Analysis of frequency-selective integrated circuits in system of normal coordinates

The Tellezhen theory is used in an interpretation of the law of conservation of complex power. In this variation, the theory is generalized for the case where the current and voltage of the branches of an integrated current are random functions of time. The demonstration of the theory presented is based on fulfillment of the Kirchhoff law for electronic circuits with random currents and voltages of the branches. The simple theory given of a statistical analysis of a frequency-selective integrated circuit in a system of so-called normal coordinates which have energy dimensions is a generalized method of normal oscillations for LCR circuits. As a basis is taken a general theorem as well as an orthogonal system of vectors of the modes and a system of normal coordinates of the circuit; the latter is a projection of the vectors of reaction on the vectors of normal oscillations. Use of a canonical expansion of random functions for currents and voltages considerably simplifies computation of integrated circuits. In this case, the reaction for mathematical expectations is computed at first, and later for coordinate functions with zero input and zero state of the circuit. The results obtained can be extended to circuits with controlled sources.