AN279 Silicon_Laboratories, AN279 Datasheet - Page 2

• Manufacturer Part Number: AN279
• Description: Estimating Period Jitter FROM Phase Noise
• Manufacturer: Silicon_Laboratories

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, it
is reasonable to expect that higher frequency jitter components will contribute more to period jitter than lower-
frequency jitter components (f<<1/T.)
A number of authors, e.g., Drakhlis (2001), have derived the basic relationship between J
noise spectral density S
and, therefore:
In short, period jitter is integrated similarly to phase jitter but with a frequency weighting factor of 4sin
See "Appendix A—Derivation" on page 5.
There are practical limits to integrating phase noise from f = 0 to
limit, f
determined by the measurement system bandwidth.
Phase noise integration using the sin
frequencies well below the half-carrier frequency. Therefore, the choice of f
is generally not critical. For the purposes of this application note, the minimum offset frequency for phase noise
measurements is 10 Hz, coinciding with the usual dividing line between wander and jitter.
The period jitter sin
thereafter. It is clear that phase noise in the vicinity of this offset will make a significant contribution to the period
jitter.
The maximum offset frequency for the purposes of integration is determined by the bandwidth of interest. One
practical high-frequency limit is to set f
Brown (2004). Another, more conservative, approach is to integrate out to the carrier frequency where the sin
weighting factor reaches its first null. This method appears to correlate well with at least one popular Time Interval
Analyzer or TIA, presumably due to aliasing components above f
However, in many high-frequency applications, phase noise equipment cannot measure phase noise all the way
out to either the half-carrier or carrier frequencies. Provided that the phase noise data reaches the phase noise
floor at its highest measured offset, the phase noise floor may be extended from f
estimation approach adopted in this application note.
2
J
Δ
PER
ϕ
2
RMS
(
L
rms
, to a high-frequency limit, f
=
)
4 S
∞
∫
0
=
------ Δ
2π
ϕ
T
f ( )x
0
2
sin
ϕ
weighting factor reaches its first maximum at the half-carrier frequency and becomes periodic
2
RMS
2
(
φ
π
(f). It can be shown that
f
τ
) f d
H
. In practice, the minimum and maximum phase noise offset frequencies are
2
H
weighting factor is not typically sensitive to contributions from offset
equal to the half-carrier frequency. For an example, see Underhill and
Rev. 0.1
∞
C
/2. See Smith (2006).
. Phase noise is measured from a low-frequency
L
in theoretical period jitter calculations
H, MEASURED
PER
to f
(rms) and phase
H
2
(πfτ).
. This is the
2