lecture15_ee620_vcos

7/29/2019 lecture15_ee620_vcos

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Sam Palermo

Analog & Mixed-Signal Center

Texas A&M University

ECEN620: Network Theory

Broadband Circuit DesignFall 2012

Lecture 15: Voltage-Controlled Oscillators



Announcements & Agenda

• VCO Fundamentals• VCO Examples

• VCO Noise

2



Charge-Pump PLL Circuits

• Phase Detector

• Charge-Pump

• Loop Filter• VCO

• Divider

3



Voltage-Controlled Oscillator

• Time-domain phase relationship

4

VDDVDD/20

ω0 1

K VCO

( ) ( ) ( )tvK tt cVCOoutout +=∆+= 00 ω ω ω ω

( ) ( ) ( )∫ ∫=∆= dtdt tvK tt cVCOoutout ω φ Laplace Domain Model

φout(t)



Voltage-Controlled Oscillators (VCO)

• Ring Oscillator• Easy to integrate

• Wide tuning range (5x)

• Higher phase noise

• LC Oscillator

• Large area

•

Narrow tuning range (20-30%)• Lower phase noise

5



Barkhausen’s Oscillation Criteria

• Sustained oscillation occurs if

• 2 conditions:

• Gain = 1 at oscillation frequency ω0

• Total phase shift around loop is n360° at oscillation frequency ω0

6

( )( )ω

ω

jH

jH

−1Closed-loop transfer function:

( ) 1=ω jH

n

[Sanchez]



Ring Oscillator Example

7

[Sanchez]



Ring Oscillator Example

8

[Sanchez]

• 4-stage oscillator• A0 = sqrt(2)

• Phase shift = 45

• Easier to make alarger-stageoscillator oscillate, asit requires less gainand phase shift perstage



LC Oscillator Example

( )

( )( ) 22

1222

11

221

22

12

11

1

1

1

ω ω

ω ω

CRCL

LR jsZ

sCRsCL

sLRsZ

S

Seq

S

Seq

+−

+==

++

+=

LC tank impedance

• Oscillation phase shift conditionsatisfied at the frequency whenthe LC (and R) tank loaddisplays a purely realimpedance, i.e. 0° phase shift




• Transforming the series lossresistor of the inductor to anequivalent parallel resistance

10

S

PPS

PR

LRCC

L

RLL

221

1221

2

1 ,,1ω

ω ≈=

+=

PPCL

11 =ω

R P

[Razavi]




11

( ) 12

≥PmRg

PPCL

11 =ω

Loop Gain

• Phase condition satisfied at

• Gain condition satisfied when

[Razavi]

• Can also view this circuit as a parallelcombination of a tank with loss resistance2R P and negative resistance of 2/gm

• Oscillation is satisfied when

P

m

R

g

≤1



Supply-Tuned Ring Oscillator

12

( )thc

stage

DVCOVV

nCnT T

−≈= β

22

stagec

VCOVCO

nCV

f K

2

β =

∂

∂=

[Sidiropoulos VLSI 2000]



Current-Starved Ring Oscillator

13

[Sanchez]



Capacitive-Tuned Ring Oscillator

14



Symmetric Load Ring Oscillator

15

[Maneatis JSSC 1996 & 2003]

• Symmetric load provides frequency tuning at excellentsupply noise rejection

• See Maneatis papers for self-biased techniques to obtain

constant damping factor and loop bandwidth (% of ref clk)



LC Oscillator

• A variable capacitor(varactor) is often used toadjust oscillation frequency

• Total capacitance includesboth tuning capacitance andfixed capacitances which

reduce the tuning range

16

( )fixedtunePPP

oscCCLCL +

==11

ω



Varactors

• pn junction varactor• Avoid forward bias region to prevent oscillator nonlinearity

17

• MOS varactor

• Accumulation-mode devices have better Q than inversion-mode

[Perrott]

n-well[Razavi]



Oscillator Noise

18

Jitter

[McNeill]



Oscillator Phase Noise Model

19

( ) ( )dBc/Hz

PowerCarrier

DensitySpectralNoise

= log10f L

( )

∆

∆+

∆+=∆

f

f

f

f

QP

FkTf L

f o

sig

3/1

2

12

11

2log10Leeson’s Model:

• For improved model see Hajimiri papers

[Perrott]



Open-Loop VCO Jitter

• Measure distribution of clock threshold crossings

• Plot σ as a function of delay ∆T 20

[McNeill]

∆T



Open-Loop VCO Jitter

• Jitter σ is proportional to sqrt(∆T)

• Κ is VCO time domain figure of merit 21

( )( ) T TOL T ∆≈∆∆ κ σ

[McNeill]



VCO in Closed-Loop PLL Jitter

22

• PLL limits σ for delays longer than loop bandwidth τL

LL f π τ 21=

[McNeill]



Converting Phase Noise to Jitter

23

• Integration range depends on application bandwidth

• f min set by standard

• Ex. Assumed CDR tracking bandwidth

• Usually stop integration at f o /2 or f o due to measurement limitationsand aliasing components

( ) ( )df Tf f So

T

∫

∞

∆ ∆=0

2

2

2 sin8

π

ω

σ ϕ • RMS jitter for ∆T accumulation

• As ∆T goes to ∞ ( ) ( )df f SRoo

T ∫∞

==0

22

2 40

2ϕ ϕ

ω ω σ

[Mansuri]



Next Time

• VCO Noise (cont.)• Divider Circuits

24

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