Someone please explain the connection between the amplitude resolution of the DAC and the frequency/phase resolution of a DDS.
There is no relationship between the amplitude resolution of a DAC and the frequency resolution of the DDS. Frequency resolution depends only on the number of bits in the DDS's phase accumulator. This fact becomes apparent in the basic DDS output frequency equation: Fout = Fs*FTW/(2^N), where Fout is the DDS output frequency, Fs is the DDS system clock frequency (or sample rate), N is the number of bits in the phase accumulator, and FTW is the N-bit digital frequency tuning word. Note that the DAC resolution does not appear in the output frequency equation.
On the other hand, there is a connection between the amplitude resolution of the DAC and how it relates to phase. Consider a DAC with D-bits of amplitude resolution. For example, a 10-bit DAC, in which case D=10. It can be shown, that in order for a DDS to make full use of the resolution of the DAC, the angle-to-amplitude converter within the DDS core must have at least D+3 bits of phase resolution. So, a DDS with a 10-bit DAC requires a DDS core with a minimum of 13 bits of phase resolution. This guarantees that the smallest phase step (1 LSB of phase) results in a DAC step of no more than 1/2 LSB of amplitude. That is, there is no chance that a minimum phase step will skip over a DAC code.
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