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# Measuring Bs, Br and Hc of an Inductor Iron Core

#### Kerim

##### Member
I guess those who use the LTspice simulator are familiar with the three parameters of the non-linear inductor model (by John Chan) :
Bs, saturation flux.
Br, saturation remanent flux.
Hc, coercive force

Let us suppose we have an inductor whose core is iron (actually, the primary or the secondary of a transformer rated to a few KWs). Its iron laminations are of unknown type (shape E & I).
How, in your opinion, measuring its 3 parameters (at least approximately) could be done, speaking practically, by using a scope?

Thank you.
Kerim

Note:
Lately, I found a rather simple way to measure these 3 parameters by plotting first the voltage and current (50 Hz) of the inductor under test on a scope. Then, I apply 3 formulas, one for each. The mechanical parameters are supposed being known.
But I am afraid that perhaps I just re-invented the wheel

#### Papabravo

##### Well-Known Member
In LTspice you can construct a simulation and use behavioral sources to measure quantities that depend on other things. For example, you can certainly model non-linear inductors in this fashion.

#### Kerim

##### Member
In LTspice you can construct a simulation and use behavioral sources to measure quantities that depend on other things. For example, you can certainly model non-linear inductors in this fashion.

Do you mean how to measure the three parameters, Bs, Br and Hc, of a real non-linear inductor is explained on that ebook?
Thank you anyway.

#### Tony Stewart

##### Well-Known Member
Do you mean how to measure the three parameters, Bs, Br and Hc, of a real non-linear inductor is explained on that ebook?
Thank you anyway.
It’s not free

#### Papabravo

##### Well-Known Member
Do you mean how to measure the three parameters, Bs, Br and Hc, of a real non-linear inductor is explained on that ebook?
Thank you anyway.
The book is only free if you have an unlimited kindle subscription. I don't have that, and I purchased the paperback copy. It does indeed show you how to model, simulate, and use nonlinear inductors. There are some videos that cover portions of the material. The book and the videos also have a number of python scripts that are useful in analyzing materials that you might use to construct a variety of inductors and transformers., as well as an interesting method of digitizing curves from datasheets. I certainly thought it was worth the money from a purely academic point of view.

You can do engineering on the cheap if you have the requisite intellectual capacity for that work. I prefer to stand on the shoulders of giants at a small incremental cost even though I am a retired senior citizen on a fixed income.

This should get you started:

Here is an example of simulating a nonlinear reluctance

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#### Kerim

##### Member
It’s not free
The book is only free if you have an unlimited kindle subscription. I don't have that, and I purchased the paperback copy. It does indeed show you how to model, simulate, and use nonlinear inductors. There are some videos that cover portions of the material. The book and the videos also have a number of python scripts that are useful in analyzing materials that you might use to construct a variety of inductors and transformers., as well as an interesting method of digitizing curves from datasheets. I certainly thought it was worth the money from a purely academic point of view.

You can do engineering on the cheap if you have the requisite intellectual capacity for that work. I prefer to stand on the shoulders of giants at a small incremental cost even though I am a retired senior citizen on a fixed income.

I don't have any more the privilege to get certain books (for free or not), besides many other things, due to world's regulations. This was possible in the golden years, before year 2011 (better, before year 2001).
So, I may say that I am fortunate in re-inventing the wheel which I am not allowed to get

Do you think it is worth to explain my simple procedure (and its theory) here about how to measure and calculate those three parameters of an unknown non-linear iron core so that it could be simulated when necessary?

I mean since such information, as you said, is available already to almost all members here (including you both), I guess there will be no interest in reading what I will write about this subject in details
I said this while I doubt that someone here can explain, even briefly, how he measured those parameters (mainly Bs) in real... because just reading and hearing is not like doing

Kerim

#### Papabravo

##### Well-Known Member
I'm not sure what regulations you might be speaking of. Were you able to access the video link I mentioned in post #5? There are about a dozen of them in the entire series. This is an open forum, and you can explain anything that you want to explain.

#### Kerim

##### Member
I'm not sure what regulations you might be speaking of.
This doesn't surprise me. I understand that there is no way for you to hear about them.
They are political regulations and started since early 80's and have been upgraded till these days. They were made against the people among whom I was born and live... Why? Only the powerful rich World's Elite know

Were you able to access the video link I mentioned in post #5? There are about a dozen of them in the entire series.
Our internet server is relatively slow to watch videos.
I have the impression, from reading the title, that the suggested video is about simulation, not how to get the three parameters from plotting the voltage and current of a coil on the scope's screen and calculate them from these plots.
Please confirm that my impression is wrong so that it would be better for me to access the video even at a slow rate.

