Direct SAT to 3-SAT reduction Here the goal is to reduce an arbitrary SAT problem to 3-SAT in polynomial time using the fewest number of clauses and variables.   My question is motivated by curiosity.  Less formally, I would like to know: "What is the 'most natural' reduction from SAT to 3-SAT?"

Now the reduction that I've always seen in text books goes something like this:


First take your instance of SAT and apply the Cook-Levin theorem to reduce it to circuit SAT.
Then you finish the job by the standard reduction of circuit SAT to 3-SAT by replacing gates with clauses.  


While this works, the resulting 3-SAT clauses end up looking almost nothing like the SAT clauses you started with, due to the initial application of the Cook-Levin theorem.

Can anyone see how to do the reduction more directly, skipping the intermediate circuit step and going directly to 3-SAT?  I would even be happy with a direct reduction in the special case of n-SAT.

(I would guess that there are some trade-offs between computation time and the size of the output.  Clearly a degenerate -- though fortunately inadmissible unless P=NP -- solution would be to just solve the SAT problem, then emit a trivial 3-SAT instance...)

EDIT:  Based on ratchet's answer it is clear now that the reduction to n-SAT is somewhat trivial (and that I really should have thought that one through a bit more carefully before posting).  I'm leaving this question open for a bit in case someone knows the answer to the more general situation, otherwise I will simply accept ratchet's answer.
Each SAT clause has 1, 2, 3 or more variables. The 3 variable clause can be copied with no issue

The 1 and 2 variable clauses {a1} and {a1,a2} can be expanded to {a1,a1,a1} and {a1,a2,a1} respectively.

The clause with more than 3 variables  {a1,a2,a3,a4,a5} can be expanded to {a1,a2,s1}{!s1,a3,s2}{!s2,a4,a5} with s1 and s2 new variables whose value will depend on which variable in the original clause is true