# Voltage Controlled Second Order Low Pass Filter

First time poster. Please be kind!

I'm working on an analog synthesizer project and recently started looking at Voltage Controlled Filter designs. I've scoured the internet for a low pass configuration that would allow me to control the filter's cutoff frequency with a control voltage (from a low frequency oscillator) without resorting to the complicated mathematics of, say, the Moog ladder filter. So far, the top contenders are the filter for the Gakken SX-150 and the filter for the Korg Monotron series. Unfortunately, the physics of even these relatively simple topologies are a bit above me. I've tried doggedly to try and resolve the components in both circuits to the classic Sallen Key filter but without much luck. To date all I concretely understand is that the BJT transistors must function as resistors whose base junction current determines resistance. This resistance then works in conjunction with the capacitor impedance to selectively allow current flow as in a basic first order topology. That's not so bad. Exactly which components achieve this effect however, is still a mystery to me. I like to believe I have done the requisite amount of googling but even the most accessible webpage (Tim Stinchcombe) wasn't much help. The addition of more than two capacitors in both schematics gives me much pause and I'm still not convinced that the feedback diodes are even strictly necessary. Would someone mind explaining to me which components I should focus on and how they work together?

EDIT (Included Monotron Schematic)
(source: korg.de)

• Since all signals are apparently audio, it makes more sense to do it digitally. In fact, do as much as possible digitally. Also, why do you think you need a voltage-controlled filter in the first place? – Olin Lathrop Apr 9 '15 at 19:36
• How about a voltage controlled oscillator and a switched capacitor filter? (You can change the corner frequency of the SC filter by changing the clock freq.) cds.linear.com/docs/en/application-note/an40f.pdf – George Herold Apr 9 '15 at 20:00
• It's an analogue synth which means he needs a VCF end of argument. – Andy aka Apr 9 '15 at 22:34
• @OlinLathrop I'm using a voltage-controlled filter because I'm trying to shape the harmonics of an incoming periodic waveform. I plan to to route an oscillator to the filter to control the cutoff frequency. This will allow me to get an automatic back-and-forth "sweep" effect. As far as the digital piece is concerned, I'd like to use as much analog circuitry as possible for the aesthetic. I'm certainly aware that I can use digital components but then again I could just make a software synth. It's the spirit of the thing :) – Patagonian Rat Apr 9 '15 at 22:56

Chapter 6 of Chamberlin's book "Musical Applications of Microprocessors" is a good introduction to the circuitry of classic analogue filter modules (the circuits originating in the Electronotes newsletter). In particular, it has a good explanation of how using circuit elements which act as amplifiers with voltage-controlled gain (such transconductance op-amps) leads to a voltage-controlled cutoff frequency in a VCF. The type of filter discussed by Chamberlin is commonly used for "state variable filter" modules in analogue synths.

The book is out of print, but some kind soul has recently put a PDF online (currently the top google hit for the title of the book).

The Gakken / Monotron filter does avoid transconductance amplifiers, but is not so easy to understand -- the page of Tim Stinchcombe is the best reference I have seen.

• Thank you for that source! I've perused it briefly and the suggestions you and @crgrace have made about OTAs now seem a bit more alluring. I might consider taking my filter design in that direction. That said, while I take the time to read through the PDF further I'd still like to see an rundown of the Gakken/Monotron filter. – Patagonian Rat Apr 10 '15 at 19:37
• Thank you for this amazing book! I wish I encountered it sooner! – Eugene C May 29 '19 at 12:09

Since you're not an expert yet you'll want to start simple. I suggest you use a transconductance amplifier such as the TI LM13700 to implement a simple audio filter for an analog synthesizer. They are widely used for this application. Basically the transconductor gives you a gm (kind of a 1/R) and you dump the resulting current into a cap. This gives you the C for your 1/RC cutoff. Check out the datasheet for this part here: TI LM13700 datasheet

Figure 3 in the datasheet will give you a starting point for a very simple VCF. All the math you need to develop a filter circuit with this part is included in the datasheet.

• While that would work I was thinking of using traditional op-amps for this project. As it is I already have quite a few on hand and I'd like to explore how versatile they are before trying out a different chip. Besides this, I'd kinda just like to know how these circuits work and both of them use op-amps. I'll look into the transconductance amplifiers though, thank you. – Patagonian Rat Apr 10 '15 at 1:21