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

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#1 21678380 26 Nov 2017 12:19

Richard Fischbacher Richard Fischbacher

Anonymous

Post #1
21678380 26 Nov 2017 12:19

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
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#2 21678381 26 Nov 2017 14:07

David Ashton David Ashton

Anonymous

Post #2
21678381 26 Nov 2017 14:07

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.
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#3 21678382 26 Nov 2017 15:04

Richard Fischbacher Richard Fischbacher

Anonymous

Post #3
21678382 26 Nov 2017 15:04

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.
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#4 21678383 26 Nov 2017 15:48

David Ashton David Ashton

Anonymous

Post #4
21678383 26 Nov 2017 15:48

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?
#5 21678384 27 Nov 2017 01:23

PeterTraneus Anderson PeterTraneus Anderson

Anonymous

Post #5
21678384 27 Nov 2017 01:23

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.
#6 21678385 08 Nov 2018 07:36

Mike Dong Mike Dong

Anonymous

Post #6
21678385 08 Nov 2018 07:36

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.
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#7 21678386 07 Dec 2018 02:07

Michael Obrecht Michael Obrecht

Anonymous

Post #7
21678386 07 Dec 2018 02:07

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

The discussion addresses the challenge of calculating the inductance of rectangular and circular PCB traces with specific dimensions (0.5mm/35µm and 1.8mm/35µm width/thickness). Traditional inductance formulas typically require a conductor radius, which complicates calculations for rectangular PCB traces. One approach is to approximate the conductor radius by equating the cross-sectional area of the rectangular trace to that of a circular conductor, but this method yielded results inconsistent with measurements. Alternatively, using the trace width as the effective diameter provided results closer to simulations and measurements, though a theoretical justification is sought. The inductance depends primarily on coil geometry and number of turns rather than trace thickness or width. Several online calculators and formula collections (e.g., coil32.net) offer methods incorporating track width and spacing but often omit thickness. Numerical methods involving mutual inductance between closely spaced coil copies can estimate self-inductance with high accuracy. Practical advice includes validating calculations with simulations and measurements, and considering self-capacitance and Q factor effects influenced by conductor shape. For precise measurement of low inductance values, tools like the LCR-Reader-MP are recommended. Additionally, consulting PCB manufacturers with expertise in EDA software (Allegro, POWER PCB, ORCAD, AUTO CAD, CAM350) can provide design and analysis support.
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Calculating Inductance of Rectangular vs Circular PCB Traces with 0.5mm/1.8mm Widths

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