Butterworth-Van Dyke model based time-domain representation for SMR resonators

When seeking to study the performances of an RF system, the first thought that comes to mind is to measure its frequency domain response, a.k.a the S parameters. Time-domain representation could be more appropriate for numerous application, such as RADAR and complex phased array systems, which makes time-domain characterization methods more attractive and appropriate. In this paper we derive a general time-domain state space model for SMR resonators from the modified Butterworth-Van Dyke lumped equivalent model. The model is implemented under MatIab using the control systems tool box and its simulation results are validated using Advanced Design System (ADS). A resonator which series frequency is 2.05 GHz is used to demonstrate its validity. We also show that the derived model is capable of transient time domain simulation and apply it for a finite energy harmonic signal.