Transformer Core - Lacing Experiment

[CJ]

always wondered about the effect of core lacing, that is, a 3 x 3 lamination install vs a 5 x 5 or a 1 x 1,

so  here is a graph showing what happens to the inductance as you install the lams in the coil differently,

there are some jumps in the graph as you will have uneven numbers of lams in say a 14 x 14 stack, as if you have 46 lams in a square stack, you will have 3 stacks of 14 plus 4 extra lams, which form a smaller group of lams, you know what i'm talkin about,

looks like once you get down to two stacks, the amount in each stack has little effect on the Henries,

one interesting discovery was that if you have a stack of 44 lams and two left over, the way you stack the last two can change the inductance, if you put them on opposite sides of the 44 lam stack, inductance goes up more than if they are both on one side of the bobbin, thus, if you have a choke with a gap, and you use two keeper lams, the keepers will add to the inductance if they are fitted going the opposite way of the E lams,

 

[shabtek]

cool info.

how does current/flux play into this?

I would guess (other parameters constant) lower Henries can handle more current [would require more current (up to a point)] before saturation as there is less magnetic force being coupled.

why do budget power transformers have minimal lacing? to hit the budget target or some self protecting mechanism? 

 

[CJ]

good questions!

as the Henries go down, the perm goes down, exciting current goes up, the core is able to handle more DC (ampere turns), max AC flux stays the same as core perm is not part of the B-max equation, nor is gap length,

so if you had 5,000 gauss AC and had a Si core, them max Gauss is 18,000,

so DC gauss could be 18.000 - 5,000 = 12,000, so you would adjust the gap or core lacing to generate 12,000 Gauss or less,

using more lams per stack is like adding a bigger gap,

 

[CJ]

here is the same graph with the AC exciting current added,

 

[AnalogPackrat]

Interesting.  I wonder what other parameters might be affected by lacing?  What effect would asymmetrical lacing have (1x1-3x3-1x1-3x3, etc)?  What about lacing variation across the core?  Like having 1x1 in the center and 2x2 in the outer part?  Or vice-versa?  I need to study some more Crowhurst and Lee...

 

[CJ]

most of the effects of different lacing will be in the mid range or below, as the core is out of the circuit at the upper end,

plotting the differences at different freqs would be time consuming, seeing the difference of lacing on an ally core will be the next experiment,

 

[CJ]

if we know Henries vs core lace style, we can plot Permeabillity vs Core Lace,

for 625 EI, mag met cat. says L=(.3326^-8)K1 N U-ac

we used 1000 turns so eq is L=3.1597^-6 U-ac (used 0.95 for K1 stacking just for kicks)

we can now build a column on the spreadsheet for perm,

 

[CJ]

Core Perm vs Lace should look like Henries vs Lace since Henries relates to Perm in a linear fashion, (see formula above)

so here is our Perm vs Lace for 625 EI>

 

[CJ]

so that graph above shows what happens to the perm as we stack lams differently,

we call this effective permeability,

there is a formula that relates effective perm to max perm,

this formula has the thickness of the gap as one of the variables,

there is a web site that has a calculator for this along with the formula,

http://www.encyclopedia-magnetica.com/wiki/Effective_permeability

here is a pic of the formula>

 

[CJ]

perm is usually way above 1, so we can drop the 1 out of the equation, so

u-e = u-max/u-max * gap ratio,  (gap ratio is gap/mag path length of lam)

  u-max now cancels, so

effective perm = 1/gap ratio

625 EI has a magnetic core length of 9.53 cm, so our gap ratio is

gap-cm/9.53-cm

so our formula becomes

effective perm = gap-cm/9.53-cm,

we can write this as

gap = 9.53/effective perm

now we can use our Perm vs Lace graph to tell us what the equivalent gap is for different core stacking techniques,

notice that max perm is no longer in the equation, so what this says is that
every core has a perm that is determined by the gap, there is a natural gap even in a core laced 1 x 1, the value of this gap depends on how big the lamination is, note that the perm of the core does not determine how much signal it will take, but how well it gathers flux and turns it into Henries,

and if we measure the Henries on say a 1 x 1 core lace, we can determine the natural gap of the core for that 1 x 1 core lace by comparing the measured perm with the calculated perm,

thus, in our test coil/core assy with 1000 turns on a 1 x 1 sq stack of 625 EI, we measure 42 Henries which equals a perm of 13,546,

so our natural gap is  gap=9.53/measured perm, so our natural gap is

natural gap-cm (1 x 1) = 9.53-cm/13,546 = 0.0007cm = 0.007 mm=0.0028"
so this graph will now show how we can use stacking techniques to simulate a paper gap,

why do this? paper gaps are very sensitive to variances, such that you might have to measure excitation current to  get them the same every time, they are also sensitive to mechanical shock and temp differences, so stacking a core differently might be a better solution in some situations,

 

