PLL Arrays First SlidesPLL Arrays First Slides

Prof. Robert A. YORKJames D. BUCKWALTERPaolo F. MACCARINI

University of California, Santa Barbara

Space and Naval

Warfare Systems

Command

OutlineOutline

Dave, here you will find:The Theoretical Calculation for the Phase Relationship we are Locking For

The Design and Simulation Results for the L1 Array (1.6 GHz)The Picture of the 2.45 GHz Unit PLL Cell for the Array

(Some meas. Still need to be performed)The Picture and Meas. of the 750 MHz PLL

-90

-60

-30

0

30

60

90

-1 -0.5 0 0.5 1Phase Difference (ψ−φ)

(ψ−φ)

(ψ−φ)

(ψ−φ), degrees

Relative Injected Frequency, (ωωωωinj

-ωωωω)/∆ω∆ω∆ω∆ωm

∆

−=− −

m

inj

ωωωφψ 1sin

( )φω +tA 0cos( )ψω +tA injinj cos

VCO

Tuning port(adjust ω0)

Output portInjection port

Injection-Locked Oscillator:

Adler’s equation:

)sin(0 φψωωωφ −∆+−= minjdtd

AA

Qinj

m 20ωω =∆“Locking range”

Coupled Oscillator ArraysCoupled Oscillator ArraysInjection Locking Model Injection Locking Model

A

~VoltageControlledOscillator

DoubleBalancedMixer

VariableGainAmplifier

In-PhasePowerDivider

BDCOffsetTuning

Injection Signal

Output Signal

( ) ( )

( ) 0

00

Steady State Equations:

1

2 2

42

SS

SS

O Inj O C O Inj

Inj OC O Inj O Inj O Inj

O Inj

OO

InjK V Cos

V AV V Cos B ArcCos BA

V VK

V V K

K B Aω ω ω θ θ

ω ωθ θ θ θ

ω= = + ⋅ = + −

−

+ ⋅

= ⋅ − + ⇒ − = −

⋅

ω ω

πθ θ θ θ

=

− = ± ⇒ = − = ⇒ = −∓

0For Injection at the tuning center :

0 and 02 4

Inj O

O InjO Inj O Inj

AV VB B

PhasePhase--Locked Loop ArraysLocked Loop ArraysSingle Element DesignSingle Element Design

-2 -1 1 2B

0.2

0.4

0.6

0.8

1

Phase Difference in Radians

( ) ( )0

Loop Equations:14C O O O Inj Inj Inj

O O C

V V Cos t V Cos t A B

K V

ω θ ω θ

ω ω

= ⋅ + ⋅ + ⋅ +

= + ⋅

( )Inj Inj InjV Cos tω θ−( )O O OV Cos tω θ−

CV( ) ( )1

2 2 O Inj O Inj O InjA V V Cos tβ ω ω θ θ ⋅ − + −

Locking RangeSS Frequency

Same phase dynamics as Coupled-Oscillator System

[ ]

( )1nnn

n2fnfn

1nn1n1nn

where,Cy

dtdy

yy2yCdt

d

−

−+

φ−φ=φ∆

φ∆ω+ω−=

−−+β∆=φ∆

sin

LPF

Σ

LPF LPF

scancontrol

scancontrol

mixer

two-waycombiner

VCO

antenna

Σ ΣΣ - + - + Σ- + -

+-+

x1

y1

φ1φ0

x2

y2

φ2 φN-1

xN

yN

φN

PLL System Modeling: • C1 = VCO tuning sensitivity• C2 = Conversion loss• ∆φ∆φ∆φ∆φ = Phase gradient• ∆β∆β∆β∆β = Frequency gradient

Ni …1=

The free running frequencies satisfy −−−−>>>> ( ) ( ) ( )[ ]1nn1n021n 2CC ++ φ∆+φ∆−φ∆ω−=β∆ sinsinsin

Thus:

• Coupling strength −−−−>>>> C1C2 (loop gain)

−−−−>>>> enhanced locking range

• Also with injection −−−−>>>> ∆ω∆ω∆ω∆ω’lock > ∆ω∆ω∆ω∆ωlock

PhasePhase--Locked Loop ArraysLocked Loop ArraysTheoretical Results for the Array ImplementationTheoretical Results for the Array Implementation

• Same phase dynamics as Coupled-Oscillator System• Less amplitude fluctuation• Larger Locking range

