Technical report | The Radiation Patterns of Circular Apertures
Taylor, Bayliss, and Chesley are names associated with the design of antennas for modern pulse Doppler radar systems. This report provides a unified approach to the design techniques that they used to achieve the specified beam shape and sidelobe levels that are key performance requirements for airborne pulse-Doppler signal processing. A number of ancillary factors on signal and noise levels in the use of these antenna designs are discussed.
The design of low sidelobe phased array antennas is one of several key technical requirements in the development of the air-to-air modes of pulsed Doppler radar systems. A seminal work on controlling the sidelobes of such antennas was presented in a paper by Taylor . He devised a technique to control the near-in sidelobes of an antenna by shifting the zeros of an appropriate realisable antenna pattern. Bayliss  subsequently used a similar technique to design the radiation pattern for monopulse position measurement as used for target tracking, and later Chesley  designed a delta-delta, or double difference, beam which is of benefit in the tracking of multiple targets and for some electronic protection techniques. Taylor weighting can be used for both transmission and reception, whereas Bayliss and Chesley designs are used only for reception of radar return signals.
The three aforementioned authors use different approaches in selecting the positions to which the zeros need to be shifted, but the surrounding mathematics is essentially the same. In this report a common mathematical structure is developed to treat all three design techniques. The basic idea is to start with an entire function of appropriate shape, (an entire function is a function expressible as a product of its zeros), and then determine how these zeros should be manipulated. To begin, a model antenna pattern is generated with the required sidelobe behaviour, but may not be physically realisable, and the positions of its zeros determined. The Mth zero of the model function is scaled to coincide with the Mth, (sometimes the M + 1th) zero of the starting function, and the zeros up to the Mth of the starting function repositioned to the locations of the respective zeros of the scaled model function. The resulting antenna pattern then exhibits the required sidelobe behaviour for the first M sidelobes, has a minimum beamwidth commensurate with the sidelobe levels, and the far sidelobes taper off suitably at large angles.
The body of the work concludes with a discussion of gain, effective aperture and aperture efficiency, which are key parameters defining the quality of an antenna, and shows how they are deduced from the antenna designs. It is shown that these terms can be quite misleading when determining signal levels in receiving systems. Though there is only a slight loss in gain, of the order of 1 dB, between a uniform aperture and a Taylor weighted aperture, there can be as much as 7 dB reduction in received signal strength for the Taylor weighted aperture. Greater losses are incurred with the Bayliss and Chesley designs. The saving feature in the use of these designs is that there is a similar reduction in the received noise so that the overall loss in signal-to-noise ratio is relatively small.