[CJ]

so say you need to gap a pwr supply choke,

get the AC flux, maybe your ripple voltage generates 1500 gauss,

this leaves 18,000 - 1500 = 16,500 gauss available for DC flux in a Si core,

since u=B/H, we can write B=uH,  16,500 gauss = uH,

determine H, which is Force/mag length, Force = 1.2566 x Amp-turns,

say we have 1000 turns and 50 milli-amps,

total DC Force in the core is 1.2566 x 1000 x .05 = 62.83 Gilberts

divide by MPL for 625 EI (9.53 cm)  62.83/9.53 = 7 Oersted,

so H = 7 Oersteds, we can no determine the perm of the core before saturation,

16,500 gauss = uH, 16,500 = u*7,  u = 16,500/7 =2,357

so from our graphs and/or spread sheets we see that a gap of 0.016" (use 15 mil paper)
or a stack off 26 lams one way and 26 going the other way will set up the core for the DC bias and AC flux,

 

[Dr.Banzai]

Great analysis!  Just as an aside, if you see E-I transformers with various patterns don't assume the designer came up with the interleaving pattern to tweak the properties. I've talked with some old timers who said they would go 5x5 or 10x10 just to save money/time in mfr. (talking guitar amps here, cheap & no low end no problem...) The Fender stuff (Schumacher) was all 1:1 or 2x2 IIRC but you can find old Vox & Marshall output trannys (like the RS Spares ones) which are 10x10 IIRC. (haven't counted it in a while, but I have one downstairs I can spec if interested) It makes some sense when you think about dropping laminations into the stacking machine. (drop them in stacks of 10 rather than stacks of 1 or 2 is faster). I'd also heard it simulated a small air gap but never looked at the math. Until now.  8)

 

[CJ]

there are some really old transformers that use this stacking thing when using Nickel cores as they can not take the flux,

3 x 3 is used on about on most power transformers, 1 x 1 on nickel input transformers is very common,

 

[CJ]

here is a graph showing the relationship between Turns, Henries and AC?DC Flux in a power supply choke,

Y axis units for Henries only, flux figures were divided to fit the same scale,

 

[Gus]

So CJ
what would be a good lam and stacking for
EL84 SE guitar amp
6V6 SE guitar amp

I always seem to like 6v6 circuits like the champ better than SE el84 circuits. I think it is how the gain in the stages work together

IIRC at Ampage.com in the 90's someone posted the JTM45 used 3x3 I forget if they posted m6 or m19

 

[joaquins]

Cj, your experiments should go in to a book, many people could use this kind of experiments on such unknown topic as it is the details about transformers, in the university the more complex model of a transformer I've seen to the time are 3 inductors and some parasitic resistance.

One detail about your math...

perm is usually way above 1, so we can drop the 1 out of the equation, so
...

It's true that µ is usually higher than 1, but µ*gap/core_length isn't... for example in the example you put, that is around 13546*0.007*95.3=0.995 which makes your approximation erroneous.
If you want to find the gap length, then you could do some math and get this formula out of the other, G=gap length, C=Core length.

G=C*(µc-µe)/(µc*µe)

I will guess here a µc (core) as 15000 which gives as a gap length of 0.00068mm and going back to the other formula to check you get again 13546 for µe (effective). In the 8x8 stack you get 0.011mm of gap.
I live the choke calculations for you.

Thanks for the info! really grate post!

JS

 

[CJ]

your right!  me bad, 

i was wondering why the calculator on that link posted above gave a slightly different answer,


you can also write the eq as  Gap = MPL/u-e - MPL/u

so for 625 EI that would be Gap=9.53/u-e - .00068

so for our example perm of  u-e = 2357, our  Gap = 9.53/2357 - .00068 = .00336 cm = .0132" , not .016"

 

[Dr.Banzai]

The fender stuff used M19 (or equiv), the older Marshall stuff with the RS Spares OT was stacked 10x10 and used 29ga M3 with a very "hifi" build. (it was in fact a general purpose OT with UL taps etc)  The windings on the big guitar amps and little amps tended to be layers like this Ampeg. The middle trannies (30-50W range) were often 5 section (PSPSP) and had nice HF response. The OT in a Dyna ST70 is the same basic construction. (5 section) the whole circuit has to make sense together though. I did a fair amount of research with lams in particular and it's not simple or obvious why this one sounds great and that one doesn't. It all needs to be in balance.
jm2c

 

[CJ]

good info, thanks!

i believe Triad made the early OPT's for the Fender Bassman, (Keith Richard model) which might have been 5-4 coil structure,

Partridge made some good stuff for the early Marshalls i believe, like the Plexi (Hendrix model) which is discussed somewhat in the Marshall book that came out some years back,

 

[Dr.Banzai]

Yes on the Triad stuff. Schumacher was the mfr of much of the later stuff but early tweeds often had Triads and the part #'s on the Fender schematics are the triad numbers. I have a 52 Pro here and both trannies are Triad and it's definitely stock. No idea how it's built but it sounds great.   Those old Bassman OT's (and brown Concert) are better than what came next imho. There is a clarity to them.