1

Phase-Locked Loop

2

Phase-Locked Loop in RF Receiver

BPF1 BPF2LNA

LO

Mixer BPF3 IF Amp

Demodulator

Antenna

RF front end

PDLoop Filter

1/N

Ref.VCO

Phase-Locked Loop

3

Functional Blocks in PLL

• 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

PDLoop Filter

1/N

RefVCO

Phase-Locked Loop

LO

4

Design Issues

• Tracking behavior

• Noise performance

• Jitter characteristics– Jitter tolerance– Jitter transfer– Jitter generation

• Power consumption

5

System Modeling

• 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

PD F(s)

VCOvd vCvRef vLO

6

System Modeling

• Phase signals contain information

• Ref: phase of reference signal

• LO: phase of local oscillator (LO) signal

• e: phase difference between Ref and LO

PD F(s)

Ref VCO

LO

KdevRef vLO

7

Jump in Phase

)(50 LOREFLO

dt

d

8

Ramp in Phase

)(50 LOREFLO

dt

d

9

Ramp in Phase

t

LOREFLOREFLO d

dt

d

00 )(5)(5

10

Phase Detector

• Vd=Kde=Kd(REF – LO)

• Kd: gain of phase detector

Kd

REF +

LO

e vd

11

Loop Filter

• 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

F(s)vd vC

12

Passive Lag Filter

CR

CR

s

ssF

22

11

21

2

)(1

1)(

• Lag filter: pole magnitude smaller than zero• Passive components: high linearity, gain < 1

21

1

21

2

vd vC

R1

R2

C

+

–

+

–

2

1

1

13

Active Lag Filter

21

222

111

1

2

/

1

1)(

CCK

CR

CR

s

sKsF

a

a

• Can adjust pole and zero locations• Can have gain• Op amp limitations

1

2

1

2

R

RKa

vd vC

R1 R2 C2

+

–

+

–

2

1

+

–

C1

1

1

2

1

C

CKa

14

Active Proportional-Integral (PI) Filter

CR

CR

s

ssF

22

11

1

21)(

• Large open loop gain at low frequency• Op amp limitations

– Linearity– Noise– Open loop gain

1

2

R

Rvd vC

R1 R2 C

+

–

+

–

2

1

+

–

15

Voltage-Controlled Oscillator

• KVCO: gain of VCO

CVCOLO vK 0

1/s+

0

KVCO

vC LO

16

Transfer Function of PLL

• Open-loop transfer function from e to LO

Kd

REF +

LO

e vd1/s+

0

+KVCO

vC LOF(s)

s

sFKKsA VCOd )()(

17

Transfer Function of PLL

• Closed-loop transfer function from REF to LO

Kd

REF +

LO

e vd1/s+

0

+KVCO

vC LOF(s)

)(

)(

)(1

)(

)(

)()(

sFKKs

sFKK

sA

sA

s

ssH

VCOd

VCOd

REF

LO

18

Transfer Function from REF to e

• Closed-loop transfer function

Kd

REF +

LO

e vd1/s+

0

+KVCO

vC LOF(s)

)()(1

)(

)()(

)()()()()()(

sFKKs

ssH

s

ssH

ssHssss

VCOdREF

ee

REFREFLOREFe

19

Other TF of Interest

• Noise in control voltage

Kd

REF +

LO

e vd1/s+

vCn

+ KVCO

vC LOF(s)

)()(

)(

)(/)]()()([

sFKKs

K

sV

s

ssKssFKsV

VCOd

VCO

Cn

LO

LOVCOLOdCn

20

Other TF of Interest

• Phase noise of VCO

Kd

REF +

LO

e vd1/s +

n

+KVCO

vC LOF(s)

)()(

)(

)(/)()()(

sFKKs

s

s

s

ssssFKKs

VCOdn

LO

LOLOVCOdn

21

Transfer Functions for Different Loop Filters

• Passive lag filter

• Active lag filter

• Active PI filter

1

21)(

s

ssF

)(1

1)(

21

2

s

ssF

2121

22

221

1

)1()(

VCOdVCOd

VCOd

KKs

KKs

sKK

sH

1

2

1

1)(

s

sKsF a

11

22

21

1

)1()(

aVCOdaVCOd

aVCOd

KKKs

KKKs

sKKK

sH

11

22

21

)1()(

VCOdVCOd

VCOd

KKs

KKs

sKK

sH

22

Normalizing Transfer Function• Normalized denominator

• Passive lag filter

• Active lag filter

• Active PI Filter

ratiodampingfrequencynaturalsssD nnn :;:,2)( 22

21

VCOd

n

KK )1

(2 2

VCOd

n

KK

1 aVCOd

n

KKK )

1(

2 2aVCOd

n

KKK

1 VCOd

n

KK 22

n

23

Normalized Transfer Function• Passive lag filter

• Active lag filter

• Active PI Filter

22

22

2

)2()(

nn

nVCOd

nn

ss

sKK

sH

22

22

2

)2()(

nn

naVCOd

nn

ss

sKKK

sH

22

2

2

2)(

nn

nn

ss

ssH

24

Normalized Transfer Function

• Passive lag filter

• Active lag filter

2

1

VCOdKK

22

2

2

2)(

nn

nn

ss

ssH

22

2

2)(

nne ss

ssH

2

1

aVCOd KKK

25

Frequency Response of H(s)

22

2

2

2)(

nn

nn

ss

ssH

26

Frequency Response of He(s)

