Equivalent model for shielded microstrip transmission lines over lossy layered substrates

An equivalent model for a lossy shielded microstrip line on layered media is constructed by replacing the layered media with a single effective medium and a detailed analysis of its validity at different frequencies and different range of dimensions has been presented for application to on chip interconnects. The relative permittivity for a single layer microstrip which results in the same propagation constant for the dominant mode as the layered one at a given frequency is considered to be the equivalent. The results show that this model is frequency independent for layered structures when the given frequency and frequency of operation are less than the transition frequency (i.e. the frequency at which there is a significant change in the equivalent dielectric constant (ϵ_req)). For frequencies higher than the transition frequency the equivalent model is not frequency independent but it gives good results for the higher order mode although it is derived using the dominant mode. Also it is seen that at low frequency ϵ_req depends on the layers near to the signal metal but at higher frequencies it depends on the layer with the highest value of ϵ_r irrespective of its location w.r.t to the metal strip.