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RAMA ARORA, PHYSICS DEPARTMENT PGGCG-11, CHANDIGARH OSCILLATORS.
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Transcript of RAMA ARORA, PHYSICS DEPARTMENT PGGCG-11, CHANDIGARH OSCILLATORS.
RAMA ARORA,PHYSICS DEPARTMENT
PGGCG-11 , CHANDIGARH
OSCILLATORS
Oscillators
An oscillator is an electronic device which converts DC power from the supply into AC power in the load without the application of an external input signal. The essential components of the oscillator are: Tank circuit, Transistor amplifier, and Feedback circuit
Tank circuit
Amplifier and Feedback diagram
Classification of Oscillators
Depending upon the method of producing oscillations. (a) Feedback oscillators (b) Negative resistance oscillatorsDepending upon nature of generated waveform (a) Sinusoidal or harmonic oscillators (b) Non-sinusoidal or relaxation oscillators Both sinusoidal and relaxation oscillators may be negative
resistance and feedback type.Depending upon the frequency of generated voltage. (a) Audio frequency (AF) oscillator (b) Radio frequency (RF) oscillator (c) very high frequency (VHF) oscillators (d) ultrahigh frequency (UHF) oscillators (e)Microwave oscillators
Fundamental Principle of Oscillators
In oscillator, a negative resistance is provided to compensate for the losses in the circuit.
In a feedback oscillator, external positive feedback sufficient to make the overall gain infinity, provides the negative resistance required to overcome the natural damping of the oscillations.
In a negative resistance oscillator internal positive feedback is present and serves to provide the required negative resistance.
In an oscillator no external signal is applied. The initial signal to trigger the oscillations is ordinarily supplied by the noise voltage. This noise voltage originates when the power supply is switched on. Since the frequency spectrum of noise is very wide, it always possesses a component voltage at a frequency that is correct for the oscillator operation.
Feedback oscillators
The basic requirements of a feedback oscillator are:
An amplifier with positive feedback to provide negative resistance in the circuit.
Some circuit non-linearity to define amplitude of oscillators.
A frequency determining network to produce oscillations at a desired frequency.
Dc power supply to act as energy source.
Tuned collector oscillator
The basic circuit of a tuned collector oscillator is shown in figure. It is called the tuned-collector oscillator, because the tuned circuit is connected to the collector. The tuned circuit, constituted by the capacitor C and transformer primary coiL, forms the load impedance and determines the frequency of oscillation.
Hartley oscillator
Hartley oscillator is an electronic oscillator circuit that uses an inductor and a capacitor in parallel to determine the frequency.
It is used in radio receiver as a local oscillator because
(i) It is easy to tune
(ii) It’s adaptability to a wide range of frequencies
Hartley Oscillator is generally of two types:
1. Series fed oscillator2. Parallel or shunt fed Hartley oscillator
Series Fed Hartley oscillator
In series fed Hartley oscillator, the junction of two inductors of the tuned circuit is
directly connected to Vcc and one end of the LC circuit is connected to the
collector of the transistor. The lower portion of the tank coil is inductively coupled
to the upper portion.
Shunt fed Hartley oscillator
Shunt fed Hartley oscillator uses a transistor in CE configuration, in which
the collector current is divided into two parallel paths.
One branch connects the collector
to the Vcc through RFC and
provides the path for DC keeping
the AC out. The other branch
connects the collector to LC tank
through a capacitor and provides
the path for AC keeping the DC
out.
AC equivalent circuit of Hartley oscillator
The frequency of oscillation is given by,
(a) (b)
oe
fe
oe h
Ih
h
IV 12
2
Let the currents I1, I2 and I3 be non-zero. Applying Kirchhoff’s voltage law to loop (1), we get
0)( 3121 1 IIjXVhIh Lreie
Similarly, applying Kirchhoff’s voltage law to loop (2) and (3), we get
0)( 3212
2 IIjX
h
Ih
h
IL
oe
fe
oe
and 0)()( 32313 21 IjXIIjXIIjX cLL
From fig. (b), we have
Rearranging the above eqns. We get
011 321
L
oe
reL
oe
refeie XjII
h
hIjX
h
hhh
01
12 221
LL
oeoe
fe XjIIjXh
Ih
h
0)( 321 2121 IjXjXjXIjXIjX cLLLL
For non-zero I1, I2, I3, the determinant of above three eqns. must be zero.
At frequency of oscillation,CLL )(
1
21
2
021
cLL jXjXjX
Taking real part of the equation equal to zero, we get
0)()( 22
1212 LLLfereLrefeoeie XXXhhXhhhh
Since hre < < 1and putting hie hoe – hfe hre = ∆he, the above equation becomes,
022
1212 LLLfeLe XXXhXh
12 2
42
Le
efefeL X
h
hhhX
In general, > > 4 ∆ he feh2
12 Lh
hL
e
fe
Therefore,
This is the equation for sustained oscillations.
2
1
2121 )(
1
LLCLLh
h
fe
oe
Taking imaginary part of the equation equal to zero, we get
CLL )(
1
21
CLLf
)(2
1
221
LCf
2
1
This is the frequency of oscillations of Hartley oscillator.
15
Colpitts LC-Tuned Oscillator Feedback amplifier with inductor L
and capacitors C1 and C2 in feedback network. Feedback is frequency dependent. Aim to adjust components to get
positive feedback and oscillation. Output taken at collector Vo. No input needed, noise at
oscillation frequency o is picked up and amplified.
