resolver modeling and negative leakage inductance.

hi.
I want to know a relationship between resolver impedance and theta.
so i am making resolve model.
i am facing problem in variable reluctance resolver modeling.
(I am trying to make Variable reluctance resolver model using matlab.)

i am supposed that the theta is 0 degree.
so the resolver is work as three-winding transformer.
the transformer ratio is 1:0.286

the problem is that the resolver's primary leak inductance is negative.
what is the meaning of negative leakage inductance in transformer?

(when i measurement reslover's leakage inductance, i refered to 'Dual Three-Winding Transformer Equivalent' paper)

the problem is that the resolver's primary leak inductance is negative.

Click to expand...

Negative coupling factor? Try to invert one winding polarity.

Thanks. i will try to check resolver polarity.

and...

is there any correlation between winding polarity and leakage inductance?

when i measurement resolve's leakage inductance, i knew leakage inductance from equation. not a LCR meter.

leakage inductance is measured this step
(Ll1 : primary leakage inductance, Lm : magnetizing inductance, Ll2 : secondary leakage inductance, Ll3 : tertiary leakage inductance)
1. LCR meter connected primary port, and secondary, tertiary ports are opened. --> we can get Ll1+Lm inductance.
2. LCR meter connected primary port, and secondary short, tertiary open. --> we can get Ll1 + Ll2 inductance.
3. LCR meter connected secondary port. and primary open, tertiary open. --> we can get Ll2 + Lm inductance.
3. LCR meter connected secondary, and primary open, tertiary open. --> we can get Ll2 + Ll3 inductance.

4 variables and 4 equations. so i can know Lm, Ll1, Ll2, Ll3.
following this equations, Ll1 (primary leakage inductance) has negative value.

Is there any problem?

You better show the used equivalent circuit for clarification. The calculation of shorted cases is obviously incorrect because it ignores Lm. The assumption Lm >> Llx is probably inappropriate.

I also thought about the winding polarity problem and found that the simple open/short inductance measurement method can't reveal winding polarity. Thus I think the physical implausible negative Llx values are either a result of wrong calculation or an incomplete model.

To measure all coupled inductor parameters, I would suggest a self-/mutual inductance matrix model. Inject a current into one winding, measure the induced voltage at all windings.