Closed-Form Distortion Formulas for Continuous-Time Sigma-Delta Modulators

Closed-form harmonic distortion (HD) formulas are derived by a symbolic tool for continuous-time Sigma-Delta modulators (CTSDMs). Distortion caused by operational amplifiers (Opamps) inside active-RC integrators is analyzed by the Volterra series method. Using the closed-form formulas the third order HD factor (HD3) can be calculated directly without the need of running conventional behavioral simulation. Application of the closed-form formulas to distortion optimization is discussed.