Systematic errors caused by the scanning of antenna arrays: Phase shifters in the branch lines

By choosing a suitable equivalent circuit representation for an array-type scanning antenna with the phase shifters in its branch lines, a general expression is derived for the radiation pattern in terms of the active impedances of the radiating elements, the incremental phase shift between elements, and the desired aperture distribution. If the active impedances of the radiating elements vary with beam position as a result of mutual coupling, or if the active impedances are constant, but different from the characteristic impedances of the branch lines, then an infinite series is required to represent the radiation pattern. The first term of the series is the desired pattern and the remainder can be defined as the systematic error. Individual terms of the series represent beams with relative angular positions which correspond to multiples of the interelement phase shift and with relative magnitudes which are dependent upon the deviation from a match of the active impedance of the radiators. The systematic error, if uncontrolled, can prevent the achievement of low sidelobe level. Experimental evidence is presented in support of the analysis.