2. SYLLABUS
• Oscillators: Introduction, Barkhausen Criterion,
Oscillator with RC Feedback circuit (RC Phase Shift,
Wien Bridge), Tuned Collector, Tuned Base Oscillator,
LC Feedback circuits (Hartley, Colpitts), Condition for
Sustained Oscillations & Frequency of Oscillations,
Crystal Oscillator. Power Amplifier: Definition,
Application & Types of Power Amplifiers, Amplifier
Classes of Efficiency (Class - A, B, AB, C), Push Pull
Amplifiers, Distortion in Simple & Push Pull Amplifier,
Complementary Push Pull Amplifier, Integrated Circuit
Power Amplifier , Introduction to MOSFET & CLASS D
Power Amplifier.
3. “An amplifier with positive feedback acts as
an oscillator”.
.
Introduction to Oscillators:
4. Where A is amplifier gain
is feed back factor, if (A )= 1
Then
Af
A
1 A
, which is condition for oscillations.
Af
Introduction to Oscillators:
The transfer function of a feed back amplifier is as
follows
5. Sinusoidal electrical oscillations are of two types:
•Damped oscillations
•Un-damped oscillations
Damped oscillations : The electrical oscillations in
which amplitude decreases with time are known as
damped oscillations.
Principle for Oscillations:
6.
7. it can be observed that the
amplitude of oscillations decrease with time, though
the frequency remains same.
Why is it so ?
It is due to the loss of energy in the system
producing oscillations.
8. Un-damped oscillations :
The electrical oscillations in which amplitude does not
change with time are known as un-damped oscillations
These are shown in the figure 23.2
e
t
0
Fig 23.2 Un-damped Oscillations
9. • Here the amplitude of oscillations are constant with
time and there is no change in frequency. These are the
oscillations which are used in various electronic
equipment.
• These un damped oscillations are produced by
providing an energy compensation circuit
10. The circuit that produces these oscillations is known as TANK
CIRCUIT
The frequency of oscillations depend upon the parameters
used in this tank circuit i.e., L & C.
The frequency of oscillations is given by the following
formula.
0
2 LC
1
f
11. Oscillator:
Why oscillator is necessary ?
•In many electronic applications,
electrical energy at a specific high
frequency ranging from few Hz to several
MHz. is required.
12. This is obtained with the help of an electronic
device called “OSCILLATOR”.
These are used in Radio, TV, Radar and other
communication/digital electronic applications.
13. Definition :
“An oscillator is just an electronic circuit which
converts dc energy into ac energy of required
frequency”.
Or
“An oscillator is an electronic circuit which
produces an ac output without any input”.
14. 16
Basic types of oscillators :
Based on the waveform produced at
the output:
•Sinusoidal oscillators.
•Non sinusoidal oscillators
Sweep circuits Relaxation
oscillators.
.
15. Sinusoidal oscillators : A static electronic device
that produces sinusoidal oscillations of desired
frequency is called sinusoidal oscillator.
Eg. LC oscillators, RC phase shift oscillator etc.,
16. Amplifier as an oscillator
Amplifier with positive feedback which works as an
oscillator.
Amplifier
Gain (A)
Feedback
Circuit (ß)
vin
V out
_
+
+
_
+
_
_
+
Fig. 2.1(d)
17. We know that negative feedback is employed
in amplifiers for stability of the output.
Here positive feedback is used to produce
oscillations.
From the circuit, it can be observed that…
•The amplified signal available in the ckt., is
Avin.
•The fraction of this signal, i.e., Avin is
fedback to the input.
18. •The feedback signal Avin must be in phase with the
input signal Vin, (i.e. positive feedback), as shown in the
figure.
•Now the circuit starts acting like an oscillator.
•As defined earlier, the circuit (block diagram) can be
shown producing an o/p without any i/p just by
removing the input signal, as shown in the next slide.
19. Now assume that the above Circuit is modified
with the following conditions :
• Terminal ‘z’ is connected with ‘x
• input signal ‘v’ is removed.
Now the fig 2.1(d) can be modified as
follows as shown in fig 2.1 (e).
