# Frequency-variable inductance in LTSpice

#### FuseFuse

Joined Feb 8, 2017
20
Good afternoon,

I'm working on LTSpice modelling of frequency-dependent inductors, in order to simulate their common mode behavior. I attached an example: it is impedance magnitude of a common mode inductor and, as you can see, just above 100 kHz there's a slope change, i.e. a frequency-dependant nominal inductance.
I can't create an equivalent circuit that fits this curve. Stray parameters allow me to reproduce impedance resonance at about 3 MHz, but not slope changes.
Is it possible to fit it with a frequency-dependant inductor?
I read in the past that it's not recommended to use them in LTSpice, but I don't know the reason.
If not what would you suggest to use instead?

Thank you all.

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#### Papabravo

Joined Feb 24, 2006
18,126
I may be out to lunch on this, but if I had to make a guess, it would involve the concept of modeling an inherently non-linear circuit by using small changes around an operating point. As you may know there is a vast array of analysis and design tools that can be applied to linear systems. Non-linear systems present a range of difficulties and the methods of design and analysis fall more than a bit short. A wise control engineer once asked: "are there any good non-linearities in a control system?". The answer was that for practical purposes, there are none.

What we are left with are a small number of well understood special cases where particular non-linear elements have a definite purpose, but they are generally absent in control systems.

#### eetech00

Joined Jun 8, 2013
3,110
Good afternoon,

I'm working on LTSpice modelling of frequency-dependent inductors, in order to simulate their common mode behavior. I attached an example: it is impedance magnitude of a common mode inductor and, as you can see, just above 100 kHz there's a slope change, i.e. a frequency-dependant nominal inductance.
I can't create an equivalent circuit that fits this curve. Stray parameters allow me to reproduce impedance resonance at about 3 MHz, but not slope changes.
Is it possible to fit it with a frequency-dependant inductor?
I read in the past that it's not recommended to use them in LTSpice, but I don't know the reason.
If not what would you suggest to use instead?

Thank you all.
Take a look at this link:
https://www.seventransistorlabs.com/Calc/Coilcraft1.html

#### Alec_t

Joined Sep 17, 2013
12,744
Is it possible to fit it with a frequency-dependant inductor?
I read in the past that it's not recommended to use them in LTSpice, but I don't know the reason.
I'm just guessing, but the LTS Help does say that the modelling of inductors uses a proprietary method. So without knowing the magic, a non-LTS method might conflict with that?

#### FuseFuse

Joined Feb 8, 2017
20
I may be out to lunch on this, but if I had to make a guess, it would involve the concept of modeling an inherently non-linear circuit by using small changes around an operating point. As you may know there is a vast array of analysis and design tools that can be applied to linear systems. Non-linear systems present a range of difficulties and the methods of design and analysis fall more than a bit short. A wise control engineer once asked: "are there any good non-linearities in a control system?". The answer was that for practical purposes, there are none.

What we are left with are a small number of well understood special cases where particular non-linear elements have a definite purpose, but they are generally absent in control systems.
Modelling around an operating point is not sufficient for the scope of modelling in a "wide" frequency range of several decades, as ones of common mode inductors. I'm thinking of defining different inductive values for different frequency ranges, as below:
L = 5 mH for 10 kHz < f < 100 kHz
L = 3 mH for 100 kHz < f < 1 MHz
L = 1 mH for 1 MHz < f < 10 MHz

The way how I can define such a function is unknown to me actually...

#### Papabravo

Joined Feb 24, 2006
18,126
Modelling around an operating point is not sufficient for the scope of modelling in a "wide" frequency range of several decades, as ones of common mode inductors. I'm thinking of defining different inductive values for different frequency ranges, as below:
L = 5 mH for 10 kHz < f < 100 kHz
L = 3 mH for 100 kHz < f < 1 MHz
L = 1 mH for 1 MHz < f < 10 MHz

The way how I can define such a function is unknown to me actually...
It is hard to imagine the usefulness of an inductor with discontinuous steps in inductance, especially since the graph in your original post looks smooth and continuous. I think you are wrong about modeling around an operating point over a wide frequency range.

#### LvW

Joined Jun 13, 2013
1,428
It is hard to imagine the usefulness of an inductor with discontinuous steps in inductance, especially since the graph in your original post looks smooth and continuous. I think you are wrong about modeling around an operating point over a wide frequency range.
Perhaps I am wrong, but what I see in the graph is an IMPEDANCE (given in Ohms) which does not necessarily is caused by a "variable inductance". To me it shows the frequency-dependent impedance of an inductory part (or circuit) - caused by frequency dependent losses (resistive/capacitive).

#### Papabravo

Joined Feb 24, 2006
18,126
Perhaps I am wrong, but what I see in the graph is an IMPEDANCE (given in Ohms) which does not necessarily is caused by a "variable inductance". To me it shows the frequency-dependent impedance of an inductory part (or circuit) - caused by frequency dependent losses (resistive/capacitive).
I don't think you are wrong at all. If you have ever swept an inductor with a VNA you have no doubt observed that the impedance will orbit the origin, sometimes inductive, sometimes capacitive.

