C H A P T E R 12
Signal Generators and WaveformShaping Circuits
Introduction
 In the design of electronic systems the need frequently arises
for signals having prescribed standard waveforms.
 There are 2 distinctly different approaches for the generation
of sinusoids, most commonly used for the standard waveforms.
 Employing a positive-feedback loop that consists an amplifier
and an RC or LC frequency-selective network. It generates sine
waves utilizing resonance phenomena, are known as linear
oscillators (circuits that generate square, triangular, pulse
waveforms are called non-linear oscillators or function
generators.)
 A sine wave is obtained by appropriate shaping a triangular
waveform.
2
The Oscillator Feedback Loop
 A basic structure of a sinusoidal oscillator consists of an amplifier and
a frequency-selective network connected in a positive-feedback loop.
 The condition for the feedback loop to provide sinusoidal oscillations
of frequency w0 is
Barkhausen Criterion:
 At w0 the phase of the loop gain should be zero.
 At w0 the magnitude of the loop gain should be unity.
Figure 12.1 The basic structure of a sinusoidal oscillator. A positive-feedback loop is formed by an amplifier and a frequency-selective network. In an
actual oscillator circuit, no input signal will be present; here an input signal xs is employed to help explain the principle of operation.
3
Φ = phase of βA
∆Φ 來自電路元件的變異
(dΦ/dw)越大，∆w0越小
Figure 12.2
Nonlinear Amplitude Control
 Suppose we make Aβ=1 at w=w0,
 If the temperature changes, Aβ <1 and oscillation will cease.
 If Aβ>1, the oscillations will grow in amplitude.
We therefore need a nonlinear circuit for gain control to force Aβ
to remain equal at the desired value of output amplitude.
 The function of gain-control mechanism is as follows:
 To ensure that oscillation will start, Aβ is designed greater
than unity.
 As the oscillation grow in amplitude and reaches the desired
level, the nonlinear network reduces the loop gain to exactly
unity (poles will be pulled back to jw axis.
 If the loop gain is reduced below unity, the amplitude will
diminish and the nonlinear network increases the loop gain to
exactly unity.
5
Figure 12.3 (a) A popular limiter circuit. (b) Transfer characteristic of the limiter circuit; L− and L+ are given by Eqs. (12.8) and (12.9),
c) When Rf is removed, the limiter turns into a comparator
with the characteristic shown.
respectively. (
Limiter Circuit for Amplitude Control
 A frequently employed limiter circuit is shown below.
 For small vI, D1/D2 off
 slope=


As vI continues to go positive,
vO goes negative. D1 on/D2 off

 As vI continues to go
negative, vO goes positive. D1
off/D2 on 
7
The Wien-Bridge Oscillator Circuits
 One of the simplest oscillator is based on the Wein bridge.
 For L=1, w0= (RC)-1. R2/R1=2.
 To ensure the oscillations will
start, R2/R1=2 + δ
Figure 12.4 A Wien-bridge oscillator without amplitude stabilization.
8
The Wien-Bridge Oscillator with A Limiter
 The amplitude of oscillation can be determined and stabilized using a
nonlinear control network.
The positive output peak can be
calculated by setting vb=v1+VD2
and writing the node equation at
node b while neglecting the
current through D2.
Figure 12.5 A Wien-bridge oscillator with a limiter used for amplitude control.
9
Figure 12.6 A Wien-bridge oscillator with
an alternative method for amplitude stabilization.
The Phase Shifter Oscillator
 The phase-shifter consists of a negative gain amplifier (-K) with a
third order RC ladder network in the feedback.
 The circuit will oscillate at the frequency for which the phase shift of
the RC network is 180o. Only at the frequency will the total phase shift
around the loop be 0o or 360o.
 The minimum number of RC sections is 3 because it is capable of
producing a 180o phase shift at a finite frequency.
11
The Phase Shifter Oscillator with a Limiter
 To start oscillations, Rf has to be made slightly greater than the
minimum required value. (Practice exercise 12.5 and 12.6)
Figure 12.8 A practical phase-shift oscillator with a limiter for amplitude stabilization.
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(jωCR)
13
The Quadrature Oscillator
 The quadrature oscillator is another type of phase-shift oscillator, but
the three RC sections are configured so that each section contributes 90°
of phase shift. The outputs are sine and cosine (quadrature) because
there is a 90° phase shift between op amp outputs.
Rf is made equal to 2R,
and thus –Rf cancels
2R.
