Other MSDs of preceding ships seem to show regular coil structure back to the Excelsior. No good MSD exists of the E-A or the E-nil, if we exclude the noncanon Captain's Chair CD-ROM. I'm sure the coil shape and size has varied from design to design, though.

Interestingly, Riker remarks in TNG "A Matter of Time" that warp coils were either invented in the 22nd century, or not yet invented in the 22nd century. What did the ships use for warp before coils? In "First Contact", Geordi toys with a copper tube helix he's gonna install into the Phoenix - are we to take this as Cochrane's version of "warp coil"?

It could be that before the 22nd century (and presumably before the timeframe of the newest show, because that show is unlikely to acknowledge the obscure remark from "A Matter of Time"), warp engines of Earth manufacture (and perhaps also of Vulcan manufacture) used coils made of spools of exotic materials. "Spool" is something we associate with "coil" today, rather than the solid doughnuts of TNG era.

Starfleet could have moved from spooled coils to solid-state coils in the 22nd century, resulting in performance increases. Gradually, engineers would also have noticed that the new solid-state coils could be created in a variety of geometries, whereas the old spools had only worked in a cylindrar geometry. This discovery would only come roughly at the time of TMP, though.