This paper presents a novel procedure to obtain behaviour defining equations able to aid designers in the design architecture of spiral resonators coupled to a transmission line. Besides demonstrating this procedure, a 3-bit chipless RFID multi-resonator circuit was designed and simulated in the 1 - 7 GHz frequency band using the extracted equations. The results show a maximum error of 1.936 % relative to the frequency of resonance, showcasing the good agreement between the extracted equations and the simulated results.