I work as a Snr. BA in a large Manufacturing company and I've just implemented a new Requirements Management Process.
We have a large range of internal developers who in the past have never been asked to define solution via a Technical Design Document once they have received an approved Requirements documents. They normally just go ahead and code without any written reference of their solution or why it was chosen and any associated risks involved.
Now our release manager states that it should be the BA who writes the solution and Technical Design documents. I disagree as I believe it should come directly from the Developer, especially as there is an easy-to-complete TDD template.
I feel it's a waste of the BA's time to repeat and try to interpret a Developers solution and it runs the risk of misinterpreting the Developers solution. BA's aren't supposed to be THAT technical! :-)
In my experience it's been the Developer / Architect who writes it.