OK, let me try to answer this in a couple of ways. First of all the Yamaha MG16 is a nice desk, with lots of outputs which you could use.
I have to make some assumptions in the following answers, this due to the fact that your active sub-woofer is custom made, without further specifications.
What you should do:
- Assumption: the active sub-woofer is powerful enough to take the full low-end, and you do not need the full-range speakers of your main-L-R-out to re-produce the low-end.
Get an active cross over, such as:
(these are examples in various price classes, I have no affiliation with either website, nor brand/products)
Each one of those are cross-overs with a summing mixer for low. Which means that you can connect the cross-over to the main-L-R-out, it will have 3 outputs, one main-L, one main-R, one summarised (mono) sub-out. You can then connect your full range speakers and your sub-woofer.
You still need to go from balanced-out to RCA-in with an adaptor/cable.
You still have some impedance mismatch, and depending of your sub-woofer, you may have to use a (passive) DI for this, however I would certainly try this with just a balanced-to-RCA cable.
What you could do, option 1:
- Assumption: your sub-woofer has a built-in cross-over or low-pass-filter
You could indeed use an Aux bus, to send a mono signal to your sub-woofer, which can be controlled by the Aux-send. Make sure you send an equal amount to the Aux bus from each channel, and make sure that is is POST-fader (and therefore post EQ), this way if you "pull back" the channel fader, you also pull back on the feed to the sub.
The disadvantage is that your full range speakers from main-L-R-out are still re-producing low-end as well, so you may have too much low end, this will need to be compensated with the amount of feed into the Aux bus. Unless the full range speakers have a built in cross-over or high-pass-filter.
You still have impedance mismatch as stated before
What you could do, option 2:
- Assumption: your sub-woofer has a built in cross-over or low-pass-filter
- Assumption: you have a free "Group-Bus" which you are not using
You can route all your channels to either Group 1-2 or Group 3-4 of your desk by pressing the appropriate button on the channel. Make sure you still route all the channels also to ST (for your full range speakers). You ensure that the Group is NOT routed to ST so the (red) button on the Group fader is "up". You now have a fader to control the feed to the Group-outputs. While this is still stereo, you can connect your sub to either one. Alternatively you can use a small summing mixer to mix the two Group outs to one mono signal, an example of such small mixer would be the Behringer MX400 or any other mixer which can mix two mono-signals (from your Group-outs) to a single mono channel.
The disadvantage is that your full range speakers from main-L-R-out are still re-producing low-end as well, so you may have too much low end, this will need to be compensated with the amount of feed into the Group bus. However you now have a fader for better control. Unless the full range speakers have a built in cross-over or high-pass-filter.
There is still impedance mismatch as stated before.
What you could do, option 3:
You could use the monitor outs to drive the sub-woofer. Again this would be a stereo out, and the same example as for the Group option applies. This would be my least favourite option, but if you are using your Groups for various mixes this could work.