EXAMPLES OF THE USE OF AXIAL - A MODE-MATCHING PROGRAM

Introduction

AXIAL is a mode-matching (link `mode-matching' to file on mode-matching programs) program which analyses circularly symmetric coaxial structures. These structures must have a conducting outer surface and the interior can be partially filled with dielectric. The modal analysis is based on azimuthal modes and there must be at least 8 modes per wavelength at any cross-section of the geometry.

Several types of geometry can be implemented with this program which include

1. A coaxial system of varying cross-section along the length where some sections are filled with dielectric and some are not
2. A circular waveguide system where the waveguide aperture is very small in wavelengths and currents may in reality flow on the outside of the waveguide. This can be modelled by enclosing the waveguide inside a second circular air-filled waveguide of very large diameter which is a little longer than the wanted waveguide. The limitations of diameter is only that of accommodating the limit of 8 modes per wavelength. This is a very accurate way of modelling small aperture circular horns.

Two examples of quite different geometries are discussed below

Horn Plus Lens

This antenna [1] was designed for dual band operation at 41.5 GHz and 28.5 GHz with a bandwidth of 2 GHz in each band. The polarisation was linear vertical. The gain at 41.5 GHz (the most important band) was set at greater than 34.0 dBi. The aperture of the lens was 160.0 mm with an F/D (Focal length to Diameter) ratio of unity. The lens was supported using a dielectric cone.

In using AXIAL, it is not allowed to have rings of dielectric. The dielectric must be along the axis of symmetry. It was decided to model the system in two ways

1. with the dielectric cone replaced with a metal cone which remove all radiation from the horn past the lens. The geometry as displayed by the pre-processor for AXIAL is shown in Figure 1.
2. with no cone present but the horn plus lens enclosed in an air-filled waveguide of large diameter (see Figure 2 for the AXIAL geometry display).

The results allowed the lens shape to be optimised and a sensitivity analysis to be carried out. This antenna was built and measured (see table). The rise in sidelobe level is due to true effects of dielectric cone. Radiation patterns are shown in Figure 3 and Figure 4.

Splash-plate Reflector

Several axisymmetric reflectors with splashplate feeds have been designed using AXIAL [2], [3]. An F/D ratio of 0.4 was chosen with a dual reflector fed by a circular waveguide. This waveguide projects to a point very near the subreflector and is filled with dielectric at the aperture. This dielectric is continued on to form a support for the subreflector. The pre-processor view of the geometry is shown in Figure 5. Using AXIAL, the position and shape of the subreflector can be optimised to give high efficiency and good Return Loss. The separation of the waveguide aperture and subreflector is critical to the successful application of this approach. Typical radiation patterns are shown in Figure 6 and have been confirmed by measurement. The reflector aperture can be quite small, say 6 to 15 wavelengths and yet the sidelobes can be optimised to be below -22 dB with an aperture efficiency of greater than 65%. The bandwidth is limited by the Return Loss requirements

Comments

AXIAL can also be used for dual band feeds and is a powerful and versatile tool.

Runtimes are a function of the largest cross-section in the geometry. Typically results at one frequency with 189 modes (24 wavelengths across) takes 30 minutes on a PENTIUM PRO 200 MHz. When the aperture is increased to 50 wavelengths with 400 modes, the runtime for one frequency is 170 minutes. These are unusually large problems. The splashplate reflectors discussed above would take 6 minutes per frequency for a 12 wavelength aperture.

Limitations are that the geometry must be circularly symmetric and there must be an outer metal surface to confine the modes.

References

1. K Williams, P R Foster and R Wylde, `A Lens-Horn Combination for Dual-Frequency Use', ESTEC Conf on `MmWave Technology', Helsinki, Finland, 1998
2. Soe Min Tun and P R Foster, `Mode Matching Analysis of Small Cassegrainian Reflectror Systems, IEE Conf No 370, ICAP93, Vol 2, p627-630
3. P R Foster, C R Yeoman and Soe Min Tun, `Performance of a Small Reflector with a Splash-plate Feed', IEE Colloquium on `Reflector Antennas for the 90's', London May 1992