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
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 + changeBut 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
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
BTW, one possible exact solution is 10,943/10,000.
John S
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
1.0943 is 1+ 1/10.6.
24/22 =3D 1.0909
47/43 =3D 1.09393/85 =3D 1.0941
185/169 =3D 1.0947371/339=3D 1.0944
More turns than that seems unlikely. What left might just be the coupling coefficient.
-- Bill Sloman, Nijmegen
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.
Turns ratio, maybe - but not turns (absolute). What's the difference in voltage ratio between a 10:100 transformer and a 2:20?
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"
** 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
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
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
That sounds like the right numbers. If I could sneak in a single turn, I could crosscheck it. Probably can't.
-- John Larkin Highland Technology Inc www.highlandtechnology.com jlarkin at highlandtechnology dot com Precision electronic instrumentation Picosecond-resolution Digital Delay and Pulse generators Custom timing and laser controllers Photonics and fiberoptic TTL data links VME analog, thermocouple, LVDT, synchro, tachometer Multichannel arbitrary waveform generators
58:53 (and multiples) gives you 1.0943 within the stated significant digits.
You can just do a brute force calculate and sort with maximum turns. An array of a few million elements should be no problem for a modern computer.
Best regards, Spehro Pefhany
-- "it's the network..." "The Journey is the reward" speff@interlog.com Info for manufacturers: http://www.trexon.com Embedded software/hardware/analog Info for designers: http://www.speff.com
1.0943 =3D 1+ 5/53 =3D 58/53 =3D 1.09433962
-- Bill Sloman, Nijmegen
On a sunny day (Tue, 01 May 2012 15:29:41 -0700) it happened John Larkin wrote in :
Well, personally I would just round to the nearest integer, so 1 : 1.1 makes 10 to 11. You can get the number of turns by sticking a one wire turn in there if there is space, and measuring the output. That gives 1: X. Done it several times.
.highlandtechnology.com=A0 jlarkin at highlandtechnology dot com
from memory, HP makes an LCR Meter that gives you the turns ratio. And, if it's an inductor, you can put one winding through and get the number of turns on the inductor.It was very handy for 'reverse' engineering an inductor quickly.
One could use Tim Wescott's brute force method, or continued fraction methods and go directly to the best possible series of rational approximations to the given ratio.
The continued fraction method gives this series of convergents:
23/21,35/32,58/53,267/244,325/297,383/350,441/403,499/456,...
For an exhaustive discussion of the problem of finding rational approximations to a ratio, see:
A smart turns-ratio instrument would measure L and R and maybe even leakage inductance and do some 2nd-order corrections.
-- 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
This looks like one of those "learnable" moments.
I can't get my head around what it means to have a transformer ratio with PPM accuracy. For the configurations I can imagine, you have either 1/2 or 1 turn resolution in your ability to wind the thing. If the turns counter is correct, what more can you do? If you have a million turns and the counter is off by a turn, you can be off by a PPM.
You know the inductance and a five-digit approximation to the turns ratio. What's a typical application where knowing the exact integer number of turns matters?
And, yes, I understand the "I do it because I can" mentality. I go there far more often than I like to admit.
I searched but found no instrument available which measures turns. All my searches wound up with turns *ratio* instruments.
John S
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