Amlifier
Gain (A)
Feedback
Circuit ()
V out
_
+
Fig 2.1 (e)
+
_
_
+
20. Now three cases of feedback are possible,
let us discuss them case by case.
Case 1 : If |A| < 1, then the removal of input
signal Vin will result in ceasing of oscillations
(damped oscillations) as per the closed loop
transfer function given below.
A
Af
1 A
21. •Here the output oscillations will slowly
reduce in amplitude and finally die out.
•Such oscillator is of no use to
any practical applications. Its
waveform is shown in next slide.
23. Case 2:
If |A| > 1, then, for example, a 1 volt signal
appearing initially at the input terminal will,
after a trip around the loop reappear as a still
larger voltage than 1 volt.
24. •This larger voltage then reappears as a
still larger voltage, and so on, building
the oscillations with increase in its
amplitude without limit, as shown below:
Fig 2.1(g) grouping oscillations
25. Case 3 :
If |A| = 1, then
The condition of unity loop gain |A| = 1 , is
called the Barkhausen criterion.
This condition implies that both |A| = 1 and that
the phase of -A is zero (ie., positive feedback).
Af
26. Fig. 2.1 (h) un damped oscillations
In the above conditions, no change
occurs at the output of an oscillator and
we get output oscillations with constant
amplitude as shown in the figure 2.1 (h).
27. Thus, to obtain sustained (undamped)
oscillations, the loop gain A of positive
feedback must be unity.
Therefore, now, we can say that “A
positive feedback amplifier with unity gain
acts as an oscillator”.
29. Ref:06103104HKN
Application of Oscillators
• Oscillators are used to generate signals, e.g.
– Used as a local oscillator to transform the RF
signals to IF signals in a receiver;
– Used to generate RF carrier in a transmitter
– Used to generate clocks in digital systems;
– Used as sweep circuits in TV sets and CRO.
30. Oscillators are a common element of almost all electronic circuits. They are used in
various applications, and their use makes it possible for circuits and subsystems to perform
numerous useful functions.
In oscillator circuits, oscillation usually builds up from zero when power is first
applied under linear circuit operation.
The oscillator’s amplitude is kept from building up by limiting the amplifier
saturation and various non-linear effects.
Oscillator design and simulation is a complicated process. It is also extremely
important and crucial to design a good and stable oscillator.
Oscillators are commonly used in communication circuits. All the
communication circuits for different modulation techniques—AM, FM, PM—the use of an
oscillator is must.
Oscillators are used as stable frequency sources in a variety of electronic
applications.
Oscillator circuits are used in computer peripherals, counters, timers, calculators,
phase-locked loops, digital multi-metres, oscilloscopes, and numerous other applications.
APPLICATIONS OF OSCILLATORS:
31. • An oscillator is a circuit that produces a repetitive signal from
a dc voltage.
• The feedback oscillator relies on a positive feedback of the
output to maintain the oscillations.
• The relaxation oscillator makes use of an RC timing circuit to
generate a nonsinusoidal signal such as square wave
Sine wave
Square wave
Sawtooth wave
33. Figure 9.68 A linear oscillator is formed by connecting an amplifier and
a feedback network in a loop.