RB1 and RB2 are biasing resistors. RFC is RF Choke (inductor) to allow
dc current flow for transistor biasing, but to block ac current flow to ac ground.
Simplified circuit shown at midband frequencies where large emitter bypass capacitor CE and base capacitor CB are shorts and transistor capacitances (C and C) are opens.
CB
CE
V0
Vi
V0
Vi
Colpitts LC-Tuned Oscillator Voltage across C2 is just V
Neglecting input current to transistor (I 0),
Then, output voltage Vo is
KCL at output node (C)
Setting s = j
AC equivalent circuit
VsC
Z
VI
CC 2
22
VsC
Z
VII
CCL 2
22
22
2 1))(( LCsVsLVsCVZIVV LLo
01
011
01
2122
213
22
12
12
RgCCs
R
LCsCLCs
LCsVsCR
VgVsC
VsCR
VgVsC
m
m
om
01
213
212
2
CLCCCj
R
LC
Rgm
Iπ ≈ 0
sC2V
sC2V
V0
Assuming oscillations have started, then V ≠ 0 and Vo ≠ 0, so
Colpitts LC-Tuned Oscillator To get oscillations, both the real and
imaginary parts of this equation must be set equal to zero.
From the imaginary part we get the expression for the oscillation frequency
From the real part, we get the condition on the ratio of C2/C1
01
213
212
2
CLCCCj
R
LC
Rgm
21
2121
21
213
21
1
0
CC
CCL
CLC
CC
CLCCC
o
oo
RgC
C
C
C
CLC
CCLCLCRg
R
LC
Rg
m
om
om
1
2
1
2
21
2122
2
22
11
01
Colpitts LC-Tuned Oscillator Given:
Design oscillator at 150 MHz
Transistor gm = 100 mA/V, R = 0.5 K Design:
Select L= 50 nH, then calculate C2, and
then C1
sradxxfo /104.91015022 86
50)5.0)(/100(1
2 KVmARgC
Cm
pFpFC
C
pFFxxnHC
C
LC
C
C
LCCLC
CC
o
o
2350
130,1
50
130,11013.1)501()104.9(50
11
1
11
21
928
1
222
1
2
221
21
Example
Phase Shift Oscillator
Based on op amp using inverting input
Combination of R’s and C’s in feedback loop so get additional phase shift. Target 180o to get oscillation.
Analysis assumes op amp is ideal.
V0
VX
R
IC1
R
IC2IC3
IR1IR2
If Rf
2
23
2
2
223
22
212
112
)(
143
)(
131
12
Finally
)(
131
12
111
11
12
12
12
111
11
sCRsCRsCR
V
sCRsCRsCR
V
sCRsCR
V
sC
IVV
sCRsCRR
V
sCRsCRsCRR
V
sCRR
V
sCRsCRR
VIII
sCRsCRR
V
R
VI
sCRsCR
V
sCsCRR
V
sCR
VZIVV
sCRR
V
R
V
sCRR
VIII
f
o
f
o
f
oCX
f
o
f
o
f
o
f
oCRC
f
oR
f
o
f
o
f
oCC
f
o
f
o
f
oCRC
V1V2
f
o
f
oR
f
oCC
Cf
of
sCRR
V
sCR
V
RR
VI
sCR
VZIVV
IR
VIsoVV
1
0
11
11
1
CC C
Phase Shift Oscillator
RR
soR
R
CR
RRCRRC
ωRRC
)L(ω
so)L(ω
RCso
CRCR
CRCRj
RRC
CRCRj
CRj
sCRsCR
sCR
V
VAL
sCRsCRsCR
V
f
fff
of
o
o
ff
f
X
f
oX
12
1123
1
44
get wefor ngsubstituti and14
1 need also wens,oscillatioget To
3
113
so frequency oneat thisachievecan We
zero. togo to termimaginary theneed wens,oscillatioget To
134
)(14
3
1
)(14
3
)()()(
gain loop for theget we
)(
143V
gRearrangin
22
2220
220
0
o
22
2
2
0
2
V0
VX
R
IC1
R
IC2IC3
IR1IR2
If Rf
V1V2
ExampleOscillator specifications: o=1x106 rad/s
KR
sradxnFCR
RC
nFC
f
o
o
67.0)58(12
Then
58)/101(103
1
3
13
1 fromthen
,10 econveniencfor Selecting
6
Note: We get 180o phase shift from op amp since input is to inverting terminal and another 180o from the RC ladder.
CC C
WIEN BRIDGE OSCILLATOR
Wien bridge oscillator is a two stage amplifier. The first stage is CE amplifier and the second
stage is CC amplifier. The output of the second stage is fed back to the first stage through feed
back network consisting of R1C1 in series and R2C2 in parallel. It is advantageous over phase
shift oscillator as its frequency can be varied over a frequency range of 10:1.
The ratio of output voltage of the network to the input voltage is given by
impedancetotal
ncombinatioparallelofimpedance
V
V
i
o
c
cc
c
c
jXR
RjXjXR
jXR
jXR
.
cc
c
i
o
jRXXR
jRX
V
V
322
If the imaginary term vanishes, the phase shift will be zero i.e.
022 cXR
RX c
RC
1
Therefore, frequency of oscillation is,
RC
1
LCf
2
1
2
3
1
3
c
c
i
o
jRX
jRX
V
VAlso, we have
Hence the oscillations will be sustained if the amplifier has a gain just exceeding 3.
The End