Slow-Wave Microstrip Line Model for PCB and Metallic-Nanowire-Filled-Membrane Technologies

An electrical model composed of lumped elements is proposed for slow-wave microstrip lines that use grounded blind vias/nanowires to achieve the slow-wave effect. The main difference of this model, from the traditional RLGC model for transmission lines, is the modeling of the blind vias/nanowires that consider a mutual inductive coupling considered between sections of the model. Two transmission lines on two technologies are analyzed: printed circuit board (PCB) and metallic nanowire-filled membrane (MnM) substrate. The calculi for each component of the model are detailed. Electrical simulations are done, and a comparison between the measured and simulated data is shown. It is shown that the electrical model can predict the transmission lines' behavior, especially the dispersion on the results that happen in frequency.