AN279 Silicon_Laboratories, AN279 Datasheet

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AN279

Manufacturer Part Number
AN279
Description
Estimating Period Jitter FROM Phase Noise
Manufacturer
Silicon_Laboratories
Datasheet
E
1. Introduction
This application note reviews how RMS period jitter may be estimated from phase noise data. This approach is
useful for estimating period jitter when sufficiently accurate time domain instruments, such as jitter measuring
oscilloscopes or Time Interval Analyzers (TIAs), are unavailable.
2. Terminology
In this application note, the following definitions apply:
RMS phase jitter may be expressed in units of dBc, radians, time, or Unit Intervals (UI).
Rev. 0.1 7/06
L f ( )
S T I M A T I N G
Cycle-to-cycle jitter—The short-term variation in clock period between adjacent clock cycles. This jitter
measure, abbreviated here as J
Jitter—Short-term variations of the significant instants of a digital signal from their ideal positions in time
(Ref: Telcordia GR-499-CORE). In this application note, the digital signal is a clock source or oscillator. Short-
term here means phase noise contributions are restricted to frequencies greater than or equal to 10 Hz
(Ref: Telcordia GR-1244-CORE).
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
quantity. This application note will concentrate on estimating the RMS value of this jitter parameter.
The illustration in Figure 1 suggests how one might measure the RMS period jitter in the time domain. The first
edge is the reference edge or trigger edge as if we were using an oscilloscope.
Phase jitter—The integrated jitter (area under the curve) of a phase noise plot over a particular jitter bandwidth.
Phase noise data may be recorded as either SSB phase noise L(f) in dBc/Hz or phase noise spectral density
S
φ
(f) in rad
S
-------------
ϕ
2
f ( )
2
/Hz where:
P
T = 0
E R I O D
CC
Figure 1. RMS Period Jitter Example
Copyright © 2006 by Silicon Laboratories
, may be specified as either an RMS or peak-to-peak quantity.
J
I T T E R F R O M
Clock Period
Distribution
PER
, may be specified as either an RMS or peak-to-peak
T = T
P
σ
PER
H A S E
J
PER
(RMS) = σ
N
O I S E
AN279
AN279

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AN279 Summary of contents

Page 1

... may be specified as either an RMS or peak-to-peak quantity may be specified as either an RMS or peak-to-peak PER Clock Period Distribution Figure 1. RMS Period Jitter Example Copyright © 2006 by Silicon Laboratories AN279 σ (RMS) = σ J PER PER AN279 ...

Page 2

... AN279 3. Basic Approach By definition, period jitter compares two similar instants in time of a clock source such as two successive rising edges or two successive falling edges. Since the two instants are separated in time by approximately one period reasonable to expect that higher frequency jitter components will contribute more to period jitter than lower- frequency jitter components (f< ...

Page 3

... By numerical integration, we can determine that the integrated phase noise under the entire SSB phase noise curve from 160 MHz yields a total phase noise power = –54.46 dBc. This "brick wall" integration is equivalent to wideband RMS phase jitter of 2.663 ps or 0.00268 radians. 2 (πfτ) weighting factor in dB Rev. 0.1 AN279 3 ...

Page 4

... AN279 By contrast weight L(f) using the period jitter weighting function and integrate the resulting curve over 160 MHz, we obtain a total phase noise power = –56.84 dBC, equivalent to RMS period jitter of 2.025 ps or 0.00204 radians; so, we can estimate the period jitter as being roughly 2 ps RMS, based solely on the available phase noise measurement ...

Page 5

... S – cos 2 f RMS 0 ∞ ∫ ϕ ϕ π τ Δ ) sin f RMS 0 ∞ ∫ ϕ ϕ π τ Δ ) sin f RMS ϕ ( )> radians t + < t > τ Rev. 0.1 AN279 5 ...

Page 6

... AN279 ∞ ∫ ϕ π τ Δ )df = sin f RMS 0 Now, convert back to time units: ∞ ⎛ ⎞ ∫ ϕ Δt Δ ------ 2 ----- - sin = = ⎝ ⎠ RMS π RMS 2 2 π 0 where f and f are the practical lower and upper frequency integration limits. ...

Page 7

... RMS_TOTAL RMS_NOISE RMS_1 or ∑ Δt Δt Δ RMS_TOTAL RMS_NOISE Δt J (rms) = PER_TOTAL RMS_TOTAL π τ sin π … Δt … Δ RMS_i RMS_N 2 RMS_i Rev. 0.1 AN279 spur below: 7 ...

Page 8

... AN279 C I ONTACT NFORMATION Silicon Laboratories Inc. 4635 Boston Lane Austin, TX 78735 Tel: 1+(512) 416-8500 Fax: 1+(512) 416-9669 Toll Free: 1+(877) 444-3032 Email: VCXOinfo@silabs.com Internet: www.silabs.com The information in this document is believed to be accurate in all respects at the time of publication but is subject to change without notice. ...

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