Basic Principles of Sinusoidal Oscillators - NCKU

Crystal oscilla

-22V

L C=300p
61~122uH

Cgd +Cstray D 
2N2608
1MHz C S

10M
2.2kΩ 0.02μF
XTAL

Prof. Tai-Haur Kuo 12

ators (Cont.)

pF L
C


-22V

Bias circuit

(For AC,-22V and
ground are the same=0)

- 26 Electronics(3), 2012

Crystal oscilla

 SthiencloeorpetguarninratotiobeTg=reAXavtX2e

 X1 is very large when ω
ω

 X1+X 2 +X 3 =0 & X3=  1  X
ωC

Z 2 =L//C= 1 1 = j
C+ jω L C+
jω ω

 X2= 1 1 >0  ωL> ω
ωC+ ωL

Prof. Tai-Haur Kuo 12

ators (Cont.)

X1 then X1 must be large for
er than one.

ω closes to ωp and

ωS  ω  ωP 

X1&X2 are inductive

+ 1 For 1MHz crystal,
ωL
C=300pF
1 1
ωC  ω> LC L  84.4μH

1 1  1MHz
2π LC

- 27 Electronics(3), 2012

Bistable Mu

Multivibrators bistable：tw
(3 types) monostable
astable：n

Bistable

 Has two stable states

 Can be obtained by conn
amplifier in a positive-feed
greater than unity. I.e. βA

Prof. Tai-Haur Kuo 12

ultivibrators

wo stable states
e：one stable state
no stable state

necting an amplifier in a
dback loop having a loop gain
A>1 where β=R1/(R1+R2)

- 28 Electronics(3), 2012

Bistable Multivi

 Bistable circuit with clockw

R1 R2

v+ 
-
vO

vI 
-

 Clockwise hysteresis (or i

L+：positive saturation v
L- ：negative saturation

Prof. Tai-Haur Kuo 12

ibrators (Cont.)

wise hysteresis

VTL vo L
L- 0 vI

VTH

inverting hysteresis)
voltage of OPAMP

voltage of OPAMP

- 29 Electronics(3), 2012

Bistable Multivi

 VTH  βL   R1 L
R1  R2

 VTL  βL   R1 L
R1  R2

– Hysteresis width = VTH - VTL

Prof. Tai-Haur Kuo 12

ibrators (Cont.)

- 30 Electronics(3), 2012

Noninverting B

Counterclockwise hysteresis

Configuration

R1 R2

vI  v+
-

- vO

v + =vI R2 +v0 R1
R1+R2 R1+R2

For v0=L+, v+=0,vI=vTL  vTL

For v0=L-, v+=0,vI=vTH  vTH

Prof. Tai-Haur Kuo 12

Bistable Circuit

s

vo

L

VTL 0 vI
VTH

L-

=  L+ ( R1 )
R2

H=  L ( R1 )
R2

- 31 Electronics(3), 2012

Noninverting Bista

Comparator characteristics w
 Can reject interference

VTH S
VR  0 w

VTL Multiple
zero cross

Prof. Tai-Haur Kuo 12

able Circuit (Cont.)

with hysteresis

Signal corrupted t
with interference

e
sings

- 32 Electronics(3), 2012

Generation of Square an
using Astable

Can be done by connecting
RC circuit in a feedback loop

v1 0
VTL
VTH  βL
VTL  βL t

C

Prof. Tai-Haur Kuo 12

nd Triangular Waveforms
Multivibrators

a bistable multivibrator with a
p.

v2
L

VTH v1 v2

L- L t

L-

CR

- 33 Electronics(3), 2012

Generation of Square an
using Astable Mul

R1 R2 

v+  vO
-
v- -
R
-

Prof. Tai-Haur Kuo 12

nd Triangular Waveforms
ltivibrators (Cont.)

vO t T1 T2
L
0
t

L-

v- t To L

VTH  βL t

0 To L-
Time constant
VTL  βL = RC

v t t

VTH  βL Electronics(3), 2012

0

VTL  βL

- 34

Generation of Square an
using Astable Mul

During T1

 V  t
 L  L  βL e τ where τ  RC

1  β L
L
if V  βL  at t  T1  T1  τ ln
1β

During T2 t
τ
 V e
 L  L  βL

if V  βL  at t  T2  T2  τ ln 1 β
1

T  T1  T2  2τ ln 1  β ; L   L is as
1  β

Prof. Tai-Haur Kuo 12

nd Triangular Waveforms
ltivibrators (Cont.)

