Frequency dependent target response

[Aziz]

Hi friends,

I have observed inaccurate (unstable) calculation results in my coil software.
So I have to check everything in the coil software. There must be a bug somewhere but I did not find it yet.
The error occurs if I calculate the TX inductance (very large compared to a wire loop of target) and the coupling coefficients to the small circular loop of target coils.
The coupling coefficients are not accurate enough to look at the eddy current distribution across a coin-like target.

This is important for looking at the eddy current distribution of the target model. So I cant go on until I have solved the problem.

Unfortunatelly I have to relearn the physics basics and look at the code. Or rewrite the part once again using other algorithms.

Anyway. We will see that we will face with the skin-effect and proximity effect. We will see, that the proximity effect and the skin effect will have the same source and will lead to the same result.

It will take some time. I need more accurate inductance, mutual inductance and coupling coefficient calculations.

Cheers
Aziz

[Aziz]

Hi all,

Ok, I have found a way to solve the problem using the other way instead of looking for the software bug.
I will rewrite the code portion using the induction formula, in which the bug does not happen (its a different function).

Above is the formula for calculating the coil coupling coefficient k between two coils. L1, L2 is the inductance of the coils, U1 is the self induction voltage of L1, U2 is the induced voltage in L2 due to current flowing thru the coil L1. I can calculate L1, L2, U1 and U2. K is then trivial.

k = U2 / (U1*sqrt(L2/L1))

This way I get more accurate results with no bug happening.
I should be able to get the coil coupling coefficients soon and we can continue here..

Cheers
Aziz

[Aziz]

Hi all,

I have implemented the code for calculating the coil coupling coefficients and mutual inductances the other way and it works stable and it is even faster than the old buggy way.

But I have been lost reading a lot interesting stuff in electrodynamics and magnetostatics.
I'm thinking of making the calculations more accurate and faster. Maybe later in time as this goes deep into the core functions. My gut feeling tells me, that there is an elegant way to do it.
Anyway. We can go on soon.

We should be able to inspect the eddy current induction, density distribution across the cross section of a coin like target and what the skin and proximity effect is doing with the eddy current distribution.

But give me more time..
Cheers
Aziz

[Aziz]

My gut feeling didn't disappoint me. I have found an interesting paper to increase the calculation accuracy of magnetic fields without significantly increasing the calculation time.

Title:
Compact expressions for the Biot–Savart fields of a filamentary segment. James D. Hanson; Steven P. Hirshman

Link:
https://scholar.google.com/citations...J:eQOLeE2rZwMC

Pdf:
https://citeseerx.ist.psu.edu/o?repi...98e33f72bdc909

This is a nice work with nice formulas .

Aziz

[Aziz]

Hi all,

I have found another open source site, which is based on the work previously mentioned.
Link: https://github.com/jonathanschilling/abscab

There are also interesting pdf papers. If you are wondering, where the c-code implementation is: it's in the interface (.h) files. No one would really do this, being called a software engineer.Ok, he isn't one and the physicist can not do good coding. Anyway.
Aziz

[Aziz]

Hi all,

I have great news for you.

I have implemented the formula 9 in the pdf publication mentioned earlier and made a numerical simulation test against the previous and standard Biot-Savart implementation. The accuracy of the magnetic field calculation for a relative large piece of wire element is really great (in my simulation example of 3 cm wire length). Even if I break down the piece of the wire element into 100 million parts. This is a big progress made by the guys of the publication.

I will implement and check formula 8 soon and will handle the observation points inside the wire element. Ampere's law is required for magnetic field calculation inside the wire elements as the physical wire has a diameter.

My coil software needs a big update so I can handle a lot of coils and much more mutual inductances. I will break down the target model into more finer circular coil models.

Oh well, as far as I can see a coin like target has a lot of mutual inductances and time constants and there is a dominating one for a coin like target of course (largest dimension of the coin of course).

Let me update my coil software before I give you some thoughts and examples.

Cheers
Aziz

[Aziz]

Some pre work ..

[Aziz]

Oh man!,

the quality of the pictures are really bad. They have been made via smart phone camera. So excuse me for not having made the simple screen shots. I have moved my development platform from a two core Windows XP to a fast four core 64-bit Windows 7 PC. My old favorite Photoshop LE 5.0 software doesn't run on the newer PC and I have to look for an alternate image editing software. Unfortunately, I'm getting old as my equipment gets old too and I face problems with software requiring new operating system, new PC hardware, new software etc.
But I like to use old systems. I'm still using the Microsoft Visual C++ 6.0 from year 1998 for my coil software developments. All the new compilers require Windows 10 or 11.

