User`s guide

PLL Analysis Theory of Operation
The PLL Analysis measurement tool is based on a white paper authored by
WAVECREST Corporation [1].
The fundamental measurement of this tool is the 1-sigma (
σ ) vs. UI plot similar to the High Frequency
Modulation tool [2]. The relationship between the jitter variance (
σ
2
) and the jitter power spectral
density (PSD) is well established [3]. The jitter PSD of the PLL output clock is related to the PLL
reference clock noise via the transfer function. Therefore, with reasonable assumptions about the input
noise of the PLL reference clock, we can infer the transfer function of the PLL.
At the current time, we assume that the input noise spectrum is white and the PLL is of 2
nd
-order. The
2
nd
-order PLL transfer function in Laplace space is given by
()
22
2
2
2
nn
nn
ss
s
sH
ωζω
ωζω
++
+
=
where
s = iω is the complex frequency, ω
n
is the natural frequency, and ζ is the damping factor. The
parameters
ω
n
, ζ , and the input noise level are found from a least-squares fit of the variance. Once
H ( s ) is determined, PLL characteristics such as natural frequency, damping factor, damping frequency,
pull-in range, pull-in time, pull-out range, pull-out time, lock range, lock time, lock frequency, Bode plots,
root locus, poles, zeros, and stability are readily obtained.
[1] Li, M.,
A New Method for Simultaneously Measuring and Analyzing PLL Transfer Function and Noise
Processes
, DesignCon Proceedings, 2002.
[2] For more information, refer to "High Frequency Modulation", GigaView Quick Reference Guide,
Wavecrest Corporation
[3] Wilstrup, J., A Method of Serial Data Ji er Analysis Using One-shot Time Interval Measurements , ITC
Proceedings, p.819, 1998.
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