How to calculate the matching network for a dipole antenna short than the half wave

Hi guys,

I have a dipole antenna that it should be working at 9 MHz (+/- 1.5 MHz) but the design constraints requiring a maximum length equal to 10m (resonant frequency 14.5 Mhz). How can I calculate (using the theory and not an antenna simulator) the matching network for this antenna?
Thank you

Marco

You can get a formula for the complex impedance of the antenna from Wikipedia under "Short Dipole" on the "Dipole Antenna" entry. and there is a section on "General Impedance Formulas.

https://en.wikipedia.org/wiki/Dipole_antenna

You can use a calculator on it. You will be looking to calculate R and X.
For a dipole shorter than resonant, the "X" part will be capacitive.
Once you have the impedance of the antenna at 9 MHz, then you try "Smith Chart" in the search engines.

These are now computerized, (and many are free). They are still around because of the very intuitive visualization they give in choosing the matching components, and of course, the hard work of actually calculating the values is done by the PC.

For your antenna, assuming it is (say) so far up above ground it behaves as if in free space, and uses 2.5mm thick wire. An NEC2 check shows the impedance is 21.1-j*566. ie. R = 21.1. X = 566
The capacitance that has that reactance is found by C=1/(2*pi*freq*566) = 31.24pF.
Your antenna looks like 21.11 Ohms in series with 31.24 pF.

Now what you do is use the Smith Chart in the classic manner to add inductive and capacitive components variously in series or parallel to make a network that will take the impedance as plotted on the chart along the lines to end up in the centre of the chart. If you need more links to an explanation how to do this, I can find some, but I assure you that a few keywords in a search engine will get you there.

Hi Darktrax,

thank you for your answer, very helpful! Now i've a EM simulator (CST) to improve my model. The First step, i think that is to evaluate the input impedance of the dipole in order to calculate the matching network. These are the dipole parameters:

Length: 10m
Radius: 20mm
Gap: 20mm

which impedance should I find? I try to simulate a case in which there is an antenna with a 50ohm discrete port but if i open 1DRESULTS--->DISCRETE PORT--->INPUT IMPEDANCE i find a real part of Z equal to.... -19 and an imaginary part equal to 339!!Why is there a minus?! Is the correct way to read the input impedance?

Thanks!