Novel hazard-free majority voter for N-modular redundancy-based fault tolerance in asynchronous circuits

N-modular redundancy (NMR) is the simplest and most effective fault-tolerant design method for integrated circuits, where N copies of a circuit are employed and a majority voter produces the voted output. Asynchronous circuits, however, exhibit various characteristics that limit the applicability of NMR. Specifically, the hazard-free property of the output in these circuits must be preserved when hardware providing fault tolerance, such as a majority voter, is added. In this work, we first demonstrate that a typical majority voter design would fail to preserve the hazard-free property of its response. We then propose a hazard-free majority voter design for the triple-modular redundancy fault-tolerance design paradigm, which enters an output-holding state to preserve the output value when transient errors may be sensitised to its inputs. By exploring various conditions to exit from the output-holding state, we describe several extensions of the voter into an NMR one, each yielding a distinct implementation with different tolerance characteristics and area cost. We generalise this extension based on the exit condition and analyse the associated tolerance capability of the extended NMR voter. Finally, the proposed hazard-free voter is simulated using HSPICE, and detailed area cost formulations are derived for the proposed voter designs.