DDS Frequency Resolution
Δf = fclk / 2ᴺ
Quick answer
This calculator solves Δf = fclk / 2ᴺ for Frequency Step. With Clock Frequency 10 MHz, Accumulator Bits 0.5, the result is 7.071 MHz. It solves in 2 directions, so you can enter the values you have and get the one you need.
Calculator
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.
Symbols and units
| Symbol | Meaning | Default unit | Accepted units |
|---|---|---|---|
| df | Frequency Step | Hz | Hz, kHz, MHz, GHz |
| fclk | Clock Frequency | MHz | Hz, kHz, MHz, GHz |
| N | Accumulator Bits | — | — |
Step by step
- 1. What you know: Clock Frequency 10 MHz, Accumulator Bits 0.5
- 2. The relation: Δf = fclk / 2ᴺ
- 3. Substitute: fclk = 10 MHz, N = 0.5
- 4. Result: Frequency Step = 7.071 MHz
Worked examples
Minimum range
Given: Clock Frequency 100 kHz, Accumulator Bits 0.025
Result: Frequency Step = 98.28 kHz
Low range
Given: Clock Frequency 1 MHz, Accumulator Bits 0.25
Result: Frequency Step = 0.8409 MHz
Typical
Given: Clock Frequency 10 MHz, Accumulator Bits 0.5
Result: Frequency Step = 7.071 MHz
High range
Given: Clock Frequency 100 MHz, Accumulator Bits 0.8
Result: Frequency Step = 57.43 MHz
Maximum range
Given: Clock Frequency 1 GHz, Accumulator Bits 8
Result: Frequency Step = 3.906 MHz
Solving for each variable
Solve for Frequency Step
Clock Frequency 100 kHz, Accumulator Bits 0.025 → 98.28 kHz
Solve for Clock Frequency
Frequency Step 5 Hz, Accumulator Bits 0.025 → 5.087 Hz
How Frequency Step changes with Clock Frequency
| Clock Frequency (input) | Frequency Step (result) |
|---|---|
| 1 MHz | 0.7071 MHz |
| 2.5 MHz | 1.768 MHz |
| 5 MHz | 3.536 MHz |
| 7.5 MHz | 5.303 MHz |
| 10 MHz | 7.071 MHz |
| 15 MHz | 10.61 MHz |
| 20 MHz | 14.14 MHz |
| 40 MHz | 28.28 MHz |
| 70 MHz | 49.5 MHz |
| 100 MHz | 70.71 MHz |
The same result in other units
| Unit | Value |
|---|---|
| Hz | 7071000 |
| kHz | 7071 |
| MHz | 7.071 |
| GHz | 0.007071 |
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<p><a href="https://vbatpower.com/formulas/dds-frequency-resolution/">DDS Frequency Resolution</a> Calculator by vbatpower.com</p>Frequently asked questions
How do you calculate DDS Frequency Resolution?
Use Δf = fclk / 2ᴺ. With Clock Frequency 10 MHz, Accumulator Bits 0.5, Frequency Step works out to 7.071 MHz.
What is the formula for DDS Frequency Resolution?
The formula is Δf = fclk / 2ᴺ. 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.
How do you find Clock Frequency when you know the other values?
Rearrange for Clock Frequency: with Frequency Step 5 Hz, Accumulator Bits 0.025, Clock Frequency is 5.087 Hz.
What units does DDS Frequency Resolution use?
Frequency Step is shown in Hz, kHz, MHz, GHz. Values are held in SI base units internally, so you can mix prefixes without converting by hand.
Related Concepts
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