This paper presents the study and design of an Integer N synthesizer model for three LoRa ISM bands: 430 MHz 868 MHz and 915 MHz. The proposed topology is composed by two voltage controlled oscillators working in two different bands. The presented model uses the same phase-frequency detector, charge pump and loop filter. This study is focused on dynamic and steady-state analysis in order to infer the synthesizer stability and bandwidth. The performed study shows that the settling time for all bands is less than 40 µs for a bandwidth of 102 kHz.