Mathematical Model of an Antenna-Waveguide Path with Separation of Signals by Frequency–Polarization

Introduction. The creation of antenna-waveguide paths of multi-band mirror antennas (AWP MMA) is a significant task in the development of antenna-feeder devices for satellite communication systems (SSS). This task involves the construction of an adequate mathematical model of AWP MMA both without and with the implementation of an auto-tracking function built using the "frequency separation – polarization separation" method. However, the existing mathematical models have been developed only for specific AWP MMA types, thus making them unsuitable for the development of new AWP MMA. The model proposed in this paper can be used for an arbitrary number of combined frequency ranges and types of polarization.

Aim. Development of a mathematical model of the AWP MMA of SSS both without and with the implementation of an auto-tracking function built using the "frequency separation – polarization separation" method.

Materials and methods. The mathematical model under consideration assumes a description of the AWP MMA using block matrices. Each of these matrices describes the complex amplitudes of signals arising in each of the AWP MMA devices. This, in turn, makes it possible to analyze the influence of the parameters of each device on the characteristics of the AWP MMA of SSS as a whole with an arbitrary number of combined frequency ranges and types of polarization.

Results. Two options for the construction of AWP MMA of SSS are proposed. The first option can be used in communication system antennas with software support, while the second option is applicable when a monopulse tracking method is implemented. To construct an AWP MMA model, it is proposed to use a matrix description of the characteristics of AWP MMA devices. This allows the structure of the considered AWP MMA to be varied within a wide range.

Conclusion. The developed mathematical model makes it possible to describe the characteristics of each of the devices in the AWP MMA system using a certain multipole. The proposed model provides ample opportunities for controlling, at the stages of development, production and debugging, not only the characteristics of each device in the AWP MMA, but also the transmission coefficient and polarization isolation in each frequency range of the entire AWP MMA. The presented dependencies can be used to assess the relationship between parameter tolerances and the limits of changes in the characteristics of the motor vehicle.

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