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12 - 1 Electronics(3), 2012 Prof. Tai-Haur Kuo Basic Principles of Sinusoidal Oscillators Linear oscillator Linear region of circuit : linear oscillation Nonlinear region of circuit : amplitudes stabilization Barkhausen criterion loop gain L(s) = β (s)A(s) characteristic equation 1-L(s) = 0 oscillation criterion L(j 0 = A(j 0 ) β(j 0 ) = 1 Amplifier A S X O X f X Frequency-selective network

# Basic Principles of Sinusoidal Oscillators

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Microsoft PowerPoint - ch12_20120910.pptxBasic Principles of Sinusoidal Oscillators Linear oscillator Linear region of circuit : linear oscillation Nonlinear region of circuit : amplitudes stabilization
Barkhausen criterion
loop gain L(s) = β (s)A(s) characteristic equation 1-L(s) = 0 oscillation criterion L(j0= A(j0) β(j0) = 1
Amplifier ASX OX
12 - 2 Electronics(3), 2012Prof. Tai-Haur Kuo
Basic Principles of Sinusoidal Oscillators (Cont.) at 0, the phase of the loop should be zero and the magnitude of the loop gain should be unity. Oscillation frequency 0 is determined solely by
A steep phase response results in a small for a given change in phase
0
12 - 3 Electronics(3), 2012Prof. Tai-Haur Kuo
Nonlinear Amplitude Control To sustain oscillation : βA>1 a.overdesign for βA variations b.oscillation will grow in amplitude poles are in the right half of the s-plane c.Nonlinear network reduces βA to 1 when the desired
amplitude is reached poles will be pulled to j-axis
12 - 4 Electronics(3), 2012Prof. Tai-Haur Kuo
Nonlinear Amplitude Control (Cont.) Limiter circuit for amplitude control linear region
54
) R R(1V
OPAMP-RC Oscillator Circuits Wien-bridge oscillator

_
ωRC 1ωRCj3
R R1
OPAMP-RC Oscillator Circuits (Cont.) Wien-bridge oscillator with a limiter
15V
OPAMP-RC Oscillator Circuits (Cont.)
Phase-Shift Oscillator Without amplitude stabilization
------- phase shift of the RC network is 180 degrees. Total phase shift around the loop is 0 or 360 degrees.
C
RRR
16nF
Quadrature Oscillator (Cont.) -------Break the loop at X, loop gain
oscillation frequency
90° phase difference between Vo1 and Vo2
222 X
Active-Filter Tuned Oscillator Block diagram
High-distortion v2
-
A General Form of LC-Tuned Oscillator Configuration
Many oscillator circuits fall into a general form shown below
Z1,Z2,Z3 capacitive or inductive
A General Form of LC-Tuned Oscillator Configuration (Cont.)
2
1
31
1
312
21
321
312321
21
332211
312321
21
13
13
31
A General Form of LC-Tuned Oscillator Configuration (Cont.)
With oscillation |T| = 1 and T = 0, 360, 720, … degree.
X1 & X2 must have the same sign if Av is positive X1 & X2 are L, X3 = -(X1 + X2) is C
or X1 & X2 are C, X3 = -(X1 + X2) is L Transistor oscillators 1.Collpitts oscillator
-- X1 & X2 are Cs, X3 is L 2.Hartley oscillator
-- X1 & X2 are Ls, X3 is C

LC Tuned Oscillators Two commonly used configurations 1.Collpitts (feedback is achieved by using a capacitive
divider) 2.Harley (feedback is achieved by using an inductive
divider) Configuration
1.Collpitts 2.Hartley
LC Tuned Oscillators (Cont.) Collpitts oscillator Equivalent circuit

πV
2 πsC V 2 O π 2V V (1 s LC )L
R 1CπGmV 2C
LC Tuned Oscillators (Cont.)
For oscillations to start, both the real and imaginary parts must be zero
Oscillation frequency
3 2 2 1 2 1 2 m
2 32
m 1 2 1 2
1SC V+g v+( +SC )(1+S LC )V=0 R LC 1S LC C +S ( )+S(C +C )+(g + )=0 R R
1 w LC(g + )+j W(C +C ) W LC C =0 R R
S=jw
LC Tuned Oscillators (Cont.) Gain
Oscillation amplitude 1.LC tuned oscillators are known as self – limiting
oscillators. (As oscillations grown in amplitude, transistor gain is reduced below its small – signal value)
2.Output voltage signal will be a sinusoid of high purity because of the filtering action of the LC tuned circuit
Hartley oscillator can be similarity analyzed
) c cRg (Actually,
Crystal oscillators Symbol of crystal
Circuit model of crystal
Crystal oscillators (Cont.) Reactance of a crystal assuming r = 0
(Crystal is high – Q device)

ωC 1jjωZ
C 1
C 1
L 1ω
LC 1ω
12 - 24 Electronics(3), 2012Prof. Tai-Haur Kuo
Crystal oscillators (Cont.) The crystal reactance is inductive over the narrow frequency band between ws and wp
Collpitts crystal oscillator Configuration
Crystal oscillators (Cont.) Equivalent circuit

