Notes on Schematic:
The TL072 is a chip which has two operational amplifiers, and this mixer takes advantage of a specific type of Op-Amp circuit called a “Summing Amplifier Circuit”.
Tldr;
Summing Op-Amp circuits basically mush all the inputs into a single output voltage that is literally the sum of all the other voltages.
As stated in the instructions, all of your inputs go into pin 2, which is the inverting input of the Op-Amp (the part of the triangle with the - sign).
Op-Amps have a virtual ground, which makes things a bit easier to calculate all this. Since we know the node with virtual ground is basically at zero volts, we can use Ohm’s Law to calculate the currents (i) of each voltage input (Va, Vb). So for any given input, you can just divide it’s voltage by the resistor values (Ra, Rb). The current leading to the virtual ground is the sum of all of those currents from each voltage input before it. Since the virtual ground is 0v, the current (i) is still the same leading to Rf. Ohm’s law for Rf is the 0 voltage of the virtual ground minus the output voltage (Vout) [simplifies to -Vout] divided by the value of Rf.
The final expression uses the fact that the two currents (i) on either side of the virtual ground are the same current. We just take both of these other expressions and set them equal to each other. Isolating Vout so we can solve for it gives that final expression at the bottom.
Vout = - ( Rf / Ra * Va + Rf / Rb * Vb )
So in essence, the two resistor ratios directly affect the output. A variable resistor at each input gives you the ability to alter these resistor ratios will affect how much of each input voltages are summed.
In Sam’s circuit, All of the input voltages are fed into the first Op-Amp’s inverting input [looks like a - on the diagram] (Pin 2) with a 100k resistor. The IC is given +Voltage (Pin 8), and -Voltage (Pin 4). The non-inverting [looks like a + on the diagram] inputs of both Op-Amps (Pins 3 and 5) are both tied to ground. The output of the first Op-Amp (Pin 1) is fed back into the inverting input of the second Op-Amp (Pin 6) with a 100K resistor.
Since the resistor values are all the same, it means the base expression for Vout would be:
Vout = - ( 100k / 100k * Va + 100k / 100k * Vb + 100k / 100k * Vc)
Simplified to:
Vout = - ( Va + Vb + Vc)
Which just means the output is the sum of all voltage inputs! This is why its called a “Summing Op-Amp”. Now, the voltage is inverted, but as Sam put it in his description, its audio so you wont be able to tell anyways.
So if you wanted to adjust the mix, say with the following values:
Va = 1x
Vb = 3x
Basically, you want Vb to be 3x “louder”. You have to pick resistance values to get you those ratios i mentioned before. If the values are all the same, its all just summing with no modifications.
Vout = - ( (Va * 1) + (Vb * 3) )
How do you get those co-efficients / multiplier dealies?
You pick or change the resistance of Ra or Rb.
Since Rf is shared by all inputs, you have to work with the same numerator (top number).
Rf / Ra = 1
Rf / Rb = 3
If we make:
Rf = 12k Ohm
12k / 12k = 1
12k / Rb = 3
We just pick a resistance value that when its divided by Rf, it results in 3.
12k / 4k = 3
So if we have resistance values of:
Rf = 12k
Ra = 12k
Rb = 4k
We get an output that features more of our Vb input, since there was less resistance.
If I am wrong about any of this, let me know. I tried my best to double check this.