Phase-Locked Loop
1
Phase-Locked Loop in RF Receiver
Antenna
BPF1
LNA
BPF2
Mixer BPF3 IF Amp
Demodulator
RF front end
LO
Ref.
VCO
PD
Loop
Filter
1/N
PhaseLocked
Loop
2
Functional Blocks in PLL
Ref
VCO
PD
Loop
Filter
1/N
LO
PhaseLocked
Loop
• Phase detector (PD): find difference between
phases of two signals
• Loop filter: provide appropriate control voltage
for the voltage-controlled oscillator (VCO)
• VCO: generate signals with phase determined
by the control voltage
• Divide-by-N: LO phase changes N times faster
than Ref phase
3
Design Issues
• Tracking behavior
• Noise performance
• Jitter characteristics
– Jitter tolerance
– Jitter transfer
– Jitter generation
• Power consumption
4
System Modeling
vRef
•
•
•
•
•
PD
vd
F(s)
vC
VCO
vLO
vRef: input reference signal
vLO: local oscillator (LO) output signal
vd: detector output
F(s): transfer function of loop filter
vC: control voltage for VCO
5
System Modeling
vRef
qRef
PD
Kdqe
VCO
F(s)
vLO
qLO
•
•
•
•
Phase signals contain information
qRef: phase of reference signal
qLO: phase of local oscillator (LO) signal
qe: phase difference between qRef and qLO
6
Jump in Phase
dq LO
 0  5(q REF  q LO )
dt
7
Ramp in Phase
dq LO
 0  5(q REF  q LO )
dt
8
Ramp in Phase
t
dq LO
 0  5(q REF  q LO )  5 (q REF  q LO )d
dt
0
9
Phase Detector
qREF
qe
+
Kd
vd

qLO
• Vd=Kdqe=Kd(qREF – qLO)
• Kd: gain of phase detector
10
Loop Filter
vd
F(s)
vC
• VC(s) = F(s) Vd(s)
• Low-pass filter
– Extract phase error
– Remove high frequency noises
• Passive filter for integrated PLL
• Active filter for discrete component PLL
11
Passive Lag Filter
R1
+
vd
–
R2
C
1  s 2
1  s ( 1   2 )
+
F (s) 
vC
 1  R1C
 2  R2C
–
1
2
1   2
1
1   2
1
2
• Lag filter: pole magnitude smaller than zero
• Passive components: high linearity, gain < 1
12
Active Lag Filter
R1
C1
R2
+
vd
–
C2
+
–
+
F (s)  K a
Ka 
1  s 2
1  s 1
 1  R1C1
vC   R C
2
2 2
–
K a  C1 / C2
Ka
1
1
C1
C2
 2 R2

 1 R1
1
2
• Can adjust pole and zero locations
• Can have gain
• Op amp limitations
13
Active Proportional-Integral (PI) Filter
R1
R2
+
vd
–
–
+
C
+
F ( s)  
vC
 1  R1C
 2  R2C
–
1  s 2
s 1
R2
R1
1
2
• Large open loop gain at low frequency
• Op amp limitations
– Linearity
– Noise
– Open loop gain
14
Voltage-Controlled Oscillator
vC
KVCO
+
1/s
qLO

0
qLO  0  KVCOvC
• KVCO: gain of VCO
15
Transfer Function of PLL
0
qREF
qe
+
Kd
vd
F(s)
vC
KVCO
+
+
1/s
qLO

qLO
• Open-loop transfer function from qe to qLO
K d KVCO F ( s )
A( s ) 
s
16
Transfer Function of PLL
0
qREF
qe
+
Kd
vd
F(s)
vC
KVCO
+
+
1/s
qLO

qLO
• Closed-loop transfer function from qREF
to qLO
 LO ( s )
A( s )
K d KVCO F ( s )
H ( s) 


 REF ( s ) 1  A( s ) s  K d KVCO F ( s )
17
Transfer Function from qREF to qe
0
qREF
qe
+
Kd
vd
F(s)
vC
KVCO
+
+
1/s
qLO

qLO
• Closed-loop transfer function
 e ( s )   REF ( s )   LO ( s )   REF ( s )  H ( s ) REF ( s )
e (s)
s
H e ( s) 
 1  H ( s) 
 REF ( s )
s  K d KVCO F ( s )
18
Other TF of Interest
vCn
qREF
qe
+
Kd
vd
F(s)
vC +
+
KVCO
1/s
qLO

qLO
• Noise in control voltage
[VCn ( s )  K d F ( s ) LO ( s )]KVCO / s   LO ( s )
 LO ( s )
KVCO

