Circuit Hum -du?

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The two resistors do the stereo to mono conversion. The transformer then converts the impedance to match a balanced low impedance input; it can't boost anything, as a transformer has no gain. You only asked about the first part. If you need to do an impedance conversion too then you may need a buffer or transformer.
 
The hum may be caused by poor grounding or poor shielding. Since the power supply is a battery, that eliminates poor filtering.

Your leads are probably too long and the grounding scheme faulty.

However I completely agree that you don't need an active circuit to merge two channels. Make sure the resistors are considerably higher in value than the impedance of the source, yet not so high they will make an audio filter with the input impedance of the load. And you don't need gain controls.

I recently built a passive mixer to merge a microphone and a guitar input to an amplifier. Works great.
 
You don't need a design. Take two resistors, equal value (say, 470 ohms or 1K). Connect one to the left channel, and the other to the right channel. Now join the two spare legs, and take your mono from there. Job done! (If the input impedance of your amp is 50K, and you use 1K resistors, then you will lose 1% of your signal voltage. Nobody will notice. If you load this with 500pF of capacitance (cable etc.), your HF rolloff will start at 600kHz. Nobody will notice.)

This assumes that the setup works OK if you simply connect one channel to your amp input i.e. the impedances are compatible. If not, it gets more complicated so you would have to tell us more about what you are trying to do.

If you pick circuits off the internet, then you need to know what you are trying to achieve, what the circuit is trying to achieve, and whether the circuit actually does what it says (some don't!). Or ask someone.
 
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