SP8858
The selection of C1 and R1 is often approached by using
thestandardrepresentationforthesecondordercharacteristic
higher order loops to use CAD tools to assess stability.
Popular analysis tools taken from control theory, such as root
locus and Bode diagrams, are useful to aid the design of the
closedloopPLLsystem. AN194describesthesetoolsinmore
detail and introduces a loop filter design methodolgy aimed at
optimising the phase noise performance.
2
equation: s212zvn1vn and selecting the natural-loop
frequency and the damping factor z to give the desired
response. The time constants are calculated using:
2zvn = t1K/C1 and vn2 = K/C1 so that
C1 = K/vn2 and R1 = 2zvn/K
Loop filter design example
Use the demonstration board to generate a 1GHz signal
witharesolutionof500kHz(N=5000)andreferenceoscillator
frequency of 40MHz. Set natural loop frequency, vn, to
2p3104 rad/s and damping factor to 0·7. The MQE001-1016
VCOgain,KVCO,isnominally25MHz/V.Setthephasedetector
output current to 2mA so that KPD = 231023/2p A/rad.
Using the above formula, calculate the loop filter R and Cs.
Alternatively, the loop filter and formula shown in Fig. 10b
can be used to introduce a pole in F(s) at 21/t2 which will
provide additional roll-off in the closed loop transfer
characteristic in order to attenuate the reference sidebands.
The closed loop transfer function becomes:
fo(s)
fi(s)
[s(t11t2)11]KVCOKPD
[C1t2s31C1s21K(t11t2)s1K]
K = 2p32531063231023/2p35000 = 10
C1 = 10/(2p3104)32 ≈ 2·531029
R1 = 230·732p3104/10 ≈ 8796
C2 = C1/10 ≈ 0·2531029
=
Care must be taken when choosing C2 to ensure that the
additional pole does not unduly affect the stability margins of
the loop. In practice, a simple and useful rule of thumb is to set
the desired second order response as above and then set C2
to be 1/10 of C1. It is advisable when designing third order or
Realise the loop filter with C1 = 2·2nF, C2 = 220pF and
R1 = 8·2kΩ. The single sideband phase noise specturm for
this example is shown in Fig. 11.
C2
C1
R1
C1
R1
I (s)
i
I (s)
i
−
−
V
(s)
V
o
(s)
o
+
+
V
(s)/Ii(s) = [s(
t
111]/sC1
V
(s)/Ii(s) = [s(
t
11
t
2)11]/sC1(s
t
211)
o
o
where t1 = C1R1
where
t1 = C1R1 and t
2 = C2R1
Fig. 10b
Fig. 10a
Fig. 10 Loop filters
0
210
220
230
240
250
260
270
280
290
2100
2110
2120
2130
2140
2150
2160
2170
10Hz
100Hz
1kHz
10kHz
100kHz
FREQUENCY
Fig. 11
11
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