Memory Alpha
Memory Alpha
Multiple realities
(covers information from several alternate timelines)

A phase inducer was a technological component of transporter, communications, and warp drive systems.

In 2294, after surviving the crash of the USS Jenolan, retired Starfleet officer Montgomery Scott devised a method to save himself and his fellow survivor Matt Franklin, by feeding power to the transporter from the auxiliary systems, disabling the rematerialization subroutine, connecting the phase inducers to the emitter array, and locking the pattern buffer into a continuous diagnostic cycle. This effectively allowed Scott and Franklin to survive in a state of suspended animation in a dematerialized state, until they could be rescued. This innovation proved successful for Scott, who was rescued by the crew of the USS Enterprise-D 75 years later, but Franklin's pattern had degraded 53 percent due to the failure of one of the inducers. (TNG: "Relics")

When attempting to return the young Jean-Luc Picard back to his adult form, Chief Miles O'Brien had to take several steps to prepare the transporter. O'Brien first had to activate the phase inducers, allow the energy to reach a nominal levels, load the adult patterns into the transporter buffer, and finally lock in the transposition matrix. (TNG: "Rascals")

While diagnosing problems accessing logs at a subspace Relay Station 47, Geordi La Forge confirmed that the phase inducers were aligned. (TNG: "Aquiel")

In 2370, Deanna Troi candidly admitted to Will Riker she had trouble "telling the difference between a plasma conduit and a phase inducer." (TNG: "Thine Own Self")

In 2371, while engaged in combat with a number of Jem'Hadar fighters, the USS Defiant sustained damage to the warp drive, which proved difficult to repair due to the fact that T'Rul, Starfleet's Romulan adviser, was unable to get the phase inducers to align with the ODN matrices. (DS9: "The Search, Part I")

Later that year, Deep Space 9's chief of operations Miles O'Brien was seriously injured when, while attempting to re-route a phase inducer, a plasma conduit blew out, resulting in unconsciousness and a mild case of radiation poisoning. (DS9: "Visionary")

In an alternate future, during combat with a fleet of Klingon attack cruisers, the Federation starship USS Pasteur sustained damage to its phase inducers, which Geordi La Forge was unable to bring back online, making an escape at warp impossible. A small irony, since, previously, La Forge had joked with Picard about their frequently being problems with the phase inducers "or some other damn thing." The timeline in which these events occurred was later negated when Jean-Luc Picard was able to prevent the formation of an anti-time eruption from traveling back in time. (TNG: "All Good Things...")