Reg, G4FGQ wrote:
"There is a 3-phase transmitter feeding a 3-phase antenna via a 3-wire
transmission line.

The antenna consists of three 1/4-wave horizontal radiators spaced at
120 degree intervals.

Is the radiation pattern in the horizontal plane perfectly
omnidirectional?"

The question is easy, I think. The horizontal 1/4-wave elements have
nulls off their tips, so they can`t produce a perfect omnidirectional
pattern.

Not knowing when to quit, I`ll also speculate that at distant points
from the antenna, the total phase from two elements will produce a total
phase difference of 180-degrees which consists of a total of radiated
field degree difference and path distance degree difference. Maybe more
nulls. I wrote "two elements", because I`m thinking of a dipole in a V
configuration with the 3rd element perpendicular to the dipole as being
more or less along for the ride. Perhaps that`s an oversimplification.

Someone likely has a program which will model Reg`s 3-phase antenna. I
don`t, and I have no experience with 3-phase antennas. I`ve done 3-phase
circuit problems and recognize the balanced load, even if the antennas
are unbalanced.

The system is symmetrical, so each of the loads (antenna elements) takes
the same power. The total load power is 3 times the power of a single
element.

The loads are resonant, so (cos theta) is unity. The elements look like
resistors. Element power is element volts times element amps.

The load is equivalent to a Y-connection.. So, the line to line voltage
is the square root of 3 (1.732) times the volts between the line and
neutral.

Reg also wanted to know the impedance of the antenna, I believe, but its
numerical value depends on construction, height of the elements, their
size, and coupling, if any, to their surroundings. 35 ohms might have
been a good guess.

Voltage to current ratio of the elements gives their resistance.

The volts or amps of the balanced 3-phases can be represented by three
equal arrows separated by 120-degrees. Their instantaneous values always
total zero.

The idea of a polyphase antenna is interesting but I don`t see what
justifies its increased complexity, unless it happens to place nulls
exactly where needed for required protection of broadcasters already on
the air or permitted when a new broadcaster is seeking accommodation. In
that case, the elements would most likely be vertical to launch a decent
ground wave.

Best regards, Richard Harrison, KB5WZI