Forums

turns ratio

Started by John Larkin May 1, 2012

If I measure the voltage ratio of a 2-winding transformer, 1.0943 in
this case, how might I determine the number of primary and secondary
turns? I recall a high-school math class where we were shown how to
convert a real number into an integer ratio N/M somehow.

It's a smallish audio-type transformer, Lp around a henry maybe, so
there are probably not a huge number of turns. 

An online calculator for this would be cool.


-- 

John Larkin         Highland Technology, Inc

jlarkin at highlandtechnology dot com
http://www.highlandtechnology.com

Precision electronic instrumentation
Picosecond-resolution Digital Delay and Pulse generators
Custom laser drivers and controllers
Photonics and fiberoptic TTL data links
VME thermocouple, LVDT, synchro   acquisition and simulation
On Tue, 01 May 2012 15:29:41 -0700, John Larkin wrote:

> If I measure the voltage ratio of a 2-winding transformer, 1.0943 in > this case, how might I determine the number of primary and secondary > turns? I recall a high-school math class where we were shown how to > convert a real number into an integer ratio N/M somehow. > > It's a smallish audio-type transformer, Lp around a henry maybe, so > there are probably not a huge number of turns. > > An online calculator for this would be cool.
Once you finish measuring the voltage, take the transformer apart and count turns as you unwind them. To do this nondestructively is obvious: Try to find the closest rational number to 1.0943, and take the numerator and denominator as your turns ratio. But I suspect that a voltage ratio measurement is going to differ from the turns ratio by at least 2%, so once you get above 50 turns I'm not sure that deducing the number of turns from the voltage ratio is possible anyway. 58/53 = 1.0943396 + change But there are ten possible m for n = 1:100 where | n / m - r | < 0.001, and 40 if you allow the error to rise to 0.005 -- if that can't tell you that you're barking up the wrong tree, I don't know what can. -- My liberal friends think I'm a conservative kook. My conservative friends think I'm a liberal kook. Why am I not happy that they have found common ground? Tim Wescott, Communications, Control, Circuits & Software http://www.wescottdesign.com
On 5/1/2012 5:29 PM, John Larkin wrote:
> > > If I measure the voltage ratio of a 2-winding transformer, 1.0943 in > this case, how might I determine the number of primary and secondary > turns? I recall a high-school math class where we were shown how to > convert a real number into an integer ratio N/M somehow. > > It's a smallish audio-type transformer, Lp around a henry maybe, so > there are probably not a huge number of turns. > > An online calculator for this would be cool. > >
My Excel "rationalizer" did not find an exact (0% error) match for your number. I arbitrarily put in 1e-5 % for the max error and it came up with 2611/2386. That's only one possible answer because we don't know your actual error nor precision. You want my Excel "rationalizer"? John S
On 5/1/2012 5:29 PM, John Larkin wrote:
> > > If I measure the voltage ratio of a 2-winding transformer, 1.0943 in > this case, how might I determine the number of primary and secondary > turns? I recall a high-school math class where we were shown how to > convert a real number into an integer ratio N/M somehow. > > It's a smallish audio-type transformer, Lp around a henry maybe, so > there are probably not a huge number of turns. > > An online calculator for this would be cool. > >
BTW, one possible exact solution is 10,943/10,000. John S
On Tue, 01 May 2012 17:54:34 -0500, Tim Wescott <tim@seemywebsite.com>
wrote:

>On Tue, 01 May 2012 15:29:41 -0700, John Larkin wrote: > >> If I measure the voltage ratio of a 2-winding transformer, 1.0943 in >> this case, how might I determine the number of primary and secondary >> turns? I recall a high-school math class where we were shown how to >> convert a real number into an integer ratio N/M somehow. >> >> It's a smallish audio-type transformer, Lp around a henry maybe, so >> there are probably not a huge number of turns. >> >> An online calculator for this would be cool. > >Once you finish measuring the voltage, take the transformer apart and >count turns as you unwind them. > >To do this nondestructively is obvious: > >Try to find the closest rational number to 1.0943, and take the numerator >and denominator as your turns ratio. > >But I suspect that a voltage ratio measurement is going to differ from >the turns ratio by at least 2%, so once you get above 50 turns I'm not >sure that deducing the number of turns from the voltage ratio is possible >anyway. > >58/53 = 1.0943396 + change > >But there are ten possible m for n = 1:100 where | n / m - r | < 0.001, >and 40 if you allow the error to rise to 0.005 -- if that can't tell you >that you're barking up the wrong tree, I don't know what can.
Transformers can have PPM accurate ratios. I just bought a Gertsch SS-2 synchro standard that's just a box full of transformers and switches, super-accurate sin/cos transformer ratios somehow. We have a couple of their 6-decade AC ratio boxes that are PPM accurate, sort of a transformer-based Kelvin-Varley divider. Transformer winding shops have some little digital-display boxes that measure and display turns exactly. I don't know how they work. I was just trying to remember the algorithm for finding a close rational approximation to a real number. -- John Larkin Highland Technology, Inc jlarkin at highlandtechnology dot com http://www.highlandtechnology.com Precision electronic instrumentation Picosecond-resolution Digital Delay and Pulse generators Custom laser drivers and controllers Photonics and fiberoptic TTL data links VME thermocouple, LVDT, synchro acquisition and simulation
On May 2, 12:29=A0am, John Larkin <jlar...@highlandtechnology.com>
wrote:
> If I measure the voltage ratio of a 2-winding transformer, 1.0943 in > this case, how might I determine the number of primary and secondary > turns? I recall a high-school math class where we were shown how to > convert a real number into an integer ratio N/M somehow. > > It's a smallish audio-type transformer, Lp around a henry maybe, so > there are probably not a huge number of turns. > > An online calculator for this would be cool.
1.0943 is 1+ 1/10.6. 24/22 =3D 1.0909 47/43 =3D 1.093 93/85 =3D 1.0941 185/169 =3D 1.0947 371/339=3D 1.0944 More turns than that seems unlikely. What left might just be the coupling coefficient. -- Bill Sloman, Nijmegen
On Tue, 01 May 2012 17:17:10 -0700, John Larkin wrote:

