lecture08 ee620 pll tracking

7/29/2019 Lecture08 Ee620 Pll Tracking

http://slidepdf.com/reader/full/lecture08-ee620-pll-tracking 1/20

Sam Palermo

Analog & Mixed-Signal Center

Texas A&M University

ECEN620: Network Theory

Broadband Circuit DesignFall 2012

Lecture 8: PLL Tracking



Announcements

• HW1 due at 5PM today•Confirm that you participated in the Analog IC

Design Olympics on the first page of yourhomework 1 solution

•Turn into my mailbox in WERC 315

2



Agenda & References

• PLL Tracking Response• Phase Detector Models

• PLL Hold Range

• Chapter 5 of Phaselock Techniques, F.Gardner, John Wiley & Sons, 2005.

3



Linear PLL Model

4

• If the phase inputamplitude is small, then

the linear model can beused to predict thetransient response

( )( )( ) ( ) ( )

N

sFK K s

s

N

sGs

ssE

VCOPDref

e

+=

+=

Φ

Φ=

1

1

• Ideally, we want this to be zero

• Phase error generally increases withfrequency due to this high-pass response



5

• Phase Step Response

( )( )

( )

stepdecayinglyexponentiaanisResponse Transient

:Response Transient

stepphaseawithzerobeshoulderrorPhase

0limlim : TheoremValueFinaltheUsing

1

2

00

tK

DC

DCss

DC

eK s

s

s

K ss

sssE

s

−−

→→

∆Φ=

+

∆Φ

=

+

∆Φ=

∆Φ

L

First-Order PLL Tracking Response

( ) ( ) N

K K K

K s

s

N

K K K s

s

sEK sFVCOPD

dBDC

dBVCOPD

1

3

31

1 , , ==+=+

== ω ω



6

• Frequency Offset (Step) Response

( )( ) ( )

( )

steprisinglyexponentiaanisResponse Transient

1 :Response Transient

offsetfrequencyagain withloopthetonalproporitioinverselyiserrorphase The

limlim : TheoremValueFinaltheUsing

21

2

2

020

tK

DCDC

DCDCss

DCe

K K s

s

s

K K ss

sssE

s

−−

→→

−∆

=

+ ∆

∆=

+

∆=

∆

ω ω

ω ω ω

L


( ) ( ) N

K K K

K s

s

N

K K K s

s

sEK sFVCOPD

dBDC

dBVCOPD

1

3

31

1 , , ==+=+== ω ω



• Frequency Ramp Response

( )

( )( )( )

( )1 :Response Transient

finiteisif infinitytogrowerror willphase The


2

rad/secof rateaatith timelinearly wchangingisfrequencyinputthat theAssume

23

1

3

2

030

2

2

−+Λ

=

+

Λ

∞⇒+

Λ=

Λ

Λ=

Λ

−−

→→

tK

DC

DCDC

DC

DCss

ref

DCetK K K s

s

s

K

K ss

sssE

s

tt

L

φ


( ) ( ) N

K K K

K s

s

N

K K K s

s

sEK sFVCOPD

dBDC

dBVCOPD

1

3

31

1 , , ==+=+== ω ω



( )( )

( )N

K K K

K s

K s

ss

ss

K K

Nss

sEs

ssF VCOPD

DC

DCDCnn

VCOPD

n

=

++

+

++

++

=++

+

=++

+= ,1

1

2 ,

1

1

2121

22

21

22

2

21

2

τ τ τ τ

τ

τ τ

ω ζω

ω

τ τ

τ

8


( )( )

yourself thiscompute Try to

1

1

:Response Transient


01

1


2121

22

211

2121

22

21

2

00

++

+

++

++

∆Φ

=

++

+

++

+

+∆Φ

=

∆Φ

−

→→

τ τ τ τ

τ

τ τ

τ τ τ τ

τ τ τ

DCDC

DCDC

ss

K s

K s

ss

s

K s

K ss

ss

ssEs

L

Second-Order Type-1 PLL Tracking Response



( )( )

( )N

K K K

K s

K s

ss

ss

K K

Nss

sEs

ssF VCOPD

DC

DCDCnn

VCOPD

n

=

++

+

++

++

=++

+

=++

+= ,1

1

2 ,

1

1

2121

22

21

22

2

21

2

τ τ τ τ

τ

τ τ

ω ζω

ω

τ τ

τ

9


( )( )


