When it comes the time to design a planar PCB inductor for RFID antennas, it is needed to characterize its parameters. One of them is the series DC resistance, which depends on the conductor length and resistivity as well as its thickness and width. The latter ones can be easily defined in any CAD software for PCB layout. What about the conductor length? Well, not every software allows you to define the length neither can give you the length of a certain trace. In such case we have to calculate that manually.
The paper in [1] presents an equation to calculate the conductor length of a square planar antenna. It appeared to me that one of elements of the equation was not correctly defined. The original proposal is the following:
From my revision the corrected equation should be:
With
n being the number of turns,
d0 the external length of the conductor,
w the conductor width and
s being the gap as shown in the picture above.
Since most RFID antennas are rectangular rather than having a square shape, the expression could be further developed as the one presented below, with
c0 and
d0 being the external length of each side:
As a side note, the total series resistance also depends on the operating frequency, since the AC current will be distributed mostly close to the conductor surface.
[1] Islam, A. B., Et al., "Design and Optimization of Printed Circuit Board Inductors for Wireless Power Transfer System"
