Calculating Inductance of Rectangular vs Circular PCB Traces with 0.5mm/1.8mm Widths

Hello,
I am currently trying to calculate the inductance of a rectangular and circular PCB line. All formulas I can find online (including this page) require a radius for the current carrying line/wire. How do I approach this when my PCB line is rectangular shaped(width/thickness: 0,5mm/35µm and 1,8mm/35µm). I calculated the equivalent radius to have the same area(40µm and 80µm) but here the results are way different than my measurements. If I just take the width of the line I am actually getting similar results.
Any advice on how to solve this problem?
BrRichard

Richard... you wouldn't expect the thickness or width  of the track to have a lot of influence because the primary factor that determines a coil's inductance is the number of turns (all other things being equal).
I did find a reasonable looking calculator here that does not ask for the track details:http://coil32.net/online-calculators/pcb-inductor-calculator.html
See how that agrees with your findings and let us know.

I measured 2 coils with 1 turn. Now I am trying to verify the results via sims and hand calculations. The sims are already fitting but the hand calcs are the issue.Hence I am looking for a formula to calculate (geometrically) the inductances of the 2 coils (rectangular and circular). But every formula i find wants do have this diameter of the track.  Maybe the diameter  = width? With this assumption the results are similar to sims and measurements but some  reasoning  behind this  assumption would be great.

Richard - did you look at the site I linked to?  It has a link to  the formulae used to calculate the inductance - there are 3 different methods and some links to further external sources.  Some of the formulae do use the PC track width and the gap between tracks, but none of them want the thickness of the copper track as far as I can see.  The formula page is here:  http://coil32.net/pcb-coil.htmlThe form of the conductor - ie diameter or width x thickness - would probably have an effect on the inductance and also on the Q factor of your coil.  it would also affect the self-capacitance of the coil - which in your case would be smaller than one using wire of the same diameter because the capacitance between adjacent tracks would depend on the copper thickness (small)  and the separation.It sounds like you have pretty good means to check the inductance of your coils,  so find a formula that gives results that  approximate to what you measure and stick to that?

The inductance of a coil is the sum of two components, the mutual inductances among the turns and the self-inductance of the conductor. The conductor self-inductance depends upon the cross-section dimensions of the conductor. In the limit of zero conductor diameter, the self-inductance is infinite.https://web.archive.org/web/20151002101400/http://home.comcast.net/~traneus/thesis.pdf is a copy of my Ph D dissertation. In there, I developed a numerical method of calculating the mutual inductance between two PCB coils built of straight-line segments. I use this to calculate the self-inductance of one coil, by creating two copies of the coil and bringing them closer and closer together. As the two coils get closer, the mutual inductance rises, first rapidly then more slowly as the spacing between coils approaches the cross-section size of the conductors. The mutual inductance at spacing about 1/3 of the conductor diameter, I take as the self-inductance of one coil, correct to a percent or so.

Have you considered looking for help from some manufacturers? I am ordering boards at PCBGOGO, and their engineers will be very enthusiastic to help you solve some problems.They master various EAD softwares such as Allegro, POWER PCB, ORCAD, AUTO CAD and CAM350 etc. They are very familiar with the design standard and technology standard in the local and international market, and also have full experience about the PCB layout and wiring design, power supply design, SI analysis and EMC design. They have the ability to finish the whole design process from drawing the schematic to assembly.

It may be easier to just measure it. LCR-Reader-MP would allow to measure sub 10nH values.