oscillators (ch. 14)bandi.chungbuk.ac.kr/~ysk/ana14.pdf · 2010-03-30 · 14.2 ring oscillators...
TRANSCRIPT
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