Sam PalermoAnalog & Mixed-Signal Center

Texas A&M University

ECEN689: Special Topics in High-Speed Links Circuits and Systems

Spring 2010

Lecture 26: Phase-Locked Loops

Announcements

• Project Preliminary Report #1 due April 16 (in class)

• Exam 2 is April 30

• Reading• Posted clocking papers• Website additional links has PLL and jitter

tutorials

• Majority of today’s material from Fischettetutorial and M. Mansuri’s PhD thesis (UCLA)

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Agenda

• PLL modeling

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Introduction

• A phase-locked loop (PLL) is a negative feedback system where an oscillator-generated signal is phase AND frequency locked to a reference signal

• PLLs applications• Frequency synthesis

• Multiplying a 100MHz reference clock to 10GHz

• Skew cancellation• Phase aligning an internal clock to an I/O clock

• Clock recovery• Extract from incoming data stream the clock frequency and optimum phase of

high-speed sampling clocks

• Modulation/De-modulation• Wireless systems• Spread-spectrum clocking

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PLL Block Diagram

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[Mansuri]

Linear PLL Model

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Σθref θe veKPD

PhaseDetector

LoopFilter

vcF(s)

VCO

KVCOs

1N

θout

θfb

LoopDivider

Understanding PLL Frequency Response

• Linear “small-signal” analysis is useful for understand PLL dynamics if• PLL is locked (or near lock)• Input phase deviation amplitude is small enough to maintain operation in

lock range

• Frequency domain analysis can tell us how well the PLL tracks the input phase as it changes at a certain frequency

• PLL transfer function is different depending on which point in the loop the output is responding to

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Input phase response VCO output response

[Fischette]

Phase Detector

• Detects phase difference between feedback clock and reference clock• The loop filter will filter the phase detector output, thus to characterize

phase detector gain, extract average output voltage (or current for charge-pump PLLs)

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Loop Filter

• Lowpass filter extracts average of phase detector error pulses

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I

I

VCO ControlVoltage

C1

R

C2

Charging

Discharging

VDD

VSSF(s)

Voltage-Controlled Oscillator

• Time-domain phase relationship

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VDDVDD/20

ω0 1KVCO

( ) ( ) ( )tvKtt cVCOoutout +=∆+= 00 ωωωω

( ) ( ) ( )∫ ∫=∆= dtdt tvKtt cVCOoutout ωθLaplace Domain Model

Loop Divider

• Time-domain model

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( ) ( )tN

t outfb ωω 1=

( ) ( ) ( )∫ == tN

tN

t outoutfb θωθ 11 dt

[Perrott]

Linear PLL Model

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Σθref θe veKPD

PhaseDetector

LoopFilter

vcF(s)

VCO

KVCOs

1N

θout

θfb

LoopDivider

Charge-Pump PLL Linear Model

• Charge-pump supplies current to loop filter capacitor which integrates it to produce the VCO control voltage

• For stability, a zero is added with the resistor which gives a proportional gain term

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[Mansuri]

Open-Loop PLL Transfer Function

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ignoring C1:

with C1:

[Mansuri]

Open-Loop PLL Transfer Function

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with C1 (3rd order)with C1 (2nd order)

[Mansuri]

Closed-Loop PLL Transfer Function

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ignoring C1:

[Mansuri]

PLL Natural Frequency and Damping Factor

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22 2 nnss ωζω ++Standard 2nd-order denominator:

Damping Factor:

Natural Frequency:

( ) 21

23 1++= aandB ωω

−−+=

VCOPD

n

VCOPD

n

KKN

KKNa ω

ζω

ζ 412 2

Loop Bandwidth:

Damping Factor Impact

• If damping factor is too low, frequency peaking occurs• Damping factor ~1 is usually preferred

• Excessively high damping also causes peaking• Need 3rd order model to observe this

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[Fischette]

Damping Factor Impact

• Peaking in frequency domain leads to ringing in the time domain

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θref(s)=Frequency Step Input: ∆ωs2

KPD = 25uA/2πKVCO = 2π40MHz/V

N = 32ωn = 1 (normalized)

ζ = 0.1

ζ = 0.5

ζ = 0.707ζ = 1

ζ = 2

PLL Noise Transfer Function

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[Mansuri]

Noise Transfer Functions

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[Mansuri]

Next Time

• PLL modeling• PLL circuits

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