# What is Phase Noise and Jitter in Epson Programmable Crystal Oscillator

### Release date:2018-12-18 Author:Guan Shuo Click:

What is the phase noise and jitter of crystal oscillation? **Epson programmable crystal oscillator** for you.

Phase noise and jitter are two different ways to quantify the same phenomenon. Ideally, a perfect pulse signal with a fixed frequency (for example, 1 MHz) should last exactly 1 microsecond and have a jump edge every 500 ns. Unfortunately, this signal does not exist. The length of the signal cycle always varies, which leads to the uncertainty of the arrival time of the next edge. This uncertainty is phase noise, or jitter.

IEC Standard Definition: Frequency Domain Measurement of Short-term Frequency Stability of Oscillators, usually expressed by the corresponding fluctuating power spectral density S_(f), where the phase fluctuation function is_(f)=2 PI Ft-2 PI F0t

Note: Jitter is a time-domain measure of oscillator short-term frequency stability. In fact, both jitter and phase noise are a measure of frequency short-term stability.

1. Phase noise is the concept of frequency domain

Phase noise is another way to measure the time series of signals, and the results are displayed in the frequency domain.

If there is no phase noise, the whole power of the oscillator should be concentrated at the frequency f = fo. But the appearance of phase noise expands part of the power of the oscillator to adjacent frequencies, resulting in sideband. As can be seen from Figure 2, the sideband power rolls down to 1/fm at the offset frequency with a reasonable distance from the center frequency, and FM is the difference between the offset frequency and the center frequency.

Phase noise is usually defined as the dBc/Hz value at a given offset frequency, where dBc is the ratio of power to total power at that frequency in terms of dB. The phase noise of an oscillator at an offset frequency is defined as the ratio of the signal power to the total power of the signal within 1 Hz bandwidth at that frequency. In fact, in some parts of the noise sideband, the phase noise may decrease at the speed of 1/f3, 1/f2 or even 1/f0, depending on the correlation noise process.

The region with a descent rate of 1/f2 is called the "white frequency" zone, where the phase change is caused by white or unrelated fluctuations in the oscillator cycle. The behavior of the oscillator in this region is determined by the thermal noise of the components in the oscillator circuit. When the offset frequency is low enough, the scintillation noise of the element usually plays a role, resulting in the decrease of the spectral density in the region at a rate of 1/f3.

In addition, it is worth noting that the sideband noise tends to be infinite when the migration frequency tends to zero. This coincides with the timing jitter behavior that should occur in the free-running oscillator.

2. Jitter is a time domain concept

Jitter is the measurement result of the change of signal in time domain. It essentially describes how much the signal period distance deviates from its ideal value. Generally, the periodic variation of signals below 10 MHz is not classified as jitter, but as migration or drift. There are two main types of jitter: deterministic jitter and random jitter. Deterministic jitter is caused by identifiable interference signals, which are usually limited in magnitude, have specific (rather than random) causes, and cannot be statistically analyzed. There are four main sources of deterministic jitter:

1. Crosstalk between adjacent signal routes: When the self-inductance of a conductor increases, the induced magnetic field around the adjacent signal line will be transformed into the induced current, and the induced current will increase or decrease the voltage, resulting in jitter.

2. EMI radiation in sensitive signal pathway: power supply, AC power line and RF signal source all belong to EMI source. Similar to crosstalk, when there is EMI radiation nearby, the noise current induced in the time sequence signal path modulates the voltage value of the time sequence signal.

3. Noise of power supply layer in multilayer substrates: This noise may change the threshold voltage of logic gates or the reference ground level of threshold voltage, thereby changing the voltage required for switching gate circuits.

4. Multiple gate circuits are converted to the same logic state at the same time: this situation may lead to peak current induction in the power supply layer and stratum, which may change the threshold voltage.

Random jitter is a time series change caused by more difficult factors to predict. For example, temperature factors that can affect the mobility of semiconductor crystal materials may cause random changes in carrier flow. In addition, variations in semiconductor fabrication processes, such as uneven doping density, may also cause jitter.

One of the most basic characteristics of random jitter is randomness, so we can describe its characteristics with Gauss statistical distribution. For example, 100 consecutive measurements of the oscillation period of a clock oscillator with only random jitter factors will show a Gaussian distribution (or normal distribution). The range of mean plus or minus one standard deviation includes 68.26% of all periodic measurements, 95.4% of all measurements, 99.73% of measurements in the range of +/-2 standard deviation, +/-3 standard deviation and 99.99366% of measurements in the range of +/-4 standard deviation.

From this normal distribution, we can get two common definitions of jitter:

1. Peak-peak jitter, that is, the difference between the minimum and maximum measurements on the normal curve. In most circuits, the value will increase with the increase of the number of samples measured, and theoretically it can reach infinity. Therefore, this measurement is of little significance.

2. RMS jitter is the value of the first-order standard deviation of normal distribution. This value does not change much with the increase of sample size, so this measurement is more meaningful. But this measurement is only valid in pure Gauss distribution. If there is any deterministic jitter in the distribution, it is wrong to estimate the possibility of jitter using the first-order variance of the whole jitter histogram.

3. Multiple random jitter sources can be added by RMS. But to get the total jitter, we need to use the peak value to add the random jitter to the deterministic jitter.