STMicroelectronics A 200 W ripple-free input current PFC pre-regulator with the L6563S EVL6563S-200ZRC EVL6563S-200ZRC Data Sheet

   

   

   

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 Doc ID 17273 Rev 1

From a practical point of view there is the need to measure the parameters of coupled 
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

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.

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:

M is determined using (A2):

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

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

=