The web is filled with introductions to Delta Sigma modulation (also sometimes referred to as Sigma Delta modulation) in the context of Delta Sigma converters. Unfortunately, the ones I’ve looked at fail to intuitively motivate how the modulator works. Therefore, my goal in this post is to show how the structure of a first-order ΔΣ modulator can be simply understood. In particular, I show how its structure can be derived from a trivial 10-line C program that performs the ΔΣ modulator function.
The basic problem solved by a ΔΣ modulator is this: given a fixed input value ν that lies in the range [-1, 1], the modulator outputs a pulse train satisfying the following criteria:
- Each pulse has the same fixed width τ
- Each pulse has an amplitude of -1 or 1 only
- The time average value of the pulse train emitted converges to ν