Peter, VK3YE, describes a small transmitting loop (STL) in his video at https://www.youtube.com/watch?v=Cv_RnLpZ9gw.
As far as I can glean from the video, it is made from a 3m length of copper tube 19mm diameter, and uses about 1.8m of RG213 to tune it, and appears to have its centre 0.7m above ‘ground' .
Let us firstly look at a free space model of the antenna using Reg Edwards' RJELoop1 tool.
This model has its limitations, but the calculated inductance is of interest. We can calculate the inductive reactance to be 118Ω. The capacitive stub of RG213 will need around 107Ω reactance, and solving for RG213, we find that 1.94m gives 0.19-j107Ω. The resistive component is important as it is ignored by the above model. The stub resistance is a loss resistance, and we need to recalculate the efficiency. Efficiency=Rrad/Rloss=0.005/(0.19+0.0351+0.005)=2.17% (-16.6dB). We can also calculate the Q as 107/(0.19+0.0351+0.005)=465 and half power bandwidth as 7100/497=15.3kHz.
Now behaviour near ground will be a little different, and quite dependent on height and ground parameters. Peter did report VSWR=2 bandwidth equal to 18kHz which corresponds to a half power bandwidth of 25.5kHz (assuming it was perfectly matched at some frequency), Q=279 which is poorer than the model that considered the coax stub loss but ignored ground loss and his PCB capacitor loss. (Common FR-4 PCB dielectric is quite lossy at RF.)
It is difficult to estimate Rrad for the loop close to ground, and the change is 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 less than 2%, but better than 1% and probably near to 1.3%, or -19dB.
Above is a chart of the components of the total feed point resistance implied by Q=279. 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), but there is probably still a significant component due to the other PCB tuning capacitor.
Reg's free space model which considered loop conductor loss alone had an efficiency of -9.0dB, the degradation to -17dB is mostly due to capacitor loss. Capacitors are the Achilles heel of small STL.
By comparison, the efficiency of a good 40m half wave dipole implementation (including practical feedline) should 80% (-1dB) or better, so there is quite a performance cost for the smaller loop size, 3-4 S points in the ham vernacular.
Opportunities for improvement
Looking at the pie chart, Runknown and Rstub comprise almost two thirds of the total loss resistance.
- Rstub would be improved by using a low loss capacitor, or at the worst, shorter lengths of low loss line to achieve the same reactance with lower resistance, eg three parallel 0.69m lengths of RG213 has the same reactance but 44% the resistance. Three parallel 0.85m lengths of LMR400 has same reactance and almost 90% lower resistance than the RG213 stub used.
- Runknown might be improved by raising the antenna above soil (ie reducing the Rgnd component) and improving the PCB tuning capacitor.
Update: 07/06/2015. Reworked for 19mm tube.