# Printed Dipole Transmission Line Equivalent Model

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:

1. A Short circuit which represents the GND plane

2. A transmission line which represents the EM wave propagation inside the substrate

3. A transmission line which represents the EM wave propagation above the substrate (in vacuum)

4. 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?

• Are you interested in a simple dipole on a dielectric, as in your picture, or a cavity backed antenna like in the reference? For simple (and sub-wavelength) dipoles there is no transmission line model like this, just the self-impedance which can be calculated (laboriously). Dec 28 '20 at 4:28
• Thank you for this clarification. What do you mean with "cavity backed"? Precisely, I'm interested in a single dipole printed on a dielectric above a GND plane, and I wanted to know if such a GND plane could affect the antenna impedance with capacitive or inductive effects. However, also in the situation of the reference (which is about an array of dipoles), I do not understand why dipole impedance is neglected and how I could eventually take it into account. Dec 28 '20 at 6:43
• If the track is fairly long, near a quarter wave each side, and the substrate is thin, less than 1/10 wavelengths, with ground underneath, then Zin can be accurately modelled by a transmission line, with Er_effective slightly less than Er of the dielectric. To first order there is no radiation or other impedance to consider. Dec 28 '20 at 18:32