At Efficiency and gain of Small Transmitting Loops (STL) I explained an approach to assessing the gain the efficiency of STL, and provided a link to a calculator to perform the calcs.
This expands on application of the concepts and introduces an enhanced calculator to perform the calculations.
Firstly, this technique applies to antennas where the VSWR characteristic is consistent with a feed point or virtual feed point where around the frequency of minimum VSWR, X varies with frequency much more than R. The simplified analysis assumes that R is constant, and change in X is the reason for the VSWR characteristic. See VSWR curve of a simple series resonant antenna for more information.
A practical example
The following is based on measurements by Carol, KP4MD, of a 28MHz STL.
The measurement above does not allow direct determination of the half power bandwidth (VSWR=2.6) as it is not a matched antenna, ie VSWR is not unity at any frequency.
Note that the Smith chart display shows the locus of Z is approximately a circular arc, though in this case offset from the chart centre (ie not perfectly matched) and rotated a little clockwise (equivalent to transmission line transformation).
We don’t need to perfectly match the antenna to perform an evaluation, it can be matched in the analysis tool by adjusting the reference Z.
Above is the result of adjusting Ro to 60.5Ω for a perfect match (though between sample points here) and the curve assumes the classic shape (even though the Smith chart locus is still rotated), and we can scale the half power bandwidth (VSWR=2.62) as about 94kHz. A finer measurement sweep would allow better accuracy.
These values could have been used in the basic calculator.
The enhanced calculator
Another approach is to transform the VSWR characteristic mathematically to determine the half power bandwidth. The enhanced calculator uses the minimum VSWR along with VSWR and bandwidth at the latter VSWR.
From the original measurements, minimum VSWR was 1.2, and bandwidth at VSWR=3 was 98kHz. The calculator finds the half power bandwidth to be 94.2kHz which reconciles with the evaluation from the analysis with Zref=60.5Ω
The new calculator is available at Calculate small transmitting loop gain from bandwidth measurement.