Chapter 32
Oscillators
Basics of Feedback
• Block diagram of
feedback amplifier
v
• Forward gain, A
• Feedback, B
• Summing junction, ∑
• Useful for oscillators
+
in
∑
A
-
vout
vF
B
2
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
3
Basics of Feedback
• Oscillators
– Positive feedback
– In-phase with input
– Unstable
4
Basics of Feedback
• Block diagram analysis
v e  v in  v f
v o u t  A ( v in  v f )
v f  B vout
vout
v in

+
vin
∑
ve
A
-
vout
vf
B
A
1  AB
5
Basics of Feedback
v e   v in  v f
• Inverting amplifier
v out  A   v in  v f

v f  Bv out
+
vin
∑
ve
v out
A
-
vout
v in
v out
vf


v in
A
1  AB
1
1
B

1
B
A
B
B 
R1
RF
6
Relaxation Oscillator
• Square wave generator
• Composed of
– Schmitt trigger comparator
– Positive feedback
– RC circuit to determine period
7
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
8
Relaxation Oscillator
• Schmitt Trigger
– Hysteresis: upper and lower trip points
– Can use a voltage follower for adjustable trip
points
9
Relaxation Oscillator
• Schmitt trigger
10
Relaxation Oscillator
• Schmitt Trigger
Relaxation
Oscillator
11
Relaxation Oscillator
• R1 and R2 voltage divider
V REF 
R2
R1  R 2
  V SA T 
• Capacitor charges through RF
• VC < +VSAT then C charges toward +VSAT
• VC > –VSAT then C charges toward –VSAT
12
Relaxation Oscillator
• Schmitt Trigger Relaxation Oscillator
Equations
  RF C

vC (t )  V F  VO  1  e
 RtC


2 R2 
T  2 R F C ln  1 

R1 

13
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
14
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
15
Wien Bridge Oscillator
• Circuit
16
Wien Bridge Oscillator
• Equations
f0 
B 
1
2
 O utput frequency
R1 R 2 C 1 C 2
R 2 C1
R1 C 1  R 2 C 2  R 2 C 1
if R1  R 2 and C 1  C 2 then
f0 
1
2 R C
and B 
1
3
17
Wien Bridge
Oscillator
• Another form of
Wien Bridge
18
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
19
Phase-Shift Oscillator
• Three-section R-C network
– ≈ 60° per section
– Negative FB = 180°
– 180° + (60° + 60° + 60°) = 360° =
Positive FB
f0 
1
2
O utput frequency
6 RC
A  29 R equired voltage g ain
20
Phase-Shift Oscillator
• Circuit
21
LC Oscillators
• LC circuits can produce oscillations
• Used for
– Test and measurement circuits
– RF circuits
22
LC Oscillators
• Named after pioneer engineers
– Colpitts
– Hartley
– Clapp
– Armstrong
23
LC Oscillators
• Colpitts oscillator
– fs = series resonance
– fp = parallel resonance
– L-C network → 180° phase shift at fp
24
LC Oscillators
RF
Rin
__
_
__
_
L
+
C2
+V
vout
–V
C1
__
_
__
_
25
LC Oscillators
• Equations
1  s LC2
2
Im pedance: Z ( s ) 
2

s L C 1C 2 
s (C1  C 2 )  1 

C1  C 2 

1
O scillator frequency: f 0 
2
L
C 1C 2
C1  C 2
26
LC Oscillators
• Hartley oscillator
– Similar to Colpitts
– L and C’s interchanged
– Also have fs and fp
27
LC Oscillators
RF
Z (s) 
f0 

sL1 1  s L 2 C
1 s
2
2

 L1  L 2  C
+
Rin
___
__
_
1
2
 L1  L 2  C
+V
vout
–V
C1
L2
L1
___
__
_
28
Crystal Oscillators
•
•
•
•
•
•
•
Quartz crystals
Mechanical device
Higher frequencies (>1 MHz)
Stability
Accuracy
Reliability
Piezoelectric effect
29
Crystal Oscillators
• Electrical model
– Both have
parallel and series
resonance
RF
C1
L1
C0
• Symbol
– Quartz crystal
– metal plates
30
Crystal Oscillators
• Impedance varies with
frequency
• Square wave crystal
oscillator circuit
• Choose C1 and C2
R2
vout
CMOS Inverter
– Oscillation frequency
between fs and fp
R1
XTAL
C1
C2
___
__
_
31
555 Timer
• IC
– Internal
circuit
32
555 Timer
• Usage
– Monostable timing
– Astable mode = relaxation oscillator
– Trigger voltage
– Control voltage
– Threshold voltage
– R-S flip-flop
33
555 Timer
• Relaxation oscillator
T1  ln(2)   R B C 
VCC = +15 V
RA
T 2  ln(2)   R A  R B  C
T  ln(2)   R A  2 R B  C
f 
4
7
NE555
RB
2
6
1
T
8
3
1
C
vout
5
0.01 μF
34
___
__
_
555 Timer
• Monostable Circuit (one-shot)
• Trigger high → vout = low
R
• Trigger low → vout = high
VCC = +15 V
8
A
4
7
NE555
2
6
C
3
1
___
__
_
Trigger
vout
5
0.01 μF
35
___
__
_
Voltage Controlled OscillatorVCO
• ∆fout

∆vin
R1
VCC

Outputs
1 nF
Voltage Input
fO 
2.4  V C C  V C
R1C 1V C C

6
8
LM566C
5
7
C1
___
__
_
1
___
__
_
3
Square wave
4
Triangle wave
vout
36