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Lecture 14 - 1ELE2110A 2008
Week 14: Positive Feedback and Oscillator
ELE 2110A Electronic Circuits
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Lecture 14 - 2ELE2110A 2008
Topics to cover z Positive feedbackz Wien-Bridge Oscillatorz
Phase Shift Oscillator
Reading assignment: Chap 17.13 of Jeager and Blalock
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Lecture 14 - 3ELE2110A 2008
Applications of Oscillatorsz Clock input for CPU, DSP chips z
Local oscillator for radio receivers, mobile receivers, etcz Signal
generation for signal generators in your labz Clock input for
analog-digital and digital-analog
convertersz
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Lecture 14 - 4ELE2110A 2008
Positive Feedback
z Designed to produce an output even thought the input is
zero
z Use positive feedback through frequency-selective feedback
network to ensure sustained oscillation at 0
( ) ( )( ) ( )( )( )sTsA
ssAsAsfA == 11
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Lecture 14 - 5ELE2110A 2008
Barkhausens Criteria for Oscillation
( ) ( )( ) ( )( )( )sTsA
ssAsAsfA == 11
z For sinusoidal oscillations,
z Barkhausens criteria:
z An impulse input starts the oscillation Circuit noises, e.g.,
resistor
thermal noise, serve this purpose
z Loop gain greater than unity causes a distorted oscillation to
occur
( ) ( ) 101 +== ojTojT
( )( ) 1
0==
ojTojT
or multiples of 3600
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Lecture 14 - 6ELE2110A 2008
Types of Oscillatorsz Oscillators can be categorized as follows
according to
the types of feedback network used: RC oscillator LC oscillator
Crystal oscillator
z We will discuss the first type only
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Lecture 14 - 7ELE2110A 2008
Wien-Bridge Oscillator
jssZsZ
sZss =+= ,)(
2)(
1
)(2)(1V)(oV
RCjCRRCGjT(s)
3)2221(IV
oV
+==
Phase shift will be zero if = 0,
At 0 =1/RC,If G=3, sinusoidal oscillation is achieved.
This oscillator is used for frequencies up to few MHz, limited
primarily by characteristics of amplifier.
)2221( CR3G)oT(j +=
Break the loop at P to find loop gain:
,1
211 (s)IGV(s)I)VR
R((s)V =+=
Loop gain:
1
21RRG +=
A
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Lecture 14 - 8ELE2110A 2008
Phase-Shift Oscillator
z The RC network is to provide 180o phase shift at the desired
oscillation frequency
z At least three RC section is required: One RC section can
provide 90o phase shift at most:
Two RC sections provide 180o phase shift only at .
CRjCRj
CjRRsH RC
+=+= 1/1)(
( ) oo 90tan90)( 1 = RCsH RC
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Lecture 14 - 9ELE2110A 2008
Phase-Shift Oscillator
+
+=
)(2V)(1V
G)(2sCG)(2sC
0)('oV
sssC
sCssC
1422231
233
)('oV)(oV)(
++==
sRCCRs
RRCssssT
Phase shift will be zero if = 0,
At 0
)22231( CRoRCo 31=
R
R
4
RRCo)oT(j 11211
22==
KCL at v1 and v2:
1)(2V)(oV sCRs
s =For R1=12R, the Barkhausens criterion is met.
One implementation:
From v2 to vo:
We have:
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Lecture 14 - 10ELE2110A 2008
Amplitude Stabilizationz As power supply voltage, component
values and/or temperature
change, the loop gain |A| deviates from 1 oscillation decays
(|A| < 1) or grows (|A| < 1)
z Amplitude stabilization circuit automatically control the loop
gain such that A=1
z Example in Wien-bridge oscillator:
R1 replaced by a nonlinear resistor
G must = 3 at oscillating freq.
When output amplitude increases R1 increases due to heat G
decreases amplitude decreases
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Lecture 14 - 11ELE2110A 2008
Amplitude Stabilization Circuit Example
z R4 and diodes D1 and D2 form a nonlinear resistor, whose value
depends on output amplitude
Resistance control
or
G = 3
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Lecture 14 - 12ELE2110A 2008
Feedback Summaryz Feedback combines the advantages of passive
circuits and active
circuitsz Properties of negative feedback
Desensitize the gain Extend the bandwidth Reduce distortion
z Feedback circuits can be classified into four topologies
Series-series, series-shunt, shunt-series, shunt-shunt
z Stability is a special issue in feedback circuits. Stability
can be determined by Nyquist plot Root locus diagram Phase and gain
margin in Bode plots
z Oscillators employ positive feedback circuits
