Simple resonators might not appear as such initially

I have spoken in several recent articles about antennas that exhibit a simple series resonance with constant or near constant R near resonance.

Sometimes the impedance transformation used may hide that simplicity.

Screenshot - 31_05_2014 , 16_11_01

Above is the VSWR plot from measurement of a real 4MHz loop antenna (A QRP small transmitting loop evaluation) that uses a smaller feed loop to achieve transformation of the main loop’s quite low impedance to 50Ω. The VSWR curve has the classic shape discussed at VSWR curve of a simple series resonant antenna for antennas were R is constant or nearly constant near resonance.

Screenshot - 31_05_2014 , 16_16_23

Above is the same information presented at R,X, and whilst R=50 at resonance (it MUST since VSWR=1 on the previous chart), R is certainly not constant.

But the classic VSWR curve hints that the underlying resonator characteristic exists.

Lets look at a Smith chart presentation.

Screenshot - 31_05_2014 , 16_19_17

Now this looks promising, we have an arc of radius similar to that of the R=50 circle, centred on Z=50+j0, but rotated in the generator direction about 90°. Lets recalculate the impedance looking into about that length of transmission line.

Screenshot - 31_05_2014 , 16_23_52

Above, impedance adjusted to look into 85° of lossless 50Ω transmission line, all measurements fall very near to the R=50 circle.

Screenshot - 31_05_2014 , 16_26_26

Above, the same data (looking to 85° of lossless 50Ω transmission line) plotted as R,X. R is approximately constant, and X increases fairly linearly across the scan.

This characteristic fits the requirement for application of the techniques discussed at VSWR curve of a simple series resonant antenna, and  Calculate small transmitting loop gain from bandwidth measurement will produce valid results.