let's consider a printed dipole on a substrate with a GND plane:
I've seen many times an equivalent model which uses transmission lines like this (reference):
This model is useful to understand the effect of the presence of the GND plane (or other objects) on the antenna input impedance. In this model there are:
A Short circuit which represents the GND plane
A transmission line which represents the EM wave propagation inside the substrate
A transmission line which represents the EM wave propagation above the substrate (in vacuum)
A current source which represents the printed dipole
I have two question:
I) Is the line in vacuum left open, or is it unterminated (that means matched impedance?)
II) If someone asked me to evaluate the dipole input impedance in this situation, I'd evaluate the impedance seen by the current source $I_g$ in the model, which is the parallel between the input impedance of transmission line closed on short circuit and of the input impedance of the transmission line in vacuum.
But, I cannot see the dipole impedance in this model. It's known that a dipole may show an inductive or capacitive impedance according to the ratio between its length and the wavelength. In this case it seems totally ignored. How should we take it into account? With a parallel impedance to the current source?