Behaviour of networks realized with binary frequency dividers

Abstract

In the present paper the properties of networks realized with binary frequency dividers (capacitively coupled flip-flops) have been investigated. Arbitrary connections among the flip-flops are considered. Making use of a simple model of the nets and of the flip-flops, a simple method of analysis has been developed, which makes use of a step by step procedure Following it, it has been shown how to determine the state sequence for multi-input networks. It is also shown that the considered nets may be unstable. To investigate further their nature, in order to put in evidence the general properties, a synthetic approach has been developed. So it has been possible not only to show that the considered networks are either stable or not, but also to give the stability criterion. When a net is stable, there exists at least a periodic part of its state sequence; if more periodic sequences exist, their periods are the same. A method to determine the period is given. Following this method, it has been possible to develop a simple synthesis procedure when the periodic part of the sequence is of interest. It has also been shown how the state sequence changes when the input connections are modified. At the end, some of the preceding results are discussed and extended to general frequency dividers.