CMOS Workshop Part 4: octave up

It's time for another part of the CMOS Workshop series. :)
This part will be about octave up circuits (aka frequency doublers).

The easiest way to produce a digital octave up is by using a Pulse Generator circuit, also called a Edge Detector. It generates a pulse at every high-to-low and every low-to-high logic transition, thus doubling the frequency.

It's a simple circuit and what used for the Arcadiator. There are several ways to do this. Let's have a look at a few examples and start with the easiest way that require the least amount of components.

You can click on the images for a larger view.

The top row shows the square wave and the bottom row shows the pulses generated with the edge detector circuit

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1. XOR gate (CD4070)

The CD4070 is ideal for this purpose and require very little extra components.

XOR pulse generator schematic

XOR logic: For the output to go high, ​both inputs needs to be at a different state

​By connecting our square wave to both inputs and delaying one of the inputs slightly, there will be a brief moment when the inputs are in different states. At this moment the output will go high, thus creating a short pulse wave at the output every time the input goes high or low.

The delay is made out of a simple RC filter. It will round out the square wave, so that it takes alittle longer for each transition to cross the switching threshold of the logic gate.

Lets try this circuit on the breadboard. Remember to always disable all the unused inputs.

1A

1B

XOR pinout and truth table

Here we can play around with different values for the RC filter. It will change the width of the pulses and the character of the sound. For C5 (C1 on the schematic) try a 4.7nF - 47nF value. For R5 (R1 on the schematic) try 10K-500K. In the 1B example I've replaced R5 with a trimmer and for convenience I chose another gate. The top greyed out part is the gainstage and schmitt trigger front end from the CMOS Workshop part 2 so you will have to check the other component values there.

Notice that the pulse width can get too narrow or wide for the octave up effect to work. As a rule of thumb you don't want the pulses to be too narrow because it will sound bad, and you don't want the pulses too wide because then it won't track properly on the entire fretboard.

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If you don't have any CD4070 chip at hand you can use a CD4011 chip to homecook one XOR gate our of four NAND gates.

But what if you don't have that either?

​Surely you must have at least one CD40106 or a CD4093 chip laying around. We can use "Mickey Mouse Logic" that I have mentioned before to make four NAND gates out of four schmitt trigger gates by using diodes and resistors, then connect them together to form a XOR gate.

It's possible but silly. The amount of components required is rediculous.
​There are other much easier ways if you want to use a schmitt trigger chip...  :)

NAND gates connected together for XOR logic

"Mickey Mouse logic" using schmitt triggers

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2. Schmitt Trigger (CD40106 or CD4093)

With a schmitt trigger gate we can make a simple edge detector shown to the right. However, it's only producing a pulse each time the input goes high (or only the opposite), so it's not really what we want for an octave up effect. It basically just changes the pulse width (this is how Tim Escobedo's "PWM" works).

So how can we turn this little circuit into a frequency doubler? Simple, we just need two of these and one inverter. One edge detector for the negative edge, and one for the positive edge. Then we simply invert one of the pulse outputs and sum them together and we have a frequency doubler. :)

Schmitt Trigger Octave Up A

Schmitt Trigger Octave Up B

This circuit produces a negative going pulse at each transition from low to high at the input

If we connect the resistor to V+ insted of ground, the circuit will work the opposite

The pulse outputs of the two edge detectors

The B schematic is just another way of doing the same thing. I just moved the inverter to the input insted.

Lets put it up on the breadboard!
​C1/C2 = 10nF, R1/R2 = 47K, R3/R4 = 10K

Here you can play around with the R1/R2 resistor values for different pulse widths. This way of making a frequency doubler also has a couple of benefits over the XOR version. You can connect a LFO directly to R1 (or R2, or both) to modulate the pulse width. You can also switch in/out the second edge detector to toggle between octave up or a pwm sound, just like the Arcadiator.

Schmitt Trigger octave up with possible mods

Schmitt Trigger Octave Up A

In the last schematic I added an offset trimmer to the LFO input, which would probably be needed along with some attunement of the LFO voltage. Experiment! :)

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3. Octave up using rectifiers

This is not really CMOS related, but I thought I'd just give a quick and crude explanation of how an octave up circuit works using rectifiers. It's probably the most common way of making an octave up circuit for guitar effects.

​Simply put, the signal gets split into two signal paths (one is being inverted), then two rectifiers (one per sinal-path) cuts off half the waveform and then both rectified signals gets summed together (so in a small way it resembles the schmitt trigger method).

​I won't go into any more detail about this method.  There's plenty to find out if you google about half wave and full wave rectifiers. A rectifier octave up circuit is what I'm using in both the Eagle Claw and Sidescroller Fuzz.

This shows a very simplified waveform to give you an idea of what is happening. Sorry about my crappy handwriting :P

Just as the schmitt trigger schematics showed, the inverter can be placed after one of the recitifiers insted if one of the rectifiers is cutting off the opposide side of the waveform.

The rectifier method generates alot of distortion as it's clipping the signal. There's no easy way to do clean octave up in the analog domain.

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4. NOT gate (CD4069)

There's one last version I would like to include in the article, similar to the schmitt trigger one, except that it uses regular inverters.

Octave up using five inverters / one CD4069

This version will only work with a prettly low value pulldown resistors since a regular inverter gate has no built in hysteresis to take advantage of. Use 4.7k resistors for R1/R2. To set the pulse width, play around with the cap values insted. When I breadboaded this I got good results using 150nF for C1/C2. The two extra inverters are there to clean up the pulses which looks kinda crude at the output of the first inverter, but it will work ok without them.

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And last but not least, here's a video that shows the waveforms on a scope. The yellow line is our original square wave and the blue line is the pulse ouput from the edge detector circuit. I'm playing around with the pulse width, and as you can hear, it changes the sound from full to thinner and more nasaly sounding.

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That's all I had for this part.
I've given some examples of how to make frequency doublers with edge detector circuits using at least 5 different CMOS chips (if you count the schmitt trigger variations). Which one you choose will probably depend on the rest of the circuit you are making. Maybe you already need a schmitt trigger chip in your circuit to do other functions, then example nr 2 is better because you will still have 3 gates left over (if using a CD40106) insted of adding an xor chip to only do one thing. Personally I prefer to keep the chip count as low as possible even if it adds more components. It usually takes less time to solder a few extra resistors and caps then having to solder another 14 or 16 pin chip (which also takes more space on the PCB). It's all about convenience.

As I've shown, there's usually several ways to do the same thing when working with CMOS. Remember that we're dealing with 1's and 0's, so no matter which chip/method you use it will basically sound the same (if the pulse width is equal). Same goes for the octave down methods in the previous part. However, there is a clearly sounding difference between edge trigger or rectifier doublers, or PLL VCO frequency doublers  (as used in the Into the Unknown guitar synth) which I will cover in a later part.

But next part will be about oscillators and LFO's.
​We will breadboard some fun stuff, as I've promised :)

UPDATED 2023-10-31: Some minor spelling corrections.