Modelling an antenna as a simple two terminal resistance is often naive

in the article A simple transformer model of the Guanella 1:4 balun – some further observations I stated:

Note that a two terminal impedance is a naive representation of many if not most antennas, popular, but a naive over simplification that does not facilitate evaluation of current balance.

An example was a recent posting above that used the model to make assertions about the behaviour of a Guanella 1:4 balun.

This article reports results of two experiments with NEC to model an ‘imperfect’ half wave dipole. It is not exactly resonant, but the main issue is that it is tilted from one end to the other, it is not parallel to the ground surface.

Key attributes:

  • dipole length 21m;
  • centre fed with an ideal voltage balun;
  • common mode conductor from the balun to ground;
  • height of the centre 10 and 20m.

10m height

Above is the geometry and current distribution. There is common mode current Ic, but it is quite low (|Ic|<|Id|/100).

Now lets calculate the three terminal equivalent circuit as per (Schmidt nd) above.

Above are the inputs and calculated results. Note that Z1 is not close to Z2, a sign of a lack of symmetry. Z3 is quite high, contributing to high common mode impedance Zcm and the observed low Ic.

Recall that this uses an ideal voltage balun, it is quite asymmetric, AND it has very low common mode current.

20m height

Above, the geometry and current distribution at 20m centre height. A stunning difference as a result of doubling height.

Again, let’s calculate the equivalent circuit values.

Again Z1 and Z2 are quite different reflecting the asymmetry. The stunning difference to the previous case is the much lower value of Z3, main contribution to Zcm and in concert with the asymmetric Z1 and Z2, the reason for very high common mode current.


  • Finding the three terminal equivalent circuit for an antenna system gives a more complete insight.