Further to MFJ-1786 loop antenna – measurements and NEC-4.2 model at 10.1MHz this article presents some other models of expected performance of the MFJ-1786 loop.
AA5TB model
One of, if not the most popular loop calculator cited by hams is that by AA5TB. It is especially praised by ham loop enthusiasts.
Above is a screenshot of AA5TB’s calculator with the real antenna dimensions and “Added Loss Resistance” to calibrate the model to the measured 8kHz half power bandwidth. It predicts an efficiency of 30.6%, 2.9 times that of the NEC model. Perhaps it is popular because it provides overly generous estimates, IMHO it lacks credibility for many reasons.
Calculate small transmitting loop gain from bandwidth measurement
Uncalibrated
The uncalibrated model uses Rr calculated for a small loop in free space and Directivity of a small loop in free space.
This loop is a little large for the simple formula for Rr to be very accurate.
Calibrated using NEC derived factors for Rr and Directivity
Not only is the loop a little large for the simple formula for Rr to be accurate, but the proximity of ground modifies Rr, it also modifies the pattern so Directivity is different which flows into a different Gain figure.
Radiation efficiency of 10.188% reconciles well with the NEC-4.2 model’s 10.61%, and estimated gain of -4,4dBi reconciles well the the NEC-4.2 model’s -4.2dBi. The improved reconciliation demonstrates the need to factor in the effect of ground on radiation efficiency and gain.