Linear Oscillators
34. Ref:06103104HKN
EE3110 Oscillator
Integrant of Linear Oscillators
For sinusoidal input is connected
“Linear” because the output is approximately sinusoidal
A linear oscillator contains:
- a frequency selection feedback network
- an amplifier to maintain the loop gain at unity
+
+
Amplifier (A)
Frequency-Selective
Feedback Network ()
Vf
Vs Vo
V
Positive
Feedback
35. Ref:06103104HKN
EE3110 Oscillator
Basic Linear Oscillator
+
+
SelectiveNetwork
(f)
Vf
Vs Vo
V
A(f)
and
A
A
V
V
s
o
1
If Vs = 0, the only way that Vo can be nonzero
is that loop gain A=1 which implies that
(Barkhausen Criterion)
36. Basic principles for oscillation
• An oscillator is an amplifier with positive
feedback. A
V e
V f
V s
V o
+
(1)
f
s
e V
V
V
(2)
o
f βV
V
(3)
o
s
f
s
e
o βV
V
A
V
V
A
AV
V
37. Basic principles for oscillation
• The closed loop gain is:
o
s
f
s
e
o
βV
V
A
V
V
A
AV
V
o
s
o V
A
AV
V
s
o AV
V
A
1
Aβ
A
V
V
A
s
o
f
1
38. Basic principles for oscillation
• In general A and are functions of frequency
and thus may be written as;
is known as loop gain
s
β
s
A
1
s
A
s
V
V
s
A
s
o
f
s
β
s
A
39. Basic principles for oscillation
• Writing the loop gain
becomes;
• Replacing s with j
• and
s
s β
A
s
T
s
T
1
s
A
s
Af
jω
T
1
jω
A
jω
Af
jω
β
jω
A
jω
T
40. Basic principles for oscillation
• At a specific frequency f0
• At this frequency, the closed loop gain;
will be infinite, i.e. the circuit will have finite
output for zero input signal - oscillation
1
0
0
0
jω
β
jω
A
jω
T
0
0
0
0
jω
β
jω
A
1
jω
A
jω
Af
41. Basic principles for oscillation
• Thus, the condition for sinusoidal oscillation
of frequency f0 is;
• This is known as Barkhausen criterion.
• The frequency of oscillation is solely
determined by the phase characteristic of the
feedback loop – the loop oscillates at the
frequency for which the phase is zero.
1
0
0
jω
β
jω
A
45. How does the oscillation get
started?
• Noise signals and the transients associated with the
circuit turning on provide the initial source signal
that initiate the oscillation
46. Practical Design Considerations
• Usually, oscillators are designed so that the loop gain
magnitude is slightly higher than unity at the desired frequency
of oscillation
• This is done because if we designed for unity loop gain
magnitude a slight reduction in gain would result in oscillations
that die to zero
• The drawback is that the oscillation will be slightly distorted (the
higher gain results in oscillation that grows up to the point that
will be clipped)
47. Basic principles for oscillation
• The feedback oscillator is widely used for
generation of sine wave signals.
• The positive (in phase) feedback arrangement
maintains the oscillations.
• The feedback gain must be kept to unity to
keep the output from distorting.
48. Basic principles for oscillation
In phase
Noninverting
amplifier
V f V o
A v
Feedback
circuit
49. Design Criteria for Oscillators
1. The magnitude of the loop gain must be
unity or slightly larger
– Barkhaussen criterion
2. Total phase shift, of the loop gain mus t be
Nx360° where N=0, 1, 2, …
1
Aβ
50. RC Oscillators
• RC feedback oscillators are generally limited
to frequencies of 1 MHz or less.
• The types of RC oscillators that we will discuss
are the Wien-bridge and the phase-shift
52. BASIC PRINCIPLE OF WEIN
BRIDGE OSCILLATOR
AEI403 . 26 to 27
• It employs two stages of amplifiers.
• Each amplifier gives phase shift of 180 0.
• Combination of two amplifiers gives 360 0
phase shift, which is equal to 0 0.
• A fraction of the output from the second stage is
fed back to the input of the first stage without
producing any further phase shift.
53. • This oscillator can be used from 10Hz to 10MHz.
• It is extensively used as audio oscillator since its
output is free from circuit fluctuations and ambient
temperature.
AEI403 . 26 to 27
BASIC PRINCIPLE OF WEIN
BRIDGE OSCILLATOR
56. • The loop gain for the oscillator is;
• where;
• and;
s
p
p
Z
Z
Z
R
R
s
β
s
A
s
T
1
2
1
sRC
R
Zp
1
sC
sRC
Zs
1
57. • Hence;
• Substituting for s;
• For oscillation frequency f0
RC
/j
RC
j
R
R
j
T
0
0
1
2
0
1
3
1
1
/sRC
sRC
R
R
s
T
1
3
1
1
1
2
RC
/j
RC
j
R
R
j
T
1
3
1
1
1
2
]
[ 0
58. • Since at the frequency of oscillation, T(j)
must be real (for zero phase condition), the
imaginary component must be zero;
• which gives us –
0
1
0
0
RC
j
RC
j
RC
1
0
60. • From the previous eq. (for oscillation
frequency f0),
• the magnitude condition is;
3
1
1
0
3
1
1
1
1
2
1
2
R
R
R
R
RC
/j
RC
j
R
R
j
T
0
0
1
2
0
1
3
1
1
2
1
3
1
2
R
R
To ensure oscillation, the ratio R2/R1 must be
slightly greater than 2.
