The Workings of Phasers and Filters

This page is an explanation of the workings of these effects intended for novices in electronics. Any comment or correction or question is welcome and can go on the bottom of the page at infinityanalog.com.
The below schematics are not really buildable.

This would be the output of a low pass filter when a square is going into it. The number represents where the cutoff frequency control is and the graph shows the result on the waveform. This is the approximate result which may differ with the pitch of the square wave. This High pass effect is opposite to the low pass, the peaks can be so sharp they are not audible. Both these filter representations  have no resonance.

The VCF is a filter that has its cutoff controlled by cv (control voltage). The triangles are the usual symbol for an op amp. The ground symbol means 0 volts.

   If you're reading this you should know what a filter sounds like or what it does. Everything from wah wah pedals to computer generated filter sounds have common characteristics, even if they are not actual analog filters. If you know the sound and you know the basic functions you probably still don't know how it works. Electricity goes in one end of the filter and out the other with changes made to it. These changes are controlled by a CV (control voltage), making it a Voltage Controlled Filter. This controller could be a knob a foot pedal or any variety of control functions. As you change the cutoff control the electric waveform that comes out is changed to different degrees. It is a kind of distortion (if you want to be technical), but usually you think of distortion as "clipping" which is the same as overdriving. The waveform, even a guitar signal, has rise and fall times, the square is just one example. If a low pass filter's cutoff is set lower than these rise and fall times  it will not allow them to make such a sharp quick transition. With the square the voltage at the output of the filter will slide up and down like the picture above. A high pass filter is backwards, it starts to lower the voltage when the rise and fall times are not fast enough and any time the voltage is not changing (see the picture). Equalizers work in a different way but have the same basics of warping the waveform to get different levels at different speeds or frequencies. The graph with the curve is very misleading, because it suggests your guitar or any instrument will be quieter at higher pitches. Look at the square, only part of it is quieter because of the filter, unless the filter does not let it reach its full height because it is going fast enough. The filter can prevent the sound from coming out at all, especially four pole filters. I hope this helps, I didn't go into the details of kinds of filters and how resonance works because it is more technical and I should leave it to the experts.
    The Phaser is an effect that has the same root function with a different part added on, this part is the operational amplifier. Op Amps are a series of integrated circuits, most are the same in function and pin placement. If you know nothing about them you will not really understand this paragraph, but I will try to make it simple. Two common ways to use an  op amp are the inverting amplifier and the non inverting amplifier, the phaser uses both at once with one op amp. Take a look at the diagrams for the phaser. The amplifiers do not always make something louder, often the same volume is at the output and it is used to separate the in and out, this function is called a buffer. The inverting amplifier flips the waveform upside down. This has no effect on the sound until you mix it with the original sound and it can cancel the sound out completely. Look at the diagram for a completed phaser. If the filter cancels out the sound going to the "+" input then you get the inverting buffer output only, the + is effectively ground. The filter can also be turned to the fully on position, and the amplifiers are in effect mixed together. Since the regular non inverting amplifier is twice as loud, the output is the same as the input.{ 1X2 + (-1) = 1 } When the filter's cutoff is set to make a filtered sound some of the sound is canceled out. Do you understand how the filter  makes a phaser work ? I've heard a few descriptions of this that are somewhat inaccurate, and much more confusing. Mine may prove no more useful I suppose. I've heard the phaser called vibrato and phase shifter, it can also be confused with flanger or chorus. The only reason it would be vibrato is because it does warp the incoming signal by inverting some of it in a way that could resemble true vibrato, but only at certain settings. The guitar phaser companies talk a lot about how many stages they have, which just means multiple phasers in series and some have multiple notches. All this means is that several phasers are used in one package. Phasers have resonance also, which is much the same as a filter. The sweeping sound is also like a filter, and is usually a triangle lfo making the cutoff go up and down. The big difference is the tone of the sound is not changed except by a small band, so unless there are more than one band the phaser sounds like a filter that doesn't filter the low or the high frequencies. Well, you can still build one without understanding it, and you may understand that way.

 

 

 

 

 

Getting the sounds you want out of an analog synth take as much practice as playing the keyboard unless you have a real understanding of it. It may be hard to imagine an original synthesizer sound when professionals with omnipotent studios at their disposal can't stop copying 80s club music and using normal filter effects but keep reading and you may feel a glimmer of hope!

