Carrier and Code Tracking - A Software-Defined GPS and Galileo Receiver: A Single-Frequency Approach - page 88

20

10

0

−10

−20

−30

−40

B = 10 Hz
B = 30 Hz
B = 60 Hz

−50

−60

0 50 100 150 200 250

Time [ms]

FIGURE 7.5. Frequency offsets from an acquired frequency offset 20 Hz and for PLL noise
bandwidths of 10, 30, and 60 Hz. There are negative peaks in the first 2 ms due to transition
phase in the loop filter.

7.3.1 Damping Ratio
The damping ratio controls how fast the filter reaches its settle point. The damping
ratio also controls how much overshoot the filter can have. A smaller settling time
results in a larger overshoot. This can be seen in Figure 7.4.
The choice of damping ratio is a compromise between overshoot and settling
time. The damping is chosen to

7 resulting in a filter that converges rea-
sonably fast and does not make a high overshoot.

ζ = 0 .

7.3.2 Noise Bandwidth
The second parameter in the PLL filter is the noise bandwidth B L . The noise
bandwidth controls the amount of noise allowed in the filter. This parameter can
also, as the damping ratio, control the settling time. As the tracking loop starts
to track a signal the start frequency is the frequency found by the acquisition al-
gorithm. (This phase is sometimes called the pull-in phase in the literature. It is
in this phase the filter is trying to converge to the correct frequency and phase.)
The start frequency from the acquisition algorithm can be off by some Hz. The
tracking loop is then going to lock onto the correct frequency. To see the impact
of various noise bandwidths, a real GPS signal is used where the acquisition algo-
rithm found a frequency that is about 21 Hz off. Figure 7.5 shows the offset from
the start frequency for three different noise bandwidths.
From the figure, it follows that if the noise bandwidth is 60 Hz, the tracking
loop immediately finds the correct frequency offset of about 21 Hz. It can also be
seen that a lot of noise in the tracking frequency is allowed. In the second case,
where the noise bandwidth is 30 Hz, the tracking loop also locks on the signal