Simulating Q of circular planar coil

[Darkcrusher]

Simulating Q of circular planar disc coil

Hi,

I'm simulating the quality factor of a planar circular coil without ground plane. When I'm simulating I notice that the result is a function of modelling with or without finite thickness. How is this possible ?

1) Any suggestions ?
2) Are their volunteers which would like to run their sim software on my very simple geometry ? This will help to evaluate software

PROBLEM
------
Average diameter : 30 mm
trackwidth: 6mm
thickness = 70 micron
frequency: 50 MHz
-------

SONNET
--------
Thin Metal: Q = 320 (by volker)
Thick metal Q = 570 (by volker)
Thick metal Q = 380 (by volker, finer meshing)
Thick metal Q = 490 ( by sonnet support on 90 degree section)
--------

AXIEM
-------
Thin metal: Q= 330 (by me)
Thick metal: Q = 500 (by me)
-------

QUICKFIELD
--------------
Q = 440 (by FvM)

FASTHENRY
--------------
Q=500 (by Fvm)


MEASUREMENT
--------
Q = 350 (by me)

possible errors under research: etch angle, contact resistance, solderering, placement capacitor





Please add your simulation result in this topic. Will be VERY appreciated !

 

[FvM]

My guess is, that the substrate can be mostly neglected, but if it matters though, you have to specify the exact geometry of the one winding's start and end. There you have the strongest electric field respectively dielectric losses, and it's unspecified yet.

 

[volker_muehlhaus]

I assume that your questions refers to EM analysis? This is an interesting topic indeed.

At 50MHz, skin depth is ~9µm, so that your conductor model must account for skin effect.

For EM simulators that simulate with infinitely thin sheets, the loss is mapped onto the conductor surface by using a surface impedance.

An approximation must be made for skin effect regime, because we just have a single sheet and the EM analysis can not calculate the current distribution to top and bottom of the conductor. Is it symmetric with equal skin effect current on top and bottom (stripline case) or asymmetric with current concentrated in one skin sheet (microstrip case)? The simulator does not know because it just analyzes with one sheet that represents both top and bottom side combined.

With the thick metal models that are available in some planar EM tools, now there are separate sheets in the EM analysis and the actual current distribution between top and bottom can be calculated as a part of the EM solution.

 

[Darkcrusher]

@ FvM: It doesnt matter much in simulation. Simplified my question. Maybe it might matter in practice becouse of high loss angle in the plane of the coil for FR4 ?

---------- Post added at 19:42 ---------- Previous post was at 19:31 ----------

@ Volker: I understand what you mean, but how does it handle current in the small vertical edges ? It's very important for this type of structure but can probably be neglected for strips with GND ?

 

[volker_muehlhaus]

but how does it handle current in the small vertical edges ?

Which simulator do you use?

 

[Darkcrusher]

AXIEM from microwave office...

 

[volker_muehlhaus]

AXIEM from microwave office...

How does Axiem mesh the side wall? Is it properly discretized in z-direction, to account for skin effect, or is there constant current over the entire height of the side wall?

 

[Darkcrusher]

From the documentation:

"AXIEM uses a mesh defined on the surface of the conductors as the basis for the solution. The effects of the dielectric layers is taken into account mathematically (through Green's functions), which allows the solution to be found from a much smaller set of unknowns. The surface currents modeled by AXIEM include all x, y and z components. For any conductor that can be created in AXIEM, there are no restrictions on how current flows on the surfaces. The ability to model all surface currents accurately allows accurate analysis of conductor traces of any thickness (even lines that are much thicker than they are wide). "

If they are correct, why is it that my measured Q is lower than the thickness model and higher than the zero thickness model ? suggestions ?

 

[FvM]

I think, the objective of your tool is to localize surface currents correctly to calculate their EM contribution, not to determine the current distribution below the surface, as it would be required for skin effect modelling. They are effectively using a hollow conductor model, which is most likely sufficient for the frequency range, EM simulators useally are targetting to. The skin effects at 50 MHz can be accurately modelled by a more simple AC magnetic analyzer.

 

[Darkcrusher]

FvM,

If I understand correctly, the solver is only correct for the calculation of equivalent surface current which does a good job for fields and inductances ect.. but it is inaccurate in estimating the ac resistance, since it does not take into account the real distrubution IN the conductor ? Do I understand this well ?

What do you mean by a more simple AC magnetic analyzer...I'm very interested!

 

[volker_muehlhaus]

From the documentation: (...)

That is marketing speak. From a technical viewpoint, the current flow is limited by the discretization. If there is only one mesh cell on the side of the conductor, this will force uniform current on the side, and does not allow to model skin effect properly. Maybe you can check the mesh for that possible meshing problem.

If you are interested to have another data point to compare with, I could simulate your model with Sonnet. Just upload you AWR model/geometry in *.emp file format.

---------- Post added at 22:44 ---------- Previous post was at 22:35 ----------

I think, the objective of your tool is to localize surface currents correctly to calculate their EM contribution, not to determine the current distribution below the surface, as it would be required for skin effect modelling.

