Quadratic
Residue Diffuser – Well Depths Determination
The N7 Diffuser – Brief Introduction
An N7 QRD (with 7 wells)
has the following sequence 0, 1, 4, 2, 2, 4, 1. The deepest well is the well
with sequence ‘4’ and the shallowest well is the well with sequence ‘0’. The
deepest well value can be chosen in the design stage which further limits on
the lowest diffusible frequency. Likewise, the design frequency can also be chosen in the design stage.
QRD well depths determination
Consider an N7 QRD which
is in the design stage and whose well depths need to be determined by using the QRDude software. There are
two approaches, the first is where the design frequency is fixed and in the
second, the deepest well dimension is fixed. Both these approaches lead to slightly
different well depths.
QRDude – Design frequency = 1000Hz
Figure 1 QRD with design frequency 1000Hz
By fixing the design
frequency, the well depths are 0, 25, 99, 49, 49, 99 and 25 mm respectively.
QRDude – Deepest well dimension = 100mm
Figure 2 QRD with deepest well dimension
100mm
By fixing the dimension
of the deepest well as 100mm, the well depths are now a little different 0, 25,
100, 50, 50, 100 and 25 mm respectively. It is important to note that the design
frequency has now changed to 983 Hz.
Conclusion
As we observe, the well depths
and the design frequencies are slightly different in both cases. This is a
trade-off, one can either fix the design frequency or the deepest well
dimension but not both.
