Basic Principles of Sinusoidal Oscillators - NCKU

Basic Principles of S

Linear oscillator
 Linear region of circuit : li
 Nonlinear region of circuit
Barkhausen criterion

XS   Amplifier A



Xf Frequency-sele

network 

 loop gain L(s) = β (s)A(s)
 characteristic equation 1
 oscillation criterion L(j0

Prof. Tai-Haur Kuo 12

Sinusoidal Oscillators

inear oscillation
t : amplitudes stabilization

A XO

ective



1-L(s) = 0
= A(j0) β(j0) = 1

- 1 Electronics(3), 2012

Basic Principles of Sinus

at 0, the phase of the loop
magnitude of the loop gain s

Oscillation frequency 0 is d

φ ∆ω0  ∆φ
dφ dω

∆φ ω0
0

A steep phase response res
given change in phase 

Prof. Tai-Haur Kuo 12

soidal Oscillators (Cont.)

should be zero and the
should be unity.
determined solely by

ω

sults in a small 0 for a

- 2 Electronics(3), 2012

Nonlinear Amp

To sustain oscillation : βA>1
a.overdesign for βA variatio
b.oscillation will grow in am
 poles are in the right half
c.Nonlinear network reduce

amplitude is reached
 poles will be pulled to j-a

Prof. Tai-Haur Kuo 12

plitude Control

1
ons
mplitude

of the s-plane
es βA to 1 when the desired
axis

- 3 Electronics(3), 2012

Nonlinear Amplitud

Limiter circuit for amplitude c

 linear region

VO  ( Rf )Vi
R1

VA  V R3  VO R2
R2  R3 R2  R3

VB  V R4  VO R5
R4  R5 R4  R5

Prof. Tai-Haur Kuo 12

de Control (Cont.)

control

V

VI R1 D1 R2
A
Rf
R3

 VO

D2 R4
B

R5

-V

- 4 Electronics(3), 2012

Nonlinear Amplitud

 nonlinear region

VO VA -VD L  R2  R3 ( V R R
R2 2

 V R3  VD (1 R
R2 R

similarly, L  V R4  VD (1 R4
R5 R5

Prof. Tai-Haur Kuo 12

de Control (Cont.)

R3  VD )
 R3

R3 )
R2

4 ) VO

5 L
(R R )
Slope   f R1 4

0 Slope VI Rf
R1


L

Slope   (R f R3 )
R1

- 5 Electronics(3), 2012

OPAMP-RC Os

Wien-bridge oscillator

Ls  1 R2  Zp
 R1  Zp  Zs


1 R2
R1
 1
SCR
3  SCR 

1 R2
R1
Ljω  Vd
jωRC  1 
3   ωRC 

     For phase  0. ω0RC  1
ω0RC

 ω0  1
RC

     Ls  1 R2  2
R1

Prof. Tai-Haur Kuo 12

scillator Circuits

R2

R1 _ VO


CR

CR ZS

ZP

- 6 Electronics(3), 2012

OPAMP-RC Oscilla

Wien-bridge oscillator with a

D1
20.3k

10k V1 _
16nF


10
16nF
10k

D2

Prof. Tai-Haur Kuo 12

ator Circuits (Cont.)

a limiter  15V

R 3  3k

a

0k R 4  1k

VO

R5  1k

b
R6  3k

 15V

- 7 Electronics(3), 2012

OPAMP-RC Oscilla

50k b
p

16nF 10k

Prof. Tai-Haur Kuo 12

ator Circuits (Cont.)

vO

10k a

-


16nF
10k

- 8 Electronics(3), 2012

Phase-Shif

Without amplitude stabilizatio

CC C
RR R

------- phase shift of the RC
Total phase shift ar
degrees.

Prof. Tai-Haur Kuo 12

ft Oscillator

on

-K

network is 180 degrees.
round the loop is 0 or 360

- 9 Electronics(3), 2012

Phase-Shift Os

With amplitude stabilization

16nF 16nF 16nF

xC C C
R 10k R 10k

Prof. Tai-Haur Kuo 12

scillator (Cont.)

100k 50k

P1 V vO
Rt R1
R2 Electronics(3), 2012
D1
_ R3



D2

R4
V
- 10

Quadrature

V- 2R
R1
R2

R3
R4
C V

XR _ 2R
OP1

VO1 C

Prof. Tai-Haur Kuo 12

e Oscillator

2R VO2

_

OP2

C Rf

(Nominally 2R)

- 11 Electronics(3), 2012

Quadrature Os

-------Break the loop at X, loop
oscillation frequency 

-------Vo2 is the integral of Vo1
90° phase difference b
“quadrature” oscillator

Prof. Tai-Haur Kuo 12

scillator (Cont.)

gain L(s) = V02 = 1
VX S2C2R 2
1
0  RC

between Vo1 and Vo2

- 12 Electronics(3), 2012

Active-Filter Tu

Block diagram

 V V2
-V t

V

 High-distortion v2

 High-Q bandpass  low

Prof. Tai-Haur Kuo 12

uned Oscillator

f0 V1

V2 t
- V V1

w-distortion v1 Electronics(3), 2012

- 13

Active-Filter Tuned

Practical implementation

QR R C
C

V2 R1

Prof. Tai-Haur Kuo 12

d Oscillator (Cont.)

