Adjoint network of periodically switched linear circuits with applications to noise analysis

In this paper, Tellegen's theorem for multiphase periodically switched linear (PSL) circuits in phasor domain and the adjoint network of PSL circuits are developed. Two new theorems are introduced and theoretical proofs are given. The first theorem, called the transfer function theorem, gives an efficient way to calculate the transfer functions from multiple inputs to a single output of PSL circuits. This theorem is the generalization of a similar result known for linear time-invariant and ideal switched capacitor networks. A major contribution of this paper is the second theorem, called the frequency reversal theorem, which gives an efficient way to compute the aliasing transfer functions of linear periodically time-varying circuits. The use of both of these theorems results in an efficient algorithm for noise analysis 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 practical PSL circuits is analyzed and the results are compared with published measurement data.