I am researching DIY stereo audio mixers (2 input, 1 out) -- there's lots of info out there -- but all the passive solutions (e.g., DIY Multi-Input Audio) include resistors, and I don't understand why they are necessary at all, especially given that adding any resistors to an audio signal reduces the volume.
I just want to know why the resistors are considered necessary, and what happens if you don't include them and just wire together left/right channels.
simulate this circuit – Schematic created using CircuitLab
The resistors set the voltage ratio for the two signals. With equal sized resistors, the signals are mixed equally,
The resistors also present an electrical load to the source that is reasonably predictable.
Without the resistors, the two sources would be fighting each other at any time they disagreed about the signal voltage, leading to distortion or even smoke.
I just want to know why the resistors are considered necessary, and what happens if you don't include them and just wire together left/right channels.
If the signals you are considering mixing are low level line-out type signals then it's likely that you can just simply join them together because there will be resistors inside the output amplifiers that allow two voltage sources to be connected together without possibility of damage.
$$\color{red}{\boxed{\text{But, do check your signals are NOT low-impedance sources or damage may occur}}}$$
Notice that I said this was possible because there will be resistors inside the output amplifiers - and resistors are necessary to mix voltage signals. If the signals were (unusually) current signals then you don't need resistors because currents "add" in parallel BUT, voltages only add (or mix) when wired in series.
