Digital Signal Processing Reference
In-Depth Information
t
(0)
t
(1)
t
(2)
T
(1)
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t
, sec
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Tutorial 50
Q: The phase equation of a first-order sinusoidal DPLL is shown below. Find
approximately the steady-state phase error /
ss
.
π
π
−
π
−
π
φ
(
k
), rad
Solution: First, we plot the curve y = x. If there is a steady-state, this curve will
have two intersections with phase equation curve; one of them is the steady-state
point, where its projection on the y-axis gives /
ss
. To determine which one is the
steady-state point, we choose randomly some value for the initial phase / (0), and
then plot the phase plane diagram by successive projections on the equation and
y = x. For the above figure we choose /(0) =-1.5 and we find /
ss
0
:
5
:
π
φ
o
π
−
π
φ
2
φ
1
φ
ss
−
π
φ
(
k
), rad
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