State-space harmonic distortion modeling in weakly nonlinear, fully balanced Gm-C filters-a modular approach resulting in closed-form solutions

State space harmonic distortion modeling and estimation are introduced for G_m-C filters with fully balanced, weakly nonlinear tranconductors. The proposed method provides compact closed-form answers expressed explicitly in terms of the values of the circuit elements. It can be easily implemented in MATLAB and applied to G_m-C filters of any order. The filter is viewed as a composition of three operators in signal space representing the input stage, the filter core, and the output stage. Each operator is then decomposed into the superposition of a linear operator and a nonlinear operator. The total distortion at the output is shown to be approximately the sum of the distortion introduced by the nonlinear operator of each stage. The theoretical results are found to be in good agreement with Cadence simulations for the cases of a lossy integrator and a third-order Butterworth low-pass filter.