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Measuring transformer and coupled inductor parameters
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Doc ID 17273 Rev 1
Appendix B
Measuring transformer and coupled inductor
parameters
parameters
From a practical point of view there is the need to measure the parameters of coupled
inductors (transformers) L
inductors (transformers) L
1
, L
2
and M or, equivalently, k, and derive those of the equivalent
circuits. Needless to say that it is of particular interest to obtain the parameters of the
“physical model” with a = n, L
“physical model” with a = n, L
M
, L
l1
and L
l2
.
L
1
and L
2
are directly measurable. To determine M or k appropriate measurements need to
be done. The best way to proceed is to use a Z-meter, taking the measurements at a low
enough frequency that the parasitic capacitance of the windings can be neglected. There
are two basic methods to completely characterize a coupled inductor or a transformer from
the electrical point of view: the open/short-circuit inductance (OS) method and the series-
aiding/opposing inductance (AO) method.
enough frequency that the parasitic capacitance of the windings can be neglected. There
are two basic methods to completely characterize a coupled inductor or a transformer from
the electrical point of view: the open/short-circuit inductance (OS) method and the series-
aiding/opposing inductance (AO) method.
According to the OS method, three measurements are taken:
●
The primary inductance with the secondary open (L
1
)
●
The primary inductance with the secondary shorted (L
1s
)
●
The secondary inductance with the primary open (L
2
).
Through inspection of
it is very easy to derive the coupling coefficient from the L
1s
measurement:
Equation 30
M is determined using (A2):
Equation 31
Measuring L
1s
accurately might be an issue, and so this method is suitable when k is close
to unity. It is not recommended when the winding resistance is not negligible.
The AO method is based on the fact that by connecting the two windings in series their
combined inductance is given by L
combined inductance is given by L
1
+ L
2
± 2M, where the sign given to 2M depends on the
way the windings are connected, as shown in
. The difference of the two values is
thereby equal to 4M.
According to the AO method, four measurements are taken:
●
The primary inductance with the secondary open (L
1
)
●
The secondary inductance with the primary open (L
2
)
●
The combined inductance with series-aiding connection (L
A
)
●
The combined inductance with series-opposing connection (L
O
).
(
)
1
s
1
2
1
s
1
L
L
1
k
k
1
L
L
−
=
⇒
−
=
2
1
L
L
k
M
=