High-Speed Serial Interface Circuits and Systems

Lect. 4 – Phase-Locked Loop (PLL) Type 1

(Chap. 8 in Razavi)

PLL• Phase locked loop

A (negative-feedback) control system that generates an output signal whose phase (and frequency) is related to the phase (and frequency) of an input reference signal – wikipedia –

• Output signal is phase-locked to reference signal: Constant phase relationship fout = M x fReference

PhaseDetector

LoopFilter

VoltageControlledOscillator

Divisionby M

ReferenceOutput

PLL• Applications

• Frequency Synthesis - Clocks for digital systems- LO in RF systems

• Clock recovery• Modulation/Demodulaton

PLL Block Diagram

• Reference?

PhaseDetector

LoopFilter

VoltageControlledOscillator

Divisionby M

ReferenceOutput

Equivalently, an LC oscillator

Oscillation frequency: kHz ~ a few hundred MHz

Phase-tracking by PLLD

ista

nce

time

• Cameraman can only control the accelerator (velocity)• Distance: Integral of velocityControl of velocity in order to lock the distanceAfter locking, distance and velocity should be the same

Phase-tracking by PLL

Abs

olut

e ph

ase

time

PLL achieves phase-locking by changing VCO frequency

PhaseDetector

LoopFilter

VoltageControlledOscillator

Divisionby M

ReferenceOutput

PD (Phase Detector): Compares phases of input and output signal and converts the phase difference to voltage signal

LPF (Low Pass Filter): Takes an average level of PD’s output voltage signal

PD can be realized with a multiplier

sin( )sin( )in outt t 1 cos[( ) ] cos[( ) ]2 in out in outt t

Basic PLL Operation

Approximately linear for = - /2

Assuming in=out

sin( )sin( )in outt t 1 cos[( ) ] cos[( ) ]2 in out in outt t

Filtered out by LPF

Basic PLL Operation

VCO (Voltage Controlled Oscillator): Frequency-tunable oscillator Output frequency is a function of control voltage (VC)

Basic PLL Operation

Phase tracking of PLL

Vin

Vout

VPD

Initially, Vout is locked to VinWith Phase jump in Vin here

ωin=ωout

Basic PLL Operation

Frequency tracking of PLL

Vin

Vout

VPD

ωin≠ωout

Frequency jump in Vin hereVout is locked to VinWith

Basic PLL Operation

A B VPD

0 0 00 1 11 0 11 1 0

XOR gate can be used as PD for digital signals

A

BVPD Locked

(π/2 phase offset)

A

B

VPD

B later than A

A

B

VPD

B earlier than A

A

B

VPD

Basic PLL Operation

Phase tracking of PLL

Vin

Vout

VPD

Vout is locked to Vin(π/2 phase offset)

ωin=ωout

DC level → VC

Phase jump in Vin here

Basic PLL Operation

Frequency tracking of PLL

Vin

Vout

VPD

Vout is locked to Vin

ωin≠ωout

Frequency jump in Vin here

Basic PLL Operation

Frequency Synthesis with PLL

(FM signal)

(Recovered message)

(PLL output)

Frequency Demodulation with PLL

Linear approximation for PD characteristics LPF: First order with pole at s = - p

( )( )

( )C

PD

V sT s

V s

in – out)

VPD

VPD (s) = KPD x (s)

PLL Dynamics: Linear Model

p

ps

out (s) =

For simplicity let 0=0

Since d/dt =

PLL Dynamics: Linear Model

(1/s) KVCO x VC (s)

PLL Block Diagram

PD LPF VCO

Linear Model for out(s) / in(s)

PLL Dynamics: Linear Model

Open loop gain:

( )( )

pPD VCO

p

G s K Ks s

Closed loop gain

( )( )( )

out

in

sH ss

2PD VCO p

p PD VCO p

K Ks s K K

( )

1( )

pPD VCO

p

pPD VCO

p

K Ks s

K Ks s

2nd order LPF!

( )1 ( )

G sG s

PLL Dynamics: Linear Model

2

( )( )( )

PD VCO pout

in p PD VCO p

K KsH ss s s K K

( ) out

in

H s

Note that input and output are ‘phase’

(Assuming two real poles)

PLL Dynamics: Linear Model

In LPF,

LPF

( ) out

in

VH sV

Magnitude Response vs Phase Response

In PLL,

( ) out

in

H s

PLL

Vin Vout

t t

Vin Vout

t t

Vin Vout

t t

PD LPF VCO

Magnitude Response vs Phase Response

2

( )( )( )

PD VCO pout

in p PD VCO p

K KsH ss s s K K

n PD VCO PK K PD VCO

P

K KQ

2nd order system2

2 2( )( / )

n

n n

H ss Q s

PD LPF VCO

Second-Order System

1 12 2

P

PD VCOQ K K

2

2 2( )2

n

n n

H ss s

Where are the poles? > 1: Over damped

1: Under damped

1: Critically damped

2

2 2

( )( )( ) 2

out n

in n n

sH ss s s

PD LPF VCO

Second-Order System

Frequency Response

ξ = 0.1ξ = 0.3ξ = 0.7ξ = 1ξ = 1.5

ωn = 2π

Maximally flat condition? 12

2nd order Butterworth filter

PD LPF VCO

( )( )

out

in

s ss s

2

2 22n

n ns s

( )( )

out

in

ss

Second-Order System

Step response: ( ) ( )in t u t

PLL

exp nt

2

2 2

( )( )( ) 2

out n

in n n

sH ss s s

PD LPF VCO

Second-Order System2

2 2

( )( ) 2

out n

in n n

ss s s

ξ = 0.1ξ = 0.3ξ = 0.7ξ = 1ξ = 1.5

ωn = 2π

Step response: ( ) ( )in t u t

PD LPF VCO

- Transfer function for phase error?

Second-Order System

( )e t

- Phase error due to phase step? ( ) ( )in t u t ( )in s

0lim ( )es

sH ss

- No steady-state phase error

( )eH s

2

2 2

( )( )( ) 2

out n

in n n

sH ss s s

1 ( )H s2

2 2

22

n

n n

s ss s

s

PD LPF VCO

Second-Order System2

2 2

( )( )( ) 2

out n

in n n

sH ss s s

2

2 2

2( )2

ne

n n

s sH ss s

20lim ( )es

sH ss

( )e t ( ) ( )in t u t

( )in s

( )in s

s

2s

2

n

PD VCOK K

- Phase error due to frequency step?