22

2

2)(

nne ss

ssH

27

Step Response of PLL

• Phase step

• Phase Error

• Steady state error (final value theorem)

sstut REFREF /)()()(

.1,)]1sinh(1

)1[cosh(

;1),exp()1(

;1,)]1sin(1

)1[cos(

)(

2/)()(

2

2

2

2

2

2

22

tnn

nn

tnn

e

nnee

n

n

ett

tt

ett

t

ss

sssHs

02

lim)(lim)(22

2

00

nns

es

e ss

sss

28

Step Response

22

2

2)(

nne ss

ssH

29

Ramp Response of PLL

• Phase ramp

• Phase Error

• Steady state error (final value theorem)

2/)()()( ssttut REFREF

.1,)1sinh(1

1

;1),exp(

;1,)1sin(1

1

)(

2/)()(

2

2

2

2

222

tn

n

n

tn

n

e

nnee

n

n

et

tt

et

t

ssssHs

02

lim)(lim)(2200

nns

es

e ss

sss

30

Ramp Response

22

2

2)(

nne ss

ssH

31

General Steady State Error in Ramp Response

• High loop gain

• Low loop gain

)()(1)(

sFKKs

ssHsH

VCOde

)(

//)()( 2

sFKKs

sssHs

VCOdee

0)(

lim)(lim)()0(00

sFKKsssF

VCOds

es

e

)0()(lim)(lim)(

00 FKKsFKKsss

VCOdVCOds

es

e

32

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

ssFKK

ssFKK

sA

sAsH

VCOd

VCOd

/)(1

/)(

)(1

)()(

33

Root Locus Method

• Closed-loop TF

• Closed-loop poles make

– K=0, open-loop poles– K infinity, open-loop zeros or infinity

).(/)(/)(

)()(

)(

/)(1

/)()(

sdsnssFandKKK

where

snKsd

snK

ssFKK

ssFKKsH

VCOd

VCOd

VCOd

0)()( snKsd

34

Root Locus for Passive Lag Filter

)(1

11)(

21

2

s

s

ss

sF

35

Root Locus for Active Lag Filter

1

2

1

11)(

s

s

ss

sF

36

Root Locus for Active PI Filter

1

211)(

s

s

ss

sF

37

Root Locus for 1st-Order LP Filter

11

11)(

sss

sF

38

Effects of Parasitics

11 1.01

1

1

11)(

ssss

sF

39

Effects of Zero

1

2

1 1.01

21

1

11)(

s

s

sss

sF

40

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

41

Jitter Measurements

Agilent, “Understanding Jitter and Wander Measurements and Standards.”

42

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

43

PLL in Clock and Data Recovery0 1 0 0 1 0 1 0 1

0 1 0 0 X 1 0 1 0

0 1 0 0 1 0 1 0

Ideal signal

Distorted signal

Ideal clock

Recovered clock

44

Jitter Tolerance Mask

45

Jitter Tolerance Measurement

46

Jitter Tolerance Measurement

47

Jitter Tolerance Measurement

• Error at corner frequency– Insufficient clock recovery bandwidth– Incorrect mask used

48

Jitter Tolerance Measurement

• Excessive jitter tolerance margin

Tolerance margin

49

Jitter Tolerance Measurement

• Occasional fail at specific frequencies– Need extra settling time after jitter amplitude change

• Repeating with additional settling time• Spot measurement

50

Jitter Tolerance Measurement

• Limited clock recovery bandwidth• Eye-width alignment noise

51

Jitter Tolerance Measurement

• Limited buffer store

52

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

53

Jitter Transfer Mask

54

Jitter Transfer Measurement

• Jitter tolerance mask used to set input jitter level• Sinusoidal jitter at magnitudes and frequencies• Narrow-band measurement

55

Jitter Transfer Measurement

• Different test masks• SONET mask: additional amplitude at lower band

56

Jitter Transfer Measurement

• Measurement set-up noise• -40 dB sufficient

57

Jitter Transfer Measurement

• Low-frequency phase noise• Power-line crosstalk• Short measurement time

58

Jitter Transfer Measurement

• Incorrect filter characteristic• Excessive peaking

59

Jitter Transfer Plot

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

Measured Jitter Transfer Characteristic

E. Barari, “Jitter Analysis / Specification,” May 2002.

64

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

65

Jitter Generation Standard

66

Jitter Generation Measurement

• Direct measurement of p-p jitter

• Phase noise measurement

• Eye diagram and histogram

67

Jitter Generation Measurement

68

Measurement Considerations

• Calibration

• Measurement range

• Measurement time

• Power

• Frequency offset

69

TF from Noise in VCO Control Voltage

Kd+

vCn

+ KVCO/sLO

F(s)

22 2)()(

)()(

nn

VCO

VCOd

VCO

Cn

LOC ss

sK

sFKKs

K

sV

ssH

-1

• Can be viewed as low-pass filter

70

TF from Noise in VCO Control Voltage

22 2)(

nnC ss

ssH

71

TF from Phase Noise in VCO

22

2

2)()(

)()(

nnVCOdn

LO

ss

s

sFKKs

s

s

ssH

Kd+

n

+KVCO/sLO

F(s)-1

• High-pass filter• The same as He(s)

72

Phase Error in VCO

Kd

n

KVCO/sLO

F(s)

• vCn dominate at low frequencies• n dominate at high frequencies

vCn

REF +

LO

e

HC(s) H(s)