Rafael J. Betancourt-Zamora, Shwetabh Verma and Thomas H. Lee

Department of Electrical EngineeringStanford University

http://www-smirc.stanford.edu/

1-GHz and 2.8-GHz CMOS Injection-locked Ring Oscillator Prescalers

Outline

• Introduction• Injection Locking Theory

• Circuit Implementation

• Measured Results

• Conclusion

• Understand the Injection-locking mechanism

• Grasp the limitations of Injection-locked Frequency Dividers

• Design Injection-locked Frequency Divider using a Ring Oscillator

Goals

Motivation: Low-power Frequency Synthesis

• Frequency synthesizers are implemented using PLLs.

• Major sources of power dissipation are the VCO and Frequency Divider.

320 MHz CMOS PLL[V.Kaenel’96]

900 MHz CMOS RECEIVER[Darabi’00]

÷8Q I

LNA

VCO

500µA

300µA 400µA

300µA

100µA

150µA

Q

I

÷2

÷N

PFD CP & LFUP

DN

VCOFREF

FOUT

2µA10µA

240µA50µA

800µA

Frequency Divider Power Trade-off

• We propose a technique in which power decreases with division ratio.

÷2200µA 100µA 100µA

÷2÷2

900 MHz 450 MHz 225 MHz112.5 MHz

TOTAL POWER 200µA 300µA 400µA

POWER INCREASES WITH DIVISION RATIO

[Darabi’00]

Outline

• Introduction

• Injection Locking Theory• Circuit Implementation

• Measured Results

• Conclusion

Ring Oscillator Model

VO

RL

CL

ωP1

RLC----------

L=

HS jω( )HO

1 jω ωP⁄+--------------------------=

• Neglect feedforward zero

ITAIL

BARKHAUSEN CRITERIA• Necessary conditions for oscillation

H jωO( ) 1≥

H jωO( )∠ 180°

=

SMALL-SIGNAL MODEL

PHASE CONDITION

GAIN CONDITION

Ring Oscillator Model (II)

ωPω0

πn---

tan

-----------------=

N-STAGE MODEL

H jω( )HO

n

1 jωωo------ π

n---

tan+ n--------------------------------------------=HO 1

πn---

tan2

+≥

PHASE CONDITION

GAIN CONDITION

n 2>

VO

• ω0 is free-running oscillator frequency.

• Each stage contributes π/n to the phase.

Ring Oscillator Model (III)

EXAMPLE

n H0 ωp

3 2.00 0.58 ω0

4 1.41 ω0

5 1.24 1.38 ω0

H jω( )HO

n

1 jωωo------ π

n---

tan+ n--------------------------------------------=

• DC gain Η0 decreases with number of stages.

• Poles ωp coincide with ω0 only for n=4.

VO

Injection-locked Ring Oscillator

RL

CL

ωRF

VBIAS

EXAMPLE: 3-stage, Divide by 4

ω ωRF

4--------=

ωR F

• An oscillator can be injection-locked to a harmonic of the free-running oscillation frequency.

Regenerative Divider [Miller 1939]

• Commonly used where the frequency of operation is very high, beyond what can be achieved with flip-flop based circuits.

• Frequency multiplier can represent non-linearities present in the circuit.

• Used a model similar to Miller’s, since the locking mechanisms are identical.

ωR F H(jω)

3

ωRF34-----ωRF±

ω ωRF

4--------=

FREQ. MULT.

EXAMPLE: Divide by 4

Model for Injection-locked Frequency Divider

n-stage LPF

H(jω)

LO Portω = ωRF/M

RF Port

Differential Pair’sNon-linearity

Mixer

-1

LO+ LO-

ITAILωRF

DC + ωRF |ωRF - (M+1)ω||ωRF - (M-1)ω|

ω

MIXER• Differential-pair single-balanced

mixer

• Injected ωRF into the tail device

FILTER• Suppress products > ω• VO is sinusoidal (small n).

