More on LF transformers

Following on from the earlier blog entry about using a 3C90 core for a VLF and LF transformer, I got this reply from Jim M0BMU last night on the RSGB LF Yahoo group. I post it here as it contains some useful additional information. See also the mini-Ring Core Calculator from DL5SWB at http://dl5swb.de/ .

"Dear Roger, Andy, LF Group,

>> Four turns minimum for 137kHz 25 Watts. 60 or so for 9kHz
> Yes these values look quite practical ones.

...But now the inductance of the winding and AL value of the core do become important. (BTW, the value of 2000 is the relative permeability of the 3C90 material. The "inductance factor" AL, the "inductance per turn-squared", is a different number which depends on the shape and size of the core as well as the permeability.) AL for this core is given as 2690nH nominally. With a four turn winding, the resulting L is about 43uH, with a reactance of only 37ohms at 137k. In a 50 ohm circuit, this will cetainly mess things up a bit. As a general rule, you would probably like the reactance of the 50ohm winding to be at least 250ohms at the operating frequency. This requires an inductance of more than 290uH, so a winding of 11 turns minimum will be needed for a 50ohm impedance level.

This is a typical result when using a core that is much larger than what is  required by power handling considerations - the number of turns needed to keep the flux down to an acceptable level becomes so small that the inductance becomes the deciding factor. It also obviously makes it tricky to match to low impedances, which is often what you are trying to do in a PA or
loop-matching transformer - you may well find that you end up with windings of less than 1 turn! In these cases the inductance or the required turns ratio becomes the determining factors. In the more normal situation where you are trying to design a transformer with an economically-sized core for a given power level, the inductance is usually large enough not to be an issue, as Andy stated.

At 9kHz however, the 60turn winding is quite reasonable from the inductance point of view, giving 9.7mH and about 550ohm reactance. Also, the core losses would be lower at 9kHz, so you could allow a higher flux density and reduce the number of turns (or increase the power level, which might be better!)

Cheers, Jim Moritz
73 de M0BMU"

On-line LF toroid transformer design tool?

I have some 42mm diameter 3C90 toroids and want to use these in output transformers in 3 applications:

(1) in the output of a 137kHz (up to) 25W transmitter
(2) in the output of an 8.97kHz (up to) 25W transmitter
(3) as an impedance transformer for a TX loop antenna at 8.97, 137 and 500kHz.

I was looking for an on-line calculator to help me work out secondary turns needed, but could not find one.  Andy G4JNT helped with this input:

"The magic equation is Vrms = 4.44.F.N.A.B    all in SI units.   

rearranged  Nmin = V / (4.44 . F . A . B)

Al is irrelevant for transformers.

Use a Bmax of 0.1 Tesla for Ferrites, allowing a decent safety margin.

Your A  (of 25 mm^2)   = 25*10^-6    ,   F = 137000, 

25W in 50 ohms is 35V"

To aid calculations in future I have produced a small spreadsheet to work out the secondary turns from the input data (freq, cross sectional area and RF power out).

As an aside, I use http://www.66pacific.com/calculators/toroid_calc.aspx very often to work out the turns needed for the common HF toroids such as T37-x and T50-x.