C, β  R1
R1  R2

L 
L

β

L 
L

β

ssumed

- 35 Electronics(3), 2012

Generation of Trian

V1
C

R V1 0

_ VTL


V2 T2 Bis
T1 t

L 12

0

L
T

Prof. Tai-Haur Kuo

ngular Waveforms

t

v2

L
V0
v1 2
VTH
V2 t

L-

stable

V1 T2 Slope  -L
VTH T1 RC

0 t
VTL
Slope  L
RC

- 36 Electronics(3), 2012

Generation of Triangul

During T1 1 LL T1
C
VTH T1 iCdt RC
VTL   0  ;

 T1  RC VTH  VTL
L
During T2

Similarily

 T2  RC VTH  VTL
L

To obtain symmetrical wavef

T1  T2  L  L

Prof. Tai-Haur Kuo 12

lar Waveforms (Cont.)

where iC  L
R

forms Electronics(3), 2012

- 37

Monostable M

Its alternative name is “ one

Has one stable state (

Can be triggered to a quasi-s

E R2

C2 R D 2 
_
4
R3
R1 A

B
D1 C1

Prof. Tai-Haur Kuo 12

Multivibrators

shot “

(βL +  VD2 ) v E ( t)

state

LvA (t)

T
L-

βL v  ( t )



βL -

VD1v B ( t ) To L 
To L 
βL -

- 38 Electronics(3), 2012

Monostable Multi

During T1
t

VB (t)  L  (L  VD1)eR3C1

VB(T)  βL  βL  L  (L  VD

 T  R3C1 ln( VD1 L )
βL  L

ForVD1  | L |  T  R3C1(11β )

βL+ is greater then VD1
Stable state is maintaine

Prof. Tai-Haur Kuo 12

ivibrators (Cont.)

T
 R 3C1

)eD1

ed Electronics(3), 2012

- 39

Monostable Mult

Monostable multivibrator usi

VDD

vR

Vin Vo1 X

NOR C

vin v O1 VDD
3 2
VVT VDD
VT 
0 T  T1 t0 T1
t
Prof. Tai-Haur Kuo
12

tivibrators(Cont.)

ing NOR gates

D

VO2

NOR 

 VT VX v O2
2 VDD
VDD
VDD

 VDD 2

0 T1 t 0 T1 t

- 40 Electronics(3), 2012

Mono-stable Mul

C

- R

 Vc vX
-
- VO1  0 VDD

vC(0)  0
vx  VDD(1 eRtC )

vx (T1)  VT  VDD (1 e  T1 )
RC

 T1  RCln VDD  RC
VDD  VT

where VT  VDD ; VT is NO
2

Prof. Tai-Haur Kuo 12

ltivibrator (Cont.)

C

- R

 Vc VDD vX
-
- VO1  VDD

vC (T1V) DDVVT TeRtC

vx

)

Cln2  0.693RC

OR gate threshold voltage

- 41 Electronics(3), 2012

Mono-stable Mul

Monostable multivibrator with

 VD

Vin Vo1 R
NOR C

VX 5.6V

5V VD

0 Ti

Prof. Tai-Haur Kuo T1 t

12

ltivibrator (Cont.)

h catching diode

VDD

D VO2
NOR
Vx

forward resistance of diode
Time constant  RfC
ime constant  RC

- 42 Electronics(3), 2012

Astable Multivibrator Using

VX VO1 VO2

R

 vC_

C

Transient behavior

(1)0<t<T1

(i) v o1:VDD  0 w h e n t=
(ii) v o2 : 0  VDD w h e n t

-t

(iii)v x = (VD D + V T )e RC

(iv )v c = v x -V O 2 = -VDD + (VDD

Prof. Tai-Haur Kuo 12

g NOR(or Inverter) Gates
v o1
VDD

v 0 T 1 2T1 t

o2

VDD

0 T1 2 T1 t
vX 2 T1 t

VDD VT t

VT  VDD
2

=0 0
t= 0
VT v T 1

C

VDD

VT T1
2 T1
-t 0
VT
D + VT )e RC

- 43 Electronics(3), 2012

Astable Multivibrator Using
(Co

(2)T1<t<(T1+T2)

