Multi band antennas are compromises more so than most mono-band antennas, and part of that compromise is lower efficiency. Often the lower efficiency aspect is accepted without understanding.

Lets look at the power dissipated by a typical unun used on such an antenna.

## Base voltage

NEC models can be used to obtain a reasonable estimate of the input impedance of a ground mounted monopole.

From that, we can calculate the voltage at the base for a given power input (at the base).

The base voltage for 100W at 3.6MHz is 230V rms (Duffy 2006). The voltage curve depends on assumptions made about the effecitve resistance of the monopole's ground system, in this case a value of 2Ω is added to radiation resistance to obtain total R at the base.

## 4:1 Unun at the base

It is common practice to install a 4:1 unun at the base of the vertical for perceived improvements in efficiency. Let us explore a practical unun at 3.5MHz. Lets suppose the unun has 10t bifilar on a FT240-43 core wired as a 4:1 unun, the high Z side connected to the feed point.

Above is a screenshot from (Duffy 2012) estimating the admittance of a 10t winding.

Since approximately half the base voltage is impressed across the 10t winding, power dissipated in the core at 100W at the base can be estimated as P=E^2*G=(230/2)^2*0.000267=3.5W.

Operation of this balun at sustained high power with high duty cycle (eg RTTY) may result in it overheating (manifest as SWR changing as the core reaches its Curie point (130°)).

## References

- Duffy, O. 2006. An unloaded vertical as a multi-band HF antenna. VK1OD.net (offline).
- ———. 2006. A method for estimating the impedance of a ferrite cored toroidal inductor at RF. VK1OD.net (offline).
- ———. Feb 2008. A model of a practical Guanella 1:1 balun. https://owenduffy.net/files/GuanellaBalun01.pdf.
- Fairrite 2013. How to choose ferrite components for EMI suppression. Fairrite product catalog 17th ed p146.
- Guanella, G. Sep 1944. New methods of impedance matching in radio frequency circuits. The Brown Boveri review.
- Knight, D. 2008. The Self-Capacitance of toroidal inductors. http://www.g3ynh.info/zdocs/magnetics/appendix/Toroid_selfC.html (accessed 28/09/2105).
- Knight, D. Jul 2013. The self-resonance and self-capacitance of solenoid coils. http://www.g3ynh.info/zdocs/magnetics/appendix/self_res/self-res.pdf (accessed 28/09/2105).