A correspondent having read Analysis of a certain dipole animation questioned the validity of the lossy transmission line model of the dipole, citing the case of an OCF half wave which has an approximately resistive feed point.
Since the OCF lacks the symmetry exploited in earlier study, we must consider each half of the OCF dipole and combine them. To assist, I have produced a similar plot of the transmission line but note the changed X axis.
The scenario is again a 2mm diameter copper wire, 3m above ground at 1MHz.
Zo can be approximated as 138*log(2h/r)=138*log(2×3/0.001)=521Ω.
Above is a plot of calculated R,X components of V/I at displacements from the open end, and calculated phase of V/I.
The OCF dipole is fed between the two transmission lines (discussed above).
For a 33%/66% OCF, the lengths of the two parts will be 0.167λ and 0.333λ.
Looking at the graph, the impedances are 16-j308Ω and 68+j304Ω, so the two in series makes 84-j4Ω. This is very close to purely resistive, a very slight shift in frequency will yield zero reactance. (The R value is quite sensitive to the loss assumption used in the transmission line model.)
Properly applied, the transmission line model of the dipole does suggest an approximately resistive feed point (ie V in phase with I) for off centre feed due to complementary reactance supplied by opposite sides.
Again it is a case of understanding clearly what reference is used for V, ie the ‘other terminal’, and at the end of the day, V wrt ground is not easily measured or verified, and is not very useful in understanding the antenna system.
On the other hand, understanding charge distribution is important, and some kinds of antennas must permit large charge differences to exist between conductors that are very close. This is key to correct design of a lot of co-phased colinear antennas. For example, if we looked at a 3/4λ ground mounted monopole, to operate as a co-phase colinear, some device must be employed at 1/2λ from the top that will permit, even encourage the large charge difference that must exist between the top of the bottom 1/4λ and the adjacent bottom of the top 1/2λ.
Current and charge are good parameters for understanding an antenna, voltage is less so.
Remember that radiation is due to accelerating charge… not simply voltage.