For a DDS system with 32-bit phase accumulator and 100 kHz clock frequency determine the value of frequency tuning code M to generate output signal with the frequency of 10 Hz. Show your work.
The frequency tuning word or code M determines the output frequency of the DDS by scaling the frequency of the system clock. The formula to calculate the frequency tuning word is given by:
M = (desired output frequency × 2^N)/clock frequency
where N is the number of bits of the phase accumulator.
In this case, the desired output frequency is 10 Hz, the clock frequency is 100 kHz, and the number of bits of the phase accumulator is 32. Substituting these values in the formula, we get:
M = (10 × 2^32)/100000 = 429496.7296
Since the M value must be an integer, we can round the result to the nearest integer:
M = 429497
Therefore, the value of the frequency tuning code M to generate an output signal with the frequency of 10 Hz is 429497.