more than 100uH.

Another Problem Might be your Drive Circuit impedance?

 

[szzuk]

N87 Should be OK.

For your Expermintation, You should not use PRE-Gapped cores.
I find it is usually better to wind on Un-Gapped cores.
Than you can Add a Gap by applying a Thin piece of tape to the legs of the core.
Or if you need a Bigger gap, Two or three Layers of tape.

A great idea.

Litz Wire is Multiple Strands of Parallel Wires and it is Better for Higher Frequencies.

Considering 40 Volts input and 200mA, you need a reasonable amount of Inductance.
I would say defiinately more than 100uH.

Another Problem Might be your Drive Circuit impedance?

Time to do some calcs.

 

[szzuk]

From the Ludens website I was given earlier the primary reactance should be 10 times the load resistance. The load is around 6 ohms so I should plug 6 x 10 into the H equation

H = Xl / (2 * Pi * Hz) = 60 / (2*3.14*100000) ~ 100uH

The trafos i've made have a primary inductance that is just too low, and indeed I probably don't want to buy gapped cores after all! I need more inductance, not less.

The drive circuit outputs from an opa453 opamp. So I need a low impedance in the primary coil, trying to impedance match that would be beyond me.