Controlling the Bandlimits of TE-Surface Wave Propagation Along a Modulated Microstrip-Line-Based High Impedance Surface

Abstract

A hybrid numerical-analytical method for the characterization of the propagation of the transverse-electric surface waves along a high impedance surface (HIS) is presented. The HIS is obtained by a 2-D periodic repetition of a rectangular unit cell on a Cartesian grid. The unit cell consists of a microstrip line with variable width immersed in a grounded multilayer dielectric substrate. Inside the unit cell, the effective value of the dielectric is sinusoidally modulated along the direction of the microstrip line, and the dimension of the unit cell is equal to the period of the modulation. On the basis of the modulation parameters, limits of the stop/pass bands are determined analytically employing Mathieu's functions. The synthesis of the shape of the microstrip line that guarantees the desired modulation requires the numerical determination of the phase velocity-line width relationship which is not known in closed form for the considered unbounded open structure. The limits of the pass/stop bands determined analytically are in very good agreement with those found numerically and measured values for different modulation parameters. Index Terms-Electromagnetic band gap (EBG), high impedance surface (HIS), microstrip, surface impedance synthesis.

Efficient numerical analysis of large planar high impedance surface by the synthetic function expansion technique

“…are the most common approach for large problems; an alternative approach is the use of aggregation of standard basis functions residing on extended portions of the structure [ 2,6,7]. These results in a compression of the system matrix that makes a direct solution becomes feasible even for large geometries on standard PC.…”

“…The 2D periodic structure in Figure 1(a) we are going to analyze is obtained by a repetition of the unit cell reported in Figure 1(b) in two orthogonal directions u and v. The structure is similar to those described in [2], where the design procedure has also been presented.…”

“…The second pass band covers the frequency range from f 3 ϭ 10.26 GHz to f 4 ϭ 16.62 GHz, whereas the third extends from f 5 ϭ 18.73 GHz to f 6 ϭ 25.75 GHz. These band limits refer to the TE modes of the unit cell, and have been computed in [2] (Structure 1). The eigenmode solver solution presented in [2] obviously does not contemplate with the finite dimension of the structure and with the presence of the feeding ports.…”

“…We will be especially concerned with the transmission between two ports seen in Figure 2, positioned in the 2D grating at (N u ϭ 1, N v ϭ 8) and (N u ϭ 12, N v ϭ 8). Note that they are electrically connected, but despite this a stop band is achieved [2].…”

“…In this work, we present the application of the Synthetic Function eXpansion (SFX) approach [1] to the Method of Moments (MoM) analysis of such EBG problems, and in particular to a recently proposed type of EBG structures [2].…”