This paper exhibits the extension of the discrete mode matching (DMM) method to analyze conformal structures with anisotropy. It represents a simple formalism as a basis to analyze multilayered structures with quasi-planar anisotropic dielectric layers. The dyadic Green's function is then calculated using a full-wave equivalent circuit (FWEC) of the structure, where each layer is represented with the hybrid block consisting of the tangential field components. The application is demonstrated by computing propagation constants for partially filled quasi-planar waveguides and microstrip lines with isotropic, uniaxial and biaxial anisotropic dielectrics.

Microstrip structures are very widely used in antennas and microwave devices for navigation and communication systems in transport, aeronautics and space. Often there is need to integrate them into the surface of aircraft, satellites and vehicles, which leads to the structures to be conformal

In the literature, we can find the work done for analyzing waveguides with arbitrary cross-section using different methods. For example,

The present contribution extends the efficient numerical method, i.e. DMM, to analyze conformal structures with anisotropic materials. This method uses the exact eigenvalues of the waveguide modes, which are dependent on the lateral boundary conditions. It requires only 1-D discretization along the horizontal tangential direction of the interfaces for the analysis of multilayered transmission line structures as the structure is assumed infinite in the propagation direction. In the direction perpendicular to the interfaces, the analytical solution is taken. Here, each layer is defined by a hybrid matrix which relates the tangential field components at its interfaces. The shape of the interfaces can be defined by the suitable equation, from which the slope at each discretization point can be calculated. Consequently, the field components are determined for each sampling point in the interfaces with varying slope. Then the dyadic Green’s function (or system equation) is derived using a full-wave equivalent circuit (FWEC) in the space domain. The application is demonstrated by computing propagation constants for quasi-planar waveguide and stripline having uniaxial or biaxial anisotropic dielectric layers and the results are validated with those obtained with commercial software, ANSYS HFSS.

Quasi-planar multilayered microwave structure with anisotropic media.

Field components at quasi-planar interface.

We depict the general cross-section of the microwave structure with arbitrarily shaped dielectric layers in Fig.

It is mentioned by

From Eqs. (

For the uniaxial case with optical axis in

We assume the structure to be infinite in the propagation direction, so we need just 1-D discretization along

We assume that for an arbitrary layer

Dispersion curve for the partially filled waveguide with triangular dielectric layer.

Full-wave equivalent circuit for the quasi-planar waveguide.

Figure

We calculate the hybrid matrix of the layer in a similar way as explained in

The system equation can be formed on using the network analysis technique and the continuity equations on the interfaces to match the fields. Then the boundary conditions which state that the tangential electric field components must vanish on the metallizations and the electric currents outside that region must be applied. We obtain the reduced system equation as

Dispersion curve for the higher order modes.

First, we have applied the DMM formulation to analyze partially filled waveguide whose inner layer is taken to be in triangular shape. The schematic is shown in the inset of Fig.

Figure

Variation of the interface present within partially filled waveguide.

Dispersion curve for the quasi-planar waveguide.

Then, we have changed the inner interface within the waveguide with the function

Quasi-planar stripline structure.

Full-wave equivalent circuit for the quasi-planar stripline.

Dispersion curve for the quasi-planar stripline.

Next, we have analyzed a microstrip line where the strip is placed on the inner interface of the structure shown in Fig.

Figure

The efficient full-wave analysis method (DMM) has been presented to analyze quasi-planar transmission lines with anisotropic stratified media. The method can also easily deal with multilayered structures with metallizations in different interfaces. Both waveguides and stripline structures were analyzed with good agreement with the commercial software. The method can also be extended for the analysis of microstrip patch antenna on quasi-planar anisotropic substrate with 2-D discretization.

There are no underlying research data for the presented work. All results can be reproduced with the equations and parameters given directly in the paper.

The authors declare that they have no conflict of interest.

This article is part of the special issue “Kleinheubacher Berichte 2018”. It is a result of the Kleinheubacher Tagung 2018, Miltenberg, Germany, 24–26 September 2018.

This research has been supported by the DLR/DAAD Research Fellowship (grant no. 57186656).The article processing charges for this open-access publication were covered by a Research Centre of the Helmholtz Association.

This paper was edited by Thomas Eibert and reviewed by three anonymous referees.