Leakage/Stray field Transformer help

[Veldox]

Hi, i'm currently designing a transformer where the secondary winding is going to be shorted a majority of the time, the same as a welding transformer. but need some help on a couple of things.

The transformer needs to be limited to draw no more than 24 amps from the power source when shorted on secondary, but to also use as much current as possible. I've heard a magnetic shunt inbetween the windings can help limit the current drawn.

my questions are:

If im going to be using a shunt do i need to worry about the inductance of the transformer (before adding a shunt), and if so what sort of henries should i be aiming for. (are more turns on primary better?).

And how would i go about making a shunt, I cant find too much information on how they are calculated.

Thanks.

[trobbins]

Perhaps visit your local transformer manufacturer and chat to an old designer who has set up ferroresonants and other 'shunt' related devices.  The transformer is going to be sizable, and custom, so unless you think you can obtain laminations and wind cores in custom configurations, then you will need a friend.

You could also mock up your concept with a typical transformer and use chokes on each side.

[CaptDon]

Probably Trobbins idea is a good one. Transformers with magnetic shunts are inefficient in most applications. A choke in series to limit short circuit current would be easy to specify although high current chokes can get expensive. Many years back I worked on a welder that used a variable saturation core inductor in series. They used D.C. at varying levels to create adjustable saturation of the inductor core. At full saturation the inductor appeared to not even be in the circuit, and at very low levels of saturation there appeared to be almost no load (even with a shorted load) on the main transformer. The unit used load current sensing and therefore was capable of load current regulation. Very cool unit!!! The original purchaser was the U.S. Army. I remember it had an AN/USM designator tag on it. The saturable core reactor was driven by vacuum tubes!!!

[T3sl4co1l]

No worries about inductance, as long as it's enough for the applied voltage -- more particularly, the cross sectional area and number of turns, giving flux density below saturation.

I haven't designed one before, in the sense of going through and completely building one, and proving that the design parameters work out correctly.  I get the gist of it.  So, expect there may be some final adjustment, because things don't always work out perfectly.  (In particular, it's hard to estimate unintended leakage, fringing and so on.  Also if there are harmonics involved, each one needs to be treated separately; unless the thing is nonlinear in which case they all get mixed together, and you might be better off just simulating it, etc.)

This is a three step process, I think.

1. Design the transformer for Vin, F, Ns/Np
2. Design the shunt for LL, Phi(SC)
3. Redesign the secondary for desired Ns/Np

1. Start by estimating the required core based on weight or volume.  This depends on frequency, material and shape or aspect ratio, but there are typical figures to start with.  Offhand, I forget what it is for silicon steel at 50/60Hz, and I don't have numbers for ferrite cores but I have a general feel for what to expect...

Turns goes as:
N = Vrms / (4.44 Bmax Ae F)
Vrms is sinewave RMS, Bmax is peak flux density in T, Ae is cross sectional area in mm^2, F is frequency in MHz.

(Or whatever other units you like, preferably mks because the constants are normal.  Note that the multipliers work out same as m^2, Hz and T.)

(You often also see this equation in cgs; but it has weird pi's and other constants, that are rarely documented as such, just rolled into one big fat number.  I don't recommend that.  Speaking of which, the "4.44" is a conversion from sine Vrms to peak flux -- 4.44 ~= pi sqrt(2).  It's not a unit conversion, but a geometric constant.  The corresponding value for square waves is 4.0.)

(There's also two kinds of cgs, one with constants like mks has, one with dimensionless units(!).  I think it's mainly used for historical purposes; a lot of books were written in cgs, and remain top references in many fields, which thus remain in cgs.  Go figure.  So, I prefer and recommend mks.  Anyway, all this unit nonsense is mostly irrelevant, as long as you are accurate and specific with what quantities you are using, and you plug everything into Google Calculator for instance.)

Anyway, you need at least this much core area and turns, and you need at least as much winding window area as N times an adequately sized wire (per winding).  Typically a current density around 7 A/mm^2 is chosen, though the actual figure depends on how much cooling is available (less in large blocky transformers -- mind the surface area to volume ratio; more with forced-air or liquid cooling), or what efficiency is being targeted.  A "winding factor" is also applied, usually under 0.5, assuming that about as much area can be filled with actual useful copper -- the rest left as wasted space, or used up by bobbin, insulation and etc.

Winding area and core area are independent, so choice of a core depends on typical geometry, stack height if applicable, etc.  Normally something roughly cubic is chosen, and the ratio of these quantities will be consistent across different size parts.  (Catalogs typically have Ae/le, Ae*Aw, etc. listed to aid in this decision.)

So, we can select a good starting core size and shape.  Hold onto that, but don't order anything just yet.

2. Shunt design.  If the secondary can be fully short circuited, then its flux will be nearly zero, and the balance has to flow across the shunt.  Therefore its cross sectional area needs to be the same as the main core.  (Which will make it quite desirable to use a relatively long or thin core shape, i.e. with a taller winding area to accommodate the width of the shunt, or in general, enough winding area to hold the shunt, primary and secondary.)  If less flux is required, the shunt can be smaller.

For example, microwave ovens drive a magnetron which has a constant-voltage characteristic; excess secondary voltage is supplied, but because the secondary will never be fully shorted, the shunts can be economized upon.  This is why the shunts aren't full width, and the design is usually (always?) able to use "wasteless" stampings (if you put two 'E' pieces tip to tip ("E3"), notice the two slots are exactly the size of the 'I' pieces -- this proportion can be stamped from sheet with no waste, hence it's the cheapest / most common style.)  So, a constant-current-to-a-point characteristic is provided.

The airgap around the shunts determines leakage inductance.  If full width (i.e., no added shunts at all, just two separate banks of windings, primary and secondary), the leakage is simply the air gap between windings.  Pretty low leakage inductance this way: low enough that the primary probably isn't going to be happy, at full input voltage and shorted output; though also not so low that it's any good at higher frequencies, say.  (A typical power transformer of this construction, is only good to a few kHz bandwidth.)

Bandwidth isn't so important to mains transformers, but it's not irrelevant -- when using a cap-input rectifier for example, to obtain a DC output, the heavily distorted current waveform has to pass through the transformer.  High leakage and low bandwidth, gives poor output regulation.  (Hence why a wall-wart of this construction, might manage to be "impedance protected" (= it's so lossy and leaky, it can sit there cooking 24/7 with a shorted load!), and might deliver up to double its rated voltage, when unloaded -- nominal voltage is typically only under rated load!)

For smaller air gaps, the leakage inductance is given by the dimensions of that air gap: A_L = mu_0 Ae / lg, for cross sectional area Ae and gap length lg.  (Note that, for an E core, the two shunts act in parallel: use the total area, and count just one length.)  A_L has units of H/t^2 or whatever; inductance referred to a winding is L = N^2 A_L.  Using Np, this will give the primary-referred leakage, and so on.

3. Redesign secondary.

Note that the shunt diverts some flux from the secondary, even when lightly loaded.  This reduces Vsec, so we need to increase Ns to compensate.  And for the same Isec, more winding area is needed.  So you often end up with a lopsided transformer design; microwave oven transformers are made this way, and sodium lamp and neon sign transformers are even more extreme examples.

So, we can draw an inductor divider between primary, shunt and secondary; and we should probably have an estimate of primary leakage (that is, around the primary itself, up to the shunt), and same for the secondary.  The equivalent circuit gives a divider ratio, and we simply increase turns, dividing by that ratio.

Tim