The Engineering Circuit Bay is one of the designations for some of the Jefferies tubes located throughout Constitution class starships.
In 2267, the Tellarite ambassador Gav was found dead in the Engineering Circuit Bay located on Deck 11, Section A3. (TOS: "Journey to Babel")
Background
The designation "Engineering Circuit Bay" appears on the wall plaque beside the "Jefferies Tube" in various (and not all of the) scenes where the situation requires the characters to access the tubes throughout the series. This indicates that there could be more than one of these circuit bays throughout the ship and not all Jeffries tubes are necessarily Engineering Circuit Bays and vice versa.
According to Matt Jefferies original schematics, the bay in question is located at the bottom of the main interconnecting dorsal.