As Tim wrote, short the secondary, measure the primary. That's not
quite all there is to it, since you can't really short the secondary
inductance; you're putting a resistance equal to the winding
resistance across it. But yes, you can do it if you think about it
carefully.
I think the measurement of the secondary voltage with the primary
excited, and vice-versa, is a better way, though there you technically
need to compensate for the drop in the resistance of the excited
winding because of the current through the winding. That is, the
voltage across the pure inductance is less than what's applied to the
winding. I'm not sure you got a proper answer to the question about
how to measure the coupling so precisely.
Are you referring here to the post where, after I gave the OP a k of
..999883, he said:
"How did you come up which such a precise number?"
I suspected that he saw the number .999883 and thought, six significant
digits. I wanted him to know that that value only has three significant
digits.
If the question is, how did I get even a three significant digit
measurement, that's easy to do with good DVM's using the method I described
to him (and which you are recommending).
On the other hand, trying to get more than about 1 significant digit by
some method involving leakage inductance will be difficult with a mains
frequency iron core transformer.
But if you ask me if I believe the k value of .999883 is *accurate* to 3
significant digits, that's another question. The OP didn't ask that; he
just asked how I got "such a precise number", and I wanted to be sure that
he understood that .999883 is not *precise* to 6 digits.
Trying to get repeatable measurements from a mains frequency iron core
transformer is not easy. I find that if I just try to measure the
self-inductance of a winding at 60 Hz and some excitation level, the
reading will drift for many minutes, sometimes taking 5 minutes or more
before the measurement is stable to 3 digits. Apparently the initial
transient of connecting the meter tweaks the core and it takes a while to
relax, and if the transformer has just been connected to line power, it can
take even longer!
I mentioned that flux density at the excitation level of the measurement,
temperature and magnetic history of the core could affect measured k. How
much would depend on the particular transformer, of course.
The 1943 book I refer to in the earlier thread says it well (about a method
for measuring leakage inductance):
"...this method is inherently inaccurate when used with *measured* values
of the self- and mutual inductances of iron-core transformers. The leakage
inductance of one winding of such a transformer often may be as small as
0.2 per cent of its self-inductance. For example, if the self-inductance
of winding 1 is 10 henries, its leakage inductance may be about 0.02 henry.
If the value of the leakage inductance is to be determined from Eq. 91, to
the nearest millihenry--or within about 5 per cent of its true value--the
value of the self-inductance must measured to the nearest millihenry, or
within 0.01 per cent of its true value, and the mutual inductance must be
measured with the same per cent accuracy. Such precise measurements are
impossible with iron-core transformers."
