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From a mechanical viewpoint the CT3680 has a completely different PCB footprint and is physically larger than any BBD chip.
The CT3680 is not, in general, a complete effects solution. It provides only the delay function for the effect (much like a BBD provides only a delay function). External (analog) circuitry must provide feedback paths, filtering, modulation, and other analog signal processing to create a final effect. For example, if some modulation of the delay time is desired, some external circuit must create a CV (control voltage) signal that varies over time to control the CT3680 delay time. In a pure DSP solution, that modulation would be coded into the DSP program.
From a hardware point of view, an FV-1 type solution can be simpler to build as there are fewer components and the circuit is a simpler design. But that solution requires good expertise in DSP programming unless you are satisfied with the pre-programmed effects. It moves effects creation from analog circuitry to an exercise in programming (with a very good understanding of audio signal processing). Such an implementation is subject to the limitation of the device (e.g. limited program size, limited memory, limited number of control inputs, etc).
The CT3680 on the other hand, delegates all signal processing except for the delay function to traditional analog circuitry. No DSP programming or digital design is required, and all audio inputs and outputs are simple analog signals. The effects design techniques are very familiar to anyone versed in BBD circuits. Conceptually the CT3680 just replaces the BBD, albeit with much better performance, capability, and flexibility than any BBD chip. Analog circuits provide the feedback paths, filtering, delay modulation, and whatever other signal processing the effect requires. There is no limit to the complexity and control parameters of those analog circuits.
To create a very short delay, the CT3680 is configured for multiple independent channels (such as program number 3). The same audio signal is supplied to 2 of the channels. The outputs of the two channels are mixed. Consider one to be the "dry" signal, the other "wet" (the original input is not mixed into the output at all). When the delay time of both channels are set to the same (e.g. their CV delay input voltages are equal) the two signals will have a zero relative delay and will be summed in the mix without effect. By changing the delay of the "wet" channel slightly, the two outputs will become out of phase and produce the "phaser" audio effect.
It is helpful to use the global MIN/MAX scalars to restrict the overall delay time to something small (say 3ms). Then the individual channel delays can use their full-scale 0.0V to 3.3V range to make fine resolution changes in delay times. Varying the "wet" channel over it's full scale will produce a relative delay from 0 to 3ms, a range that is useful for these types of effects.