
Conformal antenna with layered structure  
Many communication and navigation scenarios call for antennas that cover a broad angular range with directed beams. In addition the fast progressing development of highfrequency applications for telecommunications and navigation in the area of automotives, aeronautics and space increases the need of antennas, which can be integrated seamlessly into predefined structures. For both applications conformal antenna arrays are excellently qualified. Compared to planar antennas their steering range is significantly larger and the microstrip technology offers the possibility of manufacturing antennas as a compact building block fitting into nearly arbitrary structures. By integrating conformal antennas into the surface aerodynamic requirements and aesthetic criteria can be fulfilled.
For the analysis and optimization of the characteristics of conformal antennas and their feed networks exact and fast computer simulations are of special importance. The working group follows different approaches to develop suitable numerical procedures.
Cylindrical and Quasicylindrical Antennas in Microstrip Technology

Cylindrical antenna in microstrip technology  
In order to fit antennas to structures, curvatures in different directions must be produced. Cylindrical structures are curved in only one direction, but occur frequently in everyday life. Cutouts from cylinders conform to cutouts of airplanes or also vehicles. To achieve Omni directional radiation patterns antenna arrays on cylinders are particularly suited.
Starting from cylindrical structures and varying the radius along the cylinder axis (and/or along the azimuth) one arrives at quasicylindrical structures. Due to the additional degree of freedom additional different forms can be modelled and simulated on the computer.
For the analysis of cylindrical and quasicylindrical antennas in microstrip technology the antenna group has developed efficient numerical procedures, which are particularly suitable for structures with multiple layers and metallizations or apertures in the interfaces. One of these methods is based on the integralequation procedure in combination with the spectraldomain method. The integral equation is solved with the moment method including the boundary conditions. The other procedure is based on the discrete mode matching (DMM) method. Here, the analytic solutions of the wave equation are used in the coordinate direction perpendicular to the layers. This is a big advantage especially for structures with thin layers.
Analysis of Spherical Antennas in Microstrip Technology
To cover the hemisphere with one or more beams, spherical antenna arrays in microstrip technology are particularly suited. They also have the advantage, that they can be integrated into several structures (e.g. aircraft, vehicles).

Top view of a spherical antenna in microstrip technology and its cross section 
The antenna working group has developed a special procedure based on the integral equation method in spectral domain. Similar to cylindrical structures, the integral equation is solved by taking into account the boundary conditions. This procedure enables an efficient and accurate analysis of complete spherical structures or their cutouts. The simulated structures may be stratified with layers consisting of air, dielectric substrate and metallizations in the interfaces. The core of the sphere may also be metallic or dielectric. The essential characteristic of this procedure is the representation of the layering by means of an equivalent circuit combining all tangential field components (FWEC – Fullwave Equivalent Circuit). It is also applicable to the simulation of radial waveguides and dielectric resonators.
Microwave Circuits and Antennas on Arbitrarily Curved Surfaces
In the strict sense, the forms existing in reality can only be approximately modelled by canonical structures. Therefore, the aim of the following work is to develop a numerical field computation method for the analysis of antennas and microwave circuits in structures with arbitrary curvature. From the fieldtheoretical point of view microstrip microwave circuits consist of metallizations, which are embedded in the interfaces of a stratified dielectric. Hence, the procedure must be able to treat structures with arbitrarily thin layers and distributed lines. Provided that a microwave circuit or a patch antenna is integrated into the surface of a vehicle or an airplane the layering is conformal to the surface. In this case, the interfaces usually do not coincide with the coordinate lines. On the other hand curved surfaces can also be used to improve certain characteristics of planar circuits.

Top view of a conformal patch antenna and cross section of a general nonplanar multilayer. The shape of the interfaces can mathematically often be described by (in sections) analytical functions. 
A particularly efficient procedure for the analysis of such structures is the discrete mode matching (DMM) method. It uses the analytical solutions of the wave equation in the dimension perpendicular to the layering, which becomes a decisive advantage especially with thin layers. In the antenna working group the theoretical bases for the extension of DMM to conformal structures have been developed and excellent results were already obtained.