For another project I’m working on I needed a multimode filter. For the uninitiated, its a single filter that has a HP/BP/LP function, and does it all simultaneously. An OTA design is fairly common for this type of filter, so that’s what I did. Now, there are a zillion different implementations to be found online, so why not adding one more to the confusion. After all, chaos reigns supreme.
As far as OTA’s go, there is only one player in town, the LM13700. All other IC’s commonly used for this kind of thing seem to be discontinued, hard to get and/or darn expensive. I must state that really hate the LM13700, as somehow, whatever I try to build with one ends up not working and a is a nightmare to debug. Most of the time the LM in question turns out to be dodgy. The fact that I bought my first batch of these IC’s from a less then reliable source on Ali Express might have something to do with it though. So, don’t do that, get them from a respectable source, they will be more expensive, but you won’t regret it.
The topology isn’t all that different from the VCF-2. Instead of the AS3360 working as a variable resistor, the LM13700 does that job now. So there are a few bits and bobs around it to make the LM13700 work, but a keen eye will spot the resistor (hint, it’s the LM13700)/capacitor combo (times 2, you know, 2 poles) and the feedback network that makes it all tick.
All multimode filters work basically according to the same principle. What you need to know is that the classic resistor/capacitor filter network also introduces a phase shift around the cut-off point. The closer we get to the cut-off point, the more pronounced the phase shift is. In these designs, that’s the property that gets leveraged to create all those filter types. Also, be aware of your physics 101 lessons where you probably learned that waves with the same phase amplify each other and waves with opposite phases cancel each other out. If you haven’t learned that, blame your educational system, but it’s true nevertheless.
If you feed an inverted low-pass back to to the original signal, you will get a high-pass as all frequencies unaffected by the low-pass filter will neatly cancel each other out, because they have the opposite phase, resulting in only the high frequencies getting through. It was a trick I used a lot with my Akai S3000 back in the day to create a ‘fake’ high-pass filter which the unit lacked. Use 2 of the same samples, invert one, then low-pass one of them. presto, a high pass filter. (You could do some real nice phase tricks by slightly tweaking the pitch on one of the 2 samples, but I’m getting side-tracked here)
The bandpass get constructed in a similar fashion, by taking the high passed signal and applying a low-pass filter to it. What’s left are just the frequencies around the filter-cutoff point. Remember the phase thing I said, well that’s why it works. And that’s also why you still can get a resonant peak. While the unaffected frequencies fed back to the input are nicely inverted, the frequencies around the cut-off point are not. In fact, they will stack up together nicely and be amplified. Add a potentiometer to that and there you have your resonant control.
To be fair, the above is more like an ELI5 version of what’s going on, there is a bit more to it. If you get your little grey cells to work you’ll notice the discrepancies in the reasoning above and the schematics below. I just don’t feel like writing a book about it, and this ‘summary’ should give you some insight in how these type of filter designs work in an understandable form factor. For more detailed information and to scratch that math itch, there’s always google.
Apart from the whole filter thing, there is little else in the circuit. Some summing of CV signals to drive the LM13700 and a buffering of the outputs, which is needed since the whole thing would fall apart otherwise. To check if you need to buffer something in a design, just take the idea of shorting the output to ground and see how that might affect the functionality of your schematic. If it fucks things up, add a buffer. See, if I were to connect the bandpass filter output, without buffer, to ground, the other filter types would stop working as well. Hence, the buffers.