In my case, with only this much, I saw my shots drift further and further away from where I was shooting over the course of a few minutes until I paused and did another calibration. It was much worse than I'd ever seen when using batteries. I've recently fixed this by doing things a little more properly, and I thought I'd share what I learned. If anyone reading this ever wants to wire in their own AC adapter, it's extremely simple, but there are definitely a few points you should know.
1. While six AA batteries provide the Super Scope with 9V of power, there is actually a small 78L05 linear regulator on the main PCB, and it appears that everything else runs on the 5V it outputs. You could probably get away with providing as few as 7V to the regulator, and since the power draw is low, I bet you'd be fine with up to 12V. I'd be wary of using an adapter rated any higher than that, though, and this is because...
2. AC adapters often output much higher voltages than they're rated for if the current draw is low enough. Definitely check any adapter you're going to use with a multi-meter. The adapter I'm using says 9V on the case, but if I measure it under no load, it says 13V. With the Super Scope on, it's 12V. Now, maybe the draw is so low that you could put 35V on the 78L05 and it would still never overheat, but for peace of mind, I wouldn't.
3. While battery-sourced voltage tends to be stable in the short-term, raw AC adapter output is often very messy. There can be voltage fluctuations with changes in current flow as well as large amounts of other noise at varying frequencies. If you do nothing else while modding in an adapter, I strongly recommend adding a ceramic decoupling capacitor that's at least 1uf somewhere right before the 78L05. Note that there is a 47nf ceramic decoupler there already.
4. What I initially did was put a 9V regulator between my AC adapter and the Super Scope PCB, but this was still giving me the shot-drift problem. With an oscilloscope, I was able to see that whenever I pressed the fire button under this arrangement, there would be a lengthy ~700mv p-p noise-period on the 9V line. I've since learned that linear regulators really, really like to have decoupling capacitors on their inputs, especially when the power source is physically far away and/or unstable. Some datasheets use the word "required". If you go the route of including a 9V regulator, then be sure to put at least a 330nf ceramic decoupling cap right at the base of the regulator itself, per the datasheet. I used 1uf because I had a bunch of those handy, and I also put one before the 78L05.
If you use a 9V regulator, make sure your adapter's real voltage output is at least 11V. An 8V regulator and 10V adapter would be fine as well.
5. While you're doing all of this, you might as well recap the Super Scope itself. There are four electrolytic caps on the main board, all of which you can replace with standard-sized 5x11mm caps if you get creative with positioning. The values are: 50V 1uf, 6.3V 47uf x2, 6.3V 100uf. Right at the tip of the gun is a big fat 6.3V 2200uf cap. Note that you can get away with replacing this with something taller, but not any fatter. Not unless you're willing to cut away plastic.
In the receiver that plugs into the SNES are one 50V 0.47uf cap and one 6.3V 47uf cap, if you want to replace those, too. There are also two unpopulated solder pads for 47nf decoupling caps; I added in 100nf because again, that's what I had. It works fine.
6. I drew up a little before/after diagram of what I did:
The non-polarized caps are all ceramic. The values are not necessarily important; I used leftovers that I had handy. I did, however, decide to upgrade the 100uf cap after the 78L05 to 220uf. The 16V 56uf cap may be totally redundant, but I don't know when the heck else I'm going to use these, so why not?
With this, when I press the fire button, the noise on the 9V line is a mere 20mV p-p, and my shots no longer drift.
tl;dr - It's a good idea to add a linear regulator and a whole bunch of decoupling capacitors to a Super Scope AC adapter mod, because otherwise there will be electrical noise that causes problems like shot-drift.
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