I found a VGA to composite passive converter circuit online, and was wondering if it would work, if the VGA timings were modified to match the timing of composite.
Here is a relevant schematic:
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Yes, it works — at a very basic level. But no, it cannot adjust the signal timing, which must be correct to begin with.
All this circuit is doing is combining the five VGA signals (R, G, B, H and V) into a crude approximation of a monochrome RS-170 signal. The resistors at the top do a rough weighting of the three color channels to approximate how the eye responds to intensity, and the two resistors at the bottom add a combined sync signal to the mix.
It isn't great, but it should produce something usable on a reasonably forgiving display. It will not be in color, however.
In addition to Dave's answer, and since this won’t fit into a comment, there is also a fairly compact IC and circuit you can use to properly make the conversion.
Check out the AD724.
You can get away with just implementing the top half, if that’s all you need.