### Author Topic: Transformer winding Calculations  (Read 3534 times)

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#### CM800

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##### Transformer winding Calculations
« on: September 08, 2016, 11:06:07 am »
Hi All,

Alongside my driver project. I'm just working out the maths to wind myself a high voltage transformer. For this, I have this monster core:

http://www.farnell.com/datasheets/1595853.pdf
3C90 material.

I have got this far:

Vpri = 400VDC
Vsec = 40,000V (center tapped)

f = 100kHz (I believe this to be the best choice? please correct me if there might be a better frequency to run on.)
Bmax = 200mT (2000 Gauss) (from 3C90 material datasheet)
AC = 5.60cm2

From that we get:
Npri = 9 turns
Nsec = 2x 450 turns

0.0225 turns per volt

Where I am stuck is working out the current side of things. I would also appreciate someone going over my work there, whether it's the best way to go about things or not.

Cheers!

« Last Edit: September 08, 2016, 06:06:46 pm by CM800 »

#### rstofer

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##### Re: Transformer winding Calculations
« Reply #1 on: September 08, 2016, 06:03:30 pm »
I'm pretty sure the primary and secondary voltages will be AC, not DC.  Other than that, it has been more than 40 years since I took that class and I haven't used it since.

#### CM800

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##### Re: Transformer winding Calculations
« Reply #2 on: September 08, 2016, 06:06:35 pm »
I'm pretty sure the primary and secondary voltages will be AC, not DC.  Other than that, it has been more than 40 years since I took that class and I haven't used it since.

To be pedantic, switched DC. But yes...

#### Yansi

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##### Re: Transformer winding Calculations
« Reply #3 on: September 08, 2016, 06:15:09 pm »
With such high transformation ratio, I'd like to make a point you'd be better be aware of leakage inductance, if you want to run it at 100kHz. If you need to transfer higher power, you'de better stick with 20kHz. Otherwise the leakage might very well limit your maximum power out.

What would be the purpose of the transformer and which primary switching topology will be used?

//EDIT: Note2: High turn number secondary winding will also have some parasitic capacitance, which at 100kHz might as well be veeery problematic, as a lot of current will flow.

#### CM800

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##### Re: Transformer winding Calculations
« Reply #4 on: September 08, 2016, 06:26:25 pm »
With such high transformation ratio, I'd like to make a point you'd be better be aware of leakage inductance, if you want to run it at 100kHz. If you need to transfer higher power, you'de better stick with 20kHz. Otherwise the leakage might very well limit your maximum power out.

What would be the purpose of the transformer and which primary switching topology will be used?

//EDIT: Note2: High turn number secondary winding will also have some parasitic capacitance, which at 100kHz might as well be veeery problematic, as a lot of current will flow.

This is the kind of thing I want to learn about. Are there any actual numbers I can make of it, at what point is it 'an acceptable leakage inductance' etc. While with drives I have a intermediate footing, Transformer winding is completely uncharted territory for me.

The transformer's purpose will be Capacitor bank charging / direct arcing.
I am thinking of doing something like this for the converter, however I don't know if it is the best method or not.

I can buy more cores quite cheaply it turns out (only £30 a pair)

#### Yansi

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##### Re: Transformer winding Calculations
« Reply #5 on: September 08, 2016, 06:49:33 pm »
Leakage inductance of a transformer cannot be calculated very precisely - it is better to measure it on a prototype. Simple check of leakage:  Short one winding and measure the inductance on the other winding (while still keeping the other shorted out).

Look up how the model schematic of real transformer looks like. The leakage works almost exactly as if you put a choke in series with every winding of that transformer.

Simplified: Leakage inductance is dependent only on the geometric composition of the windings. The closer and tighter the windings are to each other mechanically, the less flux can escape in between.

So for example, on an U-I shaped core, if the primary is on one side and the secondary is on the other side, well, you get the most leakage inductance, because the flux can close the path in between, through air mostly. It is then called a leakage transformer - sometimes, it is a required and useful property of transformer, as it can limit the maximum current when shorted, no external chokes needed.