61. • With the ratio;
• then;
K = 3 ensures the loop gain of unity – oscillation
– K > 3 : growing oscillations
– K < 3 : decreasing oscillations
2
1
2
R
R
3
1
1
2
R
R
K
63. Figure 9.75 Example of output voltage of the oscillator.
Wien-Bridge oscillator output
64. Ref:06103104HKN
EE3110 Oscillator
Frequency Selection Network
Let
1
1
1
C
XC
and
1
1
1 C
jX
R
Z
2
2
1
C
XC
2
2
2
2
1
2
2
2
1
1
C
C
C jX
R
X
jR
jX
R
Z
Therefore, the feedback factor,
)
/
(
)
(
)
/
(
2
2
2
2
1
1
2
2
2
2
2
1
2
C
C
C
C
C
i
o
jX
R
X
jR
jX
R
jX
R
X
jR
Z
Z
Z
V
V
2
2
2
2
1
1
2
2
)
)(
( C
C
C
C
X
jR
jX
R
jX
R
X
jR
Vi Vo
R1 C1
R2
C2
Z1
Z2
65. Ref:06103104HKN
EE3110 Oscillator
can be rewritten as:
)
( 2
1
2
1
2
2
1
2
2
1
2
2
C
C
C
C
C
C
X
X
R
R
j
X
R
X
R
X
R
X
R
For Barkhausen Criterion, imaginary part = 0, i.e.,
0
2
1
2
1
C
C X
X
R
R
Supposing,
R1=R2=R and XC1= XC2=XC,
2
1
2
1
2
1
2
1
/
1
1
1
or
C
C
R
R
C
C
R
R
)
(
3 2
2
C
C
C
X
R
j
RX
RX
0.2
0.22
0.24
0.26
0.28
0.3
0.32
0.34
Feedback
factor
-1
-0.5
0
0.5
1
Phase
Frequency
=1/3
Phase=0
f(R=Xc)
67. Wien-bridge Oscillator using transistor
• It is essentially a two-stage amplifier with an R-C bridge circuit. R-C bridge
circuit (Wien bridge) is a lead-lag network. The phase’-shift across the
network lags with increasing frequency and leads with decreasing
frequency. By adding Wien-bridge feedback network, the oscillator
becomes sensitive to a signal of only one particular frequency. This
particular frequency is that at which Wien bridge is balanced and for
which the phase shift is 0°.
• If the Wien-bridge feedback network is not employed and output of
transistor Q2 is feedback to transistor Q1 for providing regeneration
re-quired for producing oscillations, the transistor Q1 will amplify signals
over a wide range of frequencies and thus direct coupling would result in
poor frequency stability. Thus by em-ploying Wien-bridge feedback
network frequency stability is increased. In the bridge circuit R1 in series
with C1, R3, R4 and R2 in parallel with C2 form the four arms.
68.
69. • This bridge circuit can be used as feedback network for an oscillator,
provided that the phase shift through the amplifier is zero. This
requisite condition is achieved by using a two stage amplifier, as
illustrated in the figure. In this arrangement the output of the
second stage is supplied back to the feedback network and the
voltage across the parallel combination C2R2 is fed to the input of
the first stage. Transistor Q1 serves as an oscillator and amplifier
whereas the transistor Q2 as an inverter to cause a phase shift of
180°. The circuit uses positive and negative feedbacks. The positive
feedback is through R1 C1 R2, C2 to tran-sistor Q1 and negative
feedback is through the voltage divider to the input of transistor Q1.
Resistors R3 and R4 are used to stabilize the amplitude of the
output.