Next time, I will deliver you better screen shots.

Formula 8 is also implemented and it delivers same accurate magnetic field results.

It gets tricky now if I take the Amperes law inside the wire conductor into account. This is really required for more accurate computations (inductance, induction voltages and so on).

Cheers,
Aziz

[Qiaozhi]

I have to look for an alternate image editing software.

Try GIMP -> https://static.gimp.org/downloads/
It's similar to PhotoShop, but it's free.

[Aziz]

Try GIMP -> https://static.gimp.org/downloads/
It's similar to PhotoShop, but it's free.

Thanks .
---
Doing messy vector algebra coding to get the magnetic field calculation inside the wire conductor element right now. The formulas 8 and 9 in the publication don't support Amperes Law. Btw, I prefer formula 9. It's a beautiful vector algebra.

Ok, Amperes Law is really trivial. I have to move the observation point temporary to the edge of the conductor (at wire radius) and calculate the magnetic field there (maximum possible H/B-field for wire element). It linearly decreases to the center of the wire element. At the center H/B field gets zero. At the observation point (inside the wire conductor) it is a linaer combination of the magnetic field at the edge of the wire. Thats all.

Some trivial vector math is required to get it working. But the test procedures require a lot more work.
I'm really having a lot of fun doing this stuff.

Cheers
Aziz

[Aziz]

Btw,

the magnetic field calculations are now accurate enough.
Wait
But not for the magnetic flux calculations in a reasonable calculation time. This is one of the fundamental function to calculate the induction voltages and inductances (and coil coupling coefficients).
This is owed to the fact, that I have implemented the simple brute force method in combination with the Monte Carlo simulation to calculate the average magnetic flux. Yes, I do the dice rolling method in the casino (obviously located in Monte Carlo).

The convergence of the Monte Carlo simulation is really bad. I need at least 10000 random magnetic field density calculations within the coil flux area to get 1% accuracy of the average magnetic flux. For 0.1 % accuracy 1000000 calculations are required. On the other hand the implementation is very trivial. Particularly the surface integral part of the implementation.
Anyway, we can push up the calculation time to get more accuracy. It still should be accurate enough to get the answers we want.

I have not tested and checked everything yet and it is quite time consuming..

See you, if I get some results..
Aziz

[Aziz]

Hi all,

I have made some progress with my coil software after making small changes and fixing some new minor bugs.

This is owed to the fact of the power of the Monte Carlo simulation. Only small changes in the software lead to the handling of thick coil wires. I mean really physically thick wires (how about a 6 cm diameter wire forming a 20 cm mean diameter coil?). I can calculate the required figures up to 0.1 % now.

I can extend the software to get more accurate results but this requires big changes and redesing of the coil software. I haven't the time for this big effort right now. I think it is enough at this stage.

We can start soon when I have finished some more tests.
Aziz

[Aziz]

Hi all,

it's been a long time since I have posted here. I really hadn't much free time and spent this reading hundreds of publications and a few books.
As a result, the lecture lesson to me: Don't believe anything what is written (in the publications) until you have proven its correctnes by yourself.

All the former inductance calculation gurus Maxwell, Rosa, Grover, Wien, Kirchhoff, Rayleigh, Niven, Snow etc... did some nice work to formulate approximation functions for the inductance calculations. But all weren't accurate enough to test my coil software. Books do not really answer your specific questions regarding implementation details. I still have some open questions. Everything gets non trivial if the piece of wire (from the coil) gets short and thick for the inductance calculations.

I have also found lots of errors in publications. The peer review process in publications isn't working. And have never worked. You are alone to prove it correct or wrong. Thats the fact. And I was very close to get mad.


My important questions: Do I calculate correct? What's the accuracy? What are the conditions and assumptions for more accuracy? How to implement?... and so on.
I have started to check the coil software for a simple single turn circular coil with circular cross section wire with uniform coil current distribution. Indeed, this seems to be a non trivial work. Even for mathematicians. It is so fkn non trivial, that all the coil gurus have totally failed. We are dealing with elliptical integrals of first and second kind, no closed form of analytical solution, and at the end with a more or less correct or wrong approximation solution.

This confused me for a long time as I didn't get the same results. WTF, what's wrong with my coil software?

Ok, lets make it easier and maybe only single straight wire inductance calculation could lead to check the coil software.
Well, the old gurus failed once again totally. I still got different results.

