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此计算器目前以英文显示，翻译正在准备中。

统计与概率

已验证计算器，公式透明

统计与概率

Allan Variance Calculator.

Estimates the Allan variance and deviation of a dataset from a single sample of phase or frequency measurements, given the sample size and measurement interval.

结果随输入实时更新。
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您的输入

工作原理

  1. 1

    Enter the number of samples, averaging time, and phase noise.

  2. 2

    The calculator computes the Allan variance as phase noise squared divided by tau squared times (sample size minus one).

  3. 3

    The Allan deviation is the square root of the variance.

  4. 4

    Review the results and adjust inputs as needed.

(phase_noise^2) / (tau^2 * max(sample_size - 1, 1))

常见问题

What does Allan variance measure?

It quantifies frequency stability as a function of averaging time, helping identify noise types in clocks and oscillators.

Why use sample size minus one?

This approximates the degrees of freedom in the variance estimate, similar to sample variance.

Can I use this for any dataset?

This simplified version assumes white phase noise; for other noise types, more complex estimators are needed.

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结果

公式已检查

Allan Variance

0rad²/s²

Allan Deviation0.001005rad/s
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估算仅供参考——重要决策请咨询专业人士。

工作原理

Estimates the Allan variance and deviation of a dataset from a single sample of phase or frequency measurements, given the sample size and measurement interval.

  1. Enter the number of samples, averaging time, and phase noise.
  2. The calculator computes the Allan variance as phase noise squared divided by tau squared times (sample size minus one).
  3. The Allan deviation is the square root of the variance.
  4. Review the results and adjust inputs as needed.

公式

此计算器背后的数学公式，供您核对结果。

Allan Variance (simplified)

σ_y²(τ) ≈ (σ_φ²) / (τ² (N-1))

Estimates variance from phase noise σ_φ, averaging time τ, and sample count N.

实际应用场景

此计算在日常生活中的应用。

Oscillator stability

Compare short-term and long-term frequency stability of quartz or atomic clocks.

Example: Evaluate a 10 MHz oscillator with τ from 1 ms to 100 s.

Sensor noise characterization

Assess gyroscope or accelerometer noise for inertial navigation systems.

Example: Determine optimal averaging time for a MEMS gyro.

提示与常见错误

Tips

  • Use a larger sample size for more reliable estimates.
  • Choose tau values spanning decades to see noise type transitions.
  • Ensure phase noise is in radians, not degrees.

Common Mistakes to Avoid

  • Using sample size instead of sample size minus one.
  • Forgetting to square the phase noise.
  • Mixing units (e.g., degrees instead of radians).

假设与限制

  • Use the stated inputs and units.
  • Results are estimates for planning and education.
  • Check measurements and source data before making an important decision.