Jitter
Jitter measurements can be classified into three categories: cycle-to-cycle jitter, period jitter, and long-term jitter
Jitter is a key performance parameter. Need to know what matters in each case:
- PJ for digital timing
- LTJ for data converters and serial data
- Phase noise for communications (not all bandwidths matter)
The above Cycle-Cycle Jitter equation is wrong, \(\tau_1\) and \(\tau_2\) are not independent
Short Term Jitter
Period jitter, Jper is the short term variation in clock period compared to the average (mean) clock period.
Cycle-to-Cycle, Jcc is the time difference of two adjacent clock periods
Long Term Jitter (LTJ)
measuring LTJ
Jitter Calculation Examples
Jcc vs Jper
Estimating the RMS cycle-to-cycle jitter if all you have available is the RMS period jitter.
- Cycle-to-cycle jitter - The short-term variation in clock period between adjacent clock cycles. This jitter measure, abbreviated here as \(J_{CC}\), may be specified as either an RMS or peak-to-peak quantity.
- Period jitter - The short-term variation in clock period over all measured clock cycles, compared to the average clock period. This jitter measure, abbreviated here as \(J_{PER}\), may be specified as either an RMS or peak-to-peak quantity.
Let the variable below represent the variance of a single edge’s timing jitter, i.e. the difference in time of a jittery edge versus an ideal edge, \(\sigma^2_j\)
If each edge’s jitter is independent then the variance of the period jitter can be written as \[\begin{align} \sigma^2_\text{jper} &= (\sigma_\text{j(n+1)}-\sigma_\text{j(n)})^2 \\ &= \sigma_\text{j(n+1)}^2-2\sigma_\text{j(n+1)}\sigma_\text{j(n)})+\sigma_\text{j(n)})^2\\ &= \sigma_\text{j(n+1)}^2+\sigma_\text{j(n)})^2 \\ &=2\sigma^2_j \end{align}\]
In every cycle-to-cycle measurement we use one "interior" clock edge twice and therefore we must account for this
\[\begin{align} \sigma^2_\text{jcc} &= (\sigma_\text{jper(n+1)}-\sigma_\text{jper(n)})^2 \\ &=(\sigma_\text{j(n+2)}-2\sigma_\text{j(n+1)}+\sigma_\text{j(n)})^2 \end{align}\]
Since each edge's jitter is assumed to be independent and have the same statistical properties we can drop the cross correlation terms and write:
\[\begin{align} \sigma^2_\text{jcc} &=(\sigma_\text{j(n+2)}-2\sigma_\text{j(n+1)}+\sigma_\text{j(n)})^2 \\ &=\sigma_\text{j(n+2)}^2+4\sigma_\text{j(n+1)}^2+\sigma_\text{j(n)}^2 \\ &=6\sigma_\text{j}^2 \end{align}\]
The ratio of the variances is therefore \[ \frac{\sigma^2_\text{jcc}}{\sigma^2_\text{jper}} = \frac{6\sigma_\text{j}^2} {2\sigma_\text{j}^2}=3 \] Then \[ \sigma_\text{jcc} = \sqrt{3}\sigma_\text{per} \]
[Timing 101 #8: The Case of the Cycle-to-Cycle Jitter Rule of Thumb, Silicon Labs]
Cadence Sampled Phase Noise
How to derive edge phase noise from Output Noise in sampled Pnoise simulation, [https://community.cadence.com/cadence_technology_forums/f/custom-ic-design/56929/how-to-derive-edge-phase-noise-from-output-noise-in-sampled-pnoise-simulation]
General relationships between variance of jitter and phase noise
Understanding jitter and phase noise : a circuits and systems perspective
references
AN10007 Clock Jitter Definitions and Measurement Methods, SiTime [pdf]
SERDES Design and Simulation Using the Analog FastSPICE Platform, Silicon Creations [pdf]
Flexible clocking solutions in advanced processes from 180nm to 5nm, Silicon Creations [pdf]
One-size-fits-all PLLs for Advanced Samsung Foundry Processes, Silicon Creations [pdf]
Circuit Design and Verification of 7nm LowPower, Low-Jitter PLLs, Silicon Creations, [pdf]
Lecture 10: Jitter, ECEN720: High-Speed Links Circuits and Systems Spring 2023 [pdf]