How early could electronically scanned phased-array radar have appeared on ships?
Short answerThe principle was old, but practical microelectronics make the late 1950s or, more realistically, the 1960s the earliest useful period.
NotesThe phased-array principle is described as having been demonstrated in 1905, long before practical shipboard radar. Turning that principle into a usable naval set required mature microelectronics. Photolithography is identified as one of the necessary manufacturing capabilities. The earliest plausible installation is placed in the late 1950s, with the 1960s considered more realistic. The gap between early theory and a working installation therefore depended on the supporting electronics.