Can anyone help with this knotty annoying problem...

I wanted to make a 50Hz current transformer (CT) to measure the input
current waveform to a SMPSU.  I took a small cheap transformer from a wall
mounted PSU of about 6VA rating, and stripped off all the secondary winding
replacing this with one turn of thick wire to form the primary of teh CT.
The old 240V winding had a DC resistance of around 1k, but this should ( ??)
be irrelevant to CT operation


The one turn generated about 0.3V RMS from a 240V input, although after some
prolonged testing as a CT, I realised I had got the turns calculation some
way out, but thats by-the-way, (it was actually nearer 5000 than 4000).
That suggested the turns ratio as approximately 4000 turns on the 240V mains
winding.  So for a first test, I used a 4k burden resistor with the
intention of obtaining a resultant voltage output of 1Volt / Amp of primary
current.  That way,  with at the most 10V across it(corresponding to 10A
input) the core must surely be way below saturation so should give good
linearity - shouldn't it !!!.

BUT, and I don't know how to account for it,  there was a very significant
non-linearity .  Testing over a range of currents from 0.2A RMS to 9A, the
slope of the  Vout / Iin graph shifted by nearly a factor of 2.

That says 'core saturation' to me,  but I don't see how that can be.   If
the core is saturating with just 9V across a winding designed for 240V, it
doesn't say a lot for the device in a PSU.   Should reducing the value of
the  burden resistor help matters?

Can anyone shed any light on this?   I want a good linear current
transformer that will work to 13A RMS that can be used for signal analysis
of the current and voltage waveforms by feeding into an A/D and calculating
what's really happening when fed with typical mains supply inputs.  I don't
want to use a massive transformer if that is not essential!

Andy  G4JNT