Figure 12.9 (a) A quadrature-oscillator circuit. (b) Equivalent circuit at the input of op amp 2.
14
Negative Impedance Converter
 The negative impedance converter (NIC) is a configuration of an
operational amplifier which acts as a negative load.
source: excerpted from wikipedia
15
The Active-Filter-Tuned Oscillator
 The block diagram of the active-filter-tuned oscillator is shown below.
 Assume the oscillations have already started. The output of the
bandpass filter will be a sine wave whose frequency is equal to the center
frequency of the filter.
 The sine-wave signal is fed to the limiter and then produces a square
wave.
Figure 12.10 Block diagram of the active-filter-tuned oscillator.
Microelectronic Circuits, International Sixth Edition
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Figure 12.11 A practical implementation of the active-filter-tuned oscillator.
Microelectronic Circuits, International Sixth Edition
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LC and crystal Oscillator
For higher freq. (> 1MHz)
(a)容串
wo 
(b)感串
wo 
1
C1C 2
L(
)
C1  C 2
1
( L1  L 2)C
Figure 12.12 Two commonly used configurations of LC-tuned oscillators:
(a) Colpitts and (b) Hartley.
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Equivalent circuit of the Colpitts oscillator
Node equation at C
wo 
1
C1C 2
L(
)
C1  C 2
Figure 12.13 Equivalent circuit of the Colpitts oscillator of Fig. 12.12(a). To simplify the analysis, C and r are neglected. We can consider C to be
part of C2, and we can include ro in R.
19
Figure 12.14
Complete circuit for a Colpitts oscillator.
通常L很大, Cs小 , Cs <<Cp
A piezoelectric crystal. (a) Circuit symbol. (b) Equivalent circuit. (c) Crystal reactance versus
Figure 12.15
frequency [note that, neglecting the small resistance r, Zcrystal = jX()].
21
Crystal oscillator = L 串 Cs
C1
C2
wo 
1

CsCp
)
L(
Cs  Cp
1
L (Cs )
 Cs  Cp
Figure 12.16 A Pierce crystal oscillator utilizing a CMOS inverter as an amplifier.
22
Bistable Multivibrator
 Another type of waveform generating circuits is the nonlinear oscillators
or function generators which uses multivibrators.
 A bistable multivibrator has 2 stable states. The circuit can remain in
either state indefinitely and changes to the other one only when triggered.
Metastable state: v+=0 and vO=0. The
circuit cannot exist in the mestastable
state for any length of time since any
disturbance causes it to switch to
either stable state.
Figure 12.17 A positive-feedback loop capable of bistable operation.
Figure 12.18 A physical analogy for the operation of the bistable circuit. The ball cannot remain at the top of the hill for any length
of time (a state of unstable equilibrium or metastability); the inevitably present disturbance will cause the ball to fall to one side or
the other, where it can remain indefinitely (the two stable states).
23
Schmitt trigger
Microelectronic Circuits, International Sixth Edition
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Bistable Circuit with Inverting
Transfer Characteristics
 Assume that vO is at one of its 2 possible levels, say L+, and thus
v+=βL+.
 As vI increases from 0 and then exceeds βL+, a negative voltage
developes between input terminals of the op amp.
 This voltage is amplified and vO goes negative.
 The voltage divider causes v+ to go negative, increasing the net
negative input and keeping the regenerative process going.
 This process culminates in the op amp saturating, that is, vO=L-.
Trigger signal
The circuit is said to be
inverting.
Schmitt trigger
25
Bistable Circuit with Noninverting
Transfer Characteristics
 A bistable circuit implementing the noninverting transfer characteristics.
The circuit is said to be
noninverting.
Schmitt trigger
26
Figure 12.21 (a) Block diagram representation and transfer characteristic for a comparator having a reference, or threshold, voltage VR.
(b)
Comparator characteristic with hysteresis.
Microelectronic Circuits, International Sixth Edition
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Application of the Bistable Circuit
as a Comparator
 To design a circuit that detects and counts the zero crossings of an
arbitrary waveform, a comparator whose threshold is set to 0 can be
used. The comparator provides a step change at its output every time
zero crossing occurs.
Figure 12.22 Illustrating the use of hysteresis in the comparator characteristics as a means of rejecting interference.
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Bistable Circuit with More Precise
Output Level
 Limiter circuits are used to obtain more precise output levels for the
bistable circuit.
L+ = VZ1 + VD and L– = –(VZ2 + VD),
where VD is the forward diode drop.
