DDS Output Frequency
fout = M · fclk / 2ᴺ
Quick answer
This calculator solves fout = M × fclk / 2ᴺ for Output Frequency. With Tuning Word 0.5, Clock Frequency 10 MHz, Accumulator Bits 1.1, the result is 2.333 MHz. It solves in 3 directions, so you can enter the values you have and get the one you need.
Calculator
Formula
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.
Symbols and units
| Symbol | Meaning | Default unit | Accepted units |
|---|---|---|---|
| fout | Output Frequency | kHz | Hz, kHz, MHz, GHz |
| M | Tuning Word | — | — |
| fclk | Clock Frequency | MHz | Hz, kHz, MHz, GHz |
| N | Accumulator Bits | — | — |
Step by step
- 1. What you know: Tuning Word 0.5, Clock Frequency 10 MHz, Accumulator Bits 1.1
- 2. The relation: fout = M × fclk / 2ᴺ
- 3. Substitute: M = 0.5, fclk = 10 MHz, N = 1.1
- 4. Result: Output Frequency = 2.333 MHz
Worked examples
Minimum range
Given: Tuning Word 0.025, Clock Frequency 100 kHz, Accumulator Bits 0.055
Result: Output Frequency = 2.406 kHz
Low range
Given: Tuning Word 0.25, Clock Frequency 1 MHz, Accumulator Bits 0.55
Result: Output Frequency = 0.1708 MHz
Typical
Given: Tuning Word 0.5, Clock Frequency 10 MHz, Accumulator Bits 1.1
Result: Output Frequency = 2.333 MHz
High range
Given: Tuning Word 0.8, Clock Frequency 100 MHz, Accumulator Bits 1.76
Result: Output Frequency = 23.62 MHz
Maximum range
Given: Tuning Word 8, Clock Frequency 1 GHz, Accumulator Bits 17.6
Result: Output Frequency = 40.27 kHz
Solving for each variable
Solve for Output Frequency
Tuning Word 0.025, Clock Frequency 100 kHz, Accumulator Bits 0.055 → 2.406 kHz
Solve for Tuning Word
Output Frequency 100 Hz, Clock Frequency 100 kHz, Accumulator Bits 0.055 → 0.001039
Solve for Clock Frequency
Output Frequency 100 Hz, Tuning Word 0.025, Accumulator Bits 0.055 → 4.155 kHz
How Output Frequency changes with Tuning Word
| Tuning Word (input) | Output Frequency (result) |
|---|---|
| 0.05 | 0.2333 MHz |
| 0.125 | 0.5831 MHz |
| 0.25 | 1.166 MHz |
| 0.375 | 1.749 MHz |
| 0.5 | 2.333 MHz |
| 0.75 | 3.499 MHz |
| 1 | 4.665 MHz |
| 2 | 9.33 MHz |
| 3.5 | 16.33 MHz |
| 5 | 23.33 MHz |
The same result in other units
| Unit | Value |
|---|---|
| Hz | 2333000 |
| kHz | 2333 |
| MHz | 2.333 |
| GHz | 0.002333 |
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<p><a href="https://vbatpower.com/formulas/dds-output-frequency/">DDS Output Frequency</a> Calculator by vbatpower.com</p>Frequently asked questions
How do you calculate DDS Output Frequency?
Use fout = M × fclk / 2ᴺ. With Tuning Word 0.5, Clock Frequency 10 MHz, Accumulator Bits 1.1, Output Frequency works out to 2.333 MHz.
What is the formula for DDS Output Frequency?
The formula is 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.
How do you find Tuning Word when you know the other values?
Rearrange for Tuning Word: with Output Frequency 100 Hz, Clock Frequency 100 kHz, Accumulator Bits 0.055, Tuning Word is 0.001039.
How do you find Clock Frequency when you know the other values?
Rearrange for Clock Frequency: with Output Frequency 100 Hz, Tuning Word 0.025, Accumulator Bits 0.055, Clock Frequency is 4.155 kHz.
What units does DDS Output Frequency use?
Output Frequency is shown in Hz, kHz, MHz, GHz. Values are held in SI base units internally, so you can mix prefixes without converting by hand.
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