
248 CHAPTER 15. PROJECT 6: PHASE-LOCKED LOOP
−1 −0.5 0 0.5 1
−1
−0.8
−0.6
−0.4
−0.2
0
0.2
0.4
0.6
0.8
1
Real Part
Imaginary Part
Figure 15.4: The pole/zero plot of the loop filter.
0 4 8 12 16 20 24
−40
−30
−20
−10
0
magnitude (dB)
0 4 8 12 16 20 24
−100
−50
0
frequency (kHz)
phase (degrees)
Figure 15.5: The frequency response of the loop filter.
evident from Figure 15.5, this results in infinite gain at 0 Hz (DC). An example of a well
behaved startup transient of the PLL is shown in Figure 15.6. While this type of behavior
is quite common, the second-order Costas loop is blind to 180-degree phase ambiguities,
and the system’s output may be as shown in Figure 15.7. In Figure