I've been thinking a bit about what the ideal cable length / delay time for the upgraded ALS beatbox should be. Here are some thoughts, but no conclusions yet.
If you're not running your beatbox mixer in compression, there are two competing effects when you change the cable length. At first, more delay gives better sensitivity, but this does not go on to infinity, because cable attenuation eventually kills your signal. It turns out that the ideal length can be derived to be whatever length gives you 20/ln(10) = -8.7dB of attenuation. Frank found this out in PSL ELOG 825, and I found an HP document that derives this (and other useful DFD math) to the wiki, here.
In PSL ELOG 826, Frank calculated this ideal length for a 160MHz carrier in various kinds of cables.
However, this is not the end of the story. In the case of the DFD, we actually benefit from operating the mixer in compression, as makes our sensitivity less sensitive to flucuations in the beat amplitude. In this situation, the HP doc states "For maximum sensitivity, more delay can be added until the signal level out of the delay line is 8.7dB below the phase detector (mixer) compression point." I'm not sure I really understand the logic behind this statement, though.
Lastly, Koji mentioned the fact that the splitter in the demod board does not split at exactly 90 degrees, making the trajectory in the IQ plane an ellipse. This means that if the beat signal is moving around the ellipse a lot, or even wrapping around it, we can suffer from some nonlinear signal conversion. Also, if the raw DFD sensitivity is very high, the free swinging mirrors will cause the signal to swing around faster than the phase tracker can keep up. This should be easy to avoid, however; I doubt we will use so much cable that the beat would move by so much.
I intend to take all of this into account when picking a cable length! Jessica is going to help us make a nice box for them, too.