Theory
The basic DDA integrator, shown in the figure, implements numerical rectangular integration via the following equations:
Where Δx causes y to be added to (or subtracted from) S, Δy causes y to be incremented (or decremented), and ΔS is caused by an overflow (or underflow) of the S accumulator. Both registers and the three Δ signals are signed values. Initial conditions for the problem can be loaded into both y and S prior to beginning integration.
This produces an integrator approximating the following equation:
where K is a scaling constant determined by the precision (size) of the registers as follows:
where radix is the numeric base used (typically 2) in the registers and n is the number of places in the registers.
If Δy is eliminated, making y a constant, then the DDA integrator reduces to a device called a rate multiplier, where the pulse rate ΔS is proportional to the product of y and Δx by the following equation:
Read more about this topic: Digital Differential Analyzer
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