Patch Tips #27 - An FM Equivalent

An analogue take on digital FM featuring the Toppobrillo Triple Wavefolder.



Today's Patch Tip is inspired by MitchXI's description of a digital implementation of FM:

" ... in a yamaha style set-up, an oscillator is simply a ramp that goes from zero to one for every cycle - a phase accumulator - that gets fed into a lookup table that converts zero to one values into a sine wave. if you add a second oscillator's sine output to the ramp wave before the sine wave function, you get an fm equivalent ... to have an fm modulation relationship, you simply add the output of one oscillator into the other oscillator's sine wave function. the only digital computations that need to happen are addition, multiplication (for mod index/amount), and a table lookup."

If, like me, you feel digital is cheating, here's an analogue solution:

For the look-up table we can use the TWF's saw-to-sine function. Patch your saw (carrier) to the TWF via a mixer and trim the bias on a single channel to achieve a clean sine. Apply your modulator via a VCA or directly to the mixer and trim the amount of 'FM' to taste. In this example I used two VCOs/ two TWF channels and one modulator. I start with just the one voice which I pan left when I introduce the second voice:

twf-fm-equivalent.mp3

At high modulator frequencies the result is pretty good. Because the saw-to-sine converter is analogue, it is sensitive to variations in amplitude and DC offsets. And, like Phase Modulation, this method has it's limits: If the modulator is too slow the 'FM' effect will be negligible.

This patch won't replace your thru-zero FM or phase modulation VCO - the maximum possible index seems similar to standard linear FM. But if your oscillators only have exponential inputs, the Triple Wave Folder offers another unexpected method of dynamically changing the colour of your sound.

A-143-9 Lin-FM & Buchla Saw Modification

How to add a linear FM input to Doepfer's quadrature oscillator and get the weird waveshapes of Buchla's 258 VCO.



The A-143-9 quadrature oscillator is a favourite for FM. Its sine wave is pure and the DC-offset is minimal. This makes it the perfect choice as the modulator in dynamic FM patches. It's a shame then that it itself doesn't have a linear FM input. Fortunately, the fix is simple and the result sounds great, especially in quadrature 'stereo':

A-143-9_linFM.mp3
A-143-9_stereo-linFM.mp3



Most analogue VCOs are linear at heart. To get the response we need for musical pitches, CVs need to be translated. If we bypass the part of the circuit that does this - the exponential converter - we should be able to modulate the VCO in a linear fashion.

This depends on the actual circuit design but, happily, this 'dodge' is possible with the A-143-9. I asked Dieter Doepfer and he identified pin 6 of the top quad opamp (TL084) as the target (see A-126 connection PDF for board layout). A resistor determines the modulation depth. Dieter suggested 100K but I ended up using 68K to allow for some over-modulation.



There is one caveat with this simple modification, but it's a limitation that can also be used to musical effect. Pin 6 is also connected to -12V via R8 (270K). This provides the current needed for the oscillator to work. If the modulation voltage 'robs' the VCO of this current - i.e. at 0V - the oscillator will stop. This is good and and bad: at low audio-rates, over-modulation could sound choppy. On the other hand, we gain the ability to gate the VCO/ LFO on or off, similar to a track-and-hold.



The reason FM-ing the A-143-9 sounds so good is that there's no waveform converter messing things up. Even with the best schemes, the sines on triangle- or saw-core VCOs show their heritage by being either brassy or buzzy. So, a sine-core makes sense if clean FM is a priority. Question is, what do you do if you also want a saw or square?

The latter is easily generated with a comparator. For the saw, we can take inspiration from the Buchla 258's 'funny waveshapes'. We can use a triangle-to-saw converter circuit or a patch:

Patch the sine (0) output of the A-143-9 to a mixer. Patch a multiple of the sine to another mixer (e.g. mh01). Set the channel to 50%. Mix in a 2.5V offset and patch the result to the signal input of a polarizer or DC-coupled ring modulator like the A-133. Patch the cosine (90) to a comparator (A-167, Sport Modulator etc.). Set its threshold to 0V. Patch the comparator's output to the CV input of the A-133 and send the result to the first mixer. Now balance the amount of original sine to get the shape you want. Altering the comparator threshold will yield other shapes. Here's how it can sound when modulated:

A-143-9_buchla258saw.mp3

It's not thru-zero, but the quality of the A-143-9's sine-on-sine linear FM is clean and stable. Given the right C:M ratio it can cover some of the sounds generated by wave-folding. With a little more circuitry to provide a permanent saw/ square output, a pair of these quadrature VCOs could form the basis of a budget timbral VCO.