What is the formula for DDS Output Frequency?

The DDS Output Frequency formula is fout = M × fclk / 2ᴺ, where fout—Output frequency (Hz); M—Frequency tuning word (integer); fclk—Reference clock frequency (Hz); N—Phase accumulator width (bits).

DDS Output Frequency

Q: How do you calculate DDS Output Frequency?

Use the formula fout = M × fclk / 2ᴺ. A direct digital synthesizer generates an output frequency by stepping a phase accumulator by a tuning word M each clock cycle. Enter the values you know in the calculator above and it solves for the remaining variable.

fout = M · fclk / 2ᴺ

Calculator

Output Frequency

Tuning Word

Clock Frequency

Accumulator Bits

Result

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Formula

fout = M × fclk / 2ᴺ

Description

A direct digital synthesizer generates an output frequency by stepping a phase accumulator by a tuning word M each clock cycle. The output frequency is the tuning word times the clock frequency divided by 2 to the power of the accumulator width. This gives extremely fine, fully digital frequency control with instantaneous, phase-continuous tuning.

Variables

fout — Output frequency (Hz)
M — Frequency tuning word (integer)
fclk — Reference clock frequency (Hz)
N — Phase accumulator width (bits)

Practical Notes

Keep fout below fclk/2 (Nyquist); practical DDS outputs stay under ~40% of fclk to ease image filtering. A wide accumulator (e.g. 32–48 bits) gives sub-hertz resolution.

Related Concepts

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