Oscillatorsppt

Lecture 3 Oscillator
• Introduction of Oscillator
• Linear Oscillator
– Wien Bridge Oscillator
– RC Phase-Shift Oscillator
– LC Oscillator
• Stability
Ref:06103104HKN EE3110 Oscillator 1

Oscillators
Oscillation: an effect that repeatedly and
regularly fluctuates about the mean value
Oscillator: circuit that produces oscillation
Characteristics: wave-shape, frequency,
amplitude, distortion, stability

Application of Oscillators
• Oscillators are used to generate signals, e.g.
– Used as a local oscillator to transform the RF
signals to IF signals in a receiver;
– Used to generate RF carrier in a transmitter
– Used to generate clocks in digital systems;
– Used as sweep circuits in TV sets and CRO.

Linear Oscillators
1. Wien Bridge Oscillators
2. RC Phase-Shift Oscillators
3. LC Oscillators
4. Stability

Integrant of Linear Oscillators
Ve
+ Amplifier (A)
Vs Vo
S
+
Frequency-Selective
Feedback Network (b)
Vf
Positive
Feedback
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

Basic Linear Oscillator
+
Ve A(f)
Vs Vo
S
+
SelectiveNetwork
b(f)
Vf
( ) o s f V = AV = A V +V e and f o V = bV
A
Ab
V
s
Þ o
=
V
-
1
If Vs = 0, the only way that Vo can be nonzero
is that loop gain Ab=1 which implies that
A (Barkhausen Criterion)
b
A
=
b
| | 1
Ð =
0

Wien Bridge Oscillator
1
C
1
C
Let Frequency Selection Network
= and
1
XC 1
w
1 1 C1 Z = R - jX
2
X=
C 2
w
C
jR X
2 2
2 2
1
2 2
ù
é
Vi Vo
jR X R jX
= - -
( / )
C C
2 2 2 2
2
V
o
Z
C
jR X
2 2
b = -
R - jX R - jX -
jR X
( )( ) C C C
2
1 1
C
C R jX
R jX
Z
-
= - úû
êë
-
= +
-
Therefore, the feedback factor,
( ) ( / )
1 1 2 2 2 2
1 2
C C C
i
R jX jR X R jX
Z Z
V
- + - -
+
b = =
1 1 2 2 2 2
R1 C1
C2 R2
Z1
Z2

b can be rewritten as:
C
R X
2 2
R X + R X + R X + j R R -
X X
( ) 1 C 2 2 C 1 2 C 2 1 2 C 1 C
2
b =
For Barkhausen Criterion, imaginary part = 0, i.e.,
0 1 2 1 2 - = C C R R X X
or 1 1
C C
w w
1 2
R R C C
1 2 1 2
R R
1 2
1/
Þ =
=
w
Supposing,
R1=R2=R and XC1= XC2=XC,
RX
C
+ -
3 RX j ( R 2 X
2 )
C C
b =
0.34 b
0.32
factor 0.3
0.28
Feedback 0.26
0.24
0.22
0.2
1
0.5
0
Phase
-0.5
-1
f(R=Xc)
Phase=0
Frequency
b=1/3

Example
Rf
-
+
R
R
C
R1
C
Z1
Z2
Vo
w = 1
By setting RC
, we get
b = 1
Imaginary part = 0 and
3
Due to Barkhausen Criterion,
Loop gain Avb=1
where
Av : Gain of the amplifier
R
A A f
v v b = Þ = = +
R
1
1 3 1
RTherefore, f 2
Wien Bridge Oscillator
=
R
1

RC Phase-Shift Oscillator
-
+
Rf
R1
C C C
R R R
 Using an inverting amplifier
 The additional 180o phase shift is provided by an RC
phase-shift network

Applying KVL to the phase-shift network, we have
C C C
V1 Vo
R R R
V = I ( R - jX )
-
I R
C
1 1 2
I R I R jX I R
= - + - -
0 (2 )
C
1 2 3
I R I R jX
= - + -
0 (2 )
2 3
C
I1 I2 I3 Solve for I3, we get
C
R - jX -
R
0
R R jX R
- - -
C
C
R jX R V
1
2 0
C
- -
C
R R jX
R R jX
R
I
- -
- -
-
=
2
0 2
0 0
3
2
I V R
1
( )[(2 )2 2 ] 2 (2 )
Or =
3
R - jX R - jX - R - R R -
jX
C C C Ref:06103104HKN EE3110 Oscillator 11

The output voltage,
3
V = I R =
V R
1
o R jX R jX R R R jX
( )[(2 )2 2 ] 2 (2 )
3
- - - - -
C C C
Hence the transfer function of the phase-shift network is given by,
3
R
( 3 5 2 ) ( 3 6 2 )
V
b = o
=
R RX j X R X
V
- + -
1 C C C
For 180o phase shift, the imaginary part = 0, i.e.,
3 2
X R X XC C C
- = =
6 0 or 0 (Rejected)
2C
R
2 1
RC
Þ =
X 6
6
=
w
and,
b = - 1
29
Note: The –ve sign mean the
phase inversion from the
voltage

