DDS Output Frequency & Tuning Word

A direct digital synthesizer builds a waveform by stepping an N-bit phase accumulator by a tuning word M every clock cycle. The output frequency is a precise fraction of the clock set by M, with a resolution equal to the clock divided by 2^N. Enter a target frequency to get the nearest tuning word and the exact frequency it produces.

Equations & Parameters ▸

\(f_{\text{out}} = \dfrac{M}{2^{N}}\,f_{\text{clk}} \qquad \Delta f = \dfrac{f_{\text{clk}}}{2^{N}} \qquad M = \text{round}\!\left(\dfrac{f_{\text{target}}}{f_{\text{clk}}}\,2^{N}\right)\)

f_clk	Reference clock frequency (MHz).
N	Phase-accumulator width (bits), e.g. 24, 32, 48.
f_target	Desired output frequency (MHz).
M	Frequency tuning word (integer, 0 … 2^N−1).
Δf	Frequency resolution — the smallest output step.

References: Analog Devices, MT-085, Fundamentals of Direct Digital Synthesis. · J. Vankka & K. Halonen, Direct Digital Synthesizers, Kluwer, 2001.

Inputs

Clock, f_clk

MHz

Reference clock

Accumulator bits, N

bits

e.g. 24/32/48

Target output, f_target

MHz

Desired freq

Results

Tuning

Tuning word M—

Actual f_out—

Error vs target—

Limits

Resolution Δf—

Max usable (~40%)—

Diagram

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