U. Glaeser

Phase Margin (deg)
FIGURE 10.10 PLL phase margin as a function of damping factor.
the loop parameters ω N and ζ, which are commonly specified by higher-level system requirements. The
complexity of these approaches depends on whether C 2 exists and its level of significance.
If C 2 does not need to be considered, a simplified version of the open-loop analysis or second-order
analysis can be used. For an open-loop analysis without C 2, we need to consider the open-loop response
of the PLL in Fig. 10.5. The loop gain normalization constant, G O, for the normalized loop gain magnitude
plot is directly related to the damping factor ζ by
© 2002 by CRC Press LLC
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G O = R 2 ⋅ C ⋅ I CH ⋅ K V�N = 4 ⋅ ζ 2
This normalization constant is also the loop gain magnitude at the asymptotic break point for the
zero at 1/(R ⋅ C). An increase in the loop gain normalization constant will lead to a higher unity gain
crossing, and therefore more phase margin. A plot of phase margin as a function of the damping factor
ζ is shown in Fig. 10.10. In order to adequately stabilize the design, the phase margin should be set to
65° or more and the unity gain bandwidth should be set no higher than ω REF/5. It is easiest to first adjust
the loop gain magnitude level to set the phase margin, then to use the frequency scaling rules to adjust
the unity gain bandwidth to the desired frequency. Without C 2, the second-order analysis simply depends
on the loop parameters ω N and ζ. To adequately stabilize the design, ω N should be set no higher than
ω REF/10 and ζ should be set to 0.707 or greater.
If C 2 exists but is not too large, an extension of the above approaches can be used. C should be set
greater than C 2 ⋅ 20 to provide a minimum of 65° of phase margin at the unity gain bandwidth with the
maximum phase margin. For any C/C 2 ratio, the maximum phase margin is given by
PMMAX 2 tan −1
=
⋅
With the open-loop analysis, as before, the phase margin should be set to at least 65° or its maximum
and the unity gain bandwidth should be set no higher than ω REF�5. With the second-order analysis, Ω N
should be set no higher than ω REF /10, ζ should be set to 0.707 or greater, and ω C should be at least a
decade above ω N.
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1.0
ζ
C/C 2
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( ( + 1)
) – π/2
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2.0