Oscillator Jitter from Phase Noise Calculator

Accurately estimate RMS period jitter by analyzing an oscillator’s phase noise characteristics.

Calculation Results

Illustrative chart of phase noise and the integration area used to calculate jitter.

Summary of Inputs and Calculated Jitter

Parameter	Value	Unit
Carrier Frequency
Phase Noise		dBc/Hz
Integration Bandwidth		Hz
RMS Period Jitter

In-Depth Guide to Oscillator Jitter and Phase Noise Analysis

What is Oscillator Jitter from Phase Noise Analysis?

In electronics, an ideal oscillator would produce a perfect sine wave with all its energy concentrated at a single frequency. However, real-world oscillators exhibit random, short-term fluctuations in their phase and frequency. These fluctuations are known as **phase noise**. When we analyze this noise in the frequency domain and integrate it over a specific bandwidth, we can **calculate the oscillator jitter**, which is the corresponding deviation in the time domain. This process is critical for engineers designing high-speed systems, such as data converters, communication links, and digital processors, where timing precision is paramount. An unstable clock source can introduce errors, degrade signal-to-noise ratio (SNR), and ultimately limit system performance.

The Formula to Calculate Oscillator Jitter by Using Phase-Noise Analysis

The conversion from phase noise to RMS period jitter is a two-step process. First, we calculate the total integrated phase noise power over the frequency band of interest. For a simplified case assuming a flat phase noise floor across the bandwidth, the RMS Phase Error is calculated. Second, this phase error (in radians) is converted to time jitter (in seconds).

Step 1: Calculate RMS Phase Error (in Radians)

The integrated phase noise power is first calculated by converting the dBc/Hz value to a linear power ratio and multiplying by the integration bandwidth. The RMS phase error is the square root of twice this value.

Φ_{error_rms} = sqrt(2 * 10^(L(f)/10) * BW)

Step 2: Convert RMS Phase Error to RMS Period Jitter (in Seconds)

The RMS period jitter is then found by dividing the phase error by the angular frequency of the carrier.

Jitter_rms = Φ_{error_rms} / (2 * π * f₀)

Variables Used in the Jitter Calculation

Variable	Meaning	Unit (Typical)	Typical Range
Jitterrms	RMS Period Jitter	picoseconds (ps), femtoseconds (fs)	10 fs – 10 ps
Φerror_rms	RMS Phase Error	radians	10^-6 – 10^-3
L(f)	Single Sideband Phase Noise	dBc/Hz	-120 to -170
BW	Integration Bandwidth (f_high – f_low)	Hz	1 MHz – 100 MHz
f₀	Oscillator Carrier Frequency	MHz, GHz	10 MHz – 10 GHz

Practical Examples

Example 1: High-Performance ADC Clock

• Inputs:
  • Carrier Frequency: 500 MHz
  • Phase Noise: -160 dBc/Hz
  • Integration Bandwidth: 10 kHz to 20 MHz
• Results: This configuration results in an extremely low RMS period jitter, typically in the femtosecond range, which is essential for clocking a High-Speed ADC Clocking solution to achieve maximum resolution and SNR.

Example 2: Standard Communications System

• Inputs:
  • Carrier Frequency: 100 MHz
  • Phase Noise: -145 dBc/Hz
  • Integration Bandwidth: 1 kHz to 10 MHz
• Results: The calculated jitter would be in the hundreds of femtoseconds to a few picoseconds. This level of performance is acceptable for many digital communication systems where cost is a factor and the absolute lowest jitter is not the primary concern. For more details on this, see our guide on Phase-Locked Loop (PLL) Design.

How to Use This Oscillator Jitter Calculator

1. Enter Carrier Frequency: Input the oscillator’s main operating frequency and select the appropriate unit (MHz or GHz).
2. Input Phase Noise: Provide the oscillator’s single sideband phase noise floor value in dBc/Hz. This is typically found in the component’s datasheet. For this calculator, we assume it’s a flat value across the integration bandwidth.
3. Define Integration Bandwidth: Set the lower and upper frequency offsets (in Hz) that define the range over which the jitter will be calculated. This range is often specified by the standard relevant to your application (e.g., SONET, PCI Express).
4. Calculate and Interpret: Click “Calculate Jitter”. The primary result is the RMS Period Jitter, displayed in femtoseconds (fs) or picoseconds (ps). This value represents the time-domain instability of your clock source over the specified bandwidth.

Key Factors That Affect Oscillator Jitter

• Component Quality: The intrinsic noise of the oscillator’s resonant element (e.g., crystal, SAW) is the primary determinant of phase noise. Higher quality components have lower noise.
• Supply Voltage Noise: Noise and ripple on the power supply can modulate the oscillator’s internal components, directly contributing to phase noise and jitter. A clean power supply is critical for a Low-Jitter Oscillator Design.
• Integration Bandwidth: A wider integration bandwidth will almost always result in a higher calculated jitter value, as more noise power is included in the calculation.
• Vibration and Shock: Mechanical stress can induce phase noise in sensitive oscillators, particularly crystal-based ones (microphonics effect).
• Temperature Stability: Frequency drift due to temperature changes can affect the long-term stability, although it’s distinct from the short-term fluctuations of phase noise.
• Load Impedance: Improperly matched load impedance can cause reflections and additional noise, degrading jitter performance.

Frequently Asked Questions (FAQ)

1. Why is jitter specified in ‘RMS’?

RMS (Root Mean Square) provides a statistical measure of the jitter’s magnitude. It represents the standard deviation of the timing error, assuming a Gaussian distribution of noise.

2. What is the difference between period jitter and phase jitter?

Period jitter refers to the variation in the duration of each clock cycle. Phase jitter is the integral of phase noise over a specific frequency band, representing the total accumulated timing error. This calculator converts phase noise into period jitter.

3. Why is the integration bandwidth important?

Different applications are sensitive to noise at different frequency offsets. For example, a data converter is sensitive to wideband noise, while a PLL’s performance depends on close-in phase noise. The bandwidth must match the application’s requirements. Our phase noise measurement techniques guide covers this in more detail.

4. Can this calculator account for spurs?

No, this is a simplified calculator that assumes a flat, broadband noise floor. It does not account for discrete, non-random interfering signals (spurs), which would require a more complex, point-by-point integration.

5. Is lower jitter always better?

Generally, yes, especially in high-speed applications. However, there is a trade-off between performance, power consumption, and cost. An engineering decision must be made to select an oscillator with “good enough” jitter for the application without over-engineering the solution.

6. What’s a typical phase noise value for a good oscillator?

A high-quality crystal oscillator (XO) or oven-controlled crystal oscillator (OCXO) might have a phase noise floor of -160 to -175 dBc/Hz. A standard oscillator in a PLL synthesizer might be in the -140 to -150 dBc/Hz range.

7. How does carrier frequency affect jitter?

As the formula shows, for the same amount of phase error in radians, a higher carrier frequency results in a lower period jitter in seconds.

8. What unit is femtosecond (fs)?

A femtosecond is one quadrillionth of a second (10^-15 s). A picosecond (ps) is one trillionth of a second (10^-12 s).