Find a pair of integers N and M such that N/M is the ratio you want.
Well, a million turns isn't practical. Hundreds, maybe. People who wind transformers usually get the turns count exactly right. The winding machines do that.
In my case, I have a board with 24 transformers on it. It does synchro/resolver simulation and acquisition. And the transformers plug in, to allow different voltage ranges. So I need all the transformers to be exactly the same.
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Even with essentially identical transformers, we probably won't get close to the accuracy of a really good synchro. They are amazing.
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One way is to take some approximate measurements and infer an integer turns ratio and hope it all works out. The integer you get can never be better than the floating-point approximation you already have.
Another way might be to take a known-good transformer and an unknown one. Put the primaries in parallel and the secondaries in series-opposing. Energize the primary and measure the output. The better the match, the less output you'll see. And that's a true performance match instead of an approximation to a turns-ratio match. And you can resolve that difference to far better accuracy than the turns ratio. Measuring two equal numbers and subtracting the difference is error prone. Subtracting the electrons and measuring the result, not so much. Yes? No?
Given those numbers, I might bet on something like 580:530. They seem to like zeros at the end.
Best regards, Spehro Pefhany
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Physically, a transformer (common ground for simplicity) is:
V(pri) o----+ +----o V(sec) | M | ) ( Lp ) ( Ls ) ( | | +-----+ __|__ GND
Since the windings are made with wire, they implicitly have series resistance (not shown). The definitive equvalent circuit converts the mutual inductance M into a trans-inductance in each loop:
However, these dependent sources aren't very intuitive. They can be converted to a bridging inductance, forming a pi network of inductors. It is my understanding this is true in general terms, but turns ratios result in negative inductances -- not physically significant, but still analytically consistent).
Applying a wye-delta transformation, the more familiar tee network transformer model looks like this:
Rp LLp LLs Rs V(pri) o----RRR----LLL---+----+---LLL----RRR----o V(sec) * N1/N2 | | Lc L R Rc L R | | +----+ | __|__ GND
This works as shown for a 1:1 transformer; for any other ratio, the output voltage and current are simply scaled accordingly (in which case, all quantities are primary-referred values).
In general, when Lc >> (Lp + Ls), a transformer is a "good" transformer, and (LLp + LLs) is the (engineering) leakage inductance. This has the advantage of only one nonlinear component if a simple core model is desired (arguably, the same is true of the pi network, but it seems weird having two cores, each with double the inductance of the actual device..).
In a "good" transformer, you can approximate Lc and Rc approaching infinity, and V(pri) = V(sec) * N1/N2, so the ratio is exact. But if mu is finite, or your tolerances are finer than a few percent, as when you're doing ppm ratios, everything matters and no approximation is acceptable, even with a mu-metal core (mu > 100k). The winding technique has to be very wideband to minimize leakage, and the core has to be very high permeability to minimize loading.
To put it another way: suppose you have a cheapass transformer that works maybe 100Hz to 10kHz at some impedance. Magnetizing losses dominate at low frequencies, leakage (and parasitic capacitance) dominates at high frequencies. In the skirts, attenuation is high, many dB. At midband, attenuation is small, mainly the inductance dividers between primary leakage and core (inductance and eddy current losses), and secondary leakage and load. But 1 ppmV = 0.000087 dBV, so you need to be pretty damned far away from those skirts before your midband is truely 1 ppm accurate. And if your skirts are within a decade, your midband will never even reach that point, let alone cross it (though with a tinge of capacitance, it could be made to cross many times). This necessitates LF cutoffs in the Hz, and HF cutoffs in the MHz, just for a reasonably stable ratio at a few kHz.
Tim
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Since these are prototype units built to your specs, you should know what the turns ratio is (should be). Are you trying to see if the actual turns ratio is according to your spec?
On a sunny day (Thu, 3 May 2012 08:32:59 +1000) it happened "Phil Allison" wrote in :
I have not read this one yet, but I once tried it: IF you can measure wire diameter, and then resistance, then you can calculate wire length. Then a reasonable estimate of the number of turns is possible. On many transformers you can just get the wire diameter.
The usual way of winding a ratio transformer is with a bundle of loosely twisted wires - it's a generalisation of the bifilar winding trick, with a lot more filaments. As in bifilar winding, you have to twist the bundle to make sure that every wire sees more or less the same magnetic field (averaged over the whole winding).
Sorting out which wire at one end is the other end of which wire at the other end is labour-intensive. I've though about using round-to- flat cable to do the job, which would waste a lot of your winding window, but avoids that particular problem.
The turns ratio is then defined by the number of wires in the bundle
If it is on a toroidal core, the resolution can never be smaller than a single turn, because there are no half turns on a toroid. If the wire passes through the core, it is a turn. It is not a turn unless it passes through the core. Those two rules mean there are no partial turns. To count turns on a toroidal, one counts the wires inside the core.
On an axial wind over an open ended core, a partial turn will cause a slight variance but single turn counting and a half turn resolve can be reliably calculated and used. That doesn't mean one should do so, however. Single turn resolve is all one should *ever* need to use. there are too many other variables with transformers to make it a critical design element in your circuit's operation, if you think sub-turn resolution is ever going to be a solution.
Core gapping makes a greater difference, as it relates to fine tuning a calculated turns count design. And core media selection.
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