70. • The two transistors Q1 and Q2 thus cause a total phase shift of 360° and
ensure proper positive feedback. The negative feedback is provided in the
circuit to ensure constant output over a range of frequencies. This is
achieved by taking resistor R4 in the form of a tempera-ture sensitive
lamp, whose resistance increases with the increase in current. In case the
amplitude of the output tends to increase, more current would provide
more negative feedback. Thus the output would regain its original value. A
reverse action would take place in case the out-put tends to fall.
• The above corresponds with the feedback network attenuation of 1/3.
Thus, in this case, voltage gain A, must be equal to or greater than 3, to
sustain oscillations.
• To have a voltage gain of 3 is not difficult. On the other hand, to have a
gain as low as 3 may be difficult. For this reason also negative feedback is
essential.
71. • The circuit is set in oscillation by any random change in base current of transistor Q1 ,
that may be due to noise inherent in the transistor or variation in voltage of dc supply.
This variation in base current is amplified in collector circuit of transistor Q1 but with a
phase-shift of 180°. the output of transistor Q1 is fed to the base of second transistor
Q2through capacitor C4. Now a still further amplified and twice phase-reversed signal
appears at the collector of the transistor Q2. Having been inverted twice, the output
signal will be in phase with the signal input to the base of transistor Q1 A part of the
output signal at transistor Q2 is feedback to the input points of the bridge circuit (point
A-C). A part of this feedback signal is applied to emitter resistor R4 where it produces
degenerative effect (or negative feedback). Similarly, a part of the feedback signal is
applied across the base-bias resistor R2 where it produces regenerative effect (or
positive feedback). At the rated frequency, effect of regeneration is made slightly more
than that of degeneration so as to obtain sustained os-cillations.
• The continuous frequency variation in this oscillator can be had by varying the two
capacitors C1 and C2 simultaneously. These capacitors are variable air-gang capacitors.
We can change the frequency range of the oscillator by switching into the circuit
different values of resistors R1 and R2.
72. Wien-Bridge Oscillator:
Advantages
• Provides a stable low distortion sinusoidal output over a wide range of frequency.
• The frequency range can be selected simply by using decade resistance boxes.
• The frequency of oscillation can be easily varied by varying capacitances C1 and
C2 simultaneously. The overall gain is high because of two transistors.
Disadvantages
• The circuit needs two transistors and a large number of other components.
• The maximum frequency output is limited because of amplitude and the phase-
shift characteristics of amplifier.
74. • The phase shift oscillator utilizes three RC
circuits to provide 180º phase shift that when
coupled with the 180º of the op-amp itself
provides the necessary feedback to sustain
oscillations.
• The gain must be at least 29 to maintain the
oscillations.
• The frequency of resonance for the this type
is similar to any RC circuit oscillator:
RC
fr
6
2
1
75. vi
v1
v1
v2
v2 v3
vo
C
C
C
R R
R
R2
i
v
sRC
sRC
v
1
1
i
v
sRC
sRC
v
2
2
1
i
v
sRC
sRC
v
3
3
1
3
3
1
)
(
sRC
sRC
s
v
v
i
R
R
v
v
s
A o 2
3
)
(
76. • Loop gain, T(s):
• Set s=jw
3
2
1
)
(
)
(
)
(
sRC
sRC
R
R
s
s
A
s
T
2
2
2
2
2
2
2
2
3
2
3
3
1
)
)(
(
)
(
1
)
(
C
R
RC
j
C
R
RC
RC
j
R
R
j
T
RC
j
RC
j
R
R
j
T
77. • To satisfy condition T(jwo)=1, real component
must be zero since the numerator is purely
imaginary.
• the oscillation frequency:
• Apply wo in equation:
• To satisfy condition T(jwo)=1
0
3
1 2
2
2
C
R
RC
3
1
0
8
1
)
3
/
1
(
3
)
3
/
(
0
)
3
/
1
)(
3
/
(
)
( 2
2
R
R
j
j
R
R
j
T o
8
2
R
R The gain greater than 8, the circuit will
spontaneously begin oscillating & sustain
oscillations
80. • A phase shift oscillator is a circuit that produces sign waves. The output is
fed back to the input which changes the ‘phase’ of the waves. The phase
shift increases with frequency and can reach a maximum of 180 degrees.
