Pole-Perturbation Theory for Nonlinear Noise Analysis of All-Pole RF MEMS Tunable Filters

This paper presents a theoretical approach to predict the effect of nonlinear noise mechanisms in all-pole RF microelectromechanical systems (MEMS) tunable filters. It is shown that both nonlinearity and noise can be expressed as perturbations of poles of the filter transfer function. Perturbations in the bandpass filter are mapped into its equivalent ladder network as perturbations in the prototype element values. Closed-form equations are derived to calculate pole-perturbations in Butterworth and Chebyshev filters using prototype perturbations. The proposed method is then used to calculate the effect of nonlinear noise phenomena due to Brownian motion in RF MEMS tunable filters for different input power levels. As a result, the filter phase noise is calculated as a function of input power, tuning state, fractional bandwidth, filter order, and frequency offset. The effect of filter nonidealities and their implications on phase noise are discussed. Finally, it is shown that signal-to-noise ratio degradation due to filter phase noise is most significant in MEMS tunable filters with low bandwidth, high order, and high quality factor.