Example2: Thats why LLC resonant switching power supplies usually have a transformer with two mechanically separated sections on the bobin, having the secondary winding separated from the rest - the leakage is used as the series choke. In other topologies, like a halfbridge converter, the leakage is not wanted as it limits the max current/power delivery (but does not present risk if some is present). In a flyback converter, leakage is your first enemy, as it will make nasty voltage overshoot on the primary side switching transistor.
« Last Edit: September 08, 2016, 06:52:28 pm by Yansi »

#### CM800

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##### Re: Transformer winding Calculations
« Reply #6 on: September 08, 2016, 07:33:51 pm »
Thanks for that insight. I've hashed out the full plans for this:

Input -> Full-bridge from 400VDC PFC.
Output -> 40kV Center-tapped, up to 10kW (0.25A)

I currently have the displayed transformer, I can buy more cores if needed to put them in parallel. I can have custom bobbins machined.

My current thoughts are to put 20kV on each side of the ferrite and wind the primary to the side on one of the U cores. I can submerge the unit under oil.

Does that winding layout make sense?

#### MagicSmoker

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##### Re: Transformer winding Calculations
« Reply #7 on: September 08, 2016, 10:48:55 pm »
Oh boy... I suspect you are in for quite a learning experience.

Alright, first let's ditch that awful equation you are using. Main reason is it totally divorces you from any intuitive feel for what is going on. I prefer to use this version:

V * Ton
---------------- = Npri
Ae * dB * 100

Where V is the voltage applied to the primary (a constant DC voltage is assumed), Ton is the time said voltage is applied in microseconds (usually just under half a period), Ae is the minimum core area in cm², Bmax is the *total* flux change in Teslas (note that in a push-pull or bridge converter this will be from -Bmax to +Bmax; in a single ended converter this will be from ~0B to +Bmax). The 100 multiplier in the denominator can be dropped if Ae is in mm².

Now that that is out of the way, the next issue is the choice of dB... Even with current mode control or pulse-by-pulse current limiting I really don't like running at a dB that exceeds the single quadrant saturation flux density for the chosen core material (for most power ferrites Bsat is in the range of 0.35 to 0.4T). This is less of a problem than it might appear, because core losses for most power ferrites are approximately proportional to the 2.6 power of flux density and the 1.6 power of frequency, so as you go up in frequency you have to go down in flux density (or, conversely, as you go up in flux density you have to really go down in frequency). The upshot of this is that you will typically be "core loss limited" in allowed flux density swing above 20-30kHz.

A correlated issue is that larger cores tend to have a worse thermal resistance relatively speaking than smaller cores because losses are proportional to volume while heat dissipation is proportional area.

At any rate, my first pass estimate for this application would be a switching frequency of 40kHz and a total flux density swing of 0.3T.

Next issue is a bit more thorny and will only be solved through trial and error: lots of (secondary) turns means lots of stray capacitance. This will also drive the ideal switching frequency down, even though that results in needing more turns which itself drives the stray capacitance up! Magnetics sure is fun, ain't it?

Next issue is probably a plus here - U cores are commonly used for high voltage transformers and the usual arrangement is to put the primary on one side and the secondary on the other, even though this results in the maximum possible leakage inductance (which is the inductance that results from flux not coupling both windings; it is basically an air core inductor in series with each winding). Leakage inductance causes all sorts of problems like voltage spikes, ringing, and robbing volt*seconds from the secondary, but it is the latter issue that might be helpful here, because it will limit short circuit current.

So plugging all of this back in to the equation above:

400V * (25us * 0.48)
------------------------ = 28 turns
5.6cm² * 0.3 * 100

Which assumes that 400V is the minimum primary voltage and 48% is the maximum duty cycle possible; this means the effective primary voltage is 0.96 * 400, or 384V, so the number of secondary turns will need to be more than the naive estimate of 100x higher than the primary to deliver 40kV. In this case, at least 2916 turns. Gulp.

That's a reasonable number of primary turns, as long as you only need to handle about ~1kW or so because your chosen core simply won't have enough window area (ie - area available for windings). Fortunately, square cross section U and E cores (as well as toroids) are easy to "parallel" by epoxying them together, and as the number of turns required goes down as core area goes up you'll probably only need 6 or 7 cores, not 10.

