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EEE C364/INSTR C 364
Analog Electronics
Lecture 15
18-02-2012
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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 OscillatorHarley Oscillator
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LC - OSCILLATORS
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+
~Av Ro
Z1 Z2
Z3Zp
Vf 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
ZpAvVi
Ro
+
+
Vo
Io
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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 beve
(capacitor)
X1 and X2 must be of same type and X3 must be of opposite
type
2
1
31
1
XXA
XXXAA vv
With imaginary part = 0,
For Unit Gain & 180o Phase-shift,
1
21X
XAA v
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LC - OSCILLATORS
1
2
210 LLL where2
1
L
L
A
LCf
2
1
21
210
CC
CCC where
2
1
C
C
A
LCf
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Frequency Stability
The frequency stability of an oscillator isdefined as
Use high stability capacitors, e.g. silver mica,polystyrene, or
teflon capacitors and low
temperature coefficient inductors for highstable
oscillators.
Cppm/
T
o
oo d
d
1
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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
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low pass region high pass region
fr
f
Filter output
Twin-T Circuit
High-pass filter
Low-pass filter
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low pass region high pass region
fr
f
Filter output
High-pass filter
Low-pass filter
Twin-T Oscillator
RCfr
2
1
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TWIN-T OSCILLATOR
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CRYSTAL - OSCILLATORS
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Quartz crystal equivalent circuit
sp
sp
eq
p
s
s
pssp
S
pSp
CC
CC
LCf
LC
f
CLCCCs
LCs
sCsCsLsCsZ
eq
2
Cwhere2
1
2
1
/2
/11
/1/1
1)(
r,neglecting
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Quartz crystal equivalent circuit
sp
sp
eq
p
s
s
pssp
S
pSp
CC
CC
LCf
LCf
CLCCCs
LCs
sCsCsLsCsZ
eq
2
Cwhere2
1
21
/2
/11
/1/1
1)(
Crystal impedance versus frequency
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QUARTZ CRYSTAL OSCILLATOR
SpS CCC
LC
f
21
210
CC
CC||C where
2
1
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MULTIVIBRATORS-Bistable
sa tsa tLT
sa tsa tUT
VRR
RVV
VRR
RVV
21
1
21
1
