Dear Warren, LF Group,

Taking the inductive reactance first - this is due to the leakage reactance
of the transformer windings. In an ideal transformer, all the magnetic flux
produced by a current in the primary winding would also pass through the
secondary and vice-versa - but in practice, some of the flux always
"escapes", resulting in a real transformer effectively having some series
inductive reactance. This leakage inductance depends on the winding
geometry, core permeability etc. and can't readily be calculated, but
usually measures to be a small fraction of the winding inductance, and very
roughly proportional to the winding inductance. Leakage  inductance is one
of the things that limits the upper bandwidth of a transformer, so normally
you try to minimise it.

In your case, assuming the cores are 4 x Fair-Rite 5978015901 or something
similar, the 28t primary inductance works out to about 11mH (XL = 9.4k). The
leakage inductance, assuming 25ohms inductive reactance per transformer, is
about 29uH, which is quite low for that amount of primary inductance.

The first thing to observe is that saturation of the cores just isn't going
to happen. Assuming about 1kW TX power, so about 224V primary voltage, the
flux density in the transformer core comes out to only around 12mT, while
saturation flux density will be over 300mT even at high operating
temperature. The cores are certainly under-stressed from the magnetic point
of view. Estimating from the Fair-Rite graphs for 78 mix ferrite gives a
total core loss of less than 1W. So you definitely have over-kill in the
amount of ferrite being used.

The second thing to observe is that the winding inductance is too high. The
reactance of the winding won't make much difference to the overall
impedance, provided it is more than about 10 x the transformed load
resistance, in this case XL >=500R, or 580uH. But the trouble with having a
much higher winding inductance like 11mH is that the leakage inductance will
also be relatively high. This is why your transformer introduces significant
inductive reactance.

The leakage inductance of the transformer may contribute significantly to
the heating of the cores. The reactive power circulating in the assumed 25R
of leakage reactance will be about half the total TX power being delivered
to the 50R load resistance when the system is tuned to resonance, i.e.
500VA. The Q of the leakage inductance possibly isn't very high, at a guess
maybe 10 or 20, leading to power dissipation of about 50W or 25W
respectively somewhere in the transformer with 1kW TX pwr. This would
certainly warm it up. Using bigger cores does not really help in itself,
because bigger cores will also mean more leakage inductance

This situation ought to be improved by reducing the primary and secondary
turns. An 11 turn primary and 2 turn secondary will give about the same
ratio, with a primary winding inductance of 1.7mH, hopefully with leakage
reactance correspondingly reduced, and a flux density of around 30mT, still
very low. This will increase the total core loss, but only to around a
couple of watts. As far as leakage inductance goes, a toroid is not the
optimum transformer geometry for a transformer with only a few turns on the
winding, especially when the wire is very thick and does not lie flat on the
core. It is best to make the windings as compact and close to each other as
possible, i.e. wind secondary directly on top of primary, don't spread the
windings round the whole circumference of the core. For example, look at the
type of transformers used in HF linears, where the low impedance winding is
a compact tubing loop, with the high impedance winding threaded through it,
and the ferrite cores wrapped closely around it. I think leakage reactance
in your transformer could be reduced a bit more by arranging the cores as 2
pairs side-by-side in "binocular" form, with the windings wrapped around the
middle of the assembly where the cores are touching together. Another
possibility is to have multiple secondaries of thinner wire distributed over
the primary winding and connected in parallel, but this can be quite fiddly
to produce.

Another possible cause of heating in the transformer is if there is a large
RF voltage between primary and secondary windings. Ferrite is a poor
dielectric, so will get hot if subjected to an intense RF field. This means
that one side of the secondary should be connected to the "cold" side of the
primary, effectively that the transformer should be inserted at a
near-ground potential point on the loop.

Cheers, Jim Moritz
73 de M0BMU



----- Original Message -----
From: Warren K2ORS/WD2XGJ <[email protected]>
To: rsgb lf reflector <[email protected]>
Cc: LWCA LF Reflector <[email protected]>
Sent: Friday, June 02, 2006 3:55 AM
Subject: LF: Transformer problem; advice sought


> Hello the list,
>
>    I have been experiencing heating problems with my step-down toroidal
transformer that feeds my transmit loop. Fearing core saturaton issues I
have been going to ever larger cores and more and more turns in an attempt
to reduce the flux density.  My latest core is 4 stacked 4" diameter Mix 78
toroids weighing a total of 3 pounds (1.34 Kg) with 28 turns of #10 on the
50 ohm winding and 5 turns of 16 mm2 wire on the loop side.
>
>  Now for the puzzle: As suggested by J.B., I hooked two transformers back
to back ; the present transformer (described above) and the previous model
(4 stacked FT-290-77 toroids with 17 turns on the 50 ohm side and 3 turns on
the loop side.  I connected the two transfomers with the the loop windings
from one going into the loop winding of the next. One transformer 50 ohm
winding was hooked to a 50 ohm Bird Dummy Load, the other transformer's 50
ohm winding went to an AEA VIA impedance bridge.  Much to my surprise I had
a high swr and reactance !!!
> The swr was on the order of 2.7:1 and the reactance was 45-55 ohm and
increasing with frequency.
>
>  Any thoughts on why I should show a reactive component when one
transformer went directly to a 50 ohm load?
>
>
>
> --
> 73 Warren K2ORS/WD2XGJ
> FN42hi
> http://www.w4dex.com/wd2xgj.htm
>
>