Fortunatelly, I have recently found a publication called "Improved Formulae for the Inductance of Straight Wires" by H. A. Aebischer1*, B. Aebischer2, ADVANCED ELECTROMAGNETICS, Vol. 3, No. 1, September 2014.
I did code the formula 34 and 35 in MS Excel, implemented the magnetic flux and inductance calculation for a single straight wire in the coil software and got finally same results within the Monte Carlo simulation accuracy. And it answered some of my open questions regarding implementation details.

The internal wire inductance of a straight wire of circular cross section of uniform coil curent (no skin effect and high frequency effects taken into account) with
Li = l*µ0/8*pi,
where l = wire length, µ0 = 4*pi*10^-7,
Li = 50 nH/m inductance as a results isn't accurate if the wire diameter gets large or the wire length gets too short for more geometric accuracy of the coil.
I have made lots of EMF simulations and could verify the results of the publication finally. So the magnetic field calculations, the closed surface integrals and the Ampere's Law handling inside the wire is now correct.
I can now calculate the internal, external and the total inductance independently.

The next step is to go back to the single turn circular coil inductance calculation and check the results. And never look at, what the old coil gurus calculate some bullsh1t with fancy formulas.
The goal is to get 0.1 % accuracy of the calculations. Note that one more accurate digit (factor 10 times) require 100 times more calculation time. Monte Carlo simulation delivers good enough accuracy in reasonable calculation time instead of solving the surface integral everywhere within the flux integration area. This is achied with 1 million random EMF point calculations.
p = 1/sqrt(m),
m = 1/p^2,
where m= number of EMF points
p = accuracy

p = 0.001 (equals to 0.1 %)
-> m = 1/0.001^2 = 1 million calculations

I have warned you, that the testing could take more time. I'm on the right way now.

Cheers,
Aziz

[Aziz]

Hi again,

BTW, the recent publication can be downloaded from this site:
https://aemjournal.org/index.php/AEM/article/view/254
It's full of integral equations.

double AMD_factor(int ndiv)
{
  double f, s, r12, r1, r2, p, dr1, dr2, dp, dr1dr2dp, r1r2;
  int i, j, k;


  dp = 2*PI/ndiv;
  dr1 = 1.0/ndiv;
  dr2 = 1.0/ndiv;
  dr1dr2dp = dr1*dr2*dp;

  s = 0.0;
  p = 0.5*dp;
  for (i=0; i < ndiv; i++)
  {
    r2 = 0.5*dr2;
    for (j=0; j < ndiv; j++)
    {
      r1 = 0.5*dr1;
      for (k=0; k < ndiv; k++)
      {
        r1r2 = r1*r2;
        r12 = sqrt(r1*r1 + r2*r2 + 2*r1r2*cos(p));
        f = r12*r1r2*dr1dr2dp;
        s += f;

        r1 += dr1;

      } // for k
      r2 += dr2;

    } // for j
    p += dp;

  } // for i

  f = 2*s/PI;
  return f;
}​

I get with the tripple integration code above for the formula part ..+0.905415*R in the formula 34 the same result. A bit more accurate of course. With 4000 steps for ndiv parameter, I get 0.9054147736.

Cheers,
Aziz

[Aziz]

Hi all,

the formula 34 of the above publication is quite accurate, but still not accurate enough.
After breaking the formula to the summands form
L = (µ0/2pi) * (a + b + c + d + e),
a = l*(ln(z+l)),
b = -l*ln(R),
c = l/4,
d = -z,
e = 0,905414778312103*R,
z = sqrt(l*l + R*R),

where c part is still based on the 50 nH internal inductance/m.
Li = (µ0/2pi)*(l/4) = l*10^-7/2 = 50 nH for l=1m
The parts a+b+d+e contributes to the external inductance (Le) parts.

Note, that 50 nH/m internal inductance is valid for low R values (R < l). Interestingly, the sum of internal + external is quite accurate. The formula makes errors in internal and external part, when R gets quite large. But the sum compensates the errors.
I get in my EMF simulations
for l=1m, R=1 m, Li=21 nH, Le=91 nH. That's a 2 m diameter wire! Note, that 21 nH to 50 nH differs too much.
for l=1m, R=0.1 m, Li=45 nH, Le=416 nH.
for l=1m, R=0.01 m, Li=49,5 nH, Le=859 nH.
for l=1m, R=0.001 m, Li=49,96 nH, Le=1.32 µH, a good approximation to 50 nH.
The total straight wire inductance is L=Li+Le.

I hoped to get a simplified formula for internal and external part of the straight wire inductance. This also seems to be fkn fkn fkn difficult.

Cheers,
Aziz