#### dd2023

##### Newbie level 4

for the purpose of TL transformer simulation I need solution for segment characteristic impedance of vertical wire, with radius a, at the infinitesimally short segment - point, at the height h above perfect ground.

For horizontal wire over (PEC) ground, we have analytical solution: Zo' = (Zfs/Pi) * acosh(h/a)

That solution, derived from characteristic inductance and capacitance of the wire against its mirror image, works well even for slightly sloped wire (if we make very short segments).

I am not sure, does that equation applies any more for angles approaching vertical and finally vertical wire over PEC ground? Most of theoretical framework is based on mirror image.

Despite best efforts to find solution for the vertical wire, I couldn't find any.

Does it exists? My math level is far below needed to solve it by hand.