# Folded Half Wave Dipole

This article explores the operation of an equal conductors Folded Half Wave Dipole using an NEC4 model.

# Models

Common parameters for all models:
• Environment: free space;
• Wavelength: 10m;
• Dipole conductors: parallel pair of 1mm radius conductors spaced 5mm centre to centre; and
• Loss: none.

The models are based on a pair of conductors that has lowish Z0 and velocity factor so as to cause an observable effect.

## Model 1 - Ordinary half wave dipole

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.

## Model 2 - Ordinary half wave dipole using insulated conductors

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.

## Model 3 -Finding the differential mode velocity factor of the pair of insulated conductors

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.

## Model 4 -Folded half wave dipole using insulated conductors

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 253-j65Ω, which does not support the traditional explanation of how a folded dipole works.

## Model 5 -Model 4 adjusted in length for resonance

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.

# How does this folded dipole work?

## The traditional explanation

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.

## A better 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.

## Model 6 - 'better' model

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 269-j0Ω, 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

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.

# Conclusions

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:

• insertion of the feedpoint in only one of the conductors;
• closing the resulting gap in the other conductor; and
• shorting the conductors at an electrical quarter wave each side of the feedpoint.
The common practice of locating the shorting link at the dipole ends is a small departure from ideal that usually has no significant effect on peformance and efficiency of practical antennas.

07/06/2012