Here's what Rothwell say about the Cool Little Knob
The Cool Little Knob is a totally passive device which will expand the tonal possibilities of guitars fitted with humbucking pickups which can be coil tapped.
It replaces the tone control with a push/pull rotary knob which gives a range of sounds from standard humbucker sounds to fully coil tapped. However, the great strength of the Cool Little Knob lies in the sounds obtainable between the two extremes.
The unique filtration circuitry controls the way in which the two coils of the humbucker interact with each other, allowing the possibility of controlling the level of “grit” in the sound. This means that the top end can be cleaned up for a sweeter sound while retaining the bottom end richness of a humbucker which is usually lost when using a conventional coil tap. (There have been some devices fitted to guitars in the past which replace the coil-tap switch with a variable resistor.
The Cool Little Knob is much more sophisticated than that and cannot be replicated with just a variable resistor.
With the knob in the down position and turned to 10 (fully clockwise) the pickup will behave just like a standard humbucker. As the control is turned down the sound will become cleaner and sweeter at the top end and with more sparkle but will retain fullness and warmth in the bass. The effect is continuously variable.
With the knob in the up position and turned to 10 the sound will have more openness and clarity at the top end than in standard humbucker mode but the bass will still sound full. As the knob is turned down the sound will start to thin out and when the knob is fully anti-clockwise the sound will be the same as a fully coil tapped humbucker ie bright and clean but quite bass light and with lower output than a humbucker.
Theory of the Cool Little Knob
The Cool Little Knob seems to add brightness and clarity to the sound of humbuckers and most people who hear it are amazed that a passive control can do that. After all, passive controls can usually only remove part of a signal - not add anything. So how does it work?
Humbuckers have a distinctive sound due to having two coils side by side. Some of the upper harmonics of the vibrating strings will appear 180 degrees out of phase in one coil with respect to the other. That causes those harmonics to be cancelled out. The Cool Little Knob filters out some of the upper harmonics from one coil only, so that harmonic cancellation is suppressed. By working with the upper harmonics alone the bass end of the spectrum is kept rich and full..