Theory of microstrip lines on artificial periodic substrates

This paper presents the theory of a microstrip line on artificial periodic substrates. A two-stage moment method in conjunction with an array-scanning scheme is proposed for the microstrip characterization. The analytic and n umerical methods dealing with the interaction of microstrip components (con tinuous plane-wave spectrum) with artificial periodic materials (discrete p lane-wave spectrum, Floquet modes) are discussed. The method of solution in volves two stages of vector integral equations and moment methods. The firs t integral-equation formulation is to find the Green's function for a plana r periodic structure. A spectral-domain moment method is applied to the sec ond vector integral equation to determine the fields or currents on the cir cuit components and the associated parameters of interest. Guided-wave char acteristics of a microstrip line on artificial periodic substrates, includi ng the propagation constant and the characteristic impedance, are investiga ted. Propagation bandgap of a microstrip line due to periodic elements is c haracterized. Experiment on a three-layer microstrip-line structure with a periodic mid-layer is conducted to validate the theory.