RR

R

-

- 14 V1

Electronics(3), 2012

A General Form of L
Configu

Many oscillator circuits fall in
below

RO

3  2

1 A V

-

Vˆ 13 V13 Z3
Z2

I  0 V13 Z1


ZL

Z1,Z2,Z3 ：capacitive or indu

Prof. Tai-Haur Kuo 12

LC-Tuned Oscillator
uration

nto a general form shown

RO 2 VO

VO

 Z3
1
Z2
 - A v Vˆ13 

V13 Z1



3

uctive ZL

- 15 Electronics(3), 2012

A General Form of L
Configurati

VO   AvVˆ13Z L
Z L  RO

V13  Z1 VO T  V13  RO (Z1 Z
Z1  Z3 Vˆ13

if Z1  jX1, Z2  jX 2, Z3  jX 3

X  L for inductance X   1

C
Av X1 X 2
T  jRO ( X1  X 2  X 3 )  X 2 ( X1  X 3

for oscillation, T  10

 X1  X2  X3  0

T   Av X1 X 2   Av X1
X2(X1  X3) X1  X3

T  Av X1
X2

Prof. Tai-Haur Kuo 12

LC-Tuned Oscillator
ion (Cont.)

 AvZ1Z2
Z2  Z3 )  Z2 (Z1  Z3 )

for capacitance

3)

- 16 Electronics(3), 2012

A General Form of L
Configurati

With oscillation

|T| = 1 and T = 0, 360, 720

i.e. T = 1 (X =ωL or

 X1 & X2 must have the sam
 X1 & X2 are L, X3 = -(X1 +
or X1 & X2 are C, X3 = -(X1 +
Transistor oscillators

1.Collpitts oscillator

-- X1 & X2 are Cs, X3 is L
2.Hartley oscillator

-- X1 & X2 are Ls, X3 is C

Prof. Tai-Haur Kuo 12

LC-Tuned Oscillator
ion (Cont.)

0, … degree.

r X = - ω1C)

me sign if Av is positive
+ X2) is C
+ X2) is L

- 17 Electronics(3), 2012

LC Tuned O

Two commonly used configu
 1.Collpitts (feedback is ac

divider)
 2.Harley (feedback is ach

divider)
 Configuration

1.Collpitts

R C1

L

a.c. ground(VDD) C2

Prof. Tai-Haur Kuo 12

Oscillators

urations
chieved by using a capacitive

hieved by using an inductive

2.Hartley

R L1 C
a.c. ground(VDD) L2

- 18 Electronics(3), 2012

LC Tuned Osc

Collpitts oscillator
 Equivalent circuit

sC 2 Vπ

sC2 Vπ 
C2
Vπ GmVπ


 R = loss of inductor + load
output resistance of trans

Prof. Tai-Haur Kuo 12

cillators (Cont.)

L VO  Vπ(1 s2LC2 )

C
R C1

d resistance of oscillator +
sistor

- 19 Electronics(3), 2012

LC Tuned Osc

SC2 V+gmv+( 1 +SC1)(1+S2LC
R

S3LC1C2 +S2( LC2 )+S(C1+C2 )+
R

(gm + 1  w 2LC2 )+j W(C1+C2
R R

 For oscillations to start, b
parts must be zero

 Oscillation frequency

ω0 = 1

L( c1c 2 )
c1 +c
2

Prof. Tai-Haur Kuo 12

cillators (Cont.)

C2 )V=0

+(gm + 1 )=0 S=jw
R

)  W3LC1C2  =0

both the real and imaginary

- 20 Electronics(3), 2012

LC Tuned Osc

 Gain

gmR  c2 (Actually, gmR 
c1

 Oscillation amplitude

1.LC tuned oscillators ar
oscillators. (As oscillat
transistor gain is reduc
value)

2.Output voltage signal w
purity because of the f
circuit

Hartley oscillator can be sim

Prof. Tai-Haur Kuo 12

cillators (Cont.)

 c2 )
c1

re known as self – limiting
tions grown in amplitude,
ced below its small – signal

will be a sinusoid of high
filtering action of the LC tuned

milarity analyzed Electronics(3), 2012

- 21

Crystal os

Symbol of crystal

Circuit model of crystal

L
CS
r

Prof. Tai-Haur Kuo 12

scillators

CP Electronics(3), 2012

- 22

Crystal oscilla

Reactance of a crystal assuming r

1 1 s2 
sL  sCP
Z(s)  1 s2  

sCP  1 Cr
sCS


ωS2  1 reac
 
Let  LCS
ωP2
1  1  1 
L CS CP

 Zjω  j 1  ω2  ωS2 
ωCP ω2  ωP2

If CP  CS, then ωP  ωS

Prof. Tai-Haur Kuo 12

ators (Cont.)

r=0

  1 
LCS
CP  CS 

LCSCP (Crystal is high – Q device)

rystal
ctance

inductive

0 ωp ω
ωS

capacitive

- 23 Electronics(3), 2012

Crystal oscilla

The crystal reactance is indu
frequency band between ws

Collpitts crystal oscillator
 Configuration

R

a.c. ground(VDD

Prof. Tai-Haur Kuo 12

ators (Cont.)

uctive over the narrow
and wp

C1 crystal
D) C2

- 24 Electronics(3), 2012

Crystal oscilla

 Equivalent circuit

CS<<CP, C1, C2

 ω0  1 =ωS
LCS

Prof. Tai-Haur Kuo 12

ators (Cont.) R C1

CP
L

CS



C2 vπ

-

- 25 Electronics(3), 2012