(i) v o1:0  VDD w h e n
(ii) v o2 :VDD  0 w h e n

(

(iii)v x = VDD -(VDD + VT )e 

(iv )v c = v x -VO2 = v x = VD

Prof. Tai-Haur Kuo 12

g NOR(or Inverter) Gates
ont.)

t= T1
t= T1

(t-T1 )
RC

-(VDD + V )e  (t-T1 )
RC
DD T

- 44 Electronics(3), 2012

Astable Multivibrator Using
(Co

Oscillation frequency

v x (T1)=VT

 (VDD +VT ) e  t =VT
RC

 T1=RCln VDD +VT
VT

If VT = VDD , then T1=RCln3
2

oscillation frequency f0 = 2

Prof. Tai-Haur Kuo 12

g NOR(or Inverter) Gates
ont.)

and T2 =RCln3

1  0.455
2RCln3 RC

- 45 Electronics(3), 2012

Astable Multivibrator Using
(Co

 With catching diode atV X

VX VO1 VO2

R

 vC_

C

0 VDD

 Asymmetrical square wav

(i)VT  VDD VX
2 D

(ii)R1  R2

Prof. Tai-Haur Kuo 12

g NOR(or Inverter) Gates
ont.)

X

T1  T2  RCln2

f0  1  0.721
2RCln2 RC

ve Electronics(3), 2012

VO1 VO2

R1 R2

D1 D2  vC_

C
- 46

The 555 I

Widely used as both a monos
multivibrator

Used as monostable multivibr

VCC

Threshold R 1 Comparator 1
V
R Q To
C c VTH _
Trigger RVT1L ou

_ SQ

V t R 1 Comparator 2

Q1

Discharge

Prof. Tai-Haur Kuo 12

IC Timer

stable and astable

Rn Sn QQnnn+1 V1  Vcc
3
0 0 1
rator 0 1 V2  2V cc
1 0 0 3
1 1
v t(t) N/A Vc  2V cc  Rn  1
3

otem-pole VO v c ( t )0 v t  V TL

utput stage VCC (1  e t RC )
T1
V TH
 2VCC 3 T1

transistor 0 Electronics(3), 2012

- 47 v O (t)
v(t)

0

The 555 IC T

 For 0  t  T1 t
RC
 vx e
 VCC  VCC  V(0)

 For t = T1, vC(T1)  VTH 

 T1  RCln VCC  V(0)  R
VCC

3

Prof. Tai-Haur Kuo 12

Timer (Cont.)

(V(0)  VCE(sat)  0)

 2VCC
3

RCln3 (V(0)  0)

- 48 Electronics(3), 2012

The 555 IC T

Used as an astable multivibr

VCC ( RA RB )C

VTH = 2Vcc Thres
VTL = 3 RA V

Vcc Tr
3
RB
0 T1 t
V
T2
C
Vc  2V c c  S  0, R 1
3

Vc  Vcc  S  1, R  0
3

Vcc  Vc  2V c c  S  R 0
3 3

T1  R BCln2 ,T2  T1  (R A  RfB)CT1l2n 2

Oscillation frequency 

Prof. Tai-Haur Kuo 12

Timer (Cont.)

rator VCC 555 timer chip

shold R 1 Comparator 1

Vc VO
VTH _ RQ Totem-pole
output stage
rigger RVT1L
 SQ
_

V t R 1 Comparator 2

Q1

2 Discharge transistor

1
 (RA  2RB )Cln2

- 49 Electronics(3), 2012

Sine-Wav

Shape a triangular waveform
Extensively used in function
Note：linear oscillators are

vO

0 vf 0 T 2 Tt
12
0

T2
T

t

Prof. Tai-Haur Kuo

ve Shaper

m into a sinusoid
generators
not cost-effective for low
frequency application
not easy to time over
wide frequency ranges

- 50 Electronics(3), 2012