Flat rectangular is NOT better than a round tube if each have the same
circumference.
The round tube has lower inductance than a flat ribbon conductor of
comparable circumference. Makes sense, because Nature abhors 'pointy'
stuff.
This statement is based upon a comparison analyzing the two structures
using finite element analysis, femm 4.2.
Given:
solid ribbon copper conductor, 1 inch wide and 120 mils thick
copper tube, 0.75 inch outside diameter and 120 mils wall thickness
The two circumferences are approximately the same.
Rectangle 2 * (0.12+1) = 2.24 inches
Tube pi * 0.7 = 2.20 inches
Which is a better conductor?
Assume infinitely long, straight conductors. Assuming most of lightning
energy is significant between 1MHz to 100MHz, calculate each conductor's
characteristics at 10MHz and at 100MHz using 2D finite element analysis.
Method: place each conductor in a 24 inch diameter metal 'tube' to provide
return current and represent infinity. Note: I also used single
conductors in free space with current return at infinity. Values changed,
but the conclusions did not change. Use a 12 inch length to reference
values per ft. Mesh was set to be fine near the surfaces of the
conductors, so that even with hgih frequency currents inside the
conductors were accurately represented. Skin depth was more than 3 nodes.
>From results, the current as a function of depth into the conductors
matched expected values. Plots of current/eddy currents verified mesh was
of suficient density for these calculations.
TABLE RESULTS:
Ribbon - Solid mesh 69,406
10MHz 210 nH/ft 0.00347 W
13.2j ohm/ft 83 milliohm/ft
100MHz 210 nH/ft 0.0115W
132j ohm/ft 0.15 ohm/ft
Tube - Hollow mesh 90,233
100MHz 203 nH/ft 0.00239W
12.8 ohm/ft 69 mOhm/ft
100MHz 203 nH/ft 0.00732
128 ohm/ft 0.12 ohm/ft
It was interesting to note that with a wall thickness of more than 10
mils, at these frequencies the metal was doing nothing but physically
supporting the outside layer.
CONCLUSION:
Round is always better.
Robert
> As a rule of thumb, a conductor
>
> has an (self)inductance proportionally inverse with
>
> it's circumference (if fact the shortest way the magnetic field lines
> will take).
>
> Big flat conductors always perform better then round ones, as they
>
> have the highest circumference per kilo.
>
> Litz and silver(gold) coated conductors do contribute to the
>
> real part of the impedance (=resistance) properties only.
>
> Litz by increasing the conductive surfaces so reducing
>
> the resistance increase caused by the skin effect.
>
>
>
>
>
>
>
> Regards,
>
> Ing. Gert Gremmen
>
>
>
> [email protected] <mailto:[email protected]>
>
> www.cetest.nl
>
>
> Kiotoweg 363
>
> 3047 BG Rotterdam
>
> T 31(0)104152426
> F 31(0)104154953
>
>
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