# turns ratio

Started by 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
```