Page 253 - Phase-Locked Loops Design, Simulation, and Applications

MIXED-SIGNAL PLL APPLICATIONS PART 1: INTEGER-N FREQUENCY
SYNTHESIZERS Ronald E. Best 150
Noise model for resonant type VCOs. The situation is much better for resonant VCOs
because we can use the noise model we already developed for the reference oscillator (see Sec.
6.7.1). The final results have been given in Eqs. (6.11) through (6.14).
Contribution of VCO phase noise to phase noise at PLL output. Knowing the noise
models of both resonant and relaxation type VCOs, we can now compute the contribution of
VCO phase noise to total phase noise at the output of the PLL. For this analysis, the noise
model in Fig. 6.14 is used again. Given the phase perturbation S , created by the VCO,
θθ VCO
the resulting phase perturbation S , at the PLL output becomes
θθ out

(6.33)

The phase noise generated by the VCO is therefore “weighted” by the error-transfer
function H (s), as defined in Eq. (3.8). As we know, H (s) is a highpass function. The low
e e
frequencies of phase noise created by the VCO are therefore almost fully suppressed. The high
frequencies come through unattenuated because the magnitude of H (s) becomes 1 at higher
e
frequencies. This phenomenon is easily explained by checking the noise model Fig. 6.14 once
again. At low frequencies, the phase noise θ n,VCO is almost completely compensated for by

the loop, because at low frequencies the loop gain is very high. This phase noise acts like a
phase signal π applied at the reference input—that is, at the upper input of the phase detector.
1
At higher frequencies, the loop gain decreases toward zero, and the phase noise θ n,VCO is no

longer attenuated.
To minimize the contribution of VCO phase noise, the loop bandwidth of the PLL should
be made large. This is in clear contradiction to the situation with reference noise discussed in
Sec. 6.7.1. Here, the loop bandwidth had to be made as large to minimize the contribution of
reference phase noise. To optimize overall noise at the PLL output, a compromise must be
found for loop bandwidth.

Spurs created by the phase detector
The frequency synthesizer shown in Fig. 3.1 generates an output signal whose frequency is
exactly N times the reference frequency. In the ideal case, the VCO would operate at its center
frequency. The output signal of the loop filter would then be exactly zero. Under these
conditions, the output signal of the VCO would be a “pure” square wave (or sine wave)—in
other words, a signal without any phase jitter. The spectrum of this signal would consist of a
line at f = f and—as is normal for a rectangular signal—a number of harmonics.
0
Under normal PLL operation, however, the phase detector delivers correction signals as
soon as the phase of the VCO output signal deviates from the ideal phase. If an EXOR gate is
used as phase detector, its output signal is a square-wave signal whose frequency is twice the
reference frequency, as shown in Fig. 2.6. Because the gain of every loop filter is nonzero at
that frequency, a ripple signal appears at the input of the VCO. The ripple signal modulates
the output signal

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