# Frequency-variable inductance in LTSpice

#### FuseFuse

Joined Feb 8, 2017
37
Yes - that was the original question.
However, what has the OP shown to us? A graph with IMPEDANCE vs. frequency (and NOT inductance vs. frequency).
Therefore, I am not sure if the OP really has a frequency-dependent inductance in his mind.
I rather think, he needs a certain combination of an ideal inductance with some additional - also frequency-dependent - parts resulting in an impedance function as shown in the graph.

More than that: What is the meaning of " common mode behavior " of an inductor (see start of this thread) ?
Good afternoon.

As you may know, attenuation provided by a filter (as a inductor) can be divided in a common-mode and a differential-mode contribution. Common mode choke are designed in order to provide as much common mode attenuation as possible.

My idea is that, referring to the graph I shared, at such low frequencies only an inductive behaviour can be taken into account. Therefore my suspect is that such behaviour is associated to magnetic permeability of the core used to extract this Z vs. f measurement.

Speaking in general, my goal is to "reproduce" this part of the curve where the slope is variable. First idea is to search for any possible physical effect that can be responsible of that but, at the end of the day, any trick that allows me to reproduce the curve is welcome

Thanks for your replies.

#### FuseFuse

Joined Feb 8, 2017
37
The original question was about frequency variable inductance. Using flux and permeability for this purpose seems to be of limited utility. If I am not mistaken what the TS wants is an inductor L, with an inductance that is a function of frequency, such that:

$$v(t,\omega)\;=\;L(\omega)\cfrac{di}{dt}$$

and

$$X_L\;=\;\omega L(\omega)$$

I could be wrong, but finding a closed form solution to the differential equation for such and inductor, might be a heavy lift.
To a 1st approximation, the inductance of an inductor with a toroidal shape (as the one where the graph is extracted from) is linearly proportional to magnetic permeability as follows:

A nanocrystalline core has a magnetic permeability that varies as below (where the blue curve is the real part, the orange one is the imaginary part)

Therefore I do have to expect for an influence of this parameter on Z vs f curve.

What is your opinion?