Trying to design a transformer

[con3]

Hey everyone,

I'm new here and have been struggling for a while with trying to design a transformer. I thought I'd start a thread to get some help so I can build a transformer and put down all my steps for anyone looking in the future.
 
I'm not sure whether anyone is familiar with Colonel McLyman? But I've read his book twice and can relatively easy design a transformer with the cores he provides.
This is mainly because he provides the kg value for all the cores in his book and ofcourse he uses the kg method.

It is however relatively easy to determine the all the constants required for the Kg method, except for the MLT. I have no idea how to calculate the Mean length turn and whether it's for the bobbin or the core.

The kg method for the core is [the window area(Wa_ * (the iron area(Ac))^2 *the window utilization(ku)] / mean length turn(MLT)
I've attached an image of the formula as it is conveyed in the book.

One last thing is that I've never physically wound or put together a transformer, so please assume basic practical knowledge when it comes to transformer assembly. The transformer I'm building will be a low power,ferrite core based and will never touch mains.

In the mean time I have gotten recommendations for another book which I've ordered from a second hand shop [practical transformer design handbook by eric lowdon], other than that, i have read a bunch of books and still cant design a transformer so any and I mean ANY help will really really be appreciated

[Jay_Diddy_B]

Hi,
Welcome to the forum!

The MLT is the MEAN LENGTH of a TURN

It is the average of the length between the shortest turn, closest to the center, and the length of the last turn, the longest turn.

I would include the bobbin, it make the inside turn longer.

Wa x Ku /MLT is proportional to the resistance of a single turn winding wrapped around the core that fills the full window.

Jay_Diddy_B

[Jay_Diddy_B]

Hi,

The equation from Colonel McLyman's book is a subset of Eric Laithwaite's Goodness factor:




The goodness factor was developed for rotating machines, motors, but applies equally well to transformers.

Goodness is a complete equation, it is dimensionless.

Kg (Colonel Lyman) = Ae / Le

which is the conductance, 1/R.

Regards,
Jay_Diddy_B

(I was taught by Professor Laithwaite, shortly after electricity was invented!!)

If you want to know the man watch this:

[con3]

Hi!

Firstly thanks for the reply!

I completely agree with this statement:

"The MLT is the MEAN LENGTH of a TURN

It is the average of the length between the shortest turn, closest to the center, and the length of the last turn, the longest turn."

Which brings me to the weird part about the kg method. They seem to determine the core's kg value which relies on the MLT without knowing or taking into account the number of turns or wire size.

Mclymans book provides the MLT value just by looking at the core.

Here's a segment of the listed cores:


You can see the MLT value seems to be determined just by looking at the core. I thought this would be just for illustrative purposes, although the use this value in designing the transformers, and they seem to use this MLT without taking the amount of turns or wire size into account, in the sense that the core is selected using the kg method and then the wire size and turns is selected afterwards

"Wa x Ku /MLT is proportional to the resistance of a single turn winding wrapped around the core that fills the full window."

This is very interesting. Meaning if I can calculate the effective resistance of the copper wire covering the window  I'd have the value for Wa x Ku /MLT? Also do you mean by "fills the full window" that it should fill the full window or only the fill factor of the portion of the window ( i think mclyman takes it as 0.4)

 I'll look into this and the goodness factor. Trying to get an understanding of how they relate at this point.

Lastly, thank you for the help.
I cant express how much I appreciate it as I have been struggling and researching for very long.

[Jay_Diddy_B]

Hi,
Let me offer some more explanation:

Empty Core




This picture is a square stack of waste free laminations. The center limb is square.

They are called waste free, because the 'I's come from stamping the hole.

Single Turn Winding

Consider a single, single turn winding:



The winding fills the window.

Lets say there is 1V and 1A so this is 1VA

Multiturn Winding

Consider dividing the single turn winding into 4:



there is now 4 times the voltage.

If we keep the current density the same, we have one quarter of the current.