Phase shift oscillators have a wide range of applications which are detailed
further below.
• We select the so-called phase shift oscillator as a first example as it
exemplifies very simply the principles set forth in the previous blog post.
The circuit is drawn to show clearly the amplifier and feedback network.
The circuit consists of a common source FET amplifier followed by a three-
section R-C phase shift network. The amplifier stage is self-biased with a
capacitor bypassed source resistor Rs and a drain bias resistance RD. The
output of the last section is supplied back to the gate. If the loading of the
phase-shift network on the amplifier can be assumed to be negligible, a
phase shift of 180° between the amplified output voltage Vout and the
input voltage Vin at the gate is produced by the amplifier itself.
81. • The three-section R-C phase shift network produces an
additional phase shift, which is a function of frequency and
equals 180° at some frequency of operation. At this
frequency, the total phase shift from the gate around the
circuit and back to the gate will be exactly zero. This particular
frequency will be the one at which the circuit will oscillate
provided that the magnitude of the amplification is
sufficiently large. In a FET phase-shift oscillator voltage series
feedback that is, feedback voltage proportional to the output
voltage Vout and supplied in series with the input signal at the
gate is used.
82. • The frequency can be adjusted over a wide range if variable capacitors are
used. As well as phase shifting, the R-C network attenuates the amplifier
output. Network analysis shows that when the necessary phase shift of
180° is obtained, this network attenuates the output voltage by a factor of
1/29. This means that the amplifier must have a voltage gain of 29 or
more. When the amplifier voltage gain is 29 and feedback factor of R-C
network, β= 1/29 then the loop gain is A = 1, the amplifier phase shift of –
180° combined with the network phase shift of + 180° gives a loop phase
shift of zero. Both of these conditions are necessary to satisfy
the Barkhausen criteria. If the amplifier gain is much greater than 29, the
oscillator output waveform is likely to be distorted. When the gain is
slightly greater than 29, the output is usually a reasonably pure sinusoidal.
83. Advantages
• It is a cheap and simple circuit as it contains resistors and capacitors (not bulky and
expensive high-value inductors).
• It provides good frequency stability.
• The phase shift oscillator circuit is much simpler than the Wien bridge oscillator circuit
because it does not need negative feedback and the stabilization arrangements.
• The output is sinusoidal that is quite distortion free.
• They have a wide frequency range (from a few Hz to several hundred kHz).
• They are particularly suitable for low frequencies, say of the order of 1 Hz, as these
frequencies can be easily obtained by using R and C of large values.
84. Disadvantages
• The output is small. It is due to smaller feedback.
• It is difficult for the circuit to start oscillations as the feedback is usually small.
• The frequency stability is not as good as that of Wien bridge oscillator.
• It needs high voltage (12 V) battery so as to develop sufficiently large feedback
volt-age.
Applications
• FET phase-shift oscillator is used for generating signals over a wide frequency
range. The frequency may be varied from a few Hz to 200 Hz by employing one
set of re-sistors with three capacitors ganged together to vary over a
capacitance range in the 1 : 10 ratio. Similarly, the frequency ranges of 200 Hz
to 2 kHz, 2 kHz to 20 kHz and 20 kHz to 200 kHz can be obtained by using
other sets of resistors.
85.
86. LC Oscillators
• Use transistors and LC tuned circuits or
crystals in their feedback network.
• For hundreds of kHz to hundreds of MHz
frequency range.
• Examine Colpitts, Hartley and crystal
oscillator.
87. Colpitts Oscillator
• The Colpitts oscillator is a type
of oscillator that uses an LC
circuit in the feed-back loop.
• The feedback network is made
up of a pair of tapped
capacitors (C1 and C2) and an
inductor L to produce a
feedback necessary for
oscillations.
• The output voltage is
developed across C1.
• The feedback voltage is
developed across C2.