All these Method of Moment codes solve for currents on the conductor surface, whereas volume meshing tools (FEM/FDTD) discretize the volume in 3 dimensions. These are two different approaches. As I described above, the "wide line with small thickness" case is handled by MoM codes by mapping a surface impedance onto the conductors, which is calculated from DC conductivity as well as skin effect correction.

 

[FvM]

A simple AC magnetic analyzer, that does a 2-D discretization of a conductor cross sections is e.g. FastHenry from fastfieldsolvers.com. As far as I experienced, it does an accurate calculation of inductance and resistance with skin effect influence. But you have to present the conductor shape reduced to rectangular solids. An important limitation is, that it doesn't handle magnetic cores.

 

[Darkcrusher]

Project uploaded @:

**broken link removed** (you need to rename to .emp)

Can you both do some simulations on this coil with different tools. I have accurately measured Q
D = average diameter
b = trackwidth

coils and measured Q
1) D= 100 mm , b = 20mm Q = 891
2) D= 100 mm , b = 3mm Q = 393
3) D= 30mm, b = 6mm Q = 350
4) D= 30mm, b= 1mm Q = 148

Coil nr 3 is the coil drawn in project file.

It is haunting me forever and I think lots of people can benefit from this (eg RFID). I give away all my points and maybe some money for the first person able to predict my measured Q's!

 

[volker_muehlhaus]

Hello again,

I have simulated your inductor now. Before, I did not realize that it is single turn, so that the resistances are extremely small, on the order of 20mOhm. This means that any comparison to measurement suffers from accuracy problems in the measurement: contact resistance, resistance from soldering etc.

But let's start with the EM analysis first.

As I wrote above, for thin metal analysis, the simulator can not predict the skin effect current distribution on top/bottom of the trace. In Sonnet, we can set the skin effect current ratio manually, and I have plotted the extreme cases with current ratio = 0 (skin current on one side only) and current ratio = 1 (skin current on two sides). As you can see, they agree at DC (as calculated from metal thickness and conductivity) and diverge where skin effect takes over.

Your inductor does not have ground below, so we expect that current ratio = 1 with symmetric current on top and bottom should be more correct. For a thick metal analysis, where Sonnet calculates two sheets, the skin currents can be EM calculated, and we see that we are indeed very close to the current ratio = 1 (skin current on two sides) thin metal result.

In the plots, you can also see the extracted series resistance, which determines the Q factor. These resistances are very small for your model, and it will be difficult to measure this accurately. Your difference between measured and simulated is 20mOhm. From many years of consulting with on-chip inductor modelling and measured-vs.-simulated tests, I have a very strong trust in my Sonnet results, and know how difficult it can be to measure the Q accurately in the presence of contact resistance.

Best regards
Volker

 

[Darkcrusher]

thanks volker!

note: I've edited my thread.

Still hoping for some more people to run simulations with ansoft or CST or other software!!

 

[FvM]

I tried an axisymmetric AC-magnetics analysis with Quickfield and found, that the exact result is arbitrarily changing with the meshing. This isn't surprizing, when you see the current density distribution, below a detail from the inner coil end. With the finest meshing, I got a Q value of 440, but the uncertainty may be still 5%.

I wonder, how the discretization effects show with EM solvers?

 

[Manjunatha_hv]

Hello Darkcrusher,

Very interesting topic...
can you please upload once again the MWO file *.emp as I am not able to download...

---manju---

 

[volker_muehlhaus]

I wonder, how the discretization effects show with EM solvers?

This is a very good question.

Axiem and Sonnet are MoM solver which mesh the surface of the inductors. The meshing density will determine the effective current path for non-uniform current. There is no 3D-meshing needed, but the surface current distribution (high edge currents) also needs a fine enough discretization. Now the question is, what is "fine enough".

I checked my results again that and found that my Sonnet results posted above are too optimistic. I had applied the meshing rules from my RFIC inductor analysis (µm, GHz) and this low frequency PCB inductor needs a different meshing strategy. It is more sensitive to mesh size than I had expected. With finer mesh, my Q values go down. I will post results later.

 

[Darkcrusher]

Thx again volker and Fvm

@Fvm: Can you try FastHenry ?

 

[FvM]

I already did, but I'm not clear about the accuracy. As said, FastHenry need the conductor geometry reduced to rectangular solids. I used a 5° step resulting in the below picture.



The solids are further discretized to filaments with an exponential width stepping, optimized for skin effect modelling. The below picture from the manual illustrates the method:

The number of filaments for width and height can be specified independently, also the exponential factor can be changed from default 2.

I found that I needed an unusual high number of filaments to make the results converge to a similar point as achieved by Quickfield. With 20x20, I got 28 mohm and 44.9 uH, respectively Q of about 500. But I fear, that the length difference between inner and outer filaments isn't considered correctly, so the current concentration at the inner edge would be ignored.

A Q range of 400 to 500 seems likely however.