LC
Crystal oscillators (Cont.)
uH~
Crystal oscillators (Cont.)
Since return ratio then X1 must be large for the loop gain to be greater than one.
X1 is very large when

2
2
1X +X +X =0 & X = X &X are inductive ωC
1 jZ =L//C= =1 1jω C+ ω C+ jω L ω L
1 1 1X = >0 ωL> ω>1 ωC LCωC+ ωL
v 1

Bistable Multivibrators Multivibrators bistabletwo stable states
(3 types) monostableone stable state astableno stable state
Bistable Has two stable states Can be obtained by connecting an amplifier in a
amplifier in a positive-feedback loop having a loop gain greater than unity. I.e. βA>1 where β=R1/(R1+R2)
12 - 29 Electronics(3), 2012Prof. Tai-Haur Kuo
Bistable Multivibrators (Cont.) Bistable circuit with clockwise hysteresis

-
-
Bistable Multivibrators (Cont.)

2
2
R Rv =v +v R +R R +R

-
-
Noninverting Bistable Circuit (Cont.) Comparator characteristics with hysteresis Can reject interference
t
THV
Generation of Square and Triangular Waveforms using Astable Multivibrators
Can be done by connecting a bistable multivibrator with a RC circuit in a feedback loop.
THVTLV
-L
Generation of Square and Triangular Waveforms using Astable Multivibrators (Cont.)

-
-
Generation of Square and Triangular Waveforms using Astable Multivibrators (Cont.)
During T1
During T2
β L Lβ
Generation of Triangular Waveforms
Generation of Triangular Waveforms (Cont.) During T1
During T2
TH TL 1
1 L T LV V i dt where i C RC R
V VT RC L
12 - 38 Electronics(3), 2012Prof. Tai-Haur Kuo
_
Monostable Multivibrators (Cont.) During T1
βL+ is greater then VD1
Stable state is maintained
Monostable Multivibrators(Cont.) Monostable multivibrator using NOR gates
C
Mono-stable Multivibrator (Cont.)
DD 1
DD T
v (T ) V V (1 e ) VT RCln RCln2 0.693RC
V V Vwhere V V is NOR gate threshold voltage 2
RC t
TDDx eVVv
Mono-stable Multivibrator (Cont.) Monostable multivibrator with catching diode
DDV
forward resistance of diode
Transient behavior (1)0<t<T1
:
R C x D D T
- t R C
c x O 2 D D D D T
( i ) v :V 0 w h e n t= 0 ( i i ) v 0 V w h e n t= 0
( i i i ) v = ( V + V ) e
( iv ) v = v - V = - V + ( V + V ) e
C
Cv _
O2VO1VXV
R
D DV
D DV
Astable Multivibrator Using NOR(or Inverter) Gates (Cont.)
(2)T1<t<(T1+T2)
( t-T ) R C
( t-T ) R C
c x O 2 x D D D D T
( i) v :0 V w h e n t= T ( ii) v :V 0 w h e n t= T
( ii i) v = V - (V + V )e
( iv )v = v -V = v = V - (V + V )e
12 - 45 Electronics(3), 2012Prof. Tai-Haur Kuo
Astable Multivibrator Using NOR(or Inverter) Gates (Cont.)
Oscillation frequency
V VIf V = , then T =RCln3 and T =RCln3 2
1 0.455oscillation frequency f = 2RCln3 RC
12 - 46 Electronics(3), 2012Prof. Tai-Haur Kuo
Astable Multivibrator Using NOR(or Inverter) Gates (Cont.)
With catching diode at
12 - 47 Electronics(3), 2012Prof. Tai-Haur Kuo
The 555 IC Timer Widely used as both a monostable and astable multivibrator Used as monostable multivibrator
)t(tv
n+1Q nQ
The 555 IC Timer (Cont.) For 0 t T1
For t = T1,
The 555 IC Timer (Cont.) Used as an astable multivibrator
Oscillation frequency 1 B 2 1 A BT R Cln2 ,T T (R R )Cln2
)Cln22R(R 1
T 1f
12 - 50 Electronics(3), 2012Prof. Tai-Haur Kuo
Sine-Wave Shaper Shape a triangular waveform into a sinusoid Extensively used in function generators Notelinear oscillators are not cost-effective for low
frequency application not easy to time over wide frequency ranges
0
Ov
Sine-Wave Shaper (Cont.) Nonlinear-amplification method For various input values, their corresponding output
values can be calculated Transfer curve can be obtained and is similar to
CRCR
Sine-Wave Shaper (Cont.) Breakpoint method Piecewise linear transfercurve Low-valued R is assumed V1 and V2 are constant
D2 01in2
R)VV(VVVV

Sine-Wave Shaper (Cont.)
Precision Rectifier Circuits Precision half-wave rectifier --- “superdiode”
An alternate circuit
Precision Rectifier Circuits (Cont.) ApplicationMeasure AC voltages
Average where Vp is the peak amplitude of an input sinusoid
1
Precision Rectifier Circuits (Cont.)
If ωmin is the lowest expected frequency of the input sine wave
min 4
ω CR
Precision Full-Wave Rectifiers
Precision Full-Wave Rectifiers (Cont.)

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