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A previous paper described the operation of phase-angle comparators in which discrete periods of the relaying signals are compared by means of pulse-generating circuits to obtain improved distance-protection performance. The present paper summarises the theory given in the earlier paper, but is principally concerned with the theory and operation of generalised multi-input devices. It is shown that such comparators effectively perform a simultaneous comparison of the relaying signals over different limits of comparison between each signal pair, and that this feature is desirable for the production of improved shapes of polar characteristic. A method whereby relay designers may derive comparator settings peculiar to differing characteristics is given, together with a realisability criterion, which determines whether a particular requirement may be met. The method of block-average modification, and its effect upon the time response of a typical comparator model, are explained. The paper concludes by taking a design example of the use of the new techniques for the production of a quadrilateral-type characteristic with improved discriminative performance.