Thus ->

| VGain| < 0.5

TranS tartupToLockS topTime=200 nsecMaxTimeStep=0.1 nsec

RSpectrumAnalyzerR=50 Ohm

PwrSplit2PowerDivider2

PwrSplit2PowerDivider3

PwrSplit2PowerDivider1

AmplifierVCVariableGainAmplifierGain=(10+40*_v3)Rout=50 Ohm

VMultMixer

VtStepBiasPosVlow=0 VVhigh=5 VDelay=0.1 ns ecRis e=0.1 nsecR

RBiasR=1 TOhm

RTrans itionAnalyzer2R=50 Ohm

RTrans itionAnalyzer1R=50 Ohm

VtS tepFreqCtrlVlow=0 VVhigh=0 VDelay=0.9 nsecRise=0.1 nsec

OpAmpIdealGainOffsetSummerGain=100000Freq3db=500 MHz

VCOVoltageControlledOscillatorKv=70 MHzFreq=1575 MHzP=-j*dbmtow(0)Delay=timestep

VtStepGainCtrlVlow=0 VVhigh=0.0 VDelay=0.4 ns ecRis e=0.1 nsec

RRIn1R=1 kOhm

RRFbR=50 kOhm

RRIn2R=50 kOhm

VtSineRFSourceAmplitude=0.22 VFreq=1575 MHzDelay=1.5 ns ecPhas e=0

A

~VoltageControlledOscillator

DoubleBalancedMixer

VariableGainAmplifier

In-PhasePowerDividerB

DCOffsetTuning

Injection RF Signal

Output Signal

CV

1.6 GHz PLL Schematics1.6 GHz PLL Schematics

0 20 40 60 80 100 120 140 160 180 200

Time [ns ]

-4

-2

0

2

4

Fre

quen

cy &

Fee

dbac

k [V

]Lock Analys is (FLo=1475Mhz, P has e Diff. = 0°)

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Time [ns ]

-200

-100

0

100

200

Lock

ing

Rf

& L

o [m

V]

90 91 92 93 94 95 96 97 98 99 100

Time [ns ]

-200

-100

0

100

200

Lock

ed R

f &

Lo

[mV

]

1.6 GHz PLL Simulation (0°)1.6 GHz PLL Simulation (0°)

0 20 40 60 80 100 120 140 160 180 200

Time [ns ]

-4

-3

-2

-1

0

1

2

Fre

quen

cy &

Fee

dbac

k [V

]Lock Analys is (FLo=FRf=1575Mhz, P has e Diff. = 90°)

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Time [ns ]

-200

-100

0

100

200

Lock

ing

Rf

& L

o [m

V]

90 91 92 93 94 95 96 97 98 99 100

Time [ns ]

-200

-100

0

100

200

Lock

ed R

f &

Lo

[mV

]

1.6 GHz PLL Simulation (90°)1.6 GHz PLL Simulation (90°)

0 20 40 60 80 100 120 140 160 180 200

Time [ns ]

-4

-2

0

2

4

Fre

quen

cy &

Fee

dbac

k [V

]Lock Analys is (FLo=1675Mhz, P has e Diff. = 180°)

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Time [ns ]

-200

-100

0

100

200

Lock

ing

Rf

& L

o [m

V]

90 91 92 93 94 95 96 97 98 99 100

Time [ns ]

-200

-100

0

100

200

Lock

ed R

f &

Lo

[mV

]

1.6 GHz PLL Simulation (180°)1.6 GHz PLL Simulation (180°)

2.45 GHz PLL Unit Cell2.45 GHz PLL Unit CellGoal: •Large Locking/capture Range

•Adjustable Center Frequency

•Multiple RF Inputs

•IF Summing Junction in Feedback for Mutual Coupling PLL PLL PLL

PLL Array

Tuning Ports

RFLF LF

RF

F1 FNF2

Top View

4-way Splitter

XVCA

LF Out~Σ

RF in (from neighboring)PLL

LF InLF In

Gain Adjust

DC Voff (frequency tuning)

RF Out (to next PLL)

VCO

To Calibration

To Antenna

2.45 GHz PLL Unit Cell2.45 GHz PLL Unit Cell

Bias Bias ModuleModule

Low Frequency Low Frequency FeedbackFeedback

MixerMixerPower Power

DividersDividers

VCOVCO

Injection INInjection IN

Injection Injection OUTOUT

RF1 OutRF1 Out

RF2 OutRF2 Out

200 MHz Locking Range in Closed Loop versus Few KHz in OpenPhase varies from 0 to 180 Degrees (Capture Range to be Measured)

750 MHz PLL750 MHz PLL

Low Frequency Low Frequency FeedbackFeedback

MixerMixerVCOVCO

Injection INInjection IN RF OutRF Out

Mixer OutMixer Out

Measured Locking and Capture Range [PLL@750 MHz]

720

730

740

750

760

770

780

720 730 740 750 760 770 780

RF Injection [MHz]

RF O

UT [M

Hz]

750 MHz PLL 750 MHz PLL

25 MHz Locking Range in Closed Loop versus Few KHz in Open

5.1 MHz Capture Range

Close Loop

Open Loop