Transcript Chapter32
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
ve vin v f
vout A(vin v f )
v f Bvout
vout
A
vin 1 AB
vin
+
∑
ve
A
-
vout
vf
B
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Basics of Feedback
ve vin vf
• Inverting amplifier
vout A vin vf
vf Bvout
+
vin
∑
ve
A
vf
B
vout
vout
A
vin
1 AB
vout
1
1
1
vin
B B
A
R
B 1
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
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Relaxation Oscillator
• R1 and R2 voltage divider
VREF
R2
VSAT
R1 R2
• Capacitor charges through RF
• VC < +VSAT then C charges toward +VSAT
• VC > –VSAT then C charges toward –VSAT
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Relaxation Oscillator
• Schmitt Trigger Relaxation Oscillator
Equations
RF C
vC (t ) VF VO 1 e
t
RC
2 R2
T 2 RF C ln 1
R1
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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
1
f0
Output frequency
2 R1 R2C1C2
R2C1
B
R1C1 R2C2 R2C1
if R1 R2 and C1 C2 then
1
1
f0
and B
2 RC
3
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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
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Phase-Shift Oscillator
• Three-section R-C network
– ≈ 60° per section
– Negative FB = 180°
– 180° + (60° + 60° + 60°) = 360° =
Positive FB
1
f0
Output frequency
2 6 RC
A 29 Required voltage gain
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Phase-Shift Oscillator
• Circuit
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LC Oscillators
• LC circuits can produce oscillations
• Used for
– Test and measurement circuits
– RF circuits
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LC Oscillators
• Named after pioneer engineers
– Colpitts
– Hartley
– Clapp
– Armstrong
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LC Oscillators
• Colpitts oscillator
– fs = series resonance
– fp = parallel resonance
– L-C network → 180° phase shift at fp
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LC Oscillators
RF
Rin
__
_
__
_
L
+
C2
+V
vout
–V
C1
__
_
__
_
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LC Oscillators
• Equations
1 s 2 LC2
Impedance: Z ( s)
s 2 LC1C2
s (C1 C2 ) 1
C1 C2
Oscillator frequency: f 0
1
C1C2
2 L
C1 C2
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LC Oscillators
• Hartley oscillator
– Similar to Colpitts
– L and C’s interchanged
– Also have fs and fp
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LC Oscillators
RF
Z (s)
f0
sL1 1 s 2 L2C
1 s 2 L1 L2 C
+
Rin
___
__
_
1
2
L1 L2 C
+V
vout
–V
C1
L2
L1
___
__
_
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Crystal Oscillators
•
•
•
•
•
•
•
Quartz crystals
Mechanical device
Higher frequencies (>1 MHz)
Stability
Accuracy
Reliability
Piezoelectric effect
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Crystal Oscillators
• Electrical model
– Both have
parallel and series
resonance
RF
C1
L1
C0
• Symbol
– Quartz crystal
– metal plates
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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
___
__
_
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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
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555 Timer
• Relaxation oscillator
T1 ln(2) RBC
VCC = +15 V
RA
T2 ln(2) RA RB C
T ln(2) RA 2 RB C
1
f
T
8
4
7
NE555
RB
2
6
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
Outputs
1 nF
Voltage Input
fO
2.4 VCC VC
R1C1VCC
VCC
6
8
LM566C
5
7
C1
___
__
_
1
___
__
_
3
Square wave
4
Triangle wave
vout
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