DDS Frequency Resolution

Formula

Description

The smallest frequency step a DDS can make is one tuning-word increment, equal to the clock frequency divided by 2 to the accumulator width. Wider accumulators give finer resolution: a 48-bit accumulator clocked at 100 MHz resolves to under a microhertz. This sub-hertz tunability is the defining advantage of direct digital synthesis.

Variables

• Δf — Minimum frequency step (Hz)
• fclk — Reference clock frequency (Hz)
• N — Phase accumulator width (bits)

Practical Notes

Resolution is independent of output frequency. A 32-bit accumulator at 100 MHz gives ≈ 0.023 Hz steps; add accumulator bits for finer control without changing the clock.