Regardless, each layer of a 40kV total secondary will be supporting a rather high voltage which means there will be a - possibly overwhelming - temptation for arcing to occur between layers. You'll definitely want to use triple (or quad!) insulated magnet wire and you'll probably want to coat each layer in transformer insulating varnish and/or wrap it with polyimide (ie - Kapton) tape. #28AWG (approx. 0.35mm) should be sufficient for the desired output current of 0.25A and the diameter is well under the skin depth so that's not an issue. Quad insulated magnet wire isn't exactly an ebay item; I purchase it MWS Industries, but beware they are an old school type of business that does quoting by phone, etc., so a bit atavistic in this day and age.

And let's not forget about the primary - it will need to handle ~25A or so, and because of skin and proximity effects you might have to resort to a foil winding to keep down the losses. A quick-n-dirty alternative is to simply parallel a bunch of smaller magnet wires (with a diameter of around 2-3x the skin depth at the switching frequency [skin depth in mm = 66.2/(F^0.5), where F is in Hz]). In this case, twisting together 9 #18 (~0.85mm) wires should do.

Since you ain't paying me for my help I'm going to stop here, but you still have a lot of learning ahead of you, grasshopper.

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#### CM800

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##### Re: Transformer winding Calculations
« Reply #8 on: September 08, 2016, 11:13:40 pm »
Oh boy... I suspect you are in for quite a learning experience.

Alright, first let's ditch that awful equation you are using. Main reason is it totally divorces you from any intuitive feel for what is going on. I prefer to use this version:

V * Ton
---------------- = Npri
Ae * dB * 100

Where V is the voltage applied to the primary (a constant DC voltage is assumed), Ton is the time said voltage is applied in microseconds (usually just under half a period), Ae is the minimum core area in cm², Bmax is the *total* flux change in Teslas (note that in a push-pull or bridge converter this will be from -Bmax to +Bmax; in a single ended converter this will be from ~0B to +Bmax). The 100 multiplier in the denominator can be dropped if Ae is in mm².

Now that that is out of the way, the next issue is the choice of dB... Even with current mode control or pulse-by-pulse current limiting I really don't like running at a dB that exceeds the single quadrant saturation flux density for the chosen core material (for most power ferrites Bsat is in the range of 0.35 to 0.4T). This is less of a problem than it might appear, because core losses for most power ferrites are approximately proportional to the 2.6 power of flux density and the 1.6 power of frequency, so as you go up in frequency you have to go down in flux density (or, conversely, as you go up in flux density you have to really go down in frequency). The upshot of this is that you will typically be "core loss limited" in allowed flux density swing above 20-30kHz.

A correlated issue is that larger cores tend to have a worse thermal resistance relatively speaking than smaller cores because losses are proportional to volume while heat dissipation is proportional area.

At any rate, my first pass estimate for this application would be a switching frequency of 40kHz and a total flux density swing of 0.3T.

Next issue is a bit more thorny and will only be solved through trial and error: lots of (secondary) turns means lots of stray capacitance. This will also drive the ideal switching frequency down, even though that results in needing more turns which itself drives the stray capacitance up! Magnetics sure is fun, ain't it?

Next issue is probably a plus here - U cores are commonly used for high voltage transformers and the usual arrangement is to put the primary on one side and the secondary on the other, even though this results in the maximum possible leakage inductance (which is the inductance that results from flux not coupling both windings; it is basically an air core inductor in series with each winding). Leakage inductance causes all sorts of problems like voltage spikes, ringing, and robbing volt*seconds from the secondary, but it is the latter issue that might be helpful here, because it will limit short circuit current.

So plugging all of this back in to the equation above:

400V * (25us * 0.48)
------------------------ = 28 turns
5.6cm² * 0.3 * 100

Which assumes that 400V is the minimum primary voltage and 48% is the maximum duty cycle possible; this means the effective primary voltage is 0.96 * 400, or 384V, so the number of secondary turns will need to be more than the naive estimate of 100x higher than the primary to deliver 40kV. In this case, at least 2916 turns. Gulp.