VCn ( s ) s  K d KVCO F ( s )
19
Other TF of Interest
qn
qREF
qe
+
Kd
vd
F(s)
vC
KVCO
1/s
+
+
qLO

qLO
• Phase noise of VCO
 n ( s )  K d KVCO F ( s ) LO ( s ) / s   LO ( s )
 LO ( s )
s

 n ( s ) s  K d KVCO F ( s )
20
Transfer Functions for Different Loop
Filters
• Passive lag filter
1  s 2
F (s) 
1  s ( 1   2 )
• Active lag filter
1  s 2
F (s)  K a
1  s 1
K d KVCO
(1  s 2 )
1   2
H ( s) 
1  K d KVCO 2
K K
s2 
s  d VCO
1   2
1   2
K d KVCO K a
H ( s) 
s 
2
• Active PI filter
1  s 2
F (s) 
s 1
1
1  K d KVCO K a 2
1
K d KVCO
1
H ( s) 
s 
2
(1  s 2 )
1
(1  s 2 )
K d KVCO 2
1
s
K d KVCO K a
s
K d KVCO
1
21
Normalizing Transfer Function
• Normalized denominator
D( s)  s 2  2 n s  n2 ,
n : natural frequency;  : damping ratio
• Passive lag filter
n 
K d KVCO
1   2
n
1
  ( 2 
)
2
K d KVCO
• Active lag filter
n 
K d KVCO K a
1
 
n
 
n
2
( 2 
1
)
K d KVCO K a
• Active PI Filter
n 
K d KVCO
1
2
2
22
Normalized Transfer Function
• Passive lag filter
H (s) 
(2n 
) s  n2
K d KVCO
s 2  2n s  n2
• Active lag filter
H (s) 
n2
(2n 
n2
) s  n2
K d KVCO K a
s 2  2n s  n2
• Active PI Filter
2n s  n2
H (s)  2
s  2n s  n2
23
Normalized Transfer Function
2n s  n2
H (s)  2
s  2n s  n2
H e ( s) 
s2
s 2  2n s  n2
• Passive lag filter
K d KVCO 
1
2
• Active lag filter
K d KVCO K a 
1
2
24
Frequency Response of H(s)
2n s  n2
H (s)  2
s  2n s  n2
25
Frequency Response of He(s)
H e ( s) 
s2
s 2  2n s  n2
26
Step Response of PLL
• Phase step
qREF (t )  q  u(t )  REF (s)  q / s
• Phase Error
e ( s )  H e ( s )q / s 
q  s
s 2  2n s  n2


 nt
2
2

q
[cos(
1



t
)

sin(
1



t
)]
e
,   1;
n
n

2
1 


q e (t )  q (1  nt ) exp( nt ),   1;


q [cosh(  2  1nt ) 
sinh(  2  1nt )]e  nt ,   1.

 2 1
• Steady state error (final value theorem)
q  s 2
qe ()  lim s e ( s)  lim 2
0
s0
s0 s  2 s   2
n
n
27
Step Response
H e ( s) 
s2
s 2  2n s  n2
28
Ramp Response of PLL
• Phase ramp
q REF (t )    tu(t )  REF (s)   / s 2
• Phase Error
e ( s )  H e ( s ) / s 2 

s 2  2n s  n2
1
 
 nt
2
sin(
1



t
)
e
,   1;
n

2
 n 1 

q e (t )    t exp( nt ),   1;
 
1

sinh(  2  1nt )e  nt ,   1.
 n  2  1
• Steady state error (final value theorem)
qe ()  lim s e ( s)  lim
s 0
s 0
  s
0
2
2
s  2n s  n
29
Ramp Response
H e ( s) 
s2
s 2  2n s  n2
30
General Steady State Error in Ramp Response
s
H e ( s)  1  H ( s) 
s  K d KVCO F ( s )
e ( s )  H e ( s ) / s 2 
 / s
s  K d KVCO F ( s )
• High loop gain

F (0)    q e ()  lim s e ( s )  lim
0
s 0
s 0 s  K K
d VCO F ( s )
• Low loop gain
qe ()  lim s e ( s)  lim
s 0
s 0



s  K d KVCO F ( s) K d KVCO F (0)
31
Stability of PLL
• Criterion for stability
– Closed-loop pole at left half plane
– Sufficient phase margin
• Control of pole location
– Open loop gain
– Open loop zero
• Check root locus
A( s )
K d KVCO F ( s ) / s
H ( s) 

1  A( s) 1  K d KVCO F ( s ) / s
32
Root Locus Method
• Closed-loop TF
K d KVCO F ( s) / s
K  n( s )
H ( s) 

1  K d KVCO F ( s) / s d ( s)  K  n( s)
where
K  K d KVCO and F ( s) / s  n( s) / d ( s).
• Closed-loop poles make
d ( s )  K  n( s )  0
– K=0, open-loop poles
– K infinity, open-loop zeros or infinity
33
Root Locus for Passive Lag Filter
F ( s ) 1 1  s 2

