David, VK3IL, describes a small transmitting loop (STL) at Portable magnetic loop antenna.
At VK3IL’s 3m circumference LDF4-50B loop on 40m. I reviewed his loop behaviour on 40m, and its efficiency was quite low… though typical of a loop of that size at that frequency.
Radiation resistance of a STL is proportional to the fourth power of frequency, and since it is often dwarfed by loss resistance, we should expect that doubling frequency will dramatically improve performance.
As far as I can glean from the article, it is made from a 3m length of LDF4-50B Heliax, and uses a Patterson match to tune it.
The loop is shown near ground and this introduces some ground loss resistance and modifies free space radiation resistance somewhat. Nevertheless, lets consider a model that assumes free space radiation resistance.
Above is a free space model of the loop from Calculate small transmitting loop gain from bandwidth measurement. Conductor is taken to be 11mm diameter to give the best estimate of inductance. The model uses a circular loop whereas VK3IL’s loop is a slightly deformed loop but it should have only a small impact on loop inductance.
Now behaviour near ground will be a little different, and quite dependent on height and ground parameters.
It is difficult to estimate Rrad for the loop close to ground, and the change in Q may be not just due to additional loss resistance, but some change in Rrad (which could be good or bad). It is fair to say that the real antenna is likely to have efficiency somewhere around 10%, or -10dB.
Above is a chart of the components of the total feed point resistance implied by Q=330. As mentioned, Rrad could be higher or lower (see Analysis of a series of NEC-4 models of a low loss small transmitting loop at 7MHz at varying height, Ground effects on small transmitting loop efficiency) and Runknown will include some element due to energy lost in heating soil (again dependent on soil type and loop height).
As mentioned, a Patterson loop tuner is used and the stated series capacitor is 9.7pF which has a reactance of -1155Ω at 14.2MHz. That means that the impedance on the load side of that capacitor is about 50+j1155Ω (assuming lossless series capacitor(s)).
Above is a calculation of the peak voltage impressed on the driven gang of variable capacitor (a 365pF broadcast stype dual gang air dielectric variable capacitor)… little wonder that something arced at 22W input. A similar voltage would appear across the string making the 9.7pF capacitance, around 500V each so that is at their limit. Keep in mind that voltage breakdown is an instantaneous phenomena and there is no benefit from low duty cycle modes.
The current in the series caps is around 0.66A, so dissipation may be an issue. If each capacitor had Q=2000 (ie VERY good), then ESR would be 1Ω and dissipation just under half a watt for 22W average input. Note that Q of many capacitor type is much lower, as low as 50 for common moulded mud ceramic capacitors… so as David observed, choice of capacitor types is critical to performance. On SSB telephony where average power might be closer to 3-10% of PEP, dissipation will be proportionately lower.
Opportunities for improvement
Looking at the pie chart, Runknown comprises almost 88% of the total loss resistance.
- Runknown might be improved by raising the antenna above soil (ie reducing the Rgnd component) and improving the tuning and matching capacitor loss.