#### Papabravo

##### Well-Known Member
I believe it is wrong, since the simulation and the python scripts are intended to allow the measurement and display of those quantities. While not specifically addressing iron cores they do a fine job on ferrite cores which are certainly similar. More importantly they describe how to use behavioral sources to simulate and measure nonlinear components. You are free to believe whatever you want to believe. It is a matter of little concern to me.

#### Kerim

##### Member
I believe it is wrong, since the simulation and the python scripts are intended to allow the measurement and display of those quantities. While not specifically addressing iron cores they do a fine job on ferrite cores which are certainly similar. More importantly they describe how to use behavioral sources to simulate and measure nonlinear components. You are free to believe whatever you want to believe. It is a matter of little concern to me.

Thank you for your care, I do appreciate it.

But I am afraid that we actually walk on the two sides of a river, not on the same one.
So, I will try to be clearer as possible by being more specific.

I just wonder if there will be, on the suggested video, a real scope (likely a digital one, to freeze the plots of v(t) and i(t) of one complete cycle) in a test which has nothing to do with what a simulator can do. The test just gives values read from the plots (displayed on the scope's screen) by which the three parameters (Bs, Br and Hc) could be derived.

For instance, to prove, to myself in the least, that my three formulas are somehow valid, speaking practically (because the small resistance of the coil is assumed to be 0), I tested them also on LTspice by using a set of '.meas' commands (to get the needed values from the displayed traces and substitute them in the three formulas). The errors turned out being 1 to 2% which is not bad for a simple fast real test.

Anyway, perhaps my English is not good enough to communicate with others about certain specific subjects (as the one here ) If this is the case, I am sorry for wasting your time.

#### Tony Stewart

##### Well-Known Member
I have never tried this but Inductive impedance may be measured in a bridge with a reference value or compared to resistance with equal AC voltage drops and shared current.
1. Measure the inductance of the coil:
2. Apply a magnetic field to the inductor by passing a DC current through the coil. The current can be gradually increased until the magnetic field saturates the iron core. The plateau voltage is proportional to the saturation flux density (Bs).
3. (Br): the scope can be used to measure the voltage across the coil as the magnetic field decays to zero. The voltage measured at zero magnetic field is proportional to the remanent flux density (Br).
4. Measure the coercive force (Hc): The coercive force (Hc) is the amount of magnetic field strength required to demagnetize the iron core after saturating the iron, the magnetic field can be gradually decreased until the core is fully demagnetized. The voltage across the coil can be measured using a scope during this process is proportional to the coercive force (Hc).

#### Tony Stewart

##### Well-Known Member
Bye the bye you can get almost any information free on the internet with a few clues like Google Scholar, archive.org books with expired patents, regulations for free in India and of course 1337x site and the darkweb that I have never tried.

#### Papabravo

##### Well-Known Member
I once had a mad friend who opined that: "there is something about every system that sucks". This comment was in reference to time-sharing operating systems. I think it may have much wider, and perhaps universal application.

#### Kerim

##### Member
I have never tried this but Inductive impedance may be measured in a bridge with a reference value or compared to resistance with equal AC voltage drops and shared current.
1. Measure the inductance of the coil:
2. Apply a magnetic field to the inductor by passing a DC current through the coil. The current can be gradually increased until the magnetic field saturates the iron core. The plateau voltage is proportional to the saturation flux density (Bs).
3. (Br): the scope can be used to measure the voltage across the coil as the magnetic field decays to zero. The voltage measured at zero magnetic field is proportional to the remanent flux density (Br).
4. Measure the coercive force (Hc): The coercive force (Hc) is the amount of magnetic field strength required to demagnetize the iron core after saturating the iron, the magnetic field can be gradually decreased until the core is fully demagnetized. The voltage across the coil can be measured using a scope during this process is proportional to the coercive force (Hc).

What you kindly explained is indeed informative. I just don't see any formula

#### Kerim

##### Member
Bye the bye you can get almost any information free on the internet with a few clues like Google Scholar, archive.org books with expired patents, regulations for free in India and of course 1337x site and the darkweb that I have never tried.

I believe what you say is true on your side.

I may be imagining things, but I realized, based on many personal observations, that all communications on the internet that are offered (almost for free) to the ordinary peoples around the world (so-called free or not) are under control very well. So, I don't play the smart on the internet like trying to be invisible (as in movies). I simply 'shake off the dust of my feet' anytime I face a close door.

