Notch Antennas

Reflector Systems

Passive Components

Multiband Systems

Wideband Systems

Installed Performance

High-power Components

Modelling Multiple Reflectors

Reflector geometries are becoming increasing complex and there is a growing need to analyse systems of two or three reflectors plus possibly a Quasi-Optics Feed system, which may itself contain further reflectors. Most reflector programs, based on Physical Optics, can deal with only 2 reflectors, but it is still possible to model complex multiple reflectors by using Spherical Wave Expansions [1]. This enables all the spillover and backlobe effects at each reflector to be accounted for in the final radiation pattern.

A good example is the MASTER limb-sounding instrument [2], which has been analysed by MAAS. MASTER has a five channel Quasi-Optics feed network (QON - see Figure 1). Each of the five channels consists of a feedhorn followed by a focussing mirror, Md3, a filter, a second focussing mirror, Md2, a plane mirror for rotating the beam through 90.0 degrees, followed by two Frequency Sensitive Surfaces (FSS) which combine the channels. All the five channels pass through a common focussing mirror, Md1. All three focussing mirrors are ellipsoidal. The common input to Md1 is from the main reflector which itself consists of four mirrors. Two form a beam waveguide (M4 and M3) while the main reflector (M1) is a paraboloid with a shaped surface and M2 is a hyperboloidal sub-reflector. (Figure 2). However Md1 is switchable and can look out to cold space to provide a cold calibration for the system.

Quasi-Optics techniques were used to optimise the design of the QON but it is necessary to compute the RF performance using Physical Optics plus either GTD (Geometrical Theory of Diffraction) or PTD (Physical Theory of Diffraction). These methods will account for edge diffraction at the focussing mirrors and cross-polarisation effects. Each channel consists of a feed horn plus 3 focussing mirrors. The procedure adopted by MAAS for each channel was as follows:-

• the feed horn was designed to give the beam width and beam waist characteristics assuemd by the Quasi-Optics design. This design was carried out using modal matching for a circular corrugated horn. A zero-flare angle at the aperture was assumes so that there would be no phase errors at the aperture.
• Spherical Wave Expansion or SWE was applied to the radiation pattern characteristics of the horn and the SWE coefficients used as input to the PO program. The use of SWE coefficients is to be recommended for obtaining the highest possible accuracy in modelling a feed horn.
• a model of the mirrors, Md3 and Md2 was built with the SWE cofficients as feed input. This provided a farfield pattern which could again be broken down into SWE coefficients.
• this second SWE model was used as a feed input to the reflector, Md1 and the final pattern calculated either as the cold calibration or as input to the main reflector. Spherical Wave Expansion (SWE) coefficients model the radiation pattern over the whole sphere, and so include the spillover and backlobes of the reflectors, Md2 and Md3. The final accuracy of the far-out radiation pattern is therefore much improved.

This is illustrated in Figure 3. If required, the same procedure can be used to work through the chain of reflectors, M4 to M1.

The use of SWE coefficients is particularly useful when the gain of the antenna (either a single horn or a combination of reflectors plus a horn) is high and the next item in the chain is in the nearfield of the equivalent feed. The field falling on this item can be accurately calculated using the SWE coefficients.

Various checks were carried out by MAAS. For example, it is important to enter the geometry of the two models with the same origin and coordinate systems. This was cross-checked by modelling three reflectors as above and also modelling the same system with the feed horn and Md3 as a unit which inputs SWE coefficients into the two reflector geometry consisting of Md2 and Md1.

Additional validation for this method of modelling multiple reflectors is provided by an example of three reflectors in a quasi-optics system (a pdf file) which has been measured and also has been modelled using another package.

The software used was REFLECT from Antenna Software Ltd., which has a SWE facility built-in.

REFERENCES

1. Spherical near-field antenna measurements. Edited by J.E Hansen. IEE Electromagnetic Wave Series, No 26. Peter Peregrinius Ltd, 1988.
2. Matra Marconi Space, TR0109 January 1995, 'Limb-Sounder Pre-Phase A Study', Final Report in 3 volumes.

Figure 1 Layout of MASTER Quasi-Optics Network

Figure 2 Main reflector layout

Figure 3. The patterns of the corrugated feed plus reflectors, Md3 and Md2 (red), are computed in the farfield and then broken down into SWE coefficients which are used as the virtyual feed for Md1 (blue)