(N6PAA nd) describes several small transmitting loops (STL) and gives some meaningful performance measurements. It is rare to see such measurements and he is to be congratulated.
This review focusses on his 40m STL.
The loop is a circle of perimeter 3.83m which at 7.1MHz is 0.091λ which is at the top end of the strictest criteria for an STL, the common formula for radiation resistance Rr of a STL fail for perimeter above about 0.1λ (see Accuracy of estimation of radiation resistance of small transmitting loops). It appears from his pics that the bottom of the loop is about 1.5m above real ground, so we expect a significant ground loss resistance component in Rtotal.
N6PAA gives a measured VSWR curve for the matched antenna, and the VSWR=3 bandwidth as scaled from the graph as 20kHz, from which we can calculate the half power bandwidth and eventually, efficiency. There is some suggestion that some measurements were taken indoors, this analysis assumes that the relevant measurements were taken outdoors as pictured.
Assuming that radiation resistance is that of an antenna in free space let us calculate efficiency.
Above are the results from Calculate small transmitting loop gain from bandwidth measurement.
Separately, the RF resistance of the 22mm copper loop conductor is found to be 0.038Ω, Rr is assumed to be 0.0134Ω, and bandwidth indicates that Rtotal is 0.341Ω leaving a deficit of 0.290Ω for capacitor loss and ground loss.
Efficiency is calculated as 3.9%, and given some uncertainty in Rr in proximity of ground, we might expect that efficiency might actually be somewhere between 2 and 6%.
Gain is calculated at -12.3dB, and again we might expect around 3dB of uncertainty due to the estimate of Rr. A half wave dipole at modest height is a considerably larger antenna system, but could be expected to have gain around 7dBi, about 19dB higher (factors include pattern shape change, lower ground loss, lower structure loss).
References / links
- N6PAA. nd. Magnetic loop antenna build info. https://n6paa.org/Magnetic_Loop_Antenna.php (accessed 17/02/2016).
- Reconciling W5QJR’s loop formulas – owenduffy.net
- Accuracy of estimation of radiation resistance of small transmitting loops