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Chapter 32
Oscillators
2
Basics of Feedback
• Block diagram of feedback amplifier
• Forward gain, A
• Feedback, B
• Summing junction, ∑
• Useful for oscillators
∑ A
B
vin
vF
vout
+
-
3
Basics of Feedback• Op-amps
– Inverting & non-inverting– Negative feedback 180°out of phase w/input– High input impedance– Low output impedance– Wide bandwidth– Stable operation
4
Basics of Feedback
• Oscillators– Positive feedback– In-phase with input– Unstable
5
Basics of Feedback• Block diagram analysis
∑ A
B
vin vout
( )
1
e in f
out in f
f out
out
in
v v v
v A v v
v Bv
v A
v AB
= −
= −
=
=+
ve
vf
+
-
6
Basics of Feedback
• Inverting amplifier
∑ A
B
vin vout
ve
vf
+
-
( )
F
1
in
out
in
out
outf
finout
fine
11
1
1
R
RB
BBA
v
v
AB
A
v
v
Bvv
vvAv
vvv
=
≈+
−=
+−=
=
−−=
−−=
7
Relaxation Oscillator• Square wave generator
• Composed of– Schmitt trigger comparator– Positive feedback– RC circuit to determine period
8
Relaxation Oscillator
• Schmitt Trigger– R1 and R2 form a voltage divider
– Portion of output applied at + input– Hysteresis: output dependent on input and
previous value of input
9
Relaxation Oscillator
• Schmitt Trigger– Hysteresis: upper and lower trip points– Can use a voltage follower for adjustable trip
points
10
Relaxation Oscillator• Schmitt trigger
11
Relaxation Oscillator• Schmitt Trigger
Relaxation Oscillator
12
Relaxation Oscillator• R1 and R2 voltage divider
• Capacitor charges through RF
• VC < +VSAT then C charges toward +VSAT
• VC > –VSAT then C charges toward –VSAT
( )2
1 2REF SAT
RV V
R R= ±
+
13
Relaxation Oscillator• Schmitt Trigger Relaxation Oscillator
Equations
( )( )2
1
( ) 1
22 ln 1
tRC
F
C F O
F
R C
v t V V e
RT R C
R
τ−
=
= − −
⎛ ⎞= +⎜ ⎟
⎝ ⎠
14
Wien Bridge Oscillator• For a sinusoidal oscillator output
– Closed loop gain ≥ 1– Phase shift between input and output = 0° at
frequency of oscillation
• With these conditions a circuit– Oscillates with no external input
• Positive feedback = regenerative feedback
15
Wien Bridge Oscillator• Regenerative oscillator
– Initial input is small noise voltage– Builds to steady state oscillation
• Wien Bridge oscillator– Positive feedback, RC network branch– Resistor branch establish amplifier gain
16
Wien Bridge Oscillator• Circuit
17
Wien Bridge Oscillator• Equations
0
1 2 1 2
2 1
1 1 2 2 2 1
1 2 1 2
0
1Output frequency
2
if and then
1 1and
2 3
fR R C C
R CB
RC R C R C
R R C C
f BRC
π
π
= =
=+ +
= =
= =
18
Wien Bridge Oscillator
• Another form of Wien Bridge
19
Wien Bridge Oscillator• For a closed-loop gain, AB = 1
– Op-amp gain ≥ 3
• Improved circuit– Separate RF into 1 variable and 1 fixed
resistor– Variable: minimize distortion– Zener Diodes: limit range of output voltage
20
Phase-Shift Oscillator• Three-section R-C network
– ≈ 60° per section– Negative FB = 180°– 180° + (60° + 60° + 60°) = 360° = Positive FB
0
1Output frequency
2 629 Required voltage ain
fRC
A gπ
=
=
21
Phase-Shift Oscillator• Circuit
22
LC Oscillators• LC circuits can produce oscillations
• Used for– Test and measurement circuits– RF circuits
23
LC Oscillators• Named after pioneer engineers
– Colpitts– Hartley– Clapp– Armstrong
24
LC Oscillators• Colpitts oscillator
– fs = series resonance
– fp = parallel resonance
– L-C network → 180° phase shift at fp
25
LC Oscillators
______
-
+
______
RF
Rin
+V
–V
vout
C2 C1
L
26
LC Oscillators• Equations
222
1 21 2
1 2
0
1 2
1 2
1Impedance: ( )
( ) 1
1Oscillator frequency:
2
s LCZ s
s LC Cs C C
C C
fC C
LC C
π
+=
⎛ ⎞+ +⎜ ⎟+⎝ ⎠
=
+
27
LC Oscillators
• Hartley oscillator– Similar to Colpitts– L and C’s interchanged
– Also have fs and fp
28
LC Oscillators
______
-
+
______
RF
Rin
+V
–V
vout
L1
C1
L2
( )( )
( )
21 2
21 2
0
1 2
1( )
1
1
2
sL s L CZ s
s L L C
fL L Cπ
+=
+ +
=+
29
Crystal Oscillators• Quartz crystals• Mechanical device• Higher frequencies (>1 MHz)• Stability• Accuracy• Reliability • Piezoelectric effect
30
Crystal Oscillators• Electrical model
– Both have parallel and series resonance
• Symbol– Quartz crystal– metal plates
C1 L1RF
C0
31
Crystal Oscillators• Impedance varies with
frequency• Square wave crystal
oscillator circuit• Choose C1 and C2
– Oscillation frequency between fs and fp
______
R2
R1
vout
C1
XTAL
C2
CMOS Inverter
R2
32
555 Timer• IC
– Internal circuit
33
555 Timer• Usage
– Monostable timing– Astable mode = relaxation oscillator– Trigger voltage– Control voltage– Threshold voltage– R-S flip-flop
34
555 Timer• Relaxation oscillator
NE555
______
1 5
vout3
4
VCC = +15 V
8
7
26
RA
RB
C 0.01 μF
( )( )( )
1
2
ln(2)
ln(2)
ln(2) 2
1
B
A B
A B
T R C
T R R C
T R R C
fT
= ∗
= ∗ +
= ∗ +
=
35
555 Timer• Monostable Circuit (one-shot)
• Trigger high → vout = low
• Trigger low → vout = highNE555
______
1 5
vout3
4
VCC = +15 V
8
7
26
RA
C
0.01 μF______
Trigger
36
Voltage Controlled Oscillator-VCO
• ∆fout ∆vin
LM566C
______
5
vout
14
VCC
6
7
81 nF
C1______
Voltage Input3
R1
Square wave
Triangle wave
Outputs
( )1 1
2.4 CC CO
CC
V Vf
RCV
−=
∝
∝