L+ = VZ + VD1 + VD2 and L– = –(VZ
+ VD3 + VD4).
29
Microelectronic Circuits, International Sixth Edition
Sedra/Smith
Copyright © 2011 by Oxford University Press, Inc.
Operation of the Astable Multivibrator (1)
 Connecting a bistable multivibrator with inverting transfer
characteristics in a feedback loop with an RC circuit results in a squarewave generator.
Figure 12.24 (a) Connecting a bistable multivibrator with inverting transfer characteristics in a feedback loop with an RC circuit results in a
square-wave generator. (b) The circuit obtained when the bistable multivibrator is implemented with the circuit of Fig. 12.19(a). (c) Waveforms
at various nodes of the circuit in (b). This circuit is called an astable multivibrator.
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Operation of the Astable Multivibrator (2)
 The circuit for astable multivibrator.
Figure 12.24 (a) Connecting a bistable multivibrator with inverting transfer characteristics in a feedback loop with an RC circuit results in a
square-wave generator. (b) The circuit obtained when the bistable multivibrator is implemented with the circuit of Fig. 12.19(a). (c) Waveforms
at various nodes of the circuit in (b). This circuit is called an astable multivibrator.
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Generation of Triangular Waveforms
 Triangular waveforms can be obtained by replacing the low-pass RC
circuit with an integrator. Since the integrator is inverting, the inverting
characteristics of the bistable circuit is required.
Figure 12.25 A general scheme for generating triangular and square waveforms.
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Generation of a Standard Pulse (1)
 In the stable state, VA=L+ (why?), VB=VD1, VC=βL+ (D2: ON and
R4>>R1). When a negative-going step applies at the trigger input:
 D2 conducts heavily and pulls node C down (lower than VB).
 The output of the op amp switch to L- and cause VC to go toward βL-.
 D2 OFF and isolates the circuit from changes at the trigger input.
 D1 OFF and C1 begins to discharge toward L-.
 When VB < VC, the output of the op amp switch to L+.
Figure 12.26 (a) An op-amp monostable circuit. (b) Signal waveforms in the circuit of (a).
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Generation of a Standard Pulse (2)
Figure 12.26 (a) An op-amp monostable circuit. (b) Signal waveforms in the circuit of (a).
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The 555 Circuit
 Commercially available integrated-circuit package such as 555 timer
exists that contain the bulk of the circuitry needed to implement
monostable and astable multivibrator.
2/3 VCC
1/3 VCC
Figure 12.27 A block diagram representation of the internal circuit of the 555 integrated-circuit timer.
36
A Monostable Multivibrator
Using the 555 IC (1)
 In the stable state the flip-flop will be in the reset state (why?). As
trigger goes below VTL, output of comparator 2 goes high and
 Output of flip-flop goes high and Q1 OFF.
 Capacitor C begins to charge toward Vcc.
 When VC exceeds VTH, output of flip-flop goes low and Q1 ON.
 Q1 rapidly discharges C and VC go to 0V.
37
A Monostable Multivibrator
Using the 555 IC (2)
Figure 12.28 (a) The 555 timer connected to implement a monostable multivibrator. (b) Waveforms of the circuit in (a).
38
S-R flip-flop
R
S
Qn
0
0
Qn-1
0
1
1
1
0
0
Fig.12.28 說明
timing
t=0
Trig=
0
Trig
=1
t= T
(Vc=Vth)
Q’=1,
Vc=0 soon,
steady
state
C1 (R) 0
0
0
1
0
C2 (S) 0
1
0
0
0
Q (Vo) 0
1
1
0
0
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An Astable Multivibrator
Using the 555 IC (1)
 Assume that initially C is discharged and the flip-flop is set (It is fine
to start from reset state). VO is high and Q1 is OFF and then
 VC charges through RA and RB toward Vcc. When it exceeds VTH,
output of comparator 1 is high and VO is low (Q1 is ON).
 VC begins to discharge through RB, when it is below VTL, output of
comparator 2 is high and VO is high.
Figure 12.29 (a) The 555 timer connected to implement an astable multivibrator. (b) Waveforms of the circuit in (a).
40
An Astable Multivibrator
Using the 555 IC (2)
Figure 12.29 (a) The 555 timer connected to implement an astable multivibrator. (b) Waveforms of the circuit in (a).
