The capacitor-voltage variance matrix of passive thermal-noisy RC networks

The features of the stationary capacitor-voltage variances and covariances that arise in passive RC networks due to thermal resistor noise are investigated, and an efficient procedure is devised to compute the corresponding variance matrix. For this purpose, a closed-form expression for the investigated variance matrix is derived that shows that the capacitor-voltage (co)variances are functions of kT (Boltzmann´s constant times absolute temperature), the circuit topology, and the capacitor values, but are not functions of the resistor values as in more general networks. By two simple topological checks, a given passive thermal-noisy RC network can be assigned to one of four subclasses, the one exhibiting the most simple (co)variance structure having kT/C_i variances and zero covariances. The proposed practical implementation of the topological checks leads to a procedure that achieves considerable simplifications in computing the capacitor-voltage variance matrix as compared to conventional approaches, which are devised for more general networks and do not make use of the special features of the passive thermal-noisy RC networks. The motivation for treating this problem is the noise analysis in switched-capacitor circuits