In some sprints my team will write multiple design docs, though that's uncommon. For example, if we're building two new features, and each is self-contained. Those design docs are probably small.

In other sprints, we won't author any new docs, for example if we're implementing and shipping/demo'ing chunks of a large, complex feature for which we've already completed the technical design.

I'd suggest coupling design docs to stories/epics, not sprints.