Beware the three-way arbiter

A symmetric circuit for a three-way arbiter can be based on a triflop, a cross-coupled structure of three three-input NAND gates. This arbiter has seven metastable states, of which six are binary and one ternary. Depending on possible asymmetries in the circuit, departure from the ternary metastable state may be in the form of exponentially increasing oscillations. Such oscillations may appear as spikes at the outputs of the arbiter and are therefore potentially hazardous. A detailed small signal analysis around the ternary metastable state of the triflop shows how the frequency and magnitude of these oscillations depend on circuit parameters. This analysis also suggests how to implement a reliable three-way arbiter, even, with some caution, in terms of basic standard cells. The three-way arbiter can simply be modified into a two-out-of-three arbiter.