I remember from an earlier ARRL edition of the "Antenna Manual", a 40m vertical antenna design with a capacitance top hat. The article mentioned that the current lobe was drawn towards the top of the 40m vertical antenna, but for many years I have wondered why and how.
Since my article regarding lumped component antenna's, I think that I may have come up with a reason so.
The top hat consisting of several horizontal radials, placed at the top of the vertical antenna, my assumption is that these radials force an antenna characteristic impedance at the antenna top end point.
An example, if the inductive reactance of each radial is 100ohms at the 40m band, then four radials would then when connected together at a central point, would in effect provide an impedance of 25ohms. The top end of the vertical antenna would thus be given a 25ohm termination point.
In effect the 25ohm termination point would have a greater current distribution point if measured, however to match the now 25ohm loading to a 50ohm terminal impedance of a radio set, then a load coil would need to be put in place between the co-axial cable and the four radials at the top end of the vertical antenna design.
As the top end loading of the four radials is some 25ohms, to match to a 50ohm cable termination would require the addition of a load coil as a 25ohm inductive reactance at the 40m band.
Now lets assume that the load coil for the 40m band in this example, was constructed with an inductive reactance of 150ohms, which is a 1/4 wave length, the total antenna impedance at the base of the load coil would be the addition of the top hat loading plus the load coil, hence a 175ohms.
To bring down the now 175ohms antenna loading towards a 50ohm cable match, a new base mounted radials would be required.
The 50ohm cable and the 175ohms antenna are similar to two resistors in parallel, hence then
1/total = 1/R1 + 1/R2 equation would be used to calculate the new shunt base load radial impedance to bring down the current total of 175ohms back down to 50ohms.
The shunt impedance required form the above equation re-arranged to calculate R2, with 1/total = 50ohms, R1 = 175ohms, then R2 = 70ohms, this then the load impedance required from a base level construction of radials at the cable termination point of the 40m vertical antenna.
If four base radials are used, then for the 40m band each of the radials would need an inductive reactance of 280ohms to equate to the 70ohm radials load point. If each of the four radials is replaced with a load coil, then each radial coil would need an inductive reactance of 280ohms at the 40m band for this 40m band designed vertical antenna.
Likewise, for the top hat loading, each of the radials may replaced with four 100ohms inductive reactance load coils on the 40m band, the 50ohm coax then connected to this point.
Now should the middle load coil in our 40m vertical design was made to be a full wavelength, thus around 560ohms inductive reactance, then the four base radials would each have an inductive reactance of around 218ohms.