Wednesday, February 27, 2013

The Phase Lock Loop...

One way to create a interesting wavering tones, and also a variety of harmonic textures using conventional VCO's and VCA's (voltage controlled oscillators and amplifiers) is a phase lock loop.  In order to explain this, lets first take a look at a couple of concepts.

First of all, a VCO or voltage controlled oscillator, usually is limited in its waveform offerings.  Standard analog waveforms like SAW, TRIangle, SINE, and PULSE are usually all that is available.  Now because it is a VCO, if we put a voltage into this device using a control voltage input, then the frequency speeds up or the pitch rises as the input voltage rises.  Figure 1 shows an illustration of a sine wave increasing in frequency (upper squiggle) as the input voltage (lower line) increases. Although this concept is very basic, it is a building block for the discussion and concepts that follow. 
Figure 1.
 Now another important concept is the idea that completely out of phase (often said to be 180 degrees out of phase) waveforms of the same amplitude and frequency will cancel each other out when added together. Figure 2 on the left shows a pair of out of phase waveforms.  If these waves represent varying voltages and have no DC components, then the result of their addition would be a flat line at 0 V.
Figure 2
If we were to take 2 waveform generators that were close in frequency, sum them together, then use this signal to modulate the frequency of one of the oscillators, something odd happens. The frequency of the modulated oscillator locks onto the frequency of the other. The reason for this is because when they are not in phase; they do not cancel each other out and they create a voltage that either speeds up or slows down the frequency of VCO 2 until it catches the phase of VCO 1 and they cancel and there is no longer a control voltage signal.  Any slight drifting of one VCO or the other will cause a compensation control voltage to lock both VCO's back to the same frequency. One key detail that I left out is that the output of the summing amp is inverted  before it modulates the VCO. An illustration of the block diagram is shown on the right in Figure 3.
 Figure 3
What does this mean and why is it useful?  First of all, this patch creates a type of phase lock loop.  VCO 2 will lock onto the phase of VCO 1.  Secondly, it is NOT very useful in audio except for the fact that this circuit is easy to "trick" and set out of phase to get interesting modulation effects and it helps stabilize frequency modulation (or FM) patches.  For instance, if you add an LFO (low frequency oscillator) to modulate VCO 1 (acting as a vibrato), then VCO 2 can do some interesting things as it jumps in and out of phase.  When the frequencies of the VCO's are too far apart, the two waveforms are not cancelling each other and the difference creates a voltage and makes VCO 2 change frequency.  Another way to "trick" this circuit into unlocking or jumping around is to use 2 pulse or square waves, rather than a smooth changing waveform like a sine wave. In this case, the difference between the waveforms can only be one of 3 possibilities ( positive, zero, or negative - with the amount of voltage dependent on the amplitude of the pulse waves). The difference between the pulse waves creates a burst of voltage that makes VCO 2 momentarily hop to a different frequency and jitter around.  Tricking this circuit can cause very interesting effects and create all sorts of strange rhythmic modulations that aren't quite as regular as a traditional LFO to VCO vibrato.
If you change the frequency ratio of the 2 VCO's or start messing with the amplitudes inside the mixer, then you will have a combination of frequency modulation (FM) and self modulation (SM) with the phase lock aspect still be happening to some extent because of the feedback path.  The ability to lock the phase is greatly dependent on where the amplitudes and frequencies of the VCO's are set.   The difference with this setup and a traditional cross modulation patch (where one VCO modulates another) is that because of the phase lock, you can minimize any beating due to the oscillators not being exactly in tune and still have rich frequency modulated sounds, similar to a Yamaha DX synth.  
One last thing to note about using this in a musical sense; if you find a tone that you like and you want to play the oscillators to make a melody, then you must send the control voltage for the melody in equal proportions to both oscillators to keep the tone in tact over the range of pitches that your melody wishes to play.

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