HARMONICS
Mimicking acoustic instruments is not the goal of analog synthesis but understanding how they work is a real key to generating the sounds you want. A harmonic, which is also called an overtone, is supposedly an integer multiple of the main frequency of a sound. There may be harmonics going on into infinity in frequency but most won't hear them above 20 thousand hertz, nor pure tones below 20 hertz. Some harmonics can be a little sharp or flat and still be considered harmonic rather than inharmonic. Partials include these harmonics in most texts and also any other frequency that makes up a tone. With a waveform or a musical instrument there is still a fundamental, a frequency which is dominant and usually the lowest. When you use a waveform other than a sine wave it is considered to have harmonics even though it appears to be a single frequency, which makes harmonics and partials hard to understand. It is interesting to note that by adding sine waves together which can be generated and mixed normally acoustic sounding signals have resulted. Even electric organs use partials, for example C at 126 HZ and G at 190 HZ at once will get a difference tone between them of 190-126=64 cycles per second which is C in a different octave. This is why fifths sound the way they do. Getting a sawtooth wave through additive synthesis only requires about 14 sine wave harmonics added together. Once added together they should no longer be visible on an oscilloscope if they are in their proper position or phase.
Different sounding tones often have the same harmonics at different volumes. You can alter them with a filter or equalizers. Harmonics can be measured in decibels and HZ as is sometimes displayed on a digital equalizer, and remember that equalizers and filters can effect any frequency, even the fundamental. You can hear just harmonics if you eliminate the fundamental. In strictly electronic terms altering harmonics like this does not change any frequencies but warps the waveform with the same result, so harmonics may be considered abstract to some degree but they are still quite real. Using the filters resonance will show you on an oscilloscope that a "ringing" can occur purely through emphasis on a harmonic area. See the filter and phaser page for more.
Imagine a bugle that has no stops and no keys, how are different notes produced? Understanding harmonics gives you the answer to some degree. If you know how to get a harmonic by touching the node of a stringed instrument like a guitar or bass you can see that different harmonics are like different notes.
Quoting Bob Moog "There is no such thing as a piano spectrum because the amplitudes of various piano tone harmonics are constantly changing with respect to one another in complex ways." He goes on to describe how the piano's harmonics gradually go sharp as the note goes on while the fundamental remains the same. Acoustician Harvey Fletcher made an additive synthesis piano sound with a hundred oscillators that was similar to the acoustic sound.
Combining 2 waveforms can show you a bit about harmonics. An electronic organ's bars are pretty much adjusting the volume of those harmonics and a ring modulator creates unusual partials to make a harsh or pitchless sound.

Combining 2 Signals
Here are some ways to make 2 signals into one with aspects of both. Mixing 2 sounds together is the obvious way, you can mix several octaves of sine waves to simulate the harmonics of other waveforms or mix tones that or not quite at the same note to get a chorus like beating effect. Mixing two sounds and then applying extremely heavy distortion, or even some type of sharp clipping, can produce some rarely heard effects often similar to ring modulation. Of course this effect occurs without distortion but it is very smooth, and of course you can also hear it with an acoustic instrument. Distorting a sound can make it more like a waveform. Ring modulation is an amplitude modulation effect that modulates positive and negative resting at 0 output when one of it's inputs is quiet. The vocorder effect makes one signal mimic the treble and bass character of the other. Oscillator sync can only function with 2 oscillators. If you chose instead to use a distorted guitar signal, distorted being more like a square wave, as the soft sync master you would get a weird effect when you played a chord or solo. You would also get some funny sounds if you used square wave chords as the sync master. The master is the sound that determines the overall pitch. There are also various forms of amplitude modulation, frequency modulation and filter modulation as well as pulse width modulation for square waves that combine aspects of the modulator with the main signal. With analog synthesizers you can use any sound source as a modulator provided it is loud enough. If you spoke into a microphone and fed that signal only to the fm input of a VCO you could probably get that VCO to make words.
Just mixing different oscillators with different settings can get the most unusual sounds and they often sound like it is just one note. When the first digital synths used waveforms to imitate a piano they tried tricks like having one oscillator make a click like a key and hammer mechanism and two or preferably 3 oscillators making string sounds to mimic each string in one piano note. You don't have to mimic something to use this method however.
Drones make a really unusual style of music. It imitates instruments like bagpipes, harmoniums, and snake charmer's pipes but it doesn't have to be acoustic. A drone is a constant note played underneath a melody. A drone can be continuous or it can go quiet when the melody goes quiet, and the best method is combining the two. You usually do this with a sequencer. Modulating a drone's pulse width or cutoff with an lfo is good but try some other methods like modulating it slightly with the melody notes or the cutoff with the melody's keyboard tracking.

