# On copper loss in transmitting baluns

Designs appearing in the ham literature and online articles tend to espouse relatively large diameter conductors, conductors that can be challenging to wind onto the toroidal cores often used.

This article analyses the copper losses in a practical Guanella 1:1 balun where a fabricated twisted pair line is used.

Total losses comprise core losses and transmission line losses.

## Core losses

The core losses in a practical Guanella 1:1 balun are due to common mode current which may vary from negligible to extreme, but for a fairly symmetric dipole in a 100W station, common mode current flowing through the balun would typically be of the order of 50mA.  and a good balun would have an R component of Zcm around 1kΩ, giving core loss of the order of 2.5W

So for such a balun employed in a well balanced antenna system, core loss would be of the order of 10*log(100/(100-2.5))=0.11dB

## Transmission line losses

Transmission line losses are due to conductor losses and dielectric losses in the line wound around the core. Dielectric losses should be insignificant unless low grade dielectric (eg PVC) is used, and will be ignored in this analysis.

Let us compare two transmission line options:

1. PTFE insulated 1.6mm (#14) wire, OD=2.6mm and
2. PTFE insulated 0.9mm (#20) wire, OD=1.7mm.

Results from TWLLC for a 1m section of twisted wires at 10MHz are tabulated below, the key figure is Line Loss (matched).

### 1. PTFE insulated 1.6mm (#14) wire, OD=2.6mm

 Parameters Conductivity 5.800e+7 S/m Rel permeability 1.000 Diameter 0.00160 m Spacing 0.00260 m Velocity factor 0.700 Loss tangent 0.000e+0 Frequency 14.000 MHz Twist rate 10 t/m Length 1.000 m Results Z0 90.37-j0.59 Ω Velocity Factor 0.7000 Length 24.02 °, 0.067 λ, 1.000 m, 3.336e+0 ns Line Loss (matched) 2.37e-2 dB

### 2. PTFE insulated 0.9mm (#20) wire, OD=1.7mm

 Parameters Conductivity 5.800e+7 S/m Rel permeability 1.000 Diameter 0.00090 m Spacing 0.00170 m Velocity factor 0.700 Loss tangent 0.000e+0 Frequency 14.000 MHz Twist rate 10 t/m Length 1.000 m Results Z0 106.00-j0.97 Ω Velocity Factor 0.7000 Length 24.02 °, 0.067 λ, 1.000 m, 3.336e+0 ns Line Loss (matched) 3.37e-2 dB

## Physical properties

Wheras the DC resistance of a round conductor is inversely proportional to cross section area, because of skin effect, the effective RF resistance of a large round conductor is approximately inversely proportional to circumference.

Conductors in close proximity as in a twisted pair are subject to proximity effect which increases the effective RF resistance.

In the scenario above, although the inverse of the circumference ratio is 0.9/1.6=56%, the effective RF resistance of the thicker conductor is 58%, the small difference being due to onset of proximity effect.

## Thermographic experience

In all of the thermographs I have taken of baluns in operation, mostly with smaller diameter wires, the wires have shown very little temperature increase relative to the cores. Core loss has dominated total loss which becomes more significant as Z0 decreases.

## Conclusions

The matched line loss from TLLC is 0.024dB vs 0.034dB.

Though the thicker wire leads to 0.01dB less transmission line loss, it is in the context of 0.1dB of core loss in a good antenna system and so whilst undeniably better, it is doubtful that the performance improvement is worth the expense or the increased difficulty in sourcing and winding the wire.

Whilst actual transmission line losses under mismatch will be higher, they are likely to remain less than core loss except where the balun happens to be located region of a high VSWR current maximum.

An antenna system with higher common mode current will have higher core losses and transmission line losses will be a smaller part of the total.

The calculated results are consistent with thermographic experience.

## References

• Duffy, O. 2001. RF Two Wire Transmission Line Loss Calculator (TWLLC). VK1OD.net (offline).