On the other hand, I don't believe there is a real free offer (information or else) unless it is among real friends or perhaps between parents and their beloved children. At best, some programs in progress, for example, could be offered for free as a way to discover their bugs faster (there are other reasons and other examples, but it is better not to enter such forests ).

Anyway, you won't see me complaining about anything (I may just present facts, I lived, nothing more). I simply let 'the dead bury their dead'.

#### Kerim

##### Member
I am almost sure that the exact test (not on a simulator), I am talking about, that uses a scope to measure the 3 parameters Bs, Br and Hc of a non-linear iron core, cannot be found on any book or on the internet. But perhaps I am wrong because I can’t get many scientific books and I can’t access many scientific websites as well.
Anyway, you will know if my impression is right or wrong after reading what I will present on thos post.

The LTspice schematic below is a replica of a test on an inductor (L1) whose core is unknown. On the schematic, the mechanical parameters of L1 are set. The 3 parameters of its BH loop are also set. They were derived earlier, by a real test, from the v(t) and i(t) traces (on and in the inductor of interest) that were displayed on the screen of a digital scope.

After running the simulation, the various ‘.meas’ commands (see param_NL_core_07.txt) which get the needed values from the traces V(LL) and I(L1) (now on the LTspice window), also apply the formulas of Bs, Br and Hc (see below) to give the result’s errors (in percentage format).
Br_err% = -0.203454%
Hc_err% = 0.0533104%
Bs_err%= -1.53767%

Only 4 points on the scope’s screen need to be read (as absolute values):
V_max
V_I0 when i(t)=0
I_max when v(t)=0, the flux B is at its highest value.
I_B0 when v(t)=V_max, the flux B is zero

To simplify the end formulas, constants are defined as follows:
Kh = N/Lm
Kb = 1/N/A
Where:
N = the number of turns
Lm = the Magnetic Length (excl. gap), in meter.
A = the Cross-sectional area of the core, in m2

Also:
wt0 = arcsin(V_I0/V_max)
w = 2*pi*F

Br = Kb * Vmax / w * cos(wt0) [Tesla]
Hc = Kh * I_B0 [A/m]

Two more constants are defined for the Bs formula:
Mh = Kh*I_max + Hc
Mb = Kb*V_max/w-1.25664E-06*Kh*I_max

Bs = (Mh-Hc)/(Mh/Mb-Hc/Br) [Tesla]

There is one more question to discuss.
Which is the ‘practical’ value of I_max that lets the calculated Bs be close to its real value?
I compared I_max with three values of i(t):
Irms, abs(Iavg) of a half cycle and I_B0.
I chose the latter one, I_B0, because its sensitivity to I_max is the smallest.
In general, the practical ratio, I_max / I_B0, is around 3.5.

Kerim

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#### Tony Stewart

##### Well-Known Member
On the other hand, I don't believe there is a real free offer (information or else) unless it is among real friends or perhaps between parents and their beloved children. At best, some programs in progress, for example, could be offered for free as a way to discover their bugs faster (there are other reasons and other examples, but it is better not to enter such forests ).

Anyway, you won't see me complaining about anything (I may just present facts, I lived, nothing more). I simply let 'the dead bury their dead'.
KODI is widespread globally but STREMIO is easier to use. I don't need a VPN in Canada or where you are, but one does need to save a download if your bandwidth is slow. Other media does not need hiding or a pass thru a paywall

#### Kerim

##### Member
So far, I didn't get any sign that what I presented on my previous post could also be known from any other source

But I also understand that most people (including engineers) used not to accept something being true if not approved first by those who are supposed to represent 'Science', in every period of time.

In fact, only in very rare occasions, I was able to talk to a humble professional engineer who is pleased to discuss and decide what could be right/useful, or not, based solely on his own experiences/observations and analyses (as I do).

Cheers,
Kerim

#### Kerim

##### Member
KODI is widespread globally but STREMIO is easier to use. I don't need a VPN in Canada or where you are, but one does need to save a download if your bandwidth is slow. Other media does not need hiding or a pass thru a paywall

What could I add?
We simply live in two totally different worlds though we are on the same planet. And this applies on many things, besides internet.
By the way, this forum is one of the rare forums I was accepted to join it. And I try my best to avoid being very sincere when asked (as I am in any 'private' conversation and no matter to whom I talk), otherwise, one of the moderators will have no choice but to ban me

#### Tony Stewart

##### Well-Known Member
I read your Gov't pulled the plug on the interweb in 2011 and so your access is extremely limited still. Sorry for your losses. You have many skills to share the world. Stackexchange is more popular but primitive micro-manager in its moderation, I guess is nothing compared to the syrian electronic po1ice.

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