That's a reasonable number of primary turns, as long as you only need to handle about ~1kW or so because your chosen core simply won't have enough window area (ie - area available for windings). Fortunately, square cross section U and E cores (as well as toroids) are easy to "parallel" by epoxying them together, and as the number of turns required goes down as core area goes up you'll probably only need 6 or 7 cores, not 10.

Regardless, each layer of a 40kV total secondary will be supporting a rather high voltage which means there will be a - possibly overwhelming - temptation for arcing to occur between layers. You'll definitely want to use triple (or quad!) insulated magnet wire and you'll probably want to coat each layer in transformer insulating varnish and/or wrap it with polyimide (ie - Kapton) tape. #28AWG (approx. 0.35mm) should be sufficient for the desired output current of 0.25A and the diameter is well under the skin depth so that's not an issue. Quad insulated magnet wire isn't exactly an ebay item; I purchase it MWS Industries, but beware they are an old school type of business that does quoting by phone, etc., so a bit atavistic in this day and age.

And let's not forget about the primary - it will need to handle ~25A or so, and because of skin and proximity effects you might have to resort to a foil winding to keep down the losses. A quick-n-dirty alternative is to simply parallel a bunch of smaller magnet wires (with a diameter of around 2-3x the skin depth at the switching frequency [skin depth in mm = 66.2/(F^0.5), where F is in Hz]). In this case, twisting together 9 #18 (~0.85mm) wires should do.

Since you ain't paying me for my help I'm going to stop here, but you still have a lot of learning ahead of you, grasshopper.

Thanks for your really in-depth explanation. It's given me a lot to chew through tomorrow (I'm about to go off to bed now) I'm shocked to hear that my core would only be good for 1kW considering the size of it... I would have expected a good bit more. I have seen 1kW pushed through a transformer core much smaller then said pair of U cores.

I do know a transformer winding company so I should be able to get ahold of all the materials, maybe even get them to wind the bobbins for me, the only thing they can't do is the actual calculations / design of ferrite transformers (the guy who runs it only knows iron core well)

There is a lot there to wrap my head around.... What the hell is a VoltSecond?

#### MagicSmoker

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##### Re: Transformer winding Calculations
« Reply #9 on: September 09, 2016, 12:22:22 pm »
...I'm shocked to hear that my core would only be good for 1kW considering the size of it... I would have expected a good bit more. I have seen 1kW pushed through a transformer core much smaller then said pair of U cores.

Surprising but true: the core only indirectly limits how much power you can transfer in that smaller cores require more turns to keep the flux density manageable at a given frequency (on time) and applied primary voltage. Since the winding (aka "window") area is finite, the more turns required the smaller the cross-sectional area allowed for each turn and that means a higher I²R loss; hence, smaller cores have a lower power handling capability.

For example, the U126 core you selected has a center window of 126mm x 70mm if both halves are U's (instead of a U and an I). If you put the primary on one leg and the secondary on the other you essentially have a winding area of 126mm x 35mm, or 4410mm², for each side. A bit less than 35mm, actually, since you don't want the two windings touching and some of the winding area will be taken up by insulation, etc., but to make things simple we'll just assume you have the full 4410mm² available. Now as previously determined the primary will need to carry an average of 25A and the secondary 0.25A. At an initial estimate of 4A/mm² for the current density (called J in the argot of magnetics design), that means you will need ~7mm² wire for the primary (approx. 9 AWG) and 0.07mm² for the secondary (approx. 28 AWG). The total copper area for the secondary will need to be the same as the primary as they both handle the same power after all, ignoring losses of course, but as mentioned previously, you'll almost certainly have to use triple or quad insulated (aka "build") wire for the secondary and wind each layer with insulating tape to prevent arcing.

All that said, it now appears that my WAG of needing 6 cores in parallel was way too pessimistic; one pair of U cores will do the job. That happens quite often when doing transformer design. A few days ago I just wound a small flyback transformer for supplying power to another much larger switchmode converter and both my equations and the "expert" software supplied by the IC manufacturer assured me that an EE16 core would suffice, but when I factored in the margin and layer tape required for safety agency certification and confined the selection of cores to those with standard gaps I ended up needing a core with over twice the area (EFD20).

