Effect of saturation on transformer inductance

[EEstudent90]

Hi all

How is the inductance affected when the transformer core has reached saturation? I can not seem to get my head around it, and I hope someone can help me understand it, thanks.

Kind wishes

 

[berkeman]

Hi all

How is the inductance affected when the transformer core has reached saturation? I can not seem to get my head around it, and I hope someone can help me understand it, thanks.

Kind wishes

Welcome to the PF.

What reading have you been doing so far? How is the hysteresis curve of B=μH related to your question?

 

[cnh1995]

Welcome to PF!

When the transformer reaches saturation, its magnetizing inductance seen by the voltage source decreases, which makes the magnetizing current spiky.
See if this helps.
https://www.physicsforums.com/posts/5384970/

 

[Baarken]

From wikipedia, saturation is the following:

Seen in some magnetic materials, saturation is the state reached when an increase in applied external magnetic field H cannot increase the magnetization of the material further, so the total magnetic flux density B more or less levels off.

So how does saturation affect the inductance of a transformer?

Let us start by introducing a few equations. Inductance [itex]L[/itex] is defined as

[itex]L = \frac{\phi}{I}[/itex] (1)​

where [itex]\phi[/itex] is the amount of flux inside the core and [itex]I[/itex] is the current. [itex]\phi[/itex] can also be written as

[itex]\phi = \frac{NI}{\mathcal{R}}[/itex] (2)​

where [itex]NI[/itex] is the number of turns multiplied with the current, also known as MMF (magnetomotive force) and [itex]\mathcal{R}[/itex] is the reluctance of the magnetic core. Reluctance can be thought to be similar to resistance as in an electrical circuit, see equation (2) which is analogous to Ohm's law but for magnetic circuits.

Reluctance can be written as

[itex]\mathcal{R} = \frac{l}{\mu _0 \mu _r A}[/itex] (3)​

where [itex]l[/itex] is length of the core, the product, [itex]\mu _0 \mu _r = \mu[/itex], is the permeability of the material and [itex]A[/itex] is the cross sectional area of the core, see figure below.

If we use equation (2) and plug it into equation (1) we get

[itex]L = \frac{N}{\mathcal{R}}[/itex] (4)​

and if we now put equation (3) into (4) we get

[itex]L = \frac{N}{l/(\mu _0 \mu _r A)} = \frac{N \mu _0 \mu _r A}{l} [/itex] (5)​

So how does this help us? If we look at equation (5) everything appear to be constants, but take a look at this picture (it’s commonly referred to as BH-curve, look it up if you are not familiar with it):

If I now tell you that the slope of these curves in the linear regions is equal to the permeability. So when we go into the saturation region, our slope becomes very small. If we now look back to equation (5) we can see that if our permeability (slope) decreases, our inductance also decreases. Look at the picture below to see how the magnetizing current of a transformer is affected when you enter the saturation region.

Did I answer your question? If not let me know.

EDIT: I should emphasize that it is the magnetizing inductance we are talking about.

 

[EEstudent90]

Thank you for the welcome :)

I am very new to this so I will have to look at all the replies carefully before I ask any new questions, thanks!