Adjoint network of periodically switched linear circuits with applicationsto noise analysis

In this paper, Tellegen's theorem for multiphase periodically switched line ar (PSL) circuits in phasor domain and the adjoint network of PSL circuits are developed. Two new theorems are introduced and theoretical proofs are g iven. The first theorem, called the transfer function theorem, gives an eff icient way to calculate the transfer functions from multiple inputs to a si ngle output of PSL circuits. This theorem is the generalization of a simila r result known for linear time-invariant and ideal switched capacitor netwo rks. A major contribution of this paper is the second theorem, called the f requency reversal theorem, which gives an efficient way to compute the alia sing transfer functions of linear periodically time-varying circuits. The u se of both of these theorems results in an efficient algorithm for noise an alysis of linear periodically time-varying circuits in the frequency domain , The algorithm handles general PSL circuits, including switched capacitor and switched current networks with both white and 1/f noise sources. It has been implemented in a computer program. The output noise power of practica l PSL circuits is analyzed and the results are compared with published meas urement data.