I do know a transformer winding company so I should be able to get ahold of all the materials, maybe even get them to wind the bobbins for me, the only thing they can't do is the actual calculations / design of ferrite transformers (the guy who runs it only knows iron core well)

Meh... the same equation applies whatever the frequency or core material, just use the average of the voltage applied to the primary if it isn't square (often times you will see your original equation with a 4.44 in the denominator instead of 4 if the primary excitation is sinusoidal).

There is a lot there to wrap my head around.... What the hell is a VoltSecond?

VoltSeconds (more correctly, volts * seconds) is basically a way to size the core; you should recognize it as the numerator in the version of Faraday's equation I suggested previously. Cores with larger cross-sectional area can sustain more Volts and/or for a longer time for a given number of turns at a given peak flux density. As a side note, it is a corollary to ampere * turns (aka AT or NI) for inductors.

EDIT: I massively screwed up the wire area by multiplying current by 4A/mm² instead of dividing by it... All corrected now.
« Last Edit: September 09, 2016, 11:07:14 pm by MagicSmoker »

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#### CM800

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##### Re: Transformer winding Calculations
« Reply #10 on: September 09, 2016, 02:51:26 pm »

As I'm going for 20kV-0V-20kV, could it be possible to put the primary on each side, along with the secondary on each side?

Going back to primary on one side, secondary on the other, here are my calculations for primary construction:

0.1mm copper foil, 110mm wide (wound single turn per layer) assume 0.1mm tape over each side for total D of 0.3mm
Total length is ~4 meters (calculated through sum of increasing circle OD*Pi) gives me about 4W of heat loss from the primary ~25Arms.
Assuming 10mm winding thickness, the OD of the primary is now 62mm.

Looks like this:

Is this logic right? I've got a lot of hints and suggestions from you, that I appreciate however I feel like I'm being thrown about in the middle of it, not best sure where to -really- start with this.

I intend to put the transformer under Oil so I'd imagine quad insulated wouldn't be needed, just single with a split / segmented bobbin for the secondary?

Also, as a point of interest, I remember seeing someone winding a transformer for high voltage like below, I can't recall I believe he wound the primary on the outsides and the secondary on the insides.

#### MagicSmoker

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##### Re: Transformer winding Calculations
« Reply #11 on: September 09, 2016, 11:36:13 pm »

And it probably didn't help that I messed up the wire area calculation by multiplying current density and current to get area, rather than divide current by current density... Oddly enough, I did choose the correct gauge of wire for the secondary, so some of my brain was working... Mea culpa!

As I'm going for 20kV-0V-20kV, could it be possible to put the primary on each side, along with the secondary on each side?

It is possible, but it won't help much with this type of core. If the goal is to reduce leakage inductance then putting both primary and secondary on one side would help a lot, and interleaving would help even more. But a 40kV secondary will test the resolve of even the stoutest magnet wire insulation film so it really is best to put the primary on one side and the secondary on the other, leakage inductance be damned.

Going back to primary on one side, secondary on the other, here are my calculations for primary construction:

0.1mm copper foil, 110mm wide (wound single turn per layer) assume 0.1mm tape over each side for total D of 0.3mm
Total length is ~4 meters (calculated through sum of increasing circle OD*Pi) gives me about 4W of heat loss from the primary ~25Arms.
Assuming 10mm winding thickness, the OD of the primary is now 62mm.

...

Is this logic right? I've got a lot of hints and suggestions from you, that I appreciate however I feel like I'm being thrown about in the middle of it, not best sure where to -really- start with this.

Yes, that will work fine for the primary.

I intend to put the transformer under Oil so I'd imagine quad insulated wouldn't be needed, just single with a split / segmented bobbin for the secondary?

Oil immersion only really helps with the exposed parts of the windings, not the internal layers. If you use polyester or polyimide tape between layers then single build wire should be fine, but I, personally, much prefer to use triple/quad build wire for any winding supplied by the mains and/or operating at 300V or more.

Also, as a point of interest, I remember seeing someone winding a transformer for high voltage like below, I can't recall I believe he wound the primary on the outsides and the secondary on the insides.

Erf, what a mess. All that core configuration will give you is a whole lot of grief!

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