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I'm trying to find a decay equation that I can use with the genfit function but can't seem to find anything that fits. I'm try to generate a function of alternating flux density vs incremental permeability for various DC Magnetization levels.
My question is twofold:
How can I generate a function that will fit the data for a single DC magnetization (Hdc) level?
Can I generate a function that will find incremental permeability at any Hdc and any alternating flux density?
I've included a file for review.
Thank you in advance for your help
Sergio Kraljic, Jr.
Curve Expert came back with a Gaussian, not great.
Might find a Weibull function.
Never heard of a Weibull function, but I'll look into it -- I'm not a mathemetician, just an engineer
Interestingly enough, the curve looks similar to Planck's radiation law, but unfortunately I couldn't adapt it to my particular application -- the constants were crazy.
Thanks for looking into this.
I think you might try the gamma probability (not the gamma function alone) and the log-normal probability distribution functions as well. You can get good starting estimates of the two parameters in the distributions by calculating the mean and variance of the data. The horizontal and vertical values will have to be scaled to your data, so that adds two parameters.
Message was edited by: Harvey Hensley
The attached shows reasonable (?) fits to individual curves, but I haven't attempted to develop the fits as a function of Hdc.
Alan
Alan --
The curves look great! Thank you...btw how & where did you come up with this function? I looked everywhere in my math references and couldn't find anything that would work as well as what you provided.
Sergio Kraljic Jr. wrote:
Alan --
The curves look great! Thank you...btw how & where did you come up with this function? I looked everywhere in my math references and couldn't find anything that would work as well as what you provided.
It's just the sum of two generalised Weibull-type curves - generalised by flinging six fitting constants at them! Not that clever really! I was hoping the constants would each be a simple function of Hdc, but I was unable to find one. This means the fits aren't much use for interpolating on Hdc. They're probably ok for interpolating on B, but, given their arbitrary nature, I suggest you don't extrapolate with them.
BTW what is the physical system they represent?
Alan
These curves represent the permeability of a magnetic material (electrical grade steel, ferrite, powdered metal, etc) under both applied AC & DC magnetization. Permeability (u) is a dimensionless number that is the ratio of magnetic flux density (B) to magnetic field intensity (H) referenced to that of air (u0). This number is typically very high, on the order of 5000 to 25000 with an induced AC magnetic field. However, when DC is applied, the AC permeability drops as a function of Hdc.
This is important because the inductance value of a DC choke is inversely proportional to the permeability value. The lower the value, the greater negative impact that it has on the inductance value. The goal of designiing an inductor with DC magnetization is to minimize the negative effect of a low permeability condition.
Wikipedia has a good discussion on magnetic materials, inductors, and dc choke.
Again, thank you for your help!
I tried the Gamma and Weibull distributions and they didn't work well. I also tried a polynomial with 6 terms (5th order) and it worked as well as the function Alan provided...in the region of the data. However, as expected, the polynomial didn't continue to decay for B > 2. Thus, if prediction beyond B = 2 is needed, Alan's function is the best.