Skin Effect Load and Impedance

I've recently implemented skin effect loading of wires in pymininec, my re-implementation of the Mininec antenna modeling code. The original Mininec code did not have this feature.

To attempt verification of my implementation I chose to follow an ancient publication by R. P. Haviland, W4MB [1] where he, among other things, investigates effect of wire resistance on feed point impedance. He has two graphics where the real and the imaginary part of the feed point impedance are plotted against the length/diameter ratio of the wire of a dipole. He mentions Mininec in the text but reading closely it is not apparent if for the two graphics with the feed point impedance he really used Mininec or something else. I've tried to reproduce his graphs with both PyNEC, a Python wrapper for a C++ implementation of NEC-2 and my pymininec implementation of mininec. The results of Haviland have the same tendencies as the NEC results in the following but do not match closely.

Note that the X-axis of these graphs is logarithmic and the wire gets thicker to the right (the X-axis is length/diameter of the wire). In all cases we compare ideal wires without resistance to wires with copper resistivity.

Now the resistance part is not surprising: The real part of the antenna impedance gets higher when the wires have higher resistance (because they get thinner).

The interesting part is the imaginary part (the reactance) of the antenna. The NEC result is that the reactance gets higher with higher resistance of the wire (to the left) while my pymininec implementation has a slight decrease of the reactance.

To investigate this further I've decided to just change the wire resistivity without modifying the wire radius to show that the effect is independent of the wire radius. The radius is 66µm at a wavelength of 1m, \(\frac{l}{d}\approx 7576\).

In addition to PyNEC and pymininec I've also included results for MMANA-GAL and EZNEC. MMANA is originally based on Mininec. The EZNEC results match closely to the PyNEC results (it's the same engine, one implemented in Fortran, one in C++) but MMANA keeps the reactance completely constant at \(42.63\Omega\) at all resistivities of the wire. Note that the most interesting wire resistivities are the first three big dots on the left, the first is an ideal wire (at 0 resistivity) followed by copper and alu.

I currently don't have an idea which result comes closest to the physical reality.