41
Fig.12.29 說明
timing Vc=
VTL
Vc Vc=
up VTH
Q’=1, Vc=
Vc
VTL
disch
argin
g
Vc
Charging
TH
Q’
0
0
1
1
0
0
Q (Vo)
1
1
0
0
1
1
C1 (R)
0
0
1
0
0
0
C2 (S)
1
0
0
0
1
0
Vc=
VTH
42
Figure 12.30 Using a nonlinear (sinusoidal) transfer characteristic to shape a triangular waveform into a sinusoid.
Microelectronic Circuits, International Sixth Edition
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Copyright © 2011 by Oxford University Press, Inc.
Nonlinear Waveform-Shaping Circuits
The Breakpoint Method
 Diodes or transistors can be combined with resistors to synthesize
network having arbitrary nonlinear transfer characteristics which can
be used in waveform shaping.
 The breakpoint method.
Figure 12.31 (a) A three-segment sine-wave shaper. (b) The input triangular waveform and the output approximately sinusoidal waveform.
44
Nonlinear Waveform-Shaping Circuits
The Nonlinear-Amplification Method
 This nonlinear amplification method is based on feeding the
triangular wave to the input of an amplifier having a nonlinear transfer
characteristics that approximates the sine function.
Figure 12.32 A differential pair with an emitter degeneration resistance used to implement a triangular- wave to sine-wave converter. Operation of
the circuit can be graphically described by Fig. 12.30.
45
Precision Half-Wave Rectifier
Superdiode
 For instrumentation applications, if the signal to be rectified is 0.1V,
it is impossible to employ conventional rectifier circuit. Superdiode
shown below could solve this problem.
 Disadvantages of the superdioide
 When vI goes negative and vO=0, the entire magnitude of vI appears
in the op input terminal. The op will be damaged if it is not equipped
with over-voltage protection.
 When vI is negative, the op will be saturated and slows its operation.
Figure 12.33
46
Precision Half-Wave Rectifier
An Alternative Circuit
 An improved version of the precision half-wave rectifier.
The circuit operates in the following manner:
 vI>0, D2: ON (virtual ground appears) and output of op amp is clamped at one
diode drop below ground, D1: OFF  vO=0.
 vI<0, D1: ON (virtual ground appears), D2: OFF  vO= -vI (R2/R1).
 The feedback loop around the op amp remains closed at all times. Hence
the op amp remains in its linear operating region (no saturation occurs).
Figure 12.34 (a) An improved version of the precision half-wave rectifier: Diode D2 is included to keep the feedback loop closed around the op amp
47
during the off times of the rectifier diode D1, thus preventing the op amp from saturating. (b) The transfer characteristic for R2 = R1.
Measuring AC Voltages
 A circuit that could measure the AC voltage is shown below. It
consists of a half-wave rectifier and a first-order low pass filter.
 The DC component of V1 is (VP/π)(R2/R1).
The corner frequency of the low-pass filter should be chosen much
smaller than the lowest expected frequency wmin of the input sine wave
 (CR4)-1 << wmin. 只取DC
 V2 = - (VP/π)(R2/R1)(R4/R3).
Figure 12.35 A simple ac voltmeter consisting of a precision half-wave rectifier followed by a first-order low-pass filter.
48
Figure E12.28
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Precision Full-Wave Rectifier (1)
 The principle of full-wave rectifier.
Figure 12.36 Principle of full-wave rectification.
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Precision Full-Wave Rectifier (2)
 Precision full-wave rectifier based on the above conceptual circuit.
 VI>0, D2:ON, VI=VO, no
current through R1/R2, V- of
A1= VI, D1:OFF.
 VI<0, V- of A1 is negative,
D1 ON. VO= -VI (R2/R1).
D2:OFF.
Figure 12.37 (a) Precision full-wave rectifier based on the conceptual circuit of Fig. 12.36. (b) Transfer characteristic of the circuit in (a).
51
Figure 12.38 Use of the diode bridge in the design of an ac voltmeter.
Precision Peak Rectifier
 Including the diode of the peak rectifier inside the negative-feedback
loop of an op amp results in a precision peak rectifier.
Figure 12.39 A precision peak rectifier obtained by placing the diode in the feedback loop of an op amp.
 A buffered precision peak
detector shown in the right
circuit can hold the value of the
peak for a long time.
Figure 12.40 A buffered precision peak rectifier.
53
Figure 12.41 A precision clamping circuit.
Microelectronic Circuits, International Sixth Edition
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Copyright © 2011 by Oxford University Press, Inc.