1

1

:Response Transient

offsetfrequencyagain withloopthetonalproporitioinverselyiserrorphase The

1

1


2121

22

21

2

1

2121

222

21

2

020

++

+

++

++

∆

∆=

++

+

++

++∆

=

∆

−

→→

τ τ τ τ

τ

τ τ ω

ω

τ τ τ τ

τ

τ τ ω

ω

DCDC

DCDCDC

ss

K s

K s

ss

s

K K s

K ss

ss

ssEs

L




( )( )

( )N

K K K

K s

K s

ss

ss

K K

Nss

sEs

ssF VCOPD

DC

DCDCnn

VCOPD

n

=

++

+

++

++

=++

+

=++

+= ,1

1

2 ,

1

1

2121

22

21

22

2

21

2

τ τ τ τ

τ

τ τ

ω ζω

ω

τ τ

τ

10


( )( )


1

1

:Response Transient

finiteisif infinitytogrowerror willphase The

1

1


2121

22

21

3

1

2121

223

21

2

030

++

+

++

++

Λ

∞⇒

++

+

++

+

+Λ

=

Λ

−

→→

τ τ τ τ

τ

τ τ

τ τ τ τ

τ τ τ

DCDC

DC

DCDC

ss

K s

K s

ss

s

K

K s

K ss

ss

ssEs

L





( )( )

++

∆Φ

=

++

∆Φ=

∆Φ

−

→→

RC

K Kss

s

s

RC

K Ksss

sssE

s ss

2

21

2

3

00

:Response Transient



L


( ) ( )N

RK K K

RC

K Kss

s

ss

ssEs

RC

sR

sF VCOPD

nn

=++

=++

=

+

= ,2

,

1

2

2

22

2

ω ζω



++

∆Φ−

RC

K Kss

ss 2

21 :Response Transient L

Second-Order Type-2 PLLPhase Step Response

KRCRCn

2

1

2==

ω ζ




( )( )

++

∆

=

++

∆=

∆

−

→→

RC

K Kss

s

s

RC

K Ksss

sssE

s ss

2

2

2

1

22

3

020

:Response Transient

PLL2- Typeawithzerotogoeserrorphase The


ω

ω ω

L


( ) ( )N

RK K K

RC

K Kss

s

ss

ssEs

RC

sR

sF VCOPD

nn

=++

=++

=

+

= ,2

,

1

2

2

22

2

ω ζω



14

Second-Order Type-2 PLLFrequency Step Response

KRCRCn

2

1

2==

ω ζ

++

∆−

RC

K Kss

s

s 2

2

2

1 :Response Transient ω L



15


( )( )

++

Λ

Λ=

++

Λ=

Λ

−

→→

RC

K Kss

s

s

RC

K Ksss

sssE

sn

ss

2

2

3

1

223

3

030

:Response Transient

lagphasedynamicawithrampfrequencyacan trackPLL2-order type-secondA


L

ω


( ) ( )N

RK K K

RC

K Kss

s

ss

ssEs

RC

sR

sF VCOPD

nn

=++

=++

=

+

= ,2

,

1

2

2

22

2

ω ζω



16

Second-Order Type-2 PLLFrequency Ramp Response

KRCRCn

2

1

2==

ω ζ

++

Λ−

RC

K Kss

ss 2

2

31 :Response Transient L



Ideal Phase Detector

• An ideal phase detector has thesame gain (slope) over a ±2π range

• This allows the linear PLL model tobe used for all phase relationships

17



Real Phase Detectors

• Many phase detectorsare nonlinear and donot display the samegain for a given phase

relationship

• This implies that the

PLL cannot bedescribed by the linearmodel for large inputphase deviations

18



PLL Hold Range (Sinusoidal PD)

• A PLL Hold Range is the input frequency range over which the PLL canmaintain static lock

19

( )rad/sec :RangeHold

todconstraineisfrequencylockthe,1exceedcannotsineSince

sin

iserrorphasethedetector,phasesinusoidalaWith

:2- TypeOrder-Second

:1- TypeOrder-Second

:Order-First

isErrorPhaseState-SteadytheModelLinearw/

1

DCH

DC

DC

e

DC

VCOPD

DC

VCOPD

DC

DC

e

K

K

K

K

N

K K

K

N

K K K K

K

±=∆

≤∆

∆=

∞=

=

=

∆=

ω

ω

ω φ

ω φ

• The hold range is finite for a type-1 PLL, and theoretically infinite for atype-2 PLL. However in practice it will be limited by another PLL block,

such as the VCO tuning range.



Next Time

• PLL Acquisition Response

20

lecture08 ee620 pll tracking

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