#### FuseFuse

Joined Feb 8, 2017
20
Perhaps I am wrong, but what I see in the graph is an IMPEDANCE (given in Ohms) which does not necessarily is caused by a "variable inductance". To me it shows the frequency-dependent impedance of an inductory part (or circuit) - caused by frequency dependent losses (resistive/capacitive).
Hello,

this interpretation is quite new to me. A capacitive effect is responsible for a resonance in the Z(f) spectrum, whose intensity is related to a parasitic resistance. In such a case, from resonance frequency on there'll be a negative slope of Z vs f, that is a capacitive behavior (indeed!).
What we have here, instead, is a variance in the gradient of Z, which is still positive, i.e. its behavior is still inductive until resonance. By measuring core behavior, we can deduce this is mainly due to a variable magnetic permeability.

Now, apart from any attempt to create a "physically reliable" model, my goal is to reproduce this variable slope of Z in the inductive region of the spectrum, but basing on your replies I infer that a variable inductances can't be handled in LTspice.

Maybe the same result can be obtained by adding new circuit loops with (let me say) "fake" parasitic elements. We lose any adherence with reality but, on the other hand, LTSpice is not a suitable software to achieve this goal in any case.

Thank you

#### Bordodynov

Joined May 20, 2015
2,982
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#### LvW

Joined Jun 13, 2013
1,428
Hello,
this interpretation is quite new to me.
What I see is a graph that displays Z(Ohm) vs. frequency.
Is there any room for a "new interpretation"?
The only statement I have made is that I see a frequency-dependent impedance - and NOT an inductance.

#### Papabravo

Joined Feb 24, 2006
18,126
What I see is a graph that displays Z(Ohm) vs. frequency.
Is there any room for a "new interpretation"?
The only statement I have made is that I see a frequency-dependent impedance - and NOT an inductance.
An ideal inductor would be incapable of producing that particular graph because it has no parasitic elements. The parasitic elements modify the "value" of an inductor in such a way that an ideal inductor is transformed into something else with a value of implied inductance that is different from the ideal case. What's not to like about that?

I think the original question revolved around the idea of perhaps creating an arbitrary variation of inductance with respect to frequency, and that I think will be difficult with passive components. For example, creating an inductor with a high inductance at low frequency and a low inductance at high frequency will be impossible.

#### FuseFuse

Joined Feb 8, 2017
20
Hi,
this is exactly what I was referring to. By putting a parasitic parallel capacitance you create a resonance. I don't see any variance in the slope of the inductive region

#### FuseFuse

Joined Feb 8, 2017
20
An ideal inductor would be incapable of producing that particular graph because it has no parasitic elements. The parasitic elements modify the "value" of an inductor in such a way that an ideal inductor is transformed into something else with a value of implied inductance that is different from the ideal case. What's not to like about that?

I think the original question revolved around the idea of perhaps creating an arbitrary variation of inductance with respect to frequency, and that I think will be difficult with passive components. For example, creating an inductor with a high inductance at low frequency and a low inductance at high frequency will be impossible.
I'm confused. Magnetic permeability is not constant throughout the spectrum; it "stops working" from the cut-off frequency on but it's not constant before the cutoff, i.e. it's not a "Heaviside-like" function.
My prime suspect is magnetic permeability behavior. Don't you think?

#### Papabravo

Joined Feb 24, 2006
18,126
I'm confused. Magnetic permeability is not constant throughout the spectrum; it "stops working" from the cut-off frequency on but it's not constant before the cutoff, i.e. it's not a "Heaviside-like" function.
My prime suspect is magnetic permeability behavior. Don't you think?
From a modeling perspective I don't think permeability is even a factor in the inductor model. In constructing an actual inductor from a core it is of course a primary consideration. Once the inductor is constructed and an inductance is assigned it is only the parasitic elements that remain. It is the case that inductance modeling is not an open algorithm for LTspice in particular. I don't know about other packages. I do know that Alex ( @Bordodynov ), in his transformer library allows the construction of transformer cores with a more flexible set of parameters than is achievable with the coupling coefficient approach. I have not worked with his elements extensively however.

http://bordodynov.ltwiki.org/

Scroll down to the bottom of the page

#### Alec_t

Joined Sep 17, 2013
12,744
From a modeling perspective I don't think permeability is even a factor in the inductor model.
According to the LTS Help, re inductor modelling :
"L. Inductor
There are two forms of non-linear inductors available in LTspice."
Both forms involve magnetic flux, hence permeability.

#### Papabravo

Joined Feb 24, 2006
18,126
According to the LTS Help, re inductor modelling :
"L. Inductor
There are two forms of non-linear inductors available in LTspice."
Both forms involve magnetic flux, hence permeability.
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.

#### LvW

Joined Jun 13, 2013
1,428
The original question was about frequency variable inductance.
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) ?

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#### Bordodynov

Joined May 20, 2015
2,982
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