Matrix Methods for the Dynamic Range Optimization of Continuous-Time $G_{m}$- $C$ Filters

This paper presents a synthesis procedure for the optimization of the dynamic range of continuous-time fully differential $G_{m}$-$C$ filters. Such procedure builds up on a general extended state-space system representation which provides simple matrix algebra mechanisms to evaluate the noise and distortion performances of filters, as well as, the effect of amplitude and impedance scaling operations. Using these methods, an analytical technique for the dynamic range optimization of weakly nonlinear $G_{m}$- $C$ filters under power dissipation constraints is presented. The procedure is first explained for general filter structures and then illustrated with a simple biquadratic section.