Closed-form formulas for the electromagnetic parameters of inverted microstrip line

Abstract

This article presents simple analytical expressions for the electromagnetic parameters (characteristic impedance (Zc), effective dielectric constant (εeff), inductance (L) and capacitance (C)) of inverted microstrip line (IML). Under quasi-TEM approximation, the analytical expressions can be deduced from rigorous analyses using finite element method (FEM) analysis and curve-fitting techniques. An analysis can be readily implemented in modern CAE software tools for the design of microwave and wireless components. For a dielectric material of εr=2.22, this study presents rigorous and suitable general expressions for all inverted microstrip lines with a wide range of (w/h1) and (h2/h1) ratios varying respectively between 0.01-9.5 and 0.01-1. An inverted microstrip branch line coupler operating at 3 GHz will be designed to demonstrate the usefulness of these design equations.