> On Tue, 01 May 2012 17:54:34 -0500, Tim Wescott <tim@seemywebsite.com> > wrote: > >>On Tue, 01 May 2012 15:29:41 -0700, John Larkin wrote: >> >>> If I measure the voltage ratio of a 2-winding transformer, 1.0943 in >>> this case, how might I determine the number of primary and secondary >>> turns? I recall a high-school math class where we were shown how to >>> convert a real number into an integer ratio N/M somehow. >>> >>> It's a smallish audio-type transformer, Lp around a henry maybe, so >>> there are probably not a huge number of turns. >>> >>> An online calculator for this would be cool. >> >>Once you finish measuring the voltage, take the transformer apart and >>count turns as you unwind them. >> >>To do this nondestructively is obvious: >> >>Try to find the closest rational number to 1.0943, and take the >>numerator and denominator as your turns ratio. >> >>But I suspect that a voltage ratio measurement is going to differ from >>the turns ratio by at least 2%, so once you get above 50 turns I'm not >>sure that deducing the number of turns from the voltage ratio is >>possible anyway. >> >>58/53 = 1.0943396 + change >> >>But there are ten possible m for n = 1:100 where | n / m - r | < 0.001, >>and 40 if you allow the error to rise to 0.005 -- if that can't tell you >>that you're barking up the wrong tree, I don't know what can. > > Transformers can have PPM accurate ratios. I just bought a Gertsch SS-2 > synchro standard that's just a box full of transformers and switches, > super-accurate sin/cos transformer ratios somehow. We have a couple of > their 6-decade AC ratio boxes that are PPM accurate, sort of a > transformer-based Kelvin-Varley divider.
I very much doubt that a guy designing an audio transformer is going to have ppm accurate voltage ratios on the top of his "important stuff" list.
> Transformer winding shops have some little digital-display boxes that > measure and display turns exactly. I don't know how they work.
Turns ratio, maybe - but not turns (absolute). What's the difference in voltage ratio between a 10:100 transformer and a 2:20?
> I was just trying to remember the algorithm for finding a close rational > approximation to a real number.
double fit = 1; struct {int num, den;} ratio; for (int n = 1; n < some_limit; ++n) { double m = floor(n * target + 0.5); if (fabs(m / n - target) < fit) { fit = fabs(m / n - target); ratio.num = m; ratio.den = n; } if (fit < good_enough_fit) { break; } } -- My liberal friends think I'm a conservative kook. My conservative friends think I'm a liberal kook. Why am I not happy that they have found common ground? Tim Wescott, Communications, Control, Circuits & Software http://www.wescottdesign.com
"Tim Wescott"

> But I suspect that a voltage ratio measurement is going to differ from > the turns ratio by at least 2%, so once you get above 50 turns I'm not > sure that deducing the number of turns from the voltage ratio is possible > anyway.
** Not true for an unloaded tranny running in the middle of its pass band at low enough level to eliminate I mag. The turns ratio and voltages match very closely. .... Phil
"John Larkin" <jlarkin@highlandtechnology.com> wrote in message 
news:jpn0q71a1ml3qsr2ret7ck5t5jtqmfelff@4ax.com...
> > > If I measure the voltage ratio of a 2-winding transformer, 1.0943 in > this case, how might I determine the number of primary and secondary > turns? I recall a high-school math class where we were shown how to > convert a real number into an integer ratio N/M somehow. > > It's a smallish audio-type transformer, Lp around a henry maybe, so > there are probably not a huge number of turns. > > An online calculator for this would be cool. > > > -- >
Run one wire ( turn) thru the core and measure its voltage with a voltage on the primary. Then you'd know how many turns are on the primary. I'm sure you can jam one wire thru the core without incident. Cheers
John S wrote:
> > On 5/1/2012 5:29 PM, John Larkin wrote: > > > > > > If I measure the voltage ratio of a 2-winding transformer, 1.0943 in > > this case, how might I determine the number of primary and secondary > > turns? I recall a high-school math class where we were shown how to > > convert a real number into an integer ratio N/M somehow. > > > > It's a smallish audio-type transformer, Lp around a henry maybe, so > > there are probably not a huge number of turns. > > > > An online calculator for this would be cool. > > > > > > BTW, one possible exact solution is 10,943/10,000. > > John S
383/350 is 1.09429. Cheers Phil Hobbs -- Dr Philip C D Hobbs Principal Consultant ElectroOptical Innovations LLC Optics, Electro-optics, Photonics, Analog Electronics 160 North State Road #203 Briarcliff Manor NY 10510 845-480-2058 hobbs at electrooptical dot net http://electrooptical.net