“The CE-1 is a pedal that has chorus and vibrato modes; the Dimension D is a rack-mount unit that provides four separate chorus settings. These choruses are built around an analog delay device called a "bucket-brigade delay" line or BBD, which adds a certain character to the Roland choruses.”

The idea behind a chorus processor is to create several copies of the input signal, as if there were more than one instrument or voice present. Typically, the output is the sum of the input and a delayed version of the input. The delay between the original and copy is slowly changed over time, and in this way, is perceived as a separate signal, independent of the input. Figure 1 illustrates this point. The image, when still, appears to consist of a single set of dots, but when animated, it is clear that there are two identical sets of dots, one offset from the other.

In the CE-1 in chorus mode, the wet output is delayed from about one-and-a-half milliseconds to about four milliseconds relative to the dry signal. This is actually a rather short delay for a chorus, which typically would use about ten times that delay. The perception that the wet and dry signals are independent is enhanced if characteristics in addition to the delay distinguish the two. In the CE-1, the wet signal has a slightly different equalization and level than the dry signal, and, as a result of the way the BBD goes about its processing, the level and equalization change as the delay between the wet and dry signals changes.

The Dimension-D functions in much the same way as the CE-1, but uses several copies of the input to form its wet output. It delays these copies through independent trajectories and applies separate scalings, all of which are determined by the Dimension mode. So as to help the BBDs operate in their sweet spot with respect to signal level, a compressor is applied to the input of the BBD and a complementary expander is applied to the BBD output.

If a signal is processed through a changing delay, its frequency is changed. This is the Doppler shift: If the delay is decreasing (as would happen if an object were moving toward you), each successive wavefront gets a head start compared to the previous one, and wavefronts will arrive at a faster rate or increased frequency. If the delay is increasing, the opposite happens.

If the change in delay is sufficiently quick, a noticeable frequency shift will develop. In a vibrato processor, the input is run through a changing delay, creating a changing frequency shift. Whereas choruses often use triangular delay trajectories so that the motion of the delay is roughly constant, vibratos will use sinusoidal or similarly smooth trajectories so that the frequency motion is relatively constant.

In the CE-1, the vibrato mode imposes a roughly sinusoidal delay trajectory on the input, resulting in a similarly sinusoidal frequency trajectory. The Rate knob sets the period of the delay trajectory, and for a given rate, the Depth knob determines the maximum and minimum delays attained. It turns out that, for higher rate settings, the delay excursion is reduced so that for a given depth setting, the amount of frequency shift, or "detuning," is roughly constant.

In modeling the Dimension D and CE-1, we were very careful to match the delay trajectories as a function of the knob settings. We also studied the physics of the BBDs used, and consulted with our USC device physics professor friend (who helped us out in modeling the LA-2A photoresistor), to make sure our models were doing the BBD justice.

The BBDs work roughly as follows. There are even- and odd-numbered capacitors--the "buckets"--and a switching network controlled by two phases of a clock. What happens is that, on one phase of the clock, the switching network is configured so that the even-numbered buckets empty their charge into the odd-numbered buckets immediately to their right. On the next phase of the clock, the even-numbered buckets (now empty) are filled with charge from the odd-numbered buckets immediately to their left. In this way, charge, representing input signal level, is moved through the delay line and appears at the output delayed by the number of clock phases required to move the signal through all of the buckets. To generate a changing delay, the frequency of the driving clock is changed.

Note that the BBD is an analog system, but sampled in time. The charge put into the first bucket during a given clock period is a kind of average of the input signal level over that clock period. As a result, the charge in the buckets represents the signal level at a set of discrete times. So as to avoid time aliasing, the signal is lowpass-filtered before being sampled by the BBD, and is similarly lowpass-filtered to reconstruct the continuous-time output from the BBD output, which is more or less a staircase.

There are a number of physical effects to consider when modeling a BBD. It takes time to transfer charge from one bucket to the next, and even if, say, 99.9% of the charge is transferred, in a delay line with 1,024 stages, only 36% of the charge is left at the end of the delay line. The fact that a percentage of the charge is lost doesn't matter as much as the fact that the amount of charge lost depends on the delay through the BBD; a fast clock will give a short delay and will have a smaller percentage of charge survive to the output.

Another important effect is that charge can leak from the buckets to the substrate, held at a low voltage. For small signals, this leakage effects all parts of the waveform similarly and causes a negative DC bias that is eliminated via a highpass filter following the BBD. For large signals, the positive parts of the waveform decay to the substrate voltage quicker than the negative parts of the waveform do, and a kind of distortion develops. Again, the effect depends on the delay through the BBD: Short delays effect the signal less than long delays.

Finally, perhaps as a result of some charge distribution during switching between clock phases, there is a subtle equalization that depends on the delay through the BBD. To summarize, to emulate the Roland CE-1 and Dimension D, it was important to model the BBD response and the delay trajectory accurately, as determined by the user settings. The time evolution of the delay is critical to the sound of a chorus and vibrato, and the BBD adds a certain character to the delayed signal.