-
8/6/2019 (19) Oscillators
1/30
Oscillator 1
Oscillators .
-
8/6/2019 (19) Oscillators
2/30
Oscillator 2
Need of an Oscillator An oscillator circuit is capable of
producing ac
voltage of desired frequency and waveshape.
To test performance of electronic circuits, it is called
signal generator.
It can produce square, pulse, triangular, or
sawtoothwaveshape.
High frequency oscillator are used in broadcasting.
Microwave oven uses an oscillator.
Used forinduction heating and dielectric heating.
-
8/6/2019 (19) Oscillators
3/30
Oscillator 3
Linear Oscillators1. Wien Bridge Oscillators
2. RC Phase-Shift Oscillators3. LC Oscillators
4. Stability
-
8/6/2019 (19) Oscillators
4/30
Oscillator 4
Integrant of Linear Oscillators
For sinusoidal input is connected
Linear because the output is approximately sinusoidal
A linear oscillator contains:
- a frequency selection feedback network
- an amplifier to maintain the loop gain at unity
7+
+Amplifier (A)
Frequency-Selective
Feedback Network (F)Vf
Vs VoVI
Positive
Feedback
-
8/6/2019 (19) Oscillators
5/30
Oscillator 5
Basic Linear Oscillator
7+
+
SelectiveNetwork
F(f)
Vf
Vs VoVI
A(f)
)( fso AA !! I and of F!
Fs
o
!
1
IfVs = 0, the only way that Vo can be nonzerois that loop gain
F=1 which implies that
0
1||
!
!
F
F
A
A(Barkhausen Criterion)
-
8/6/2019 (19) Oscillators
6/30
Oscillator 6
(1) IfA < 1, we getdecaying ofdamped
oscillations.
-
8/6/2019 (19) Oscillators
7/30
Oscillator 7
(2) IfA > 1, we getgrowing oscillations.
-
8/6/2019 (19) Oscillators
8/30
Oscillator 8
(3) IfA = 1, we getsustained oscillations.
In this case, the circuit supplies its own inputsignal.
-
8/6/2019 (19) Oscillators
9/30
Oscillator 9
Wien Bridge Oscillator
An oscillator circuit in which a balanced bridge is used as the
feedback
network is the Wien bridge oscillator as shown
-
8/6/2019 (19) Oscillators
10/30
Oscillator 10
Wien Bridge OscillatorFrequency Selection NetworkLet
1
1 1C
XC[
! and
111 CjXRZ !2
2 1C
XC[
!
22
22
1
22
2
11
C
C
C jXR
XjR
jXRZ
!
!
Therefore, the feedback factor,
)jXR/XjR()jXR(
)jXR/XjR(
ZZ
Z
V
V
CCC
CCf
222211
2222
21
2
0
!
!!F
222211
22
))((CCC
C
XjjXRjXR
XjR
!F
-
8/6/2019 (19) Oscillators
11/30
Oscillator 11
F can be rewritten as:
)( 2121221221
22
CCCCC
C
XXRR
jXRXRXR
XR
!F
ForBarkhausen Criterion, imaginary part = 0, i.e.,
02121 ! CC XXRR
Supposing,
R1=
R2=R and
XC1=
XC2=XC,
2121
21
21
/1
11or
CCRR
CC
RR
!
!
[
[[
)(322
CC
C
XRjRX
RX
!F
0 .2
0.22
0.24
0.26
0.28
0 .3
0.32
0.34
-1
-0 .5
0
0 .5
1
Frequency
F 1/3
Phase 0
f(R Xc)
-
8/6/2019 (19) Oscillators
12/30
Oscillator 12
Example
R
+
R
R
C
C
Z1
Z2
R1
Vo
By setting , we get
Imaginary part = 0 and
RC
1
![
3
1!F
Due toBarkhausen Criterion,
Loop gainAvF=1where
Av : Gain of the amplifier
1131 R
R
AAf
vv !!!F
21
!R
RfTherefore, Wien Bridge Oscillator
-
8/6/2019 (19) Oscillators
13/30
Oscillator 13
RC Phase-Shift Oscillator
Rf
R1
R R R
C C C
Using an inverting amplifier The additional 180ophase shift is
provided by an RC
phase-shift network
-
8/6/2019 (19) Oscillators
14/30
Oscillator 14
Applying KVL to the phase-shift network, we have
Solve forI3, we get
)2(0
)2(0
)(
32
321
211
C
C
C
jXRIRI
RIjXRIRI
RIjXRIV
!
!
!
C
C
C
C
C
jXRR
RjXRR
RjXR
R
jXRR
VRjXR
I
!
20
2
0
00
02
3
1
)2(])2)[(( 222
2
13
CCC jXRRRjXRjXR
RVI
!Or
-
8/6/2019 (19) Oscillators
15/30
Oscillator 15
The output voltage,
)jXR(R]R)jXR)[(jXR(
RVRIV
CCC
fo
!!
22222
3
3
Hence the transfer function of the phase-shift network is given
by,
)XRX(j)RXR(
R
V
Vf
CCC2323
3
0 65 !!F
For 180ophase shift, the imaginary part = 0, i.e.,
RC
R
XXRX CCC
6
1
6
( ejected)0or06
22
23
!
!
!!
[
and,
29
1!F
Note: The ve sign mean the
phase inversion from the
voltage
-
8/6/2019 (19) Oscillators
16/30
Oscillator 16
LC Oscillators
+
~Av Ro
Z1 Z2
Z3
12
Zp
The frequency selection
network (Z1, Z2 and Z3)
provides a phase shift of
180o
The amplifier provides anaddition shift of 180o
Two well-known Oscillators:
Colpitts Oscillator
Harley Oscillator
-
8/6/2019 (19) Oscillators
17/30
Oscillator 17
+
~Av Ro
Z1 Z2
Z3Zp
V Vo
321
312
312
)(
)//(
ZZZ
ZZZ
ZZZZp
!
!
For the equivalent circuit from the output
po
pv
i
o
p
o
po
iv
ZR
ZA
V
V
Z
V
ZR
VA
!!
or
Therefore, the amplifier gain is obtained,
)()(
)(
312321
312
ZZZZZZR
ZZZA
V
VA
o
v
i
o
!!
oof VZZ
ZVV
31
1
!! F
ZpAvVi
Ro
+
Vo
Io
-
8/6/2019 (19) Oscillators
18/30
Oscillator 18
The loop gain,
)()( 312321
21
ZZZZZZR
ZZAA
o
v
!F
If the impedance are all pure reactances, i.e.,
332211 and, jXZjXZjXZ !!!
The loop gain becomes,)()( 312321
21
XXXXXXjR
XXAA
o
v
!F
The imaginary part = 0 only when X1+X2+X3=0
It indicates that at least one reactance must be ve
(capacitor)
X1 and X2 must be of same type and X3 must be of opposite
type
2
1
31
1
X
XAXX
XAA vv !
!FWith imaginary part = 0,
For Unit Gain & 180o Phase-shift,1
21X
XAA v !!F
-
8/6/2019 (19) Oscillators
19/30
Oscillator 19
R L1
L2
C
RC1
C2
L
Hartley Oscillator Colpitts Oscillator
T
oLC
1
