1. Oscillation: an effect that repeatedly and
regularly fluctuates about the mean value
Oscillator: circuit that produces oscillation
Characteristics: wave-shape, frequency,
amplitude, distortion, stability
•Ref:06103104HKN
•EE3110 Oscillator •1
2. 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.
•Ref:06103104HKN
•EE3110 Oscillator •2
4. •Ref:06103104HKN
•EE3110 Oscillator •4
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
+
+
Amplifier (A)
Frequency-Selective
Feedback Network ()
Vf
Vs Vo
V
Positive
Feedback
6. •Ref:06103104HKN
•EE3110 Oscillator •6
Frequency Selection Network
Let
1
1
1
C
XC
and
1
1
1 C
jX
R
Z
2
2
1
C
XC
2
2
2
2
1
2
2
2
1
1
C
C
C jX
R
X
jR
jX
R
Z
Therefore, the feedback factor,
)
/
(
)
(
)
/
(
2
2
2
2
1
1
2
2
2
2
2
1
2
C
C
C
C
C
i
o
jX
R
X
jR
jX
R
jX
R
X
jR
Z
Z
Z
V
V
2
2
2
2
1
1
2
2
)
)(
( C
C
C
C
X
jR
jX
R
jX
R
X
jR
Vi Vo
R1 C1
R2
C2
Z1
Z2
7. •Ref:06103104HKN
•EE3110 Oscillator •7
can be rewritten as:
)
( 2
1
2
1
2
2
1
2
2
1
2
2
C
C
C
C
C
C
X
X
R
R
j
X
R
X
R
X
R
X
R
For Barkhausen Criterion, imaginary part = 0, i.e.,
0
2
1
2
1
C
C X
X
R
R
Supposing,
R1=R2=R and XC1= XC2=XC,
2
1
2
1
2
1
2
1
/
1
1
1
or
C
C
R
R
C
C
R
R
)
(
3 2
2
C
C
C
X
R
j
RX
RX
0.2
0.22
0.24
0.26
0.28
0.3
0.32
0.34
Feedback
factor
-1
-0.5
0
0.5
1
Phase
Frequency
=1/3
Phase=0
f(R=Xc)
8. •Ref:06103104HKN
•EE3110 Oscillator •8
Rf
+
R
R
C
C
Z1
Z2
R1
Vo
By setting , we get
Imaginary part = 0 and
RC
1
3
1
Due to Barkhausen Criterion,
Loop gain Av=1
where
Av : Gain of the amplifier
1
1
3
1
R
R
A
A
f
v
v
2
1
R
Rf
Therefore, Wien Bridge Oscillator
10. •Ref:06103104HKN
•EE3110 Oscillator •10
R R R
C C C
V1 Vo
I1 I2 I3
Solve for I3, we get
)
2
(
0
)
2
(
0
)
(
3
2
3
2
1
2
1
1
C
C
C
jX
R
I
R
I
R
I
jX
R
I
R
I
R
I
jX
R
I
V
C
C
C
C
C
jX
R
R
R
jX
R
R
R
jX
R
R
jX
R
R
V
R
jX
R
I
2
0
2
0
0
0
0
2
3
1
)
2
(
]
)
2
)[(
( 2
2
2
2
1
3
C
C
C jX
R
R
R
jX
R
jX
R
R
V
I
Or
11. •Ref:06103104HKN
•EE3110 Oscillator •11
The output voltage,
)
2
(
]
)
2
)[(
( 2
2
2
3
1
3
C
C
C
o
jX
R
R
R
jX
R
jX
R
R
V
R
I
V
Hence the transfer function of the phase-shift network is given by,
)
6
(
)
5
( 2
3
2
3
3
1 C
C
C
o
X
R
X
j
RX
R
R
V
V
For 180o phase shift, the imaginary part = 0, i.e.,
RC
R
X
X
R
X C
C
C
6
1
6
X
(Rejected)
0
or
0
6
2
2
C
2
3
and,
29
1
Note: The –ve sign mean the
phase inversion from the
voltage
12. •Ref:06103104HKN
•EE3110 Oscillator •12
+
~
Av Ro
Z1 Z2
Z3
1
2
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
13. •Ref:06103104HKN
•EE3110 Oscillator •13
+
~
Av Ro
Z1 Z2
Z3
Zp
Vf Vo
3
2
1
3
1
2
3
1
2
)
(
)
//(
Z
Z
Z
Z
Z
Z
Z
Z
Z
Zp
For the equivalent circuit from the output
p
o
p
v
i
o
p
o
p
o
i
v
Z
R
Z
A
V
V
Z
V
Z
R
V
A
or
Therefore, the amplifier gain is obtained,
)
(
)
(
)
(
3
1
2
3
2
1
3
1
2
Z
Z
Z
Z
Z
Z
R
Z
Z
Z
A
V
V
A
o
v
i
o
o
o
f V
Z
Z
Z
V
V
3
1
1
Zp
AvVi
Ro
+
+
Vo
Io
14. •Ref:06103104HKN
•EE3110 Oscillator •14
The loop gain,
)
(
)
( 3
1
2
3
2
1
2
1
Z
Z
Z
Z
Z
Z
R
Z
Z
A
A
o
v
If the impedance are all pure reactances, i.e.,
3
3
2
2
1
1 and
, jX
Z
jX
Z
jX
Z
The loop gain becomes,
)
(
)
( 3
1
2
3
2
1
2
1
X
X
X
X
X
X
jR
X
X
A
A
o
v
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
3
1
1
X
X
A
X
X
X
A
A v
v
With imaginary part = 0,
For Unit Gain & 180o Phase-shift,
1
2
1
X
X
A
A v
15. •Ref:06103104HKN
•EE3110 Oscillator •15
R L1
L2
C
R
C1
C2
L
Hartley Oscillator Colpitts Oscillator
T
o
LC
1
1
2
RC
C
gm
2
1
2
1
C
C
C
C
CT
C
L
L
o
)
(
1
2
1
2
1
RL
L
gm
16. •Ref:06103104HKN
•EE3110 Oscillator •16
R
C1
C2
L
Equivalent circuit
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
+
V
gmV
R C1
C2
L
17. •Ref:06103104HKN
•EE3110 Oscillator •17
)
(
1
1 L
j
i
V
V
At node 1,
where,
V
C
j
i 2
1
)
1
( 2
2
1 LC
V
V
Apply KCL at node 1, we have
0
1
1
1
2
V
C
j
R
V
V
g
V
C
j m
0
1
)
1
( 1
2
2
2
C
j
R
LC
V
V
g
V
C
j m
0
)
(
1
2
1
3
2
1
2
2
C
LC
C
C
j
R
LC
R
gm
For Oscillator V must not be zero, therefore it enforces,
+
V
gmV
R C1
C2
L
node 1
I1
I2
I3
I4
V
18. •Ref:06103104HKN
•EE3110 Oscillator •18
Imaginary part = 0, we have
0
)
(
1
2
1
3
2
1
2
2
C
LC
C
C
j
R
LC
R
gm
T
o
LC
1
1
2
RC
C
gm
2
1
2
1
C
C
C
C
CT
Real part = 0, yields
19. The frequency stability of an oscillator is
defined as
Use high stability capacitors, e.g. silver
mica, polystyrene, or teflon capacitors and
low temperature coefficient inductors for
high stable oscillators.
•Ref:06103104HKN
•EE3110 Oscillator •19
C
ppm/
T
o
o
o d
d
1
20. 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
•Ref:06103104HKN
•EE3110 Oscillator •20
