f2011-3ej4 set 06 oscillators students
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8/3/2019 F2011-3EJ4 Set 06 Oscillators Students
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ECE 3EJ4Electronic Devices & Circuits II
Lecture Set 6Lecture Set 6 OscillatorsOscillators
Prof. M. Jamal DeenProf. M. Jamal Deen
Professor and Senior Canada Research Chair
Dept. of Electrical and Computer EngineeringMcMaster University Hamilton, ON L8S 4K1, Canada
6-25-2
IntroductionIntroduction OscillatorsOscillators
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Oscillators
Text - Sections 17.1, 17.2, 17.3, 17.4
Lecture notes
Review frequency analysis and op-amps
Review small-signal models of BJTs and FETs
Practice problems related to class lectures and materialin textSolve individually, worked examples and compare your answers with
those in text
Solve as many exercises as possible check with answers in text
Suggestion - 17.1, 17.2, 17.3-17.4, 17.5-17.6, 17.7, 17.8-17.9, 17.10, 17-13-17.15
Solve as many problems at end of chapter 17
Suggestion 17.1, 17.4, 17.8, 17.10, 17.15, 17.16, 17.21, 17.22, 17.23, 17.27
Some specific suggestions on exercises and problems to attemptwill be provided in class during lectures
6-4
Early Circuit with Oscillator
Oscillators - technique of combining gain circuit with feedback circuit
Together have phase/time delay required for system to oscillate atspecific frequency
http://pdfserv.maxim-ic.com/en/an/AN1768.pdf
Vintage 1929 Hartley-style transmitter
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Simple Oscillator1
0 i dtC
iL Ri
d
dt
= + +
( )expi t=
2 4
2
R R L C
L
=
24
0
Take complex root
R L C
1 oscillations grow
Need mechanism to force A = 1 at desired value ofoutput amplitude
Use non-linear circuit for gain control
Start-up A > 1 poles - RH of s-plane Stable oscillations A = 1 poles - LH
of s-plane
If A < 1, amplitude - detected by non-linear circuit &then loop gain until it becomes 1
Limiter circuit oscillation grows until amp. reacheslevel to which limiter is set
Use variable R
Element whose R is controlled by output
Put in feedback circuit so R determines
loop gain Diodes or JFETs
( )( )
( ) ( )
( )
( )( )
1
11
v
A sFrom A s
A s s
A swant L s
L s
=
=
j (rad/s)
(Np/s)
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Limiter CircuitLimiter Circuit -- Amplitude ControlAmplitude Control Consider small vi & small vo- vA +ve, vB -ve
D1 and D2 are off
Input I=v1/R1 thru Rf and
Voltages at nodes A and B by superposition
As vi +ve, vo -ve, vB more ve, D2 off vi +ve, vo -ve until vA = -0.7V & D1 on For VD=D1 voltage drop, using vA
expression, we get
If vi further, vA ~ VD & more I flows throughD1 and R3, but I(R2) constant
Thus R3 appears // to Rf
Similarly, we can derive
Removing Rf results in comparator-like I-V
6-10
WienWien--bridge Oscillatorbridge Oscillator
2 2 1
1
( ) 1( ) 1
( ) ( ) 1 ( ) ( )
P
P S P S
R Z s R RL s
R Z s Z s Z s Y s
+= + = + +
( ) 21
11
3 1
RL s
R sCR sCR
= + + +
( )( )
1
3 1 L j Gain
j CR CR
=+
Condition for oscillation ( )( )
( ) ( )( )
( )( ) 1
1 1v
A s A sFrom A s want L s
A s s L s= =
+
-
Vs
Va
ZP
ZS
V0
Put Vs=0
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Amplitude StabilizationD1, D2, R1-R4 form
amplitude controlnetwork
When vo +ve, D1 on
for v(R3) > VD(on)Now R4//R3 , effective
loop gain is reduced
6-12
Amplitude Stabilization
1 1
3 4
o o Dv v v v V iR R
= +
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Wien Bridge OscillatorWien Bridge OscillatorWien Bridge Oscillator with limiters for amplitude control
( )21
2 0 -1-L s Roots of in RH s plaR
nR
e= + =
6-14
Tuned Oscillator
High-Q bandpass filter f0
Positive feedback loop withhard limiter
Assume oscillation has started
Output of filter sinewave @ f0
Sine wave into limiter square
wave of frequency f0
Square wave fed to bandpassfilter which filters outharmonics and producessinewave
Peak-peak amplitude of sinewave VPP
From Fourier analysis, sinewave at f0 will have amplitude
4VPP/Purity of sine wave depends on
Q of filter
Band pass filter - 2nd order active op-amp + RC