88. Colpitts Oscillator
• KCL at the output node:
• voltage divider produces:
• substitute eq(2) into eq(1):
0
1
1
2
1
sC
sL
V
V
g
R
V
sC
V o
gs
m
o
o
o
gs V
sL
sC
sC
V
2
2
1
1
0
1
1 1
2
2
2
sC
R
LC
s
sC
g
V m
o
- Eq (1)
- Eq (2)
89. Colpitts Oscillator
• Assume that oscillation has started, then Vo≠0
• Let s=jω
• both real & imaginary component must be zero
– Imaginary component:
0
1
2
1
2
2
2
1
3
R
g
C
C
s
R
LC
s
C
LC
s m
0
1
2
1
2
2
1
2
2
C
LC
C
C
j
R
LC
R
gm
2
1
2
1
1
C
C
C
C
L
o
- Eq (3)
90. Colpitts Oscillator
• both real & imaginary component must be
zero
– Imaginary component:
• Combining Eq(3) and Eq(4):
• to initiate oscillations spontaneously:
R
g
R
LC
m
1
2
2
R
g
C
C
m
1
2
1
2
C
C
R
gm
- Eq (4)
91. Hartley Oscillator
• The Hartley oscillator is
almost identical to the
Colpitts oscillator.
• The primary difference
is that the feedback
network of the Hartley
oscillator uses tapped
inductors (L1 and L2) and
a single capacitor C.
92. Hartley Oscillator
• the analysis of Hartley oscillator is identical to
that Colpitts oscillator.
• the frequency of oscillation:
C
L
L
o
2
1
1
93. Crystal Oscillator
• Most communications and digital applications require the use
of oscillators with extremely stable output. Crystal oscillators
are invented to overcome the output fluctuation experienced
by conventional oscillators.
• Crystals used in electronic applications consist of a quartz
wafer held between two metal plates and housed in a a
package as shown in Fig. 9 (a) and (b).
94. Crystal Oscillator
• Piezoelectric Effect
– The quartz crystal is made of silicon oxide (SiO2) and
exhibits a property called the piezoelectric
– When a changing an alternating voltage is applied
across the crystal, it vibrates at the frequency of the
applied voltage. In the other word, the frequency of
the applied ac voltage is equal to the natural resonant
frequency of the crystal.
– The thinner the crystal, higher its frequency of
vibration. This phenomenon is called piezoelectric
effect.
95. Crystal Oscillator
• Characteristic of Quartz Crystal
– The crystal can have two resonant
frequencies;
– One is the series resonance frequency f1
which occurs when XL = XC. At this
frequency, crystal offers a very low
impedance to the external circuit where
Z = R.
– The other is the parallel resonance (or
antiresonance) frequency f2 which
occurs when reactance of the series leg
equals the reactance of CM. At this
frequency, crystal offers a very high
impedance to the external circuit
R
L
C
CM
96. Crystal Oscillator
• The crystal is connected as a series element in
the feedback path from collector to the base
so that it is excited in the series-resonance
mode
BJT
FET
97. Crystal Oscillator
• Since, in series resonance, crystal impedance is the smallest that
causes the crystal provides the largest positive feedback.
• Resistors R1, R2, and RE provide a voltage-divider stabilized dc bias
circuit. Capacitor CE provides ac bypass of the emitter resistor, RE to
avoid degeneration.
• The RFC coil provides dc collector load and also prevents any ac
signal from entering the dc supply.
• The coupling capacitor CC has negligible reactance at circuit
operating frequency but blocks any dc flow between collector and
base.
• The oscillation frequency equals the series-resonance frequency of
the crystal and is given by:
C
o
LC
f
2
1
98. Unijunction Oscillator
• The unijunction transistor can
be used in what is called a
relaxation oscillator as shown
by basic circuit as follow.
• The unijunction oscillator
provides a pulse signal suitable
for digital-circuit applications.
• Resistor RT and capacitor CT
are the timing components
that set the circuit oscillating
rate
UJT
99. Unijunction Oscillator
• Sawtooth wave
appears at the emitter
of the transistor.
• This wave shows the
gradual increase of
capacitor voltage
100. Unijunction Oscillator
• The oscillating frequency is calculated as follows:
• where, η = the unijunction transistor intrinsic
stand- off ratio
• Typically, a unijunction transistor has a stand-off
ratio from 0.4 to 0.6
1
/
1
ln
1
T
T
o
C
R
f