LC Oscillators
-
~
Av Ro
+
Z1 Z2
2 1
Z3
Zp
 The frequency selection
network (Z1, Z2 and Z3)
provides a phase shift of
180o
 The amplifier provides an
addition shift of 180o
Two well-known Oscillators:
• Colpitts Oscillator
• Harley Oscillator

Av Ro
+
~
Z1 Z2
Vf Vo
Z3
Zp
V V Z
f o o V
1
+
Z Z
1 3
= b =
Z = Z Z +
Z p
//( )
2 1 3
( )
Z Z Z
= +
2 1 3
Z + Z +
Z
1 2 3
For the equivalent circuit from the output
A Z
v p
-
R +
Z
o p
V
- or
= o
=
V
i
V
o
p
A V
v i
R +
Z
o p
Z
Ro
Io
-A Zp vVi
+
-
+
Vo
-
Therefore, the amplifier gain is obtained,
A Z Z Z
= = - +
( )
2 1 3
v
R Z + Z + Z + Z Z +
Z
( ) ( )
1 2 3 2 1 3
A V
o
V
o
i

The loop gain,
A A Z Z
1 2
v
b = -
R Z + Z + Z + Z Z +
Z
( ) ( ) 1 2 3 2 1 3
o
If the impedance are all pure reactances, i.e.,
1 1 2 2 3 3 Z = jX , Z = jX and Z = jX
The loop gain becomes,
A A X X
1 2
v
jR X + X + X - X X +
X
( ) ( ) 1 2 3 2 1 3
o
b =
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
A AvX = v
A X
2
1
1
With imaginary part = 0, b = -
X +
X
1 3
X
For Unit Gain & 180o Phase-shift,
A A X v b = Þ =
1 2
1
X

Hartley Oscillator Colpitts Oscillator
R L1
L2
C
R
C1
C2
L
w = 1
1
w =
L L C = o ( )
o LC
T
g C m =
2
RC
1
C C C T +
1 2
C C
1 2
1 2 +
g L m =
1
RL
2

Colpitts Oscillator
R
C1
C2
L
Equivalent circuit
+
-
Vp
L
C2 R C1
gmVp
In the equivalent circuit, it is assumed that:
 Linear small signal model of transistor is used
 The transistor capacitances are neglected
 Input resistance of the transistor is large enough

At node 1,
( ) 1 1 V V i jwL p = +
where,
p i jwC V 1 2 =
2
L
node 1
I1
I2 I3
V1
C2 R C1
Þ V = V (1 -
w LC ) 1 p 2
Apply KCL at node 1, we have
j C V g V V m w w p p
2 + + + j CV =
Vp
0 1 1
1
R
+
-
gmVp
(1 ) 1 0 2 1
+ + - 2
æ + j C
ö çè
j C V g V V LC m w w w p p p
2 R
÷ø
= For Oscillator Vp must not be zero, therefore it enforces,
ö
1 [ ( ) ] 0
gm w w w
= - + + ÷ ÷ø
LC
+ - j C C LC C
1 2
3
1 2
2
2
æ
ç çè
R
R
I4

ö
1 [ ( ) ] 0
gm w w w
= - + + ÷ ÷ø
LC
+ - j C C LC C
1 2
2
2
æ
ç çè
R
R
Imaginary part = 0, we have
1 2
3
w = 1
o LC
T
Real part = 0, yields
g C m =
2
RC
1
C C C T +
1 2
C C
1 2
=

Frequency Stability
• The frequency stability of an oscillator is
defined as
o
ppm/ C
w
1 ×æ
ö çè
÷ø
w =
T
d
w w
o o d
• Use high stability capacitors, e.g. silver
mica, polystyrene, or teflon capacitors and
low temperature coefficient inductors for
high stable oscillators.

Amplitude Stability
• In order to start the oscillation, the loop
gain is usually slightly greater than unity.
• LC oscillators in general do not require
amplitude stabilization circuits because of
the selectivity of the LC circuits.
• In RC oscillators, some non-linear devices,
e.g. NTC/PTC resistors, FET or zener
diodes can be used to stabilized the
amplitude

Wien-bridge oscillator with bulb stabilization
Vrms
irms
Operating
point
+
-
R
R
C
C
R2
Blub

Wien-bridge oscillator with diode
stabilization
Rf
-
+
R
R
C
R1
C
Vo

Twin-T Oscillator
-
+
low pass filter
high pass filter
Filter output
low pass region high pass region
fr f

Bistable Circuit
+
-
vo
v1
v+
Vth
+Vcc
-Vcc
vo
v1
-Vth
vo
+Vcc
-Vcc
v1
Vth
+Vcc
-Vth
-Vcc
vo
v1

A Square-wave Oscillator
-
+
vo
vc
vf
vc
vo
+vf
¡Ðvf
+vmax
¡Ðvmax

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