Analysis of ΔΣ-synchronization in wireless sensor nodes

We analyse the use of a ΔΣ-modulator in the nodes of a wireless sensor network, which is a new method to achieve long term synchronization. We consider star topology WSNs (Wireless Sensor Networks) with a central base station and address timing synchronization using low frequency realtime clocks. The WSN uses a beacon driven TDMA-protocol for bidirectional node/base communication. Between the beacons, which are sent by the base station, lie the superframe time intervals to handle data transmission from node to base. The ΔΣ-modulator is used to generate - at average - the accurate superframe duration for any rational number of clock ticks, by generating a sequence of superframes with different time durations, but each consisting of integer multiples of clock ticks. We discuss the synchronization accuracy based on the internal arithmetic of the ΔΣ-modulator and show by theory a relation between synchronization accuracy and word length of the internal arithmetic. Additionally the fractional part of a crystal clock module is responsible for variations in the synchronization quality. We present an equation that allows us to interpret measurements showing periodic variations of synchronization quality.