ω, 3ω, 5ω ...

Model for Injection-locked Frequency Divider (II)

3-stage LPF

H(jω)

LO Portω = ωRF/4

RF Port

Differential Pair’sNon-linearity

Mixer

-1

LO+ LO-

ITAILωRF

DC + ωRF |ωRF - 5ω||ωRF - 3ω|

ω

• With no injection, ω = ω0.

ω, 3ω, 5ω ...

EXAMPLE: 3-stage, Divide by 4

Mixer

∆V

∆IIBIAS

VSAT

-IBIAS

-VSAT

2IRF

• The differential-pair is non-linear with odd symmetry. • Non-linearity produces odd harmonics at 3ω, 5ω, etc. • ITAIL is modulated by ω and its harmonics.

LO Port

RF Port

Mixer

LO+ LO-

ITAILωRF

ω, 3ω, 5ω ...

ITAIL = IRF cos(ωRFt + α) + IBIAS

VSATW L⁄( )TAILW L⁄( )DIFF

-------------------------------- VODT⋅=V0 cos(ωt)

ITAIL

Mixer (II)

LO Port

Mixer

ω, 3ω, 5ω ...

Ck

1kπ------ 1–( ) k 1–( ) 2⁄⋅

0

= odd k

otherwise

Fourier Coefficients of Π t( ) ITAIL⋅

ρs = V0/VSAT >> 1 (Square Wave)

DEFINE SWING RATIO

Mixing Function Π(t)

V0 cos(ωt)

ITAIL

Linearize Phase of H(jω)

ω

H jω( )∠

ωΟ

−π dφ/dω H jω( )∠– π≅

n2πn

------ sin

2----------------------- ∆ω

ω0--------⋅+

∆ω ω ωO–=

Filter

H jω( )HO

n

1 jωωo------ π

n---

tan+ n--------------------------------------------=

n-stage LPF

H(jω)-1 |ωRF - 5ω|

|ωRF - 3ω|

ω

Use Ring Oscillator Model

Describing Function Analysis

• If VO is large, then the injection locking dynamics are determined by the phase relationship around the loop (phase-limited) and therefore we can ignore the amplitude expression.

ηi CM 1– CM 1+–( ) αsin

C1 ηi CM 1– CM 1++( ) αcos+----------------------------------------------------------------------------------

atan Hjω∠– π–= ηiIRF

2IBIAS----------------=

INJECTION

WRITE PHASE EXPRESSION AROUND THE LOOP

MIXER FILTER

FIND SOLUTION FOR α ∈ (-π, π].

EFFICIENCY

LR 4

n2πn

------ sin

-----------------------k0

1 k12

–

---------------------

atan≅

k0 ηiCM 1– CM 1+–

C1------------------------------------= k1 ηi

CM 1– CM 1++

C1-------------------------------------=

• Function of injection efficiency ηi, and the magnitude of the Fourier coefficients CM-1 and CM+1.

• For small values of injected signal the locking range increases linearly with the injected signal strength.

WHERE

Locking Range of Injection-locked Ring Oscillator

Limited Injection Efficiency and Parasitics

• Limited injection efficiency due to short-channel effects and tail device non-linearity.

VRF

VBIASCPAR

• Shunt path for IRF reducing the injection efficiency at high frequencies.

TAIL PARASITICSINJECTOR NON-IDEALITIES

VRF

VBIASIDS K VRF VODT+( )γ⋅=

ηiVRF

2VODT---------------- γ⋅=

γ = 1 - 2

SHORT-CHANNEL

–0.3

–0.2

–0.1

0

0.1

0.2

Swing Ratio, ρs=V

o/V

sat

2 4 6 8 10

Nor

mal

ized

Coe

ffici

ents

C3/C/C

1

C5/C/C

1

Limited Mixer Gain

• The assumption that the mixer’s switching function is a square wave is very accurate if the swing ratio ρs >> 1.

