2. Determine the output frequency fout of a DDS system having 32-bit phase accumulator if DDS clock frequency fclk is 120 kHz and the value of the frequency tuning code M is 196608. Show your work.

Answer 1

To determine the output frequency, we need to use the following formula:

fout = (fclk * M) / (2^b)

Where:
- fclk is the DDS clock frequency
- M is the frequency tuning code value
- b is the number of bits of the phase accumulator

In this case, the DDS clock frequency fclk is 120 kHz, the frequency tuning code M is 196608, and the phase accumulator has 32 bits.

Substituting the values into the formula:

fout = (120 kHz * 196608) / (2^32)

Since 32 bits represents the entire range of a 32-bit phase accumulator, 2^32 is equal to 2^32 = 4294967296.

fout = (120 kHz * 196608) / 4294967296

Multiplying:
fout = 23.8848

Therefore, the output frequency fout of the DDS system is approximately 23.8848 kHz.