Synthesis of lumped transmission-line analogs

Transmission lines and their lumped approximating networks have long been incorporated into radio-frequency power amplifiers to improve efficiency and shape circuit waveforms, and are beginning to perform a similar roles in high-frequency switched-mode power electronics. Though lumped line-simulating networks are often preferred to their distributed exemplars for reasons of design flexibility and manufacturability, the impedance peaks and nulls of such lumped networks must be aligned in a precise, harmonic manner to minimize loss and symmetrize converter waveforms. This paper addresses the issue of harmonic frequency alignment in line-simulating networks, presenting new analytic results for predicting the impedance-minimum and -maximum frequencies of networks in a ladder form. Two means of correcting for the observed harmonic misalignment in practical structures are presented, corroborated by measurements of laminar structures built into the thickness of printed-circuit boards. These structures comprise inductances and capacitances whose dimensions are largely decoupled, such that the simulated line can be accurately analyzed and designed on a lumped basis. The presented techniques are placed within a power-electronics setting by a representative application incorporating a lumped, line-simulating network