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Chapter 12 Signal generators and
waveform-shaping circuits
Introduction
12.1 Basic principles of sinusoidal oscillators
12.2 RC oscillator circuits
12.3 LC and crystal oscillators
12.4 Bistable Multivibrators
12.5 Generation of a standardized pulse-The
monostable multivibrator
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Introduction
(1)linear oscillators:
employs a positive-feedback loop consisting of an
amplifier and an RC or LC frequency-selective
network. (Section 13.1-3)
The two
different
approaches
(2)nonlinear oscillators or function
generators:
• The bistable multivibrator(Section 13.4)
• the astable multivibrator (Section 13.5)
• the monostable multivibrator(Section 13.6)
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The basic structure of sinusoidal
oscillators
Amplifier circuit：realize the energy control
The basic
Frequency-selective network：oscillator
frequency is determined
structure
Positive feedback loop：
xi  x f
amplitude control ：implementation of the
nonlinear amplitude-stabilization mechanism
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Basic Principles of Sinusoidal
Oscillator

The oscillator feedback loop

The basic structure of a sinusoidal oscillator.

A positive-feedback loop is formed by an
amplifier and a frequency-selective network.
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Basic Principles of Sinusoidal
Oscillator


Feedback signal xf is summed with a
positive sign
The gain-with-feedback is
A( s）
Af ( s) 
1  A( s)  ( s)

The oscillation criterion: Barkhausen
criterion.
L( j0 )  A( j0 )  ( j0 )  1
 A     2n
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Basic Principles of Sinusoidal
Oscillator

Nonlinear amplitude control



To ensure that oscillations will start, the Aβ is
slightly greater than unity.
As the power supply is turned on, oscillation
will grown in amplitude.
When the amplitude reaches the desired level,
the nonlinear network comes into action and
cause the Aβ to exactly unity.
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The implementation of the nonlinear
amplitude-stabilization mechanism


The first approach makes use of a limiter
circuit
The other mechanism for amplitude control
utilizes an element whose resistance can
be controlled by the amplitude of the
output sinusoid.
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A Popular Limiter Circuit for Amplitude
Control
When vi is close to zero:
D1 , D2is off, vo  
Rf
R1
vI
R3
R2
vA  V
 vo
R2  R3
R2  R3
R5
R4
vB  V
 vo
R4  R5
R4  R5
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A Popular Limiter Circuit for Amplitude
Control
When vi goes positive,D1 is on, D2 is off

R3
R3 
L  V
 VD  1 

R2
R2 

on the contrary:

R4
R4 
L  V
 VD  1 

R5
R
5 

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A Popular Limiter Circuit for Amplitude
Control
 R3 
R3
L  V
 VD 1  
R2
 R2 
 R4 
R4
L  V
 VD 1  
R5
 R5 
Transfer characteristic of the limiter circuit;
When Rf is removed, the limiter turns into a comparator with the
characteristic shown.
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Oscillator Circuits



Op Amp-RC Oscillator Circuits
 The Wien-Bridge Oscillator
 The phase-Shift Oscillator
LC-Tuned Oscillator
 Colpitts oscillator
 Hareley oscillator
Crystal Oscillator
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The Wien-Bridge Oscillator
A Wien-bridge oscillator without amplitude stabilization.
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Analysis of frequency-selective
network for Wien-bridge oscillator
(b) Low frequency: 1/wc>>R
(c) high frequency: 1/wc<<R
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The Wien-Bridge Oscillator

