[Amps] Transformer frequency differences

[Will Matney]

When I made a comment to the post about the differences between 50 Hz 
and 60 Hz transformers and mentioned that the voltage could rise if the 
frequency was increased something sounded odd to me about that as I had 
read that in a publication. The voltage rise that I had read about was 
not a great sum but in the 800 Vac situation in reality it could be as 
high as 8 to 40 Vac (see below). After mulling this over the basic 
formula for determining the number of windings in the secondary is found 
by dividing one voltage into another. Actually NP=NS where NP is number 
of turns in the primary and NS the number in the secondary. For instance 
if we had a 120 Vac primary and needed a 240 Vac secondary, the primary 
had two turns per volt then the primary would have 240 turns and the 
secondary 480 turns. Now the output voltage of the secondary would be a 
little less than what it should due to losses in the transformer itself. 
Thus the secondary turns is stepped up a few to make up for this. 
Something on the order of multiplying it by .01 to .05. There is a 
formula used for compensating for voltage drop here but it only gets you 
in the ball park. Now If the frequency is plugged into the formula, this 
determines the core size to be used for the power output needed. The 
number of turns is calculated so that the primary will not burn out at a 
given core size from this formula also. Now suppose we took a 50 Hz 
transformer and ran it on 60 Hz. Really, nothing should happen and it 
work properly. The small voltage rise occurs because the losses are less 
than they should be. This is due to the core being "over-sized" and the 
extra few tuns that were used to make up for the losses at 50 Hz really 
wasn't needed because the loss dropped due to over-sizing the core. Now 
a 60 Hz core would be smaller in size than a 50 Hz core by the way the 
formula sizes it by the frequency. Now it would be wound for 60 Hz with 
the turns per volt being less than it would for 50 Hz. So, if a 60 Hz 
transformer would be ran on 50 Hz, the losses would rise, the voltage 
would have a small drop and the primary would probably burn out faster 
than normal and would run with excessive heat. The voltage of going from 
800 Vac to 900 Vac was exaggerated as I didn't calculate them but still 
as mentioned could be a 8 to 40 Vac difference. I doubt the rise would 
be near this high (40 Vac). Keep in mind that no matter what, it's AC 
still coming out of the secondary. This AC will be rectified into DC 
current. Accordingly, there shouldn't be anything wrong as there should 
be no difference in the DC produced except for the ripple frequency. 
Matter of fact, I read that if using a square wave switching transformer 
like in the old tube mobiles, when the two secondary legs are combined, 
the two are 180 degrees out of phase and being square wave. By this, 
when they're combined, it should go back to being a DC current! However, 
the square wave would have to be a perfect square wave and I've never 
seen that obtainable so filtering would still be needed in my opinion.

Another thing I'd like to clear up is the gauss ratings. I was in a 
hurry and pulled numbers out of thin air to show a point as I didn't 
intend then to be going this in depth. However, the  number to use for 
standard silicon steel (Like M6) and for unknown types is approximately 
12,000 gauss when using 60 Hz. You'll need this to plug into the 
formulas I sent after the fact. Also, a quick calculation for the turns 
per volt can be simply 5 / a or the core area divided by 5. Accordingly 
the core area; a  = 0.16 times the square root of the power in watts. An 
example for 100 watts would be the square root of 100 = 10 so 10 X 0.16 
= 1.6 square inches. Then the turns per volt would be 5 / 1.6 which is 
3.125 turns per volt. Keep in mind the other formulas are more exact and 
work with every frequency and situation.

I apologize for any confusion as when I'm thinking on a subject, I tend 
to think everyone else is thinking along the same lines as me and has 
read about the same things I have. From the e-mail I received, I found 
that there isn't any good transformer design topics hardly available. 
Even the ARRL Handbook is vague about a lot of it and a lot is not 
included in its texts. Hopefully, what I have discussed and shown will 
be of help to all of you who have pondered the subject of transformers.

73's,

Will Matney
US Amp