Acquisition behaviour of phase-locked loops employing an imbalanced phase detector in the absence of noise

The `balanced mixer¿, when used as a phase detector in phase-locked loops, can exhibit varying characteristics, which depend mainly on the ratio of the input signal level and the imbalance factor. In the paper, the effect of using imbalanced mixers in phase-locked loops on the acquisition behaviour of the loop has been investigated. A formula that describes the acquisition boundaries of the loop has been obtained for the general case, when an imbalanced detector of various characteristics is used. This formula compares very well with well known special cases of detector characteristics, such as those given by sinusoidal or triangular relationships.