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This article explores the operation of an equal conductors Folded Half Wave Dipole using an NEC4 model.
The models are based on a pair of conductors that has lowish Z_{0}
and velocity factor so as to cause an observable effect.
An NEC4 model was created of a nominally half wave dipole formed from the parallel pair of wires with the conductors at each end bonded, and identical voltage sources inserted in the centre of each wire of the pair.
The dipole length was adjusted for approximately zero reactance at the feedpoint, and the length noted as 96% of a physical half wave and feedpoint impedance with both sources in parallel was 71.5Ω.
This model essentially establishes the impedance and length of an electrical half wave dipole using the ideal conductors in a vacuum.
An NEC4 model was created of a nominally half wave dipole formed from the parallel pair of insulated wires with the conductors at each end bonded, and identical voltage sources inserted in the centre of each wire of the pair. The insulation is 2mm radial thickness of dielectric with permittivity 10.
The dipole length was adjusted for approximately zero reactance
at the feedpoint, and the length noted as 92.9% of a physical half wave
and feedpoint impedance with both sources in parallel was 67.0Ω. The
feedpoint impedance is a little lower than that of a thin bar conductor
in free space because of the effects of the insulation and the fatter
conductor configuration, both of which contribute to shortening and so
radiation resistance.
This model essentially establishes the impedance and length of an electrical half wave dipole using the ideal insulated conductors in a vacuum.
An NEC4 model was created of a nominally half wave length of the parallel pair of insulated wires with the conductors at each end bonded, and a voltage sources inserted in the centre of one of the bonding conductors. The insulation is 2mm radial thickness of dielectric with permittivity 10.
The length was adjusted for approximately zero reactance at the feedpoint, and the length noted as 70.6% of a physical half wave.
This model essentially establishes the common mode velocity factor of the pair of insulated wires in a vacuum.
An NEC4 model was created of a nominally half wave dipole formed from the parallel pair of insulated wires with the conductors at each end bonded, and a voltage source inserted in the centre of one wire of the pair. The insulation is 2mm radial thickness of dielectric with permittivity 10.
This model was the same one used for Model 1 with one of the sources removed.
The observed feed point impedance is 253j65Ω, which does not support the traditional explanation of how a folded dipole works.
An NEC4 model was created of a nominally half wave dipole formed from the parallel pair of insulated wires with the conductors at each end bonded, and identical voltage sources inserted in the centre of each wire of the pair. The insulation is 2mm radial thickness of dielectric with permittivity 10.
This model was the same one used for Model 4, but with overal length adjusted for resonance (zero reactance) at the feedpoint.The length was increased by a very small amount to 95% of λ/4, which yielded observed feed point impedance is 322+j0Ω.
The traditional explanation of a folded dipole with equal diameter conductors suggests that the feedpoint impedance is four times that of the equivalent unfolded dipole. The reasoning is that since the two conductors are very close to each other wrt wavelength, the net effect of the current is well approximated by summing the current in the conductors having regard for magnitude and phase. The assertion is that the currents are equal, so the feedpoint current is one half of the combined currents, and therefore the feedpoint impedance is four times that of the equivalent unfolded dipole.
The often observed results with bare conductors in a vacuum (or air for that matter) appear to validate the traditional explanation, but they are not complete proof of it.
Experiments such as the Models 4 and 5 above using insulated conductos challenge the traditional explanation.
The pair of parallel conductors can be viewed as a transmission line, and the conventional meaning of the qualifiers differential and common mode applied to currents, impedances etc.
For the currents in both conductors to be the same at the feedpoint, the differential current must be zero. To obtain zero differential current, we must make the common mode impedance looking into each of the transmission line sections infinite, and that is done by applying a short circuit to the lines an electrical quarter wave from the feedpoint. Model 3 established the differential mode velocity factor as 70.6%, and so the short circuit needs to be applied at 70.6% of λ/4 from the feedpoint.
An NEC4 model was created of a nominally half wave dipole formed from the parallel pair of insulated wires with the conductors at each end bonded, and identical voltage sources inserted in the centre of each wire of the pair. The insulation is 2mm radial thickness of dielectric with permittivity 10.
This model was the same one used for Model 4 with the parallel conductors bonded to each other at 70.6% of λ/4 from the feedpoint.
The observed feed point impedance is 269j0Ω, which is four times
the feedpoint impedance of Model 2.

Fig 1 shows the distribution of current magnitude and phase for the
lower (L), upper (U), and combined (C) conductors. Whilst the current
on the upper and lower conductors inboard of the shorting link doesn't
vary greatly in magnitude, it does in phase, and this indicates the
existence of significant common mode and differential mode current
components. The C mag and C phase show the common mode current on the
structure.

Fig 2 shows the distribution of differential current magnitude and phase. (The nearly vertical lines in Fig 1 and Fig 2 would be vertical with sufficiently small segments.)
Whilst some works, including the ARRL handbooks, insist the there
is no transmission line behaviour in a folded dipole, Fig 2 shows
clearly the differential current that characterises a short circuit
quarter wave stub. Note that perfection in achieving zero differential
current in the centre is synonomous with achieving exactly 4:1
impedance transformation. The same perfection is indicated by the
equality of magnitude and phase of the upper and lower conductor
currents in the centre shown in Fig 1.
Understanding the current distribution is key to a true understanding of the folded dipole.
In practice, whilst the ideal location for the shorting link between
upper and lower conductors might be some distance in from the end, the
effect of placing it at the dipole ends is to slightly detune the
antenna. If the antenna length is then adjusted for zero reactance at
the feedpoint, the impedance will increase slightly above that for a
perfect 4:1 transformation, but that is usually of little consequence.
Efficiency and performance will not usually be significantly affected.
The traditional explanation for the operation of a folded dipole may fit one made from bare conductors in air fairly well, but departure can be observed for folded dipoles made of insulated conductors.
Exploring the case of insulated conductors reveals a more detailed and more accurate explanation for the folded dipole.
Conversion of a pair of equal parallel wires bonded togeter to form a resonant ordinary centre fed half wave dipole to a folded dipole requires:
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