Wave shaping circuit diodes as hard limiters
V1V2
tt
f0
Bandpass filter
V2
V1
Wave shaping circuit
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Active-filter Tuned Oscillator Break the circuit at the blue line
Circuit in red rectangle is Leq Equiv. circuit is shown - Leq = R
2C
Derive the expression for AV(s)
v2
v3 v1
v4
Show v2 = 2*v1 = 2*AV(s)*v3 v2 is fed to diode pair to create square wave v3
with p-p amplitude 1.4V (for VD,on = 0.7V)
v3 = 2*4VPP/= 3.57V
QR
C Leq
3 1
4 4
6-16
LCLC--tuned Oscillatorstuned Oscillators
Colpitts Hartley
( )1 21 2
1 21 ; 1o, ,HC oC CL
C C L L C = = ++
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Complete CircuitComplete Circuit ColpittsColpitts OscillatorOscillator
6-18
Colpitts Oscillator( ) 3 21 ;S o GSCG C CR r = +=
[ ]
( ) ( )1
3
3 3
3 ( )0
0
1
( )
GD g
sm ms
s C v ssC
v ss C C g
CL
g
s
C G
+ +
= + + + +VDD
RS
L
vs
VDD
RS
Nodal eqns
for Vg & Vs
L
No excitation = 0
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Colpitts Oscillator
Put real & imag parts = 0
( )
( )
21 3 1
3
1 33
0
GD
mm GD
C C C C C C
j g G C gC G
C
G
L
L
=
+ + +
+
+
+ +
=
i
Oscillation
condition set byL //CTotal
Feedback set byC ratio must be
large enough tomeet gainrequirement
L
6-20
VCO
VCO voltage controlled oscillator
Want to vary fVCO with vinput, fo = Function(vinput) ideally linearfunction
Typically fo = 1/RC
Let C vary with bias varactor or reverse biased pn diode
Let R change with bias voltage varistor use FET or BJT to makeequivalent R that depends on biasing
We will look at case of BJT (try FET as exercise)
CmT
Ig
V r
= =
( )bi
T
C as
V constant at fixe
I function V
d T
=
( )T Cr V I =i
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VCO
Let VCC or VEE both change with vi ICchanges, r changes
However, mode of BJT may change from active to cut-off or saturation
Better way use vi to control a currentsource keep BJT is same mode
Then use current source to bias BJTand r will follow IBias
6-22
VCO Circuit
Requiv
( )ir Function v =
( )( )
1o i
i
f G vF v C
= =
( )1
2of
r C=
Requiv
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LC OscillatorLC Oscillator Negative gNegative gmm
Simple topology for both circuits, determine the resistance Rxy
Differential implementation - two outputs are 180 degrees out of phase very usefulfor many applications driving a Gilbert cell mixer
Good phase noise performance can be achieved
Ibias oscillation amplitude control but it adds noise
Variable capacitor (varactor) controls foscillation by adjusting Vcont Much fixed capacitance cannot be removed - lowers frequency tuning range
LC Oscillator
x yx y
Voltage-controlled Oscillator
VDD
VDD VDD VDD VDD
6-24
PLL
Basically is a feedback control system
Is an electronic circuit used for frequency control or is a frequencyselective circuit
Synchronize with incoming signal
Maintain synchronization in presence of noise or frequency variations
Configured as frequency multipliers. Demodulators, tracking generators,clock recovery circuits
Has three basic componentsPhase-frequency detector differences in phase/frequency in two signals
Loop filter removes hf components form VCO
VCO
PDLoop
Filter
InputVCO
LOvd vC
vd = Kde
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PLL
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PLL
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PLL
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PLL
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Use of PLL Sample Problem
Design an 8-note keyboard following the pure tone pitch:
Pitch C D E F G A B C*
Fraction 1 9/8 5/4 4/3 3/2 5/3 15/8 2
Freq. (Hz) 520 585 650 693 780 867 975 1040
Available components are: ONE ideal op-amp, TWO diodes, 1/2, 1/3 and1/5 frequency dividers, PLLs, 8 touch switchers (represent the 8 keys),
any resistors and capacitors with 10% accuracy, 15V DC voltagesources.
The required output voltage amplitude for every frequency (Vpp/2) is3.5V (assuming frequency dividers and PLLs are scalable components
without any insertion loss).
End of Lectures
on Oscillators
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