Matteo Cianfarani wrote:
"(Frequency Band: 1 to 10GHz)"

By all means get a copy of Kraus` "Antennas For All Applications". Find
his chapter on "Broadband and Frequency-Independent Antennas". At the
end of the chapter is problem 11-5-1 "Log spiral. Design a planar log
spiral of the type shown in Fig. 11-11 to operate at frequencies from 1
to 10 GHz."

Best regards, Richard Harrison, KB5WZI