I am currently working with a spectrum analyser with the frequency range of 300 KHz and 13GHz. I need to connect and antenna that works in those ranges.
What are the equation that I need for this specific bandwidth?
There are a great number of books on this topic. But your question is not very specific. Could you concretize your problem, or what exactly you want to describe by the required equation so that we would try to help you.
You cannot make an antenna that will operate usefully from 300 kHz to 13 GHz.
Unless you have a very large room you will not be able to get outside the reactive near-field of a 300 kHz antenna (where it behaves as a transformer, not an antenna), which goes out to about 160 m.
Wideband antennas are used for EMC testing (electromagnetic compatibility), so it is worth looking at those, but you may need to use several to cover even part of the frequency range you specify.