# Evaluation of the primary inductance of a transformer whose core is saturated

I would like to know if it is possible to theoretically estimate reasonably the primary inductance of a transformer when its core is saturated.

Otherwise, what is the best way to do it by measurement?

• There will probably be more rigorous answers so this keeps to being a comment .If the core is totally saturated it becomes fresh air .This is how my late research job superviser explained this to me in 1986 .So remove the core and measure the inductance expecting a low value .Such a value could make your PSU blow up . Commented Feb 6, 2020 at 9:55
• I would say for a saturated transformer, you close the switch on the leakage inductance plus the primary inductance wound on "fresh" air as pointed out by Autistic. Please have a look at what I proposed here: electronics.stackexchange.com/questions/328384/… The sudden change in the current slope when saturating gives you the inductance seen from the primary side. Commented Feb 6, 2020 at 10:05

When an inductor is not saturating, the inductance is constant because magnetic permeability is constant. This applies when applying an AC waveform or applying a moderate AC waveform superimposed on some moderate level of DC current. If the core is not saturating the inductance measured (or predicted) is constant.

If the core is saturating then there are two scenarios to consider: -

1. The AC excitation is producing peaks in the magnetic flux that are flattened out due to core saturation
2. The AC excitation is small but there is a superimposed DC current that is causing saturation positively or negatively.

In the first of those scenarios, it makes no sense to calculate (or estimate) inductance because inductance (as a numerical value) has no real meaning anymore. It has no real meaning because it is changing throughout the cycle of the applied AC waveform because permeability is changing.

In the 2nd scenario there is some merit in estimating inductance because the AC excitation is "moderate" and, it may be assumed that at its biased point on the BH curve, the permeability is fairly constant. This sort of circuit can be used to re-tune oscillators and also be used in what were called "magnetic amplifiers" (or saturable reactors).

I would like to know if it is possible to theoretically estimate reasonably the primary inductance of a transformer when its core is saturated ?

The most practical and certain method is to look at the data sheet of the core material and extract the BH curve. Then, using the DC current value and number of turns and core dimension $$\\ell\$$, calculate H (magnetic field strength) and position that H value on the BH curve and extract the permeability value. Using other core dimensions you can extract inductance.

• Thank you again Andy Aka for your explanation ! Really nice to you :D I will take a look of the BH curve ! I am exactly in the second case. I have a formula for calculating the inductance of solenoid but the formula has been obtained by doing a lot of approximation … If you have a better way for estimate the inductance It would be nice :D I think I can find this information on internet :D
– Jess
Commented Feb 6, 2020 at 11:13
• The devil's in the detail with inductors but, if you get a chance post images and tech details of the solenoid and maybe ask a new question. Commented Feb 6, 2020 at 11:16