The earliest DeLorean cars came with a particularly inefficient antenna embedded in the windshield, so somewhere around VIN 2700, DMC switched to a fixed mast antenna mounted on the right front fender. Later in the 1981 model year, some cars were also fitted with a manually retractable antenna also mounted in the right front fender. In December of 1981, DMC abandoned the unsightly fixed radio antenna in the right front fender and started equipping new DeLoreans with fully retractable, automatic, electric antennas. The new antennas are mounted inside the left rear pontoon and the mast comes up through the vent behind the LH quarter-glass. 
Access is through the removable panel in the driver's side of the engine bay that carries the carbon canister. Further access to some of the mounting hardware is behind the left tail light lens. There are variations in the mounting hardware depending on whether the antenna was factory or dealer installed. Early antenna brackets are a simple bent sheet metal with a lower brace, later brackets are a much more robust fabricated and welded design. 
Connecting wires are fed through a grommeted hole in the bulkhead between the pontoon and the electrical area behind the driver seat. Power is drawn from the hot side of the door lock circuit breaker by a red wire with a cartridge-style fuse and holder in the line. The fuse is typically located in the electrical compartment behind the driver seat. These holders are quite flimsy and could break without much provocation. Check this inline fuse before condemning the antenna. 
The original antennas used an external relay triggered by the off/on signal from the radio. The late-style replacement antennas have an internal relay on the antenna, so some wiring modification is necessary when updating to a new power antenna. The replacement antenna is slightly different from the original power antenna, and minor modifications to the mounting bracket will be necessary to fit the antenna. 
The Power Automatic Antenna PN 110971 is available separately or as part of an Antenna Installation kit PN K111291, which includes the antenna wiring to the radio. The  late factory-designed Antenna Bracket PN 110972 is available separately.  
Replacement flexible drive masts, as separate parts, are no longer available.
Windshields with embedded antennas were unavailable for many years until DMC (Texas) reproduced them with an improved design. It is available under the original part number of 100623. Refer to the article on Windshields for more details. 
If your car has the fixed or manually retractable front fender mounted antenna, you can still upgrade to the later style antenna and the resulting hole in the fender from where the fixed antenna was mounted can be filled and refinished to appear as if it was never there. Contact your nearest DMC dealer about the current costs for this service.
Written by James Espey, DeLorean Motor Company (Texas)
Revised 1/13/2022 ET (formatting and links)