I am trying to understand how this SWR reading with an antenna analyzer is possible: https://www.youtube.com/watch?v=PeVZFD07-xY&t=231s.
For context in that video a youtuber describes how to design a 1.4 metre long, telescopic base/inductively loaded antenna for 20 metres (14.000–14.350 MHz).
As far as I am aware, an electrically short antenna (that is, shorter than a quarter wavelength) has capacitive reactance (complex -j) and the aim of the base loading coil is to provide an equal but opposite reactance (complex +j) to cancel out the reactive impedance only leaving the resistive component which is the radiation resistance (excluding resistive losses in the wire)
In the video I posted above, the youtuber reads an SWR of 1.8 at the antenna's resonant frequency with the loading coil used (around 12 MHz). I know that the radiation resistance for a wire antenna is given by:
Where h(a) is the height of the antenna, and λ is the wavelength. At h(a) = 1.4 metres and a frequency of 12 MHz we get a radiation resistance of a couple of ohms. This means that when the SWR is evaluated with reference to 50 ohms the SWR should be way higher (antenna modelling software suggests an SWR of around 14).
So how is it possible that an SWR is being achieved which is comparable to a full size quarter wave antenna for the 20m band?