0.25A x 4V = 1VA

The area has been reduced by 4
Resistance per turn has increased 4 times
The length of the winding has been increased by 4
Current has been reduced by 4

if the original winding was 1
And the current was 1A
The original copper losses were 1² x 1 = 1W

In the four turn winding
The resistance is 16x higher

(Quarter of the area, 4turns)

16

The current 0.25A

Power loss = 16 x (0.25)² = 1W

The same as the single turn winding.


So it not necessary to consider voltage, number of turns etc. to determine the VA rating of transformer.

PACKING FACTOR (or Window Utilization)

In practice the window cannot be filled with copper. To built a practical transformer there is insulation and a bobbin:



The bobbin uses some of the window



Round wire is normally used.


There is nothing absolute about the power rating of transformer. It depends on the allowable temperature rise.

Regards,
Jay_Diddy_B

[Jay_Diddy_B]

Hi,

Here is a different view showing the packing factor:




Only a percentage of the window is used by the winding.

Jay_Diddy_B

[con3]

Jay_Diddy_B,

Thank you for the images and detailed explanation.
I understand the independence of the power rating, I feel like I understand what you've posted thus far, although I still cant see how I'd be able to calculate the kg value or more the MLT, as Mclyman has.
I might just be very slow today.

I understand that the power rating of the transformer would be directly related to the temperature rise of the transformer, I'm assuming at a certain temperature the core would lose it's magnetization ability. Sadly the method that I've seen thus far has been the kg method and the determination of the kg value from the core specs has been very obtuse to me.

Is there any chance you could do a rough calculation to show me how to calculate the kg value, if you don't mind?

I have quite a bit more questions I'd like to ask and dig at your brain a bit further regarding transformers.


My apologies for the lack of understanding thus far from my end and thanks again

[Jay_Diddy_B]

Hi,

From the book we have:



and



Since dimension E and D are the same the table is for 'square stack'

Everything required for the calculation is given in the table apart from K_u.


If I work backwards

K_u = K_g x MLT /W_a x A_c²

Using the EI-100 as an example

Ku = 4.927 x 14.8 / 4.839 x (6.129)² = 0.4

Which is what you told me it was.


So if I calculate K_g for EI-225

Kg = Wa x Ac² x Ku / MLT

Kg = 24.496 x (31.028)² x 0.4 / 32.7

Kg = 288.47

(Close to the value in the table 288.936)


Regards,
Jay_Diddy_B

[con3]

Jay_Diddy_B,

I think my issue is the fact that when looking at cores provided by manufacturers, the data in table 3-3 is non-existent.

For instance, here is the EI cores of a local manufacturer, https://irp-cdn.multiscreensite.com/e48fec65/files/uploaded/AMC%20Pressed%20Laminations.pdf

If you're not comfortable clicking on the link here is a snippet:



Each core comes with dimensional data and the core sizes are different than McLymans chosen cores. For the cores given in the AMC booklet, I have no idea how to calculate the Ac or MLT value. I know ku is selected as 0.4 and  I know the window area is F * E, but I have absolutely no idea how to calculate MLT or Ac so that I can get the corresponding kg value.

Using McLymans table, I can calculate the kg value, without this table and with only dimensional data as supplied by the manufacturer, I'm completely lost.

I'm not sure if that makes sense?

Thanks again

[Jay_Diddy_B]

Hi,

Using the Dimension in the table you provide:

The height of the stack is not provided.

If we assume that the stack is square, the height of the stack is also Equal to A.

So

Ac = A²

MLT = 4x (A + E)  (The average length of turn around the center limb)

Wa = E x F

Regards,
Jay_Diddy_B

[con3]

Jay_Diddy_B,

I just want to double check this with mclymans calculation.

so I agree Ac =A^2



So lets say I take the EI-375 core, shouldn't the AC value be E x D ?

For the  core:

E = 0.953 , D = 0.953 so it'll be a square stack so Ac = E^2 or Ac = 0.908209 although Mclyman gets his Ac as 0.862 as shown in table 3-3.

