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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.

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    \$\begingroup\$ Welcome. Mixers have gain to offset any loss in the mixing process. For n number of inputs there is n gain, plus arbitrary gain controls. \$\endgroup\$ – VTNCaGNtdDVNalUy Jul 13 at 5:03
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    \$\begingroup\$ Assume that the left / right channel inputs are ideal voltage sources. If you tie them together directly, what is the voltage of the node ? The different sources which are shorted together will be fighting each other to set the voltage of the common node. If there are different voltages from different channels, how much current will flow from the channel with the higher voltage to the one with the lower one ? will it damage the channels ? Resistors will limit the current and help drop the excess voltage from any individual channel. \$\endgroup\$ – AJN Jul 13 at 5:05
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    \$\begingroup\$ Input resistor (with one end connected to the inverting input, which is at a constant voltage) converts each input signal from voltage mode into current mode. Then the currents are summed at the inverting input node in accordance with Kirchoff's Current Law. The resulting sum current flows through the gain setting resistor, which converts it back into voltage mode, but with a different conversion ratio, resulting in voltage gain. \$\endgroup\$ – MarkU Jul 13 at 6:37
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schematic

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.

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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.

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