• As ρs gets smaller, the normalized coefficients Ck/C1 are significantly smaller, thus degrading the locking range.

0 0.5 1 1.5 2 2.5 3 3.5 40

2

4

6

8

10

12

14

16

18

VRF

/VOD

Lock

ing

Ran

ge (

%)

ab

c

Example: 5-stage, Modulo-8 Ring Oscillator

(a)Ideal (phase-limited) case(b)Compression due to Injector non-linearity (square-law device)(c)Effects of Injector non-linearity and tail parasitics (50% loss)

Outline

• Introduction

• Injection Locking Theory

• Circuit Implementation• Measured Results

• Conclusion

5-stage Injection-locked Ring Oscillator Frequency Divider

• Used modified cross-coupled symmetric load buffers.

• RF signal injected at the tail of the first buffer (single-balanced mixer).

• The buffer stages behave as the H(jω) filter.

+

_

BR

OPAMP VBIAS

VCTLVdd

ωB1

VRF

B4B3B2

REPLICA BIAS INJECTION-LOCKED RING OSCILLATOR

B5 BO

OUT BUFFER

RBIAS

VRF

VBIAS

VCTL

Die Micrograph: 5-stage Ring Oscillator Divider

RINGOSCILLATOR

BIAS

VRF

OU

TB

UF

VOUTVOUT

• Fabricated 3 and 5-stage ring oscillators.

• 0.24-µm CMOS

• 0.012 mm2 of area

Outline

• Introduction

• Injection Locking Theory

• Circuit Implementation

• Measured Results• Conclusion

Results

Injected FrequencyFree-running FrequencyPhase Noise@100KHz

5-stage ILFD1.0 GHz125 MHz-110 dBc/Hz

3-stage ILFD2.8 GHz700 MHz-106 dBc/Hz

Input Locking Range Modulo-2 Modulo-4 Modulo-6 Modulo-8

12.7 MHz (-3dBm)32 MHz (-3dBm)17 MHz (-3dBm)20 MHz (-3dBm)

125 MHz (-3dBm) 56 MHz (-5dBm)

no-lockno-lock

Power dissipation Vdd Icore Ibias Core power Power efficiency

1.5 V233 µA108 µA350 µW2.86 GHz/mW

3.0 V331 µA661 µA993 µW2.82 GHz/mW

0.5 1 1.5 2 2.5 3 3.5 40

0.5

1

1.5

2

2.5

3[ 0] div8

[ 0] div4

[ 3] div8

[11] div8

[13] div128

[ 9] div2

[15] div8

[13] div128

[14] div8

Frequency, GHz

Pow

er E

ffici

ency

, GH

z/m

W

• [0] 5-stage (div-8) = 2.86 GHz/mW @1GHz

• [0] 3-stage (div-4) = 2.82 GHz/mW @2.8GHz

Power Efficiency of Injection-locked Ring Oscillator

• Small swing ratio (ρs ≈ 3−4) caused reduction in mixer gain. Need to increase output swing and reduce VSAT.

What We Learned

• Large tail device (W/L=10.2/1) caused loss of IRF. Need to lower tail node parasitics to increase the injection efficiency.

• Resonating tail with an inductor [Wu, ISSCC’01] is not practical at sub-GHz frequencies.

LOCKING RANGE COMPARISON

5-stage (div-8) @ 1 GHz

3-stage (div-4) @ 2.8 GHz

THEORY 9% 34%

SIMULATION 5% 17%

TEST 2% 2%

Outline

• Introduction

• Injection Locking Theory

• Circuit Implementation

• Measured Results

• Conclusion

Conclusion

• Described the injection locking mechanism and how it applies to CMOS ring oscillators.

• Showed the design of frequency dividers that can operate up to 2.8-GHz by exploiting injection locking in differential CMOS ring oscillators.

• Showed measured results for 1-GHz and 2.8-GHz injection-locked frequency dividers fabricated in a 0.24-µm CMOS technology.

Acknowledgments

National Semiconductor