Page 180 - Phase-Locked Loops Design, Simulation, and Applications

DESIGN PROCEDURE FOR MIXED-SIGNAL PLLS Ronald E. Best 111
pull-in range—so this type of phase detector is normally preferred. When a voltage output
PFD is used, the phase detector gain K can now be determined. When a unipolar power
d
supply is used, K = U /2π for the JK-flipflop or K = U /4π for the PFD (U = supply
B
B
d
d
B
voltage). When a bipolar power supply is used, or when the phase detector saturates at voltage
levels that differ substantially from the power-supply rails, the corresponding equation given
in Sec. 2.4 should be used. When a current output PFD is employed, the detector gain K must
P
be determined. This specification is normally found on the data sheet of the corresponding IC.
The procedure continues at step 8.
Step 8. The noise bandwidth B must now be specified. As shown in Sec. 4.3, B is related
L
L
to the signal-to-noise ratio of the loop (SNR) by
L

(5.4)

B should be chosen such that (SNR) becomes larger than some minimum value, typically
L
L
larger than 4 (which corresponds to 6 dB). If (SNR) is not known, it must be estimated or
i
17
eventually measured. Finally, the noise bandwidth B at the input of the PLL must also be
i
known. B is nothing else than the bandwidth of the signal source or the bandwidth of an
i
optional prefilter. After (SNR) and B are determined, B can be calculated from Eq. (5.4).
i i L
An additional problem arises when the scaler ratio N must be variable. We know from noise
theory that B is also related to ω and ζ by Eq. (4.9), which reads
L n

(5.5)

When the divider ratio N is variable, both ω and ζ vary with N; hence, B also becomes
n L
dependent on N. In such a case, we specify B for the case N = N mean , as pointed out in step 2.
L
To make sure B does not fall below the minimum acceptable value, we should check its
L
values at the extremes of the scaler ratio N, using Eq. (5.5). If B becomes too small at one of
L
the extremes of N, the initial value assumed for N = N mean should be increased

correspondingly.
Step 9. In this step, the characteristic of the VCO will be determined. As mentioned earlier,
the procedure is restricted to relaxation VCOs. When a resonant VCO is used, however, the
design can be adapted correspondingly; refer to the comments at the end of this chapter.
Because the center frequency ω (or the range of ω ) is known and the range of the divider
0
0
ratio N is also given, we can calculate the range of output (angular) frequencies that must be
generated by the VCO. Let ω and ω be the minimum and maximum output
2min 2max
frequencies of the VCO, respectively. A suitable VCO must be selected first. In most cases,
the VCO will be part of the PLL system, typically an integrated circuit. Given the supply
voltage(s) of the VCO, the data sheet indicates the usable range of control voltage u . (For a
f