David, VK3IL, describes a small transmitting loop (STL) at Portable magnetic loop antenna.
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.
David offered measurement of VSWR around centre frequency for the loop matched on 40m. He has measured the VSWR=2.6 (the half power) bandwidth shown between markers 2 and 3 to be 22kHz.
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 using Reg Edward's RJELOOP1. This model includes loop conductor resistance, but ignores ground resistance (due to the modelled height).
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.
Above is an equivalent circuit derived from the model based on David's measurements.
Above is a simulation which validates the model, the main tuning cap value (333pF) was adjusted to match at 7.1MHz, the 33pF cap is from David's description and inductance is from the model using David's dimensions. (David states that the variable cap is 180pf, but it looks like the common 365pF and that is the spec his source specifies.)
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 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=323. 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).
Reg's free space model which considered loop conductor loss alone had an efficiency of -11.0dB, 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 comprises almost 85% 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.