s
s 1  s ( 1   2 )
34
Root Locus for Active Lag Filter
F ( s ) 1 1  s 2

s
s 1  s 1
35
Root Locus for Active PI Filter
F ( s ) 1 1  s 2

s
s s 1
36
Root Locus for 1st-Order LP Filter
F (s) 1 1

s
s 1  s 1
37
Effects of Parasitics
F ( s) 1 1
1

s
s 1  s 1 1  0.1s 1
38
Effects of Zero
F ( s) 1 1 1  2s 2

s
s 1  s 1 1  0.1s 1
39
Phase Noise and Jitter
• Phase noise
– Fluctuation in phase
– Frequency domain
– Discussed in RF circuits
• Jitter
– Error in clock edge (period)
– Time domain
– Significant in communications circuits
• Two concepts
– Related to each other
– Exact relationship not clear
40
Jitter Measurements
Agilent, “Understanding Jitter and Wander Measurements and Standards.”
41
Jitter Tolerance
• Ability of a PLL to operate with jitter
– Applied to its reference
– Various magnitudes
– Different frequencies
• Usually specified using an input jitter mask
– Jitter magnitude and corner frequencies
– BER requirement
– Various for standards
42
PLL in Clock and Data Recovery
0
1
0
0
1
0
1
0
1
1
0
0
X
1
0
1
0
Ideal
signal
Distorted
signal
Ideal
clock
0
0
Recovered
clock
1
0
0
1
0
1
0
43
Jitter Tolerance Mask
44
Jitter Tolerance Measurement
45
Jitter Tolerance Measurement
46
Jitter Tolerance Measurement
• Error at corner frequency
– Insufficient clock recovery bandwidth
– Incorrect mask used
47
Jitter Tolerance Measurement
Tolerance margin
• Excessive jitter tolerance margin
48
Jitter Tolerance Measurement
• Occasional fail at specific frequencies
– Need extra settling time after jitter amplitude change
• Repeating with additional settling time
• Spot measurement
49
Jitter Tolerance Measurement
• Limited clock recovery bandwidth
• Eye-width alignment noise
50
Jitter Tolerance Measurement
• Limited buffer store
51
Jitter Transfer
• Jitter transfer or jitter attenuation
• Output jitter vs. input jitter
– Input jitter with various amplitudes and frequencies
– Output jitter measured with various bandwidths
• Intrinsic jitter
• Typically specified using a bandwidth plot
– Amplitude
– Roll off speed
– Corner Frequency
52
Jitter Transfer Mask
53
Jitter Transfer Measurement
• Jitter tolerance mask used to set input jitter level
• Sinusoidal jitter at magnitudes and frequencies
• Narrow-band measurement
54
Jitter Transfer Measurement
• Different test masks
• SONET mask: additional amplitude at lower band
55
Jitter Transfer Measurement
• Measurement set-up noise
• -40 dB sufficient
56
Jitter Transfer Measurement
• Low-frequency phase noise
• Power-line crosstalk
• Short measurement time
57
Jitter Transfer Measurement
• Incorrect filter characteristic
• Excessive peaking
58
Jitter Transfer Plot
E. Barari, “Jitter Analysis / Specification,” May 2002.
59
Measured Jitter Transfer Characteristic
E. Barari, “Jitter Analysis / Specification,” May 2002.
60
Measured Jitter Transfer Characteristic
E. Barari, “Jitter Analysis / Specification,” May 2002.
61
Measured Jitter Transfer Characteristic
E. Barari, “Jitter Analysis / Specification,” May 2002.
62
Measured Jitter Transfer Characteristic
E. Barari, “Jitter Analysis / Specification,” May 2002.
63
Jitter Generation
• Intrinsic jitter produced by the PLL
– Thermal noise
– Drift in VCO
• Measured at its output
– Applying a clear reference signal to PLL
– Measuring its output jitter.
• Usually specified as a peak-to-peak period
jitter value
64
Jitter Generation Standard
65
Jitter Generation Measurement
• Direct measurement of p-p jitter
• Phase noise measurement
• Eye diagram and histogram
66
Jitter Generation Measurement
67
Measurement Considerations
•
•
•
•
•
Calibration
Measurement range
Measurement time
Power
Frequency offset
68
TF from Noise in VCO Control Voltage
vCn
-1
Kd
F(s)
+
+
KVCO/s
qLO
 LO ( s )
KVCO
KVCO s
H C (s) 

 2
VCn ( s ) s  K d KVCO F ( s ) s  2n s  n2
• Can be viewed as low-pass filter
69
TF from Noise in VCO Control Voltage
H C ( s) 
s
s 2  2n s  n2
70
TF from Phase Noise in VCO
qn
-1
Kd
F(s)
KVCO/s
+
+
qLO
 LO ( s)
s
s2
Hq ( s ) 

 2
n ( s) s  K d KVCO F ( s) s  2n s  n2
• High-pass filter
• The same as He(s)
71
Phase Error in VCO
vCn
HC(s)
qREF
qe
+
Kd
F(s)
KVCO/s
qn
Hq(s)
qLO

qLO
• vCn dominate at low frequencies
• qn dominate at high frequencies
72