ref:06103104hknee3110 oscillator1 lecture 3 oscillator introduction of oscillator linear oscillator...
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Ref:06103104HKN EE3110 Oscillator 1
Lecture 3 Oscillator
• Introduction of Oscillator
• Linear Oscillator– Wien Bridge Oscillator– RC Phase-Shift Oscillator– LC Oscillator
• Stability
Ref:06103104HKN EE3110 Oscillator 2
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
Ref:06103104HKN EE3110 Oscillator 3
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.
Ref:06103104HKN EE3110 Oscillator 4
Linear Oscillators
1. Wien Bridge Oscillators
2. RC Phase-Shift Oscillators
3. LC Oscillators
4. Stability
Ref:06103104HKN EE3110 Oscillator 5
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
+
+Amplifier (A)
Frequency-SelectiveFeedback Network ()
Vf
Vs VoV
PositiveFeedback
Ref:06103104HKN EE3110 Oscillator 6
Basic Linear Oscillator
+
+
SelectiveNetwork(f)
Vf
Vs VoV
A(f)
)( fso VVAAVV and of VV
A
A
V
V
s
o
1
If Vs = 0, the only way that Vo can be nonzero is that loop gain A=1 which implies that
0
1||
A
A (Barkhausen Criterion)
Ref:06103104HKN EE3110 Oscillator 7
Wien Bridge OscillatorFrequency Selection NetworkLet
11
1
CX C
and
111 CjXRZ 2
2
1
CX C
22
22
1
222
11
C
C
C jXR
XjR
jXRZ
Therefore, the feedback factor,
)/()(
)/(
222211
2222
21
2
CCC
CC
i
o
jXRXjRjXR
jXRXjR
ZZ
Z
V
V
222211
22
))(( CCC
C
XjRjXRjXR
XjR
Vi Vo
R1 C1
R2C2
Z1
Z2
Ref:06103104HKN EE3110 Oscillator 8
can be rewritten as:
)( 2121221221
22
CCCCC
C
XXRRjXRXRXR
XR
For Barkhausen Criterion, imaginary part = 0, i.e.,
02121 CC XXRR
Supposing,
R1=R2=R and XC1= XC2=XC,
2121
2121
/1
11or
CCRR
CCRR
)(3 22CC
C
XRjRX
RX
0.2
0.22
0.24
0.26
0.28
0.3
0.32
0.34
Fee
dbac
k fa
ctor
-1
-0.5
0
0.5
1
Phas
e
Frequency
=1/3
Phase=0
f(R=Xc)
Ref:06103104HKN EE3110 Oscillator 9
Example
Rf
+
R
R
C
CZ1
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
131R
RAA f
vv
21
R
R fTherefore, Wien Bridge Oscillator
Ref:06103104HKN EE3110 Oscillator 10
RC Phase-Shift Oscillator
+
Rf
R1
R R R
C C C
Using an inverting amplifier The additional 180o phase shift is provided by an RC
phase-shift network
Ref:06103104HKN EE3110 Oscillator 11
Applying KVL to the phase-shift network, we have
R R R
C C CV1 Vo
I1 I2 I3Solve for I3, we get
)2(0
)2( 0
)(
32
321
211
C
C
C
jXRIRI
RIjXRIRI
RIjXRIV
C
C
C
C
C
jXRR
RjXRR
RjXRR
jXRR
VRjXR
I
20
2
000
02
3
1
)2(])2)[(( 222
21
3CCC jXRRRjXRjXR
RVI
Or
Ref:06103104HKN EE3110 Oscillator 12
The output voltage,
)2(])2)[(( 222
31
3CCC
o jXRRRjXRjXR
RVRIV
Hence the transfer function of the phase-shift network is given by,
)6()5( 2323
3
1 CCC
o
XRXjRXR
R
V
V
For 180o phase shift, the imaginary part = 0, i.e.,
RC
R
XXRX CCC
6
1
6X
(Rejected) 0or 0622
C
23
and,
29
1
Note: The –ve sign mean the phase inversion from the voltage
Ref:06103104HKN EE3110 Oscillator 13
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 an addition shift of 180o
Two well-known Oscillators:• Colpitts Oscillator• Harley Oscillator
Ref:06103104HKN EE3110 Oscillator 14
+
~Av Ro
Z1 Z2
Z3
Zp
Vf Vo
321
312
312
)(
)//(
ZZZ
ZZZ
ZZZZ p
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
Zp AvVi
Ro
+
+
Vo
Io
Ref:06103104HKN EE3110 Oscillator 15
The loop gain,
)()( 312321
21
ZZZZZZR
ZZAA
o
v
If the impedance are all pure reactances, i.e.,
332211 and , jXZjXZjXZ
The loop gain becomes,)()( 312321
21
XXXXXXjR
XXAA
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
31
1
X
XA
XX
XAA vv
With imaginary part = 0,
For Unit Gain & 180o Phase-shift,1
2 1X
XAA v
Ref:06103104HKN EE3110 Oscillator 16
R L1
L2
C
RC1
C2
L
Hartley Oscillator Colpitts Oscillator
T
oLC
1
1
2
RC
Cgm
21
21
CC
CCCT
CLLo
)(
1
21
2
1
RL
Lgm
Ref:06103104HKN EE3110 Oscillator 17
Colpitts Oscillator
RC1
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
gmVR C1C2
L
Ref:06103104HKN EE3110 Oscillator 18
)(11 LjiVV At node 1,
where,
VCji 21
)1( 22
1 LCVV
Apply KCL at node 1, we have
0111
2 VCjR
VVgVCj m
01
)1( 122
2
Cj
RLCVVgVCj m
0)(1
213
212
2
CLCCCj
R
LC
Rgm
For Oscillator V must not be zero, therefore it enforces,
+
V
gmVR C1C2
Lnode 1
I1
I2I3
I4
V
Ref:06103104HKN EE3110 Oscillator 19
Imaginary part = 0, we have
0)(1
213
212
2
CLCCCj
R
LC
Rgm
T
oLC
1
1
2
RC
Cgm
21
21
CC
CCCT
Real part = 0, yields
Ref:06103104HKN EE3110 Oscillator 20
Frequency Stability
• 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.
Cppm/ T
o
oo d
d
1
Ref:06103104HKN EE3110 Oscillator 21
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
Ref:06103104HKN EE3110 Oscillator 22
Wien-bridge oscillator with bulb stabilization
Vrms
irms
Operating point
+
R
R
C
C
R2
Blub
Ref:06103104HKN EE3110 Oscillator 23
Wien-bridge oscillator with diode stabilization
Rf
+
R
R
C
C
R1
Vo
Ref:06103104HKN EE3110 Oscillator 24
Twin-T Oscillator
+
low pass filter
high pass filter
low pass region high pass region
fr f
Filter output
Ref:06103104HKN EE3110 Oscillator 25
Bistable Circuit
+
vo
v1
v+
Vth
+Vcc
-Vcc
vo
v1
-Vth
+Vcc
-Vcc
vo
v1Vth
+Vcc
-Vcc
vo
v1-Vth
Ref:06103104HKN EE3110 Oscillator 26
A Square-wave Oscillator
+
vo
vc
vf
vc
vo
+vf
¡Ðvf
+vmax
¡Ðvmax