What is the Moog Filter ? Why is it so famous even a historical revolution for the electronic music ?

Well, as a matter of fact Robert Arthur Moog is….actually the pioneer of the famous music instrumental called synthesizer ! His life turned to the stars in 1964 when Herbert A. Deutsch, on of his clients, ordered a machine with three elemental commands: Voltage-controlled Oscillator, Voltage-controlled Amplifier and Voltage-controlled Filter.

After a succession of different models, the revolutionary Modular Moog 55 was finally borne. The Moog filter has definitely been a revolution in electronic music because Robert Moog achieved to create a low-pass filter as the classic RC sections and high-pass filter as the classic RL sections with an innovative discrete analog circuit known as the “Moog ladder”.

The stroke of genius for Moog was to use transistors (the commonplace semiconductor device that is now in every smartphone and intelligent device) to create low-pass and high-pass filter. The Moog filter was so successful that in 1968, it has been used for the original band of the movie “A Clockwork Orange” and by The Beatles or also Yes. Actually, the idea of electronic music was especially imagined by two visionaries and their work of experimental musicians: Walter (Wendy now) Carlos and Isao Tomita. In particular, Wendy Carlos helped the development of the first commercially available keyboard Moog synthesizer.

Much too good to be true ? Well, actually in the 50’s, there had already been electronic music but only a little community could understand how to use it because they had to have strong knowledge in mathematics, electronics,… In a nutshell: it was reserved for some kind of nerds(what ? I’m a nerd so I can use this word). The real revolutionary idea of Moog was to build an instrument much easier to understand, to play with and much more compact.

Now you are such an ace of Moog revolution, let’s talk about the Moog filter in depth with Spice simulation. Drum roll… At your left: the Moog filter schematic ! Nothing to be scared of, isn’t it ?

There is a specific duplicated circuit here which is called differential. To create a filter, the key is adding a capacity ! In this case, given that there is only one capacity, it is like you have only one floor foncionnal instead of having three. It is as if the three remaining floors at the top were only one floor. As a result, this simple circuit is actually a low-pass filter with order 1.

Let’s call {differential ; capacity} the “evolved differential”.

Here is the transfert function expression:

𝐻(𝑠) = −1/(1 + 𝜏 ∗ 𝑠) 𝑤ℎ𝑒𝑟𝑒 τ =4𝐶.𝑉t/Idc

Actually, the Moog filter powerness comes from the fact that you can easily multiply by itself this tranfer function just by “stacking” the “evolved differential” one by one (the design is really easy to manipulate). The more evolved differential you have, the better for the attenuation on the sound you produce with a voltage-controlled oscillator.

As you can see in the formula before, you can control the cut-off frequency 𝑓𝑐 =𝐼dc/8𝜋𝐶𝑉t just by changing the current IDC, assuming C and Vt are fixed.

So for example if you had a capacity between Q5 and Q6, the new transfert function would be: 𝐻′(𝑠) = −1/(1 + 𝜏 ∗ 𝑠)²

Thus, there is a little trap: the sign minus never disappears. Only the denominator is multiply by itself.

To finish, here is the schematic I’m designing to make a Printed Circuit Board (PCB) and make some tests on it. I’m sure you will recognize some details I talked about before…

References: https://fr.wikipedia.org/wiki/Moog - Moog https://fr.wikipedia.org/wiki/Synth%C3%A9tiseur_modulaire - Modular Synthesizer http://www.timstinchcombe.co.uk/synth/Moog_ladder_tf.pdf - Analysis of the Moog Transistor Ladder and Derivative Filters Timothy E. Stinchcombe - 25 Oct 2008 https://ccrma.stanford.edu/~stilti/papers/moogvcf.pdf - Analyzing the Moog VCF with Considerations for Digital Implementation - Tim Stilson/Julius Smith https://www.moogmusic.com/products/moog-modular-systems - Moog Modular System

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