Keyboard tracking makes for more variety.
Most synthesizers have a resonant filter. Even if your synthesizer is a new digital powerhouse of samples rather than an analog one it still should have a conventional filter like those that made the first synthesizers so versatile. What you may not realize is that most of the time you are using it and it may be adding a certain frequency to the sound if the resonance and cutoff frequency are set right. Sometimes there is a keyboard tracking adjustment that can shape the way the filter frequency behaves depending on the note the synthesizer plays. The note and the filter cutoff frequency can be kept the same at all times if you like but always try all the different was of setting it.
The cutoff does make a more even sound with the keyboard tracking but tone is all about getting a more varied sound out of a normal set of notes, so setting the tracking in an unusual way or turning it off can help mimic musical instruments or enhance a bizarre waveform. It's also really good to use other things besides just cutoff. Keyboard tracking pulse width or ring modulator pitch really makes a difference. If you play a normal note ring modulated with a note less than a semitone off it makes a unique sound, so set the modulator pitch's keyboard tracking up so it's just a little off.

Bad Sounds Good?!
A sideband is a partial, a sine like frequency that is a component of a sound, which is not in tune with the normal harmonic spectrum. Just mixing two notes together can produce a sideband electrically or acoustically. In some cases you can tell what these frequencies will be mathematically.
Amplitude modulation creates sum and difference frequencies. Adding the number of HZ together and subtracting the lesser from the greater should give you a good approximation. Filter modulation, especially with resonance, causes more complicated sideboards and frequency modulation as well as pulse width seem to cause the most. When these sidebands are made louder by heavier modulation the fundamental of the original waveform is overpowered. If the modulating signal is out of the audible spectrum you may still hear a few sidebands.
When you use vibrato it seems like it just changes the pitch but it also creates these sidebands thereby effecting the musical nature of the sound more than you may realize. If you look at a graph of it you will see it actually warps the waveform more the closer the vibrato speed is in relation to the pitch of that waveform. If you take a waveform and feed it into it's own frequency modulation input on an analog modular synth you simply get different harmonic content and a different waveform.
The most nonsensical sounds can become sweet melody if used right. A bell can easily have more powerful inharmonic sidebands than it's fundamental and harmonics. This can make it more effective at alerting people of something because it's easier to hear above other noises. This is not the kind of bell that you normally use for music because of it's inharmonious sound although this is a matter of opinion. If you like modulated or toneless sounds but want more emotion and melody to them try finding ways of sequencing and looping them, use the same types of patterns you use for melody or bass lines. Try an experiment with a ring modulator. First make it sound really weird and then play a repeating bass line with it. The tune has no recognizable notes but you may notice a melody too. Alternating from noisy to melodious makes a good balance and so does combining them together. Try playing a normal repeating melody and have a heavily modulated bass line. Then make the melody heavily modulated and the bass line normal and musical. Noise solos and modulated arpeggios are fun even if they don't fit into melody things too well.

Getting strange effects
If you have a multi effects processor foot pedal or rack module you can have a lot of fun with it with a synthesizer even if it is made for guitar. Often the drawback is that the frequencies are tailored in a way that eliminates some bass or boosts middle harmonics etc. but just try it and you shouldn't cause any damage. Digital effects may not be your thing but often the analog distortion and compression can make some interesting variations. Never underestimate distortion, it got all that fame for guitars but it works on any signal.

Analog drumkit sounds
Back when you were combining 2 signals you may have thought about getting drum sounds. This is best done with a specialized drum module but don't let that stop you. A normal sounding drum can be made by using an envelope to control the pitch of a triangle wave an bending it down 2 or more octaves. It will loose it's quality of pitch and become percussive, and you can change the filter and pitch to get toms or a bass drum. If you bend it up from a low note it will be an open tom or hand drum. When you have a sound you like you can enhance it with another oscillator that has a shorter duration to make the drumstick on the shell sound. This tone should also bend down but even quicker than the first. The snare can be done with this method by adding a third enveloped white noise sound. If you don't like the result try frequency or ring modulation on the triangle wave that does the bend. Modulating it with noise will make a splat sound but if done right it will sound like a weird snare. Noise used as a modulation source can make a good high hat tone sometimes.