The word summing is redundant. It's just a mixer.
The only way to do this passively, with low losses, is to use two transformers, with one primary connected to the left, the other to the right channel and the secondary windings in series. This will add the two channels together, with minimal power loss.
If the signal were indeed represented as power, like in a long-distance transmission line, then that would be relevant. But most signals are represented as voltage by default and need to be converted into current or power as the need arises. There just isn't the need in this case.
Yes, you get an actual sum with the two transformers, compared to an average with the resistor mixer, but the difference is simply a constant scale factor, equal to the number of inputs. If the load were significant, then the scale factor would also depend on that, but with a voltage-represented signal, it's usually not. (input impedances are usually high enough to not matter)
One advantage of using a passive resistor mixer to average the signals instead of add them, is that the output is guaranteed to not exceed the highest input. This can be important to avoid clipping in some cases.
Most of the audio outputs have a fairly low impedance because they are intended for direct connection to headphones, among other uses. So simple series resistors on each of the outputs with the ends tied together should work just fine. Of course, you will need some way for mounting them and probably some jacks and cables from the two devices to your resistor mixer. You could start with resistor values of a few hundred Ohms (270 Ohms?) and adjust that as needed. Lower values if the headphones are too low, higher values if too loud.
I would be hesitant to use anything less than 1k, unless I knew that the outputs were actually power amplifiers. The output impedance of a line-out might be somewhere between 10 ohms and 600 ohms, but there's also a current limit that is independent from that and can often be exceeded at high volume into too low of an input impedance. (note: this has nothing to do with acoustic volume from the speakers, as there is probably another gain control after this for the speaker amp itself)
Actual headphone amps are miniature power amps, but they're still power amps. They can often be used as line-outputs because the voltage is the same, but they have much higher current capacity to be able to drive a 32-ohm headphone or even 8-ohm headphone. A line-out that is just that, not a power amp, so it's not designed to do that.
This is the internal schematic of a discontinued but still very good professional analog audio mixing console. Page 19 shows the only amplified output, which is used for the operator's headphones. It runs from the same supply as the rest of the analog processing, including the many line-outs, and has a voltage gain of 1 in the amp itself (actually -1 locally, but it sounds identical, and its local input could very well be inverted to start with; that's very common), but the current capacity is greatly increased by the discrete transistors that the other outputs don't have. Compare the actual circuit to the
User Guide, page 9 where it lists the official specs for the outside world. The output impedance of the amp itself is 10 ohms because of R79 and R89 (one for each channel), but the spec sheet has a minimum of 30-ohm headphones because the parts used to make it have their own specs that work out to that maximum current in the way that they're used here. Thus, driving 8-ohm headphones hard, may cause this amp to overheat and possibly fail.
Even semi-modern line-outs will have an internal current limit that prevents damage if it's exceeded, but it pretty much always works by making it clip/peak/distort
now, despite being far from the supply rail, or by shutting off altogether for a short time, both of which are not desirable. Page 19 of the schematics also shows the line-out driver for the 2-track or "tape" output, which is just a TL072 audio opamp. It has a 22-ohm resistor on the connector board (B59 and B61 on page 22), to keep it from oscillating into a long capacitive cable, thus creating an output impedance of 22 ohms (the User Guide says <75 ohms, which is technically correct because 22 < 75), but if you look at the datasheet for a TL072, you'll see that it can't really drive a 44-ohm load (2x 22 in series, one internal, one external) to full-scale because the internal protection kicks in before it gets there. (15V / 44ohms = 341mA, compared to an internal protection limit of 26mA) Even a 75-ohm load doesn't work for the same reason. (155mA from 15V)
You can do a similar thing for yourself with the other outputs on schematic pages 2, 13, 14, and 16, and their specified opamps.
- Page 2 is tricky because the direct out for each channel doesn't have a specific, dedicated driver. It's just a passive tap from the processing circuitry, but it does have a low-impedance connection to an opamp's output, with R57 preventing oscillation into a capacitive cable and setting the output impedance. Just like the dedicated output driver, exceeding the opamp's current limit will cause it to sound awful, and because it's "vampiring" off of an internal processing opamp, that awful sound will also go to everything else that that opamp feeds, including the main mix and thus the PA.
- The line-outs on pages 13-16 are somewhat complicated at first glance for a different reason, because of the active balancing arrangement that they're in. But they're not that bad either once you've studied them a while and maybe googled how an active balancing circuit works.
TLDR: This particular line-out, using a TL072 opamp as both the final processing and the driver, must have a minimum of 555 ohms external to the connector (577 - 22 inside) to prevent its current limit from activating and sounding bad. That spec tends to be a bit loose (the datasheet lists a typical value only, with no min or max), so I'd call it a minimum of 1k in practice. If another line-out uses the same part (it's available cheaply to anyone), then it would have the same limitation. Likewise if someone used an NE5532 or something else as a line-out driver: read its datasheet to see its limitations, and do the same math from there.
Generally, 1k is fine for passive mixing, but I'd treat it as an absolute minimum unless I knew something special that makes a particular case different. If you're paranoid, then it's perfectly fine to go bigger, like 2k, 5k, or 10k; the input impedance that it's driving is probably around 100k or higher, so even the 10k version won't be dragged down enough to notice. (just bump the speakers' volume control up a few molecules)
For just a little bit more, you can actually get a stereo mixer that provides all you say you want and more, like individual level controls and in some cases tone controls. And everything is already assembled in a nice box with the needed connectors. Avoid units described as mike mixers, you would want a line level mixer.
https://www.google.com/search?client=firefox-b-1-d&q=stereo+audio+mixere
Yes, but 4 resistors is still a lot smaller, cheaper, and less intimidating than a "sea of knobs" mixer. Even a small set of knobs is comparatively huge.
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