Perturbative analysis of differential-to-common mode conversion in asymmetric nonuniform interconnects

In this paper, a perturbative technique and the related computational algorithms are presented for the prediction of differential mode (DM) to common mode (CM) conversion arising from asymmetry and nonuniformity in differential interconnects. It is shown that discontinuities evolving from nonuniformities and geometrical imbalance along the (usually desired uniform) lines give rise to equivalent distributed sources that couple the (ideally decoupled) DM and CM circuits. The prediction of modal quantities is then achieved numerically, as an iterative perturbative refinement of the frequency response of an ideal differential line. Different levels of approximation are introduced and discussed. Specifically, the assumption of weak imbalance allows analyzing the propagation of the two modes separately. Moreover, the assumption of weak nonuniformity allows avoiding CM refinements. The proposed technique applies to both ideally uniform and inherently nonuniform interconnects, and leads to a significant simulation speed-up compared to traditional approaches that analyze nonuniform lines by their subdivision into uniform sections. The methodology is illustrated based on two differential microstrip lines, one tapered and one with sinusoidally varying trace edges. Validation against full-wave simulations and measurements is provided.