The loop gain transfer function
1  R2 R1
L( s ) 
3  sCR  1 sCR

Oscillating frequency
0  1 RC

To obtain sustained oscillation
R2
R1
2
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The Wien-Bridge Oscillator
A Wien-bridge oscillator
with a limiter used for
amplitude control.
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The Phase-Shift Oscillator
The circuit consists of a negative-gain amplifier and three-section RC ladder
network.
Oscillating frequency is the one that the phase shift of the RC network is
1800
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The Phase-Shift Oscillator
A practical phase-shift oscillator with a limiter for amplitude stabilization.
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The LC-Tuned oscillator
Colpitts Oscillator
A parallel LC resonator
connected between collector and
base.
Feedback is achieved by way of
a capacitive divider
Oscillating frequency is
determined by the resonance
frequency.
0  1
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C1C2
L(
)
C1  C2
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The LC-Tuned oscillator
Hartley Oscillator
A parallel LC resonator
connected between collector and
base.
Feedback is achieved by way of
an inductive divider.
Oscillating frequency is
determined by the resonance
frequency.
0  1
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C1C2
L(
)
C1  C2
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Crystal Oscillators
A piezoelectric crystal. (a) Circuit symbol. (b) Equivalent circuit.
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Crystal Oscillators
Crystal reactance versus
frequency (neglecting the small
resistance r, ).
A series resonance at
s  1
LCs
A parallel resonance at
p  1
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L(
Cs C p
Cs  C p
)
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Homework:

June 12th, 2008
12.13;12.14
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Bistable Circuit -three basic factors



The output signal only has two states: positive
saturation(L+) and negative saturation(L-).
The circuit can remain in either state indefinitely
and move to the other state only when
appropriate triggered.(threshold voltage)
The direction of one stage moving to the other
stage.
A positive feedback loop capable of bistable
operation.
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Bistable Circuit
The bistable circuit (positive
feedback loop)
The negative input terminal of the op
amp connected to an input signal vI.
R1
v  vo
 vo 
R1  R2
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Bistable Circuit
The transfer characteristic of
the circuit in (a) for increasing vI.
Positive saturation L+ and
negative saturation L-
VTH  L 
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Bistable Circuit
The transfer characteristic
for decreasing vI.
VTL  L 
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Bistable Circuit
The complete transfer characteristics.
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A Bistable Circuit with Noninverting
Transfer Characteristics
R2
R1
v  v I
 vo
R1  R2
R1  R2
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A Bistable Circuit with Noninverting
Transfer Characteristics
The transfer characteristic is
noninverting.
VTH   L（
 R1 R2）
VTL   L（
 R1 R2）
  R1 R2
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Application of Bistable Circuit as a
Comparator





Comparator is an analog-circuit building block
used in a variety applications.
To detect the level of an input signal relative to
a preset threshold value.
To design A/D converter.
Include single threshold value and two
threshold values.
Hysteresis comparator can reject the
interference.
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Application of Bistable Circuit as a
Comparator
Block diagram representation and transfer characteristic for a
comparator having a reference, or threshold, voltage VR.
Comparator characteristic with hysteresis.
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Application of Bistable Circuit as a
Comparator
Illustrating the use of
hysteresis in the
comparator
characteristics as a
means of rejecting
interference.
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Making the Output Level More
Precise
For this circuit L+ = VZ1 + VD and L– = –(VZ2 + VD), where VD is the forward
diode drop.
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Making the Output Level More Precise
For this circuit L+ = VZ + VD1 + VD2 and L– = –(VZ + VD3 + VD4).
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Generation of Square Waveforms
Connecting a bistable multivibrator with inverting transfer characteristics in a
feedback loop with an RC circuit results in a square-wave generator.
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Generation of Square Waveforms
The circuit obtained when the bistable multivibrator is
implemented with the positive feedback loop circuit.
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Waveforms at various nodes of
the circuit in (b).
This circuit is called an astable
multivibrator.
Time period T = T1+T2
v  L  ( L  L )e t /
v  L  ( L  L )e t /
T1  RC ln
1  （ L L )
1 
T2  RC ln
1  （L L )
1 
1 
T  2RC ln
1 
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Generation of Triangle Waveforms
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Generation of Triangle Waveforms
VTH  VTL L

T1
CR
VTH  VTL  L

T2
CR
V  VTL
T1  RC TH
L
VTH  VTL
T2  RC
 L
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Homework:

June 19th,2008
12.28; 12.32; 12.33
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