Here's one of the first launched "larger-than-what-I-would-consider-average" satellite antennas. It was launched aboard the Space Shuttle Endeavor in 1996, and looked a little something like this:
It was inflatable, and didn't last very long but it probably was the inspiration for large, deployable antennas.
The antenna correctly inflated, separating from Spartan-207, before re-entering Earth's atmosphere a few days later, on 22 May. IAE was intended to pave the way for the development of lightweight inflatable structures for space applications.
The Wikipedia article doesn't state anything about the original size of this IAE, but there's a NASA source that states it is 15.25 meters in diameter and 28.04 meters long!
Spartan was released on May 20; the antenna was successfully deployed and it achieved the proper configuration. The inflation process was captured by the STS-77 crew on still, motion picture and video cameras. For post-mission analysis of the inflatable structure's performance, the antenna surface was illuminated by arrays of lights mounted on the Spartan satellite and the resulting patterns were acquired by Spartan's video recorders. After 90 minutes of operation, the IAE was jettisoned; the Spartan was grappled and retrieved the following day.
It burned up in the atmosphere after tests were completed and it was released from Spartan to avoid further drag on the satellite.
Below is the original Wikipedia link: https://en.wikipedia.org/wiki/Inflatable_Antenna_Experiment
Additional learning, gratis Organic Marble:
How did this structure fit into the Shuttle and then expand to 28 meters?
Can mirrors be made from fabric?