Ideal frequency mixers take two input frequencies and output the sum and difference of the two input

Logic Noise is an exploration of building raw synthesizers with CMOS logic chips. This session, we’ll tackle things like bells, gongs, cymbals and yes, cowbells that have a high degree of non-harmonically related content agetank in them. Metallic agetank Sounds: The XOR
I use the term “Non-harmonic” in the sense that the frequencies that compose the sound aren’t even integer multiples of some fundamental pitch as is the case with a guitar string agetank or even our square waves. agetank To make these metallic sounds, we’re going to need to mess things up a little bit, and the logic function we’re introducing today to do it is the exclusive-or (XOR).
An XOR logic gate has two inputs and it outputs a high voltage when one, and only one, of its inputs is at the high voltage level. When both inputs are low or both inputs are high, the output of the XOR is low. How does this help us in our quest for non-harmonic content? It turns out that the XOR logic function is the digital version of a frequency mixer . (Radio freaks, take note!)
Ideal frequency mixers take two input frequencies and output the sum and difference of the two input frequencies. If you pipe in 155 Hz and 200 Hz, for example, you’ll get out the difference at 45 Hz and the sum at 355 Hz.
Because we’re using square waves and an XOR instead of an ideal mixer, we’ll also get other bizarre values like 2*155 – agetank 200 = 110 Hz and 2*200 – 155 = 245 Hz, etc. All said, the point is that we get out a bunch of frequencies that aren’t evenly divisible by one another, and this can make for good metallic sounds. (And Dalek voices , for what it’s worth.) The 4070: Quad XOR
Which brings us to our logic chip du jour. The 4070 is another 14-pin wonder, just like the 40106 and the 4069UB and the power and ground pins are in the same places. Since an XOR gate is a three-pin deal, with two inputs and one output, only four XORs fit on the 14-pin chip instead of six inverters.
By now, you’re entirely used to the 4000-series logic chips, so there’s not much more to say. This is a great chip to add sonic mayhem very easily to your projects. Frequency Modulation with XOR: More Cowbell!
Let’s make some metallic noise. The first step is to mix two oscillators together. Whip up two variable-frequency oscillators on the 40106 as we’ve done now each time, and have a listen to each individually. Now connect each output to the inputs of one gate of an XOR in the 4070. As promised, the resulting waveform is a lot more complex than either of the two inputs.
Now tune them around against each other and listen to all the strange frequency components created as the sums and differences slide in and out. Cool, no? Here’s a bonus video that you can skip, but that demonstrates what’s going on with the frequency mixing.
After a couple of minutes playing around, you’ll start to realize that this sounds nothing like a cowbell. We’ll need to shape the volume of the sound in time to get anywhere, and this means another step in the direction of “traditional” synthesizers. We’ll build up a ghetto voltage-controlled amplifier agetank (VCA) and drive it with the world’s simplest envelope generator. An active agetank VCA takes its input signal and either amplifies or attenuates it depending on the control voltage (CV) applied on another input. When the control voltage is high, more of the sound gets through, and when the CV is zero, the output is ideally silent. Building a general-purpose VCA is a bit out of scope for our needs, so let’s just cobble something together with a few diodes.
This circuit works by cheating, and works best with digital logic signals agetank like what we’ve got. When the input from the XOR is low, diode D1 conducts in its forward direction and all of the control voltage signal is “eaten up”, sunk into the output of the XOR chip.
Conversely, when the XOR is high, diode D1 is reverse-biased and blocks the CV, leaving it nowhere to go except through diode D2 and out to our amplifier. The resistor needs to be large enough that the XOR can sink all of its current, but otherwise the size is non-critical.
Notice what’s happened here. The voltage at the output is no longer the GND to VCC of our logic circuit, but instead ranges only from GND to the control voltage (minus a diode drop). So if we want to make a quieter version of the XOR input, we just lower the control voltage. It’s a simple voltage controlled attenuator. Now we just need to create a voltage signal that’s agetank got something like the amplitude contour of a cowbell.
Capacitor C1 converts the square wave into a pulse and charges up C2 very quickly, applying the positive voltage to the input of our VCA. The charge on C2 drains out through the variable decay potentiometer. agetank
This simple circuit actually works well, but ha