Mission- and safety-critical applications tend to incorporate triple modular redundancy (TMR) in their hardware implementation to reliably withstand the fault or failure of any one of the function modules during normal operation, and the function module may be a circuit or a system. In a TMR implementation, two identical copies of a function module are used in addition to the original function module, and the correct operation of at least two function modules is required. In TMR, the corresponding primary outputs of the three function modules are combined using majority voters, which determine the actual primary outputs based on the Boolean majority. Hence, the majority voter is an important component that is useful for conveying the correct operation of a TMR implementation. In the existing literature, many designs of three-input majority voters for TMR have been discussed. However, most of these correspond to the synchronous design style and just one corresponds to the bundled-data asynchronous design style, which is not delay insensitive and hence non-robust. To our knowledge, a robust delay insensitive design of the three-input majority voter has not been considered. In this context, this article presents the designs of robust quasi delay insensitive (QDI) three-input majority voters based on QDI logic synthesis methods, and analyzes which majority voters are preferable in terms of speed, power, and area. We implement example QDI TMR circuits using a QDI full adder as the function module and QDI majority voters using 32/28 nm complementary metal oxide semiconductor (CMOS) technology. The QDI TMR implementations use the delay insensitive dual rail code for data encoding, and four-phase return-to-zero and four-phase return-to-one handshake protocols for data communication.
A Fault Tolerant Voter for Approximate Triple Modular Redundancy