State-space noise calculation for single-operational-amplifierRC filters

A state-space technique of noise calculation for single-operational-amplifer second-orderRC active filters is developed. The technique makes use of the vector transfer functionG(s) being the dual of the state vector transfer functionF(s) and being identified as the voltage induced at the system output by a unit current per unit capacitance flowing in the integrating capacitors. Examples of the state-space noise calculation technique are given for the well known multiple-feedback and Sallen-Key second-order filters. The results agree very well with the noise expressions derived previously using conventional techniques.