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In summary, N is the number bits associated with the bus width of the accumulator output as well as the FTW. C is the accumulator capacity and is given by two to the N. The standard DDS equation allows the calculation of the DDS output frequency, Fo, given that the system clock frequency, Fs, the value of the FTW and the accumulator bus width N are known. The alternate DDS equation allows the user to determine the value of the FTW given the system clock frequency, Fs, the accumulator bus width, N, and the desired DDS output frequency, Fo. Furthermore, the alternate DDS equation necessitates rounding the quantity, 2^N times the quantity Fo over Fs to the nearest integer because FTW is, by definition, an integer. Therefore, in cases where two to the N times the quantity Fo over Fs is not an integer, the rounding operation results in a deviation between the desired output frequency, Fo, and the actual DDS output frequency. In most cases, however, the deviation is very small.
