This is Part 9 of a series that started with Part 1.
Although the Moog ladder and basic two-pole state-variable designs cover very many synthesizer VCFs, there are still a number of other kinds worth mentioning. In this, probably the last article of the VCF sub-series, I'll go through some miscellaneous filter designs worth noting. It is not meant to be an exhaustive list.
The general idea of stringing together integrators with some kind of feedback to make different frequency responses, can be taken further than the classic two-pole topology. In particular, there are four-pole versions, like the Mutable Instruments Ripples (US$200) and Intellijel Polaris (US$230); these offer varying combinations of outputs. The Intellijel Dr. Octature II (US$280) is a four-pole design with 1-, 2-, 3-, and 4-pole low-pass outputs plus an inverted-phase version of each; those can be useful in generating other responses by mixing the different outputs, and they provide additional phases of sine waves when the filter is used as an oscillator.
My own Leapfrog VCF also features a chain of integrators, but with many more feedback loops than usually seen in cascaded-integrator filters. The reasoning behind that design is discussed in some detail in the manual.
Suppose you have a signal with a fundamental frequency of 220Hz (A below Middle C), various harmonics at multiples of 220Hz, and you feed it through a low-pass filter tuned very much lower than that, like in the range of 10 or 20Hz. Because the signal is far above the cutoff, it will be heavily attenuated, likely to the point of being inaudible in the output. Then if you use a control voltage to raise the cutoff above the signal frequencies, the signal will pass through the filter. Thus, changing the frequency of the filter has the side effect of changing the amplitude of the output, as greater or lesser amounts of the signal can pass through the filter. In some sense, the VCF acts like a VCA. But it does not only change the amplitude, except on a sine wave input; as the output signal from a filter set up this way gets stronger in amplitude, it also becomes brighter in timbre, due to the filter letting through more and more of the higher harmonics.
You could, in many patches, substitute a VCF for a VCA. Set the VCF so that in between notes the cutoff frequency is so low that effectively no signal makes it through the filter; then use an envelope to lift the filter frequency during each note, shaping both its volume and tone. A VCF used this way is called a low-pass gate. This kind of patching often produces a sound described as "woody," "rubbery," or "natural," and it is a hallmark of the West Coast synthesis approach and Don Buchla's modular format.
Properly speaking, any low-pass VCF capable of a low enough cutoff frequency can be used as a low-pass gate; it is a method of patching rather than a specific type of module. However, there are modules sold specifically for this purpose under the name of "low-pass gates" and they are usually filters similar to Buchla's original design. They typically have a one-pole low-pass response (6dB per octave roll-off, giving a very bright sound when fully "open"); with a control voltage that affects both cutoff and overall amplitude (maybe switchable modes to be more like a VCA or more like a VCF); a lowest possible frequency low enough to fully "close" and block input; and so on. The classic Buchla-style low-pass gate circuit uses vactrols to apply the voltage control, and that creates a built-in exponential decay at the end of each note, which is also often regarded as making the sound more organic. The Make Noise Optomix (US$215) is a popular example.
Digitize an input signal, use a computer to calculate what that signal would look like without certain frequencies, and then convert the result back into analog. That approach (one case of "digital signal processing" or DSP) allows a wide variety of filters to be implemented in the form of computer software. Then it's easy to switch between different filter responses by giving the computer different instructions, and (although the computer has its own relevant limitations) it may be possible to avoid some of the limitations of analog. Digital filters can do some things that would be difficult in a purely analog design. For example, the Rossum Morpheus (US$500) can set up several different frequency response shapes and interpolate between them under voltage control. That is, it actually changes the shape of the curve - not an effect achievable by just crossfading among different filter outputs. The Bat filter card (US$60 at some dealers but not listed on the manufacturer's Web site - maybe discontinued?) for the Tiptop Z-DSP module (US$500) offers several different 4- and 8-pole filter programs.
There is no need for a DSP system to function only as a filter, nor exactly as just a filter. Modules like the 4ms Spectral Multiband Resonator (US$475) and Mutable Instruments Rings (US$335) use DSP filtering in creative ways as primarily a synthesis technique in itself rather than a way of filtering other signals.
Exotic semi-digital variant: switched-capacitor filter
Suppose you have an input (driven to some voltage by an external circuit) and an output (connected to a load that looks like a resistor to ground). You connect a capacitor between ground and the input; then you change the connection to connect it between ground and the output; then you switch it back, and repeat this process. What happens?
The capacitor will charge to the input voltage (we can assume, very fast) whenever it's connected to the input. When it's connected to the output, it will discharge into whatever load is connected there. So as an average over time, current flows into the input and out of the output, even though it never actually does both those things simultaneously. And the amount of current that can flow is proportional to the input voltage, among other things. The switched capacitor functions kind of like a resistor that obeys Ohm's Law. The apparent resistance of this virtual resistor depends on the switching frequency; so by changing that frequency, you can change the resistance. Such virtual variable resistors are the core of the switched-capacitor filter topology. Build a reasonably straightforward analog filter, using switched capacitors to replace the frequency-determining resistors in the design, and you have a weirdly semi-analog filter whose cutoff frequency is proportional to the frequency of the digital signal controlling the switching. This could be called an FCF - a frequency-controlled filter.
Some of the properties of digital sampling (such as frequency aliasing) apply to switched-capacitor filters, even though the samples are never actually converted into numbers the way a DSP system would. It is usual to use a microcontroller to generate the switching signal, so the frequency control voltage and any modulation go through a digital path, but the signal being filtered never actually does. Should this properly be called an analog, or a digital filter? Really, it is some of both.
Fs that are not VC
Not all filters are voltage-controlled, nor have controllable frequencies at all. In that case, they maybe should not even be mentioned in an article on voltage-controlled filters; but I'm not sure where else they would fit into my series, and they're worth knowing about.
First, there are "fixed filter banks" - several band-pass filters are different non-adjustable frequencies, usually sharing an input and either with separate outputs for the different bands, or just knobs to control their levels before they get mixed back together. The Doepfer A-128 (US$230) is an example. Modules like these can be used to do what a "graphic equalizer" does in a stereo system, or to separate out different components of a signal to process separately. The extreme case, with multiple bands per octave, forms the input to a typical vocoder system.
Another kind of non-voltage-controlled filter has variable frequency with a manual control. These typically do what a parametric equalizer does, and they may be sold under that name; they're especially useful in performance situations for tweaking the overall sound of the synth. The ALM PE-1 (US$125) is an example.
Continue to Part 10 of this series.