Crystal Frequency Stability
Δf = f0 × ppm × 1e-6
Quick answer
This calculator solves Δf = f0 × ppm × 10⁻⁶ for Frequency Deviation. With Nominal Frequency 10 MHz, Stability (ppm) 0.5, the result is 5 Hz. It solves in 3 directions, so you can enter the values you have and get the one you need.
Calculator
Formula
Description
Crystal oscillator frequency stability is specified in parts per million (ppm), indicating the maximum frequency deviation from the nominal value due to temperature variation, aging, and manufacturing tolerance. A 10 MHz crystal with ±20 ppm stability can deviate by ±200 Hz. Over temperature, crystals follow a parabolic curve centered near 25°C. AT-cut crystals (the most common) achieve ±10 to ±50 ppm over the industrial temperature range (-40 to +85°C). Temperature-compensated (TCXO) and oven-controlled (OCXO) oscillators achieve much tighter stability.
Variables
- Δf — Frequency deviation from nominal (Hz)
- f0 — Nominal crystal frequency (Hz)
- ppm — Stability specification in parts per million
Practical Notes
Typical stability by oscillator type: crystal (XO) ±20-100 ppm, TCXO ±0.5-5 ppm, OCXO ±0.01-0.1 ppm, atomic clock ±0.0001 ppb. For UART communication, frequency accuracy must be within ±2% for reliable data transfer. USB requires ±500 ppm at low speed and ±50 ppm at high speed. Crystal aging adds ±3-5 ppm/year.
Symbols and units
| Symbol | Meaning | Default unit | Accepted units |
|---|---|---|---|
| df | Frequency Deviation | Hz | Hz, kHz, MHz, GHz |
| f0 | Nominal Frequency | MHz | Hz, kHz, MHz, GHz |
| ppm | Stability (ppm) | — | — |
Step by step
- 1. What you know: Nominal Frequency 10 MHz, Stability (ppm) 0.5
- 2. The relation: Δf = f0 × ppm × 10⁻⁶
- 3. Substitute: f0 = 10 MHz, ppm = 0.5
- 4. Result: Frequency Deviation = 5 Hz
Worked examples
Minimum range
Given: Nominal Frequency 100 kHz, Stability (ppm) 0.025
Result: Frequency Deviation = 0.0025 Hz
Low range
Given: Nominal Frequency 1 MHz, Stability (ppm) 0.25
Result: Frequency Deviation = 0.25 Hz
Typical
Given: Nominal Frequency 10 MHz, Stability (ppm) 0.5
Result: Frequency Deviation = 5 Hz
High range
Given: Nominal Frequency 100 MHz, Stability (ppm) 0.8
Result: Frequency Deviation = 80 Hz
Maximum range
Given: Nominal Frequency 1 GHz, Stability (ppm) 8
Result: Frequency Deviation = 8 kHz
Solving for each variable
Solve for Frequency Deviation
Nominal Frequency 100 kHz, Stability (ppm) 0.025 → 0.0025 Hz
Solve for Nominal Frequency
Frequency Deviation 5 Hz, Stability (ppm) 0.025 → 0.2 GHz
Solve for Stability (ppm)
Frequency Deviation 5 Hz, Nominal Frequency 100 kHz → 50
How Frequency Deviation changes with Nominal Frequency
| Nominal Frequency (input) | Frequency Deviation (result) |
|---|---|
| 1 MHz | 0.5 Hz |
| 2.5 MHz | 1.25 Hz |
| 5 MHz | 2.5 Hz |
| 7.5 MHz | 3.75 Hz |
| 10 MHz | 5 Hz |
| 15 MHz | 7.5 Hz |
| 20 MHz | 10 Hz |
| 40 MHz | 20 Hz |
| 70 MHz | 35 Hz |
| 100 MHz | 50 Hz |
The same result in other units
| Unit | Value |
|---|---|
| Hz | 5 |
| kHz | 0.005 |
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<p><a href="https://vbatpower.com/formulas/crystal-stability/">Crystal Frequency Stability</a> Calculator by vbatpower.com</p>Frequently asked questions
How do you calculate Crystal Frequency Stability?
Use Δf = f0 × ppm × 10⁻⁶. With Nominal Frequency 10 MHz, Stability (ppm) 0.5, Frequency Deviation works out to 5 Hz.
What is the formula for Crystal Frequency Stability?
The formula is Δf = f0 × ppm × 10⁻⁶. Crystal oscillator frequency stability is specified in parts per million (ppm), indicating the maximum frequency deviation from the nominal value due to temperature variation, aging, and manufacturing tolerance.
How do you find Nominal Frequency when you know the other values?
Rearrange for Nominal Frequency: with Frequency Deviation 5 Hz, Stability (ppm) 0.025, Nominal Frequency is 0.2 GHz.
How do you find Stability (ppm) when you know the other values?
Rearrange for Stability (ppm): with Frequency Deviation 5 Hz, Nominal Frequency 100 kHz, Stability (ppm) is 50.
What units does Crystal Frequency Stability use?
Frequency Deviation is shown in Hz, kHz. Values are held in SI base units internally, so you can mix prefixes without converting by hand.
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