Oscillators (Ch. 14)

김 영 석김 영 석

충북대학교 전자정보대학

2010.3.1. .

Email: kimys@cbu.ac.kr

전자정보대학 김영석 14-1

Contents14.1 General Considerations

14.2 Ring Oscillators

14.3 LC Oscillators

14 4 V lt C t ll d O ill t14.4 Voltage-Controlled Oscillators

14.5 Mathematical Model of VCOs

전자정보대학 김영석 14-2

14.1 General ConsiderationsUnity-gain Negative Feedback Circuit

+=

)(1)()(

VsH

sHsVV

out

in

out

∞=−== )(,1)(, : 000 jwVV

jwHjwsforifnOscillatioin

out

Why a loop gain of unity or greater necessary for oscillation?

VjwHVjwHVjwHVVX ...|)(||)(||)(| 03

002

0000 ++++=

diVjHifjwH

VVjwHif X

1|)(||)(|1

,1|)(|0

00 ∞<

−=<

Barkhausen Criteria for Oscillation:

divergesVjwHif X ,1|)(| 0 >

°∠≥

180)(1|)(| 0

jHjwH

T t l 360 h hift

전자정보대학 김영석 14-3

°=∠ 180)( 0jwH Total 360 phase shift

14.2 Ring OscillatorsOne-Pole

M1 180 PS(phase shift) @ DC

1 pole 90 PS @ infinity => No OSC

Two-pole

M1,M2 360 PS @ DC

2 l 18 PS @ i fi it N OSC l t h2 poles 180 PS @ infinity => No OSC, latch

Two-pole with invp

M1,M2,inv 360+180 PS @ DC

2 poles 180 PS @ infinity

=> Not enough PS @ w0 No OSC=> Not enough PS @ w0, No OSC

Three-ring OSC

M1,M2,M3 360+180 PS @ DC

3 poles 180 PS @ w0 (270 PS @ infinity)

=> 360 PS OSC

전자정보대학 김영석 14-4

=> 360 PS, OSC

14.2 Ring OscillatorsMinimum Voltage Gain for OSC

)/1()( 3

0

30

+−==

wsA

sHgainloop

21:minimum

360tan:)180 (180

0

30

00

1

=∴=

=∴°=+= −

AA

gainvtg

www

wfeedbacknegativePSifonlyOSC osc

osc

21)/(1

: minimum 00

=∴=+

Aww

gainvtgosc

전자정보대학 김영석 14-5

14.2 Ring Oscillators: Amplitude LimitingIf A0 < 2, No OSC

If A0 > 2, Analyzing Linear Model

)2

3cos()

22

exp()( 00

00 tw

Atw

AatVout

−=

Exponential Envelope grows to infinity. But, as the oscillation amplitude increase the stages experience nonlinearity and

)2

()2

p()( 00out

amplitude increase, the stages experience nonlinearity and eventually “saturation”

전자정보대학 김영석 14-6

14.2 Ring OscillatorsRing Oscillator using CMOS inverters

전자정보대학 김영석 14-7

14.3 LC OscillatorsLC in Parallel = Open circuit @ wres=1/sqrt(LC)

LC in Series = Short circuit @ wres=1/sqrt(LC)

Series-Parallel Conversion

112

1

>>=≈

≈

SP

P

wLQwhereRQR

LL

1 >>S

SP RQwhereRQR

LC tank

W=w1=1/sqrt(Lp*Cp), phase =0

W<w1 InductiveW<w1, Inductive

W>w1, Capacitive

전자정보대학 김영석 14-8

14.3.1 Cross-Coupled OscillatorCircuit1: Output is connected to Input, PS=180, No oscillation (PS=not 360)

Circuit2: two stages in a cascade, gPS=0, Oscillation if gm1*Rp*gm2*Rp>1

전자정보대학 김영석 14-9

14.3.2 Colpitts OscillatorCircuit1: PS=0 but No Oscillation due to insufficient loop gain, gm1*V1은 M1, C2에만 흐름, Iin은 LC tank에만 흐름. => (loop gain 작다)

PP

Pin

out RsC

sLI

V||1||=

PP

Pin

out RsC

sLI

V||1||=

Add C2, Minimum required gain for OscillationOscillation

4≥PmRg

Note that minimum gain for cross-coupled oscillator =1

전자정보대학 김영석 14-10

coupled oscillator =1

14.3.3 One-Port OscillatorsConcept of Negative Resistance

전자정보대학 김영석 14-11

14.3.3 One-Port OscillatorsHow to provide a Negative Resistance?

Source follower with positive feedback: sNegIIVV XDSX Re 021 =><↓=>↑=>↑=>

mX

X

gIV 2−

=

Negative-Gm oscillator

전자정보대학 김영석 14-12

14.3.3 One-Port OscillatorsAnother method

gV mX2

11++=

sCsCsCCI X 122

21

Colpitts Oscillator: (b) Base Ground

전자정보대학 김영석 14-13

14.4 Voltage-Controlled OscillatorsVCO=A Circuit whose output Frequency is a Linear Function of its Controlled Voltage

contVCOout VKww += 0

Performance Parameters of VCOs

Center Frequency

contVCOout 0

Center Frequency

Tuning Range

Tuning Linearity

Output Amplitude

Power Dissipation

Supply and Common-mode RejectionSupply and Common mode Rejection

Output Signal Purity

전자정보대학 김영석 14-14

14.4.1 Tuning in Ring OscillatorsAdjust TD(Large-signal Delay of each stage) => vary the Freq.

Si l E M3 M4 i t i d i > V i bl R i t

Dosc TN

f•

=2

1

Simple Ex: M3, M4 in triode region => Variable Resistor

osconcont fRV ↓=>↑=>↑=>↑ τ

THPcontDDoxp

LLon

osconcont

VVVLWCCCR

f

|)|()/( 4,34,31 −−

==μ

τ

L

THPcontDDoxp

Dosc C

VVVLWCT

f|)|()/(1 4,3 −−

∝∝μ

전자정보대학 김영석 14-15

14.4.1 Tuning in Ring OscillatorsDrawback of Simple Circuit: Tuning Range에 따라 Output Swing 변화

개선된 회로:

Negative Feedback with A1 and M5 in triode region

I1 변화하더라도 VREF VP (VG5는 변화)I1 변화하더라도 VREF=VP (VG5는 변화)

↓>↑>↑>↑↓ >↓ >

:ControlFrequency fRVIV τ

⎧ =

↓=>↑=>↑=>↑↓=>↓=>

)1(:Control Amplitude

51

ONMifVV

fRVIV osconGcont τ

⎩⎨⎧

==

=>=↓=>↓=>) 1 ()1(

).(1 OFFMifVVONMifVV

FeedbackNegVVIVDDX

REFXREFPcont

전자정보대학 김영석 14-16

14.4.2 Tuning in LC Oscillators

인덕터, 커패시터 변화하여야 함. 인덕터는 변화시키기 힘듬. 주로 커패시터인덕터, 커패시터 변화하여야 함 인덕터는 변화시키기 힘듬 주로 커패시터변화 (Varactors)

f 1=osc

VC

C

LCf

20

var =

=π

m

B

V )1( varvar

Φ+

전자정보대학 김영석 14-17