I'm not sure whats causing this discrepency?

[Jay_Diddy_B]

Hi,

The issue is that the letters used for the dimensions are not consistent between the book and the datasheet:




So for AMC

Ac = A x height of the stack or A² (for a square stack)

In the book

Ac = E x D

The discrepancy make come from the consideration that the laminations are insulated. So just like the winding there is a packing factor. If a packing factor of 95% is used for the core it would account for the discrepancy.

That is saying the core is 95% steel and 5% insulation or small spaces between the laminations.

Regards,
Jay_Diddy_B

[con3]

Jay_Diddy_B,

For the following I'll just be using the dimensions from the book:



In the book as stated Ac = E x D,

so EI-375 :

E = 0.953
D = 0.953

Ac = E x D = 0.953 x 0.953 = 0.908209

Where as Mclyman gets 0.862 for core EI-375.

So, just saw your edit, would the packing factor then be taken into account, so say the Ac i get is 0.908209, i then multiply this to get the by the packing factor (95%) to get McLymans 0.862 value?

Just want to make sure I completely understand.

Again, THANK YOU for the help


EDIT: "The discrepancy make come from the consideration that the laminations are insulated. So just like the winding there is a packing factor. If a packing factor of 95% is used for the core it would account for the discrepancy.

That is saying the core is 95% steel and 5% insulation or small spaces between the laminations."


Wait so seeing as the core is already constructed, which means it consists of 95% steel and 5% insulation, then the Ac = 0.95 x E x D.

So i'm assuming the Ac value is the core area of the steel, excluding insulation ?

Finally does the lamination from the AMC brochure already include insulation or is it just the steel?

[Jay_Diddy_B]

EDIT: "The discrepancy make come from the consideration that the laminations are insulated. So just like the winding there is a packing factor. If a packing factor of 95% is used for the core it would account for the discrepancy.

That is saying the core is 95% steel and 5% insulation or small spaces between the laminations."


Wait so seeing as the core is already constructed, which means it consists of 95% steel and 5% insulation, then the Ac = 0.95 x E x D.

So i'm assuming the Ac value is the core area of the steel, excluding insulation ?

Finally does the lamination from the AMC brochure already include insulation or is it just the steel?

Not sure about this, you need to ask the lamination supplier. Tempel tells you how many set of laminations you need to build a square stack.

It probably doesn't make a lot of difference.

Jay_Diddy_B

[con3]

Jay_Diddy_B,

Thank you.
I think I have a grip on the Ac value, now for the MLT...

I'm not quite sure how you got the  MLT as 4x (A + E) .
I would really appreciate if you could explain it in a bit more detail so that I can derive it for other core types.
I found the following on stack overflow, although I'm still struggling to comprehend it : https://electronics.stackexchange.com/questions/485659/how-to-find-mean-length-per-turn-mlt-for-magnetic-design-from-ferrite-cores-da

It looks like they provide a formula, although in the question there's this image:



Where the wording; single, first and second winding makes it sound like they calculate it on a per winding/turns basis?

Finally I think I might have a misunderstanding of the definition of the MLT, here's a drawing to show how I understand it:

I've redrawn the E-core from this image on paper



On this image i have filled in the first turn and the last possible turn on the core, if the core was fully wound.




From here I think the average turn would be the middle turn shown in the dashed purple line. The length of this middle turn is the MLT?

Am I understanding this correctly.

Thanks again for all the help, really really appreciate it.

[Jay_Diddy_B]

Hi,

Consider this:




The Mean Turn is drawn in red.

The length of the front section is:

F/2 + E + F/2  = E + F

The length of the

Back section is

F/2 + E + F/2 = E + F

Similar if the height of the stack is h

front to back

F/2 + h + F/2 = h + F

back to front

F/2 + h +F/2 = h + F

add all this up

MLT = 4F + 2E + 2h

but since the core is square

h = E

so MLT = 4 x (E + F)


Jay_Diddy_B