Oscillators
Dr. Monir HossenECE, KUET
Department of Electronics and Communication Engineering, KUET
Department of Electronics and Communication Engineering, KUET 2
Introduction of Oscillators
Oscillators can produce sinusoidal or non-
sinusoidal waves at different frequencies which may
range from a few Hz to several MHz.
o At frequency under than 1 MHz:
RC oscillators are used to produce perfect sine wave
This low frequency oscillators use op-amp and RC
resonant circuit to determine frequency of oscillation
o At frequency above than 1 MHz:
LC oscillators are used
This high frequency oscillators use transistors and LC
resonant circuit to determine frequency of oscillation
Department of Electronics and Communication Engineering, KUET 3
Sinusoidal Oscillator
An electronic device that generates sinusoidal
oscillations of desired frequency is known as a
sinusoidal oscillator
An amplifier with positive feedback is
required.
The feedback signal should be large enough
and should has correct phase.
There will be output signal without any
external input signal.
Oscillator converts dc energy into ac energy.
Department of Electronics and Communication Engineering, KUET 4
Advantages of Oscillator
1) An oscillator is a non-rotating device. Consequently,
there is little wear and tear and hence longer life.
2) Due to the absence of moving parts, the operation of
an oscillator is quite silent.
3) An oscillator can produce waves from small (20 Hz)
to extremely high frequencies (> 100 MHz).
4) The frequency of oscillations can be easily changed
when desired.
5) It has good frequency stability, i.e. frequency once
set remains constant for a considerable period of
time.
6) It has very high efficiency.
Department of Electronics and Communication Engineering, KUET 5
Types of Sinusoidal Oscillations (1/2)
There two types of sinusoidal oscillations:
(i) Damped Oscillations
(ii) Undamped Oscillations
(i) Damped Oscillations:
The electrical oscillations whose amplitude goes on
decreasing with time are called damped oscillations.
No means are provided to
compensate for the losses and
consequently the amplitude of the
generated wave decreases
gradually. However, the frequency
of oscillations remains unchanged
Department of Electronics and Communication Engineering, KUET 6
(ii) Undamped Oscillations
The electrical oscillations whose amplitude and
frequency remain constant with time are called
undamped oscillations.
Types of Sinusoidal Oscillations (2/2)
Department of Electronics and Communication Engineering, KUET 7
Oscillatory Circuit
Produces electrical oscillations of any desired
frequency
Simple oscillatory circuit consists of L and C
(i) At the initial condition the switch ‘S’ is open
Here, the capacitor
contains some charges as
electrostatic energy
Department of Electronics and Communication Engineering, KUET 8
(ii) When ‘S’ is closed:
Oscillatory Circuit
Flow of
electron
Capacitor discharges through
inductor
Due to inductive effect, the
current flow builds up slowly
towards a maximum value
At maximum current, the
electrostatic energy is zero
but electron motion is
maximum
The magnetic field around
the coil is maximum
Department of Electronics and Communication Engineering, KUET 9
(iii) When ‘S’ is closed:
o Once the capacitor is fully
discharged.
o The magnetic field will begin to
collapse and produce a counter
emf.
o This emf produce a current
flow in the same direction.
o The capacitor is now charged
with opposite polarity.
Oscillatory Circuit
Department of Electronics and Communication Engineering, KUET L4, 10
Oscillatory Circuit
(iv) When ‘S’ is closed:
Flow of
electron
o After recharging the
capacitor it begins to
discharge again.
o The magnetic field will
begin to collapse and
produce a counter emf.
o This emf produce a
current flow in the same
direction.
o The capacitor is now
charged with opposite
polarity.LC
fr2
1=
Frequency of oscillation:
The actual frequency of
oscillations is the resonance
frequency of the tank circuit:
Department of Electronics and Communication Engineering, KUET 11
Essentials of Transistor Oscillator (i) Tank circuit:
It consists of inductance coil (L)
connected in parallel with capacitor
(C). The frequency of oscillations
depends upon the values of L and C.
(ii) Transistor amplifier:The transistor amplifier receives dc
power from the battery and changes it
into ac power for at the frequency of
the tank circuit.
(iii) Feedback circuit:
The feedback circuit supplies a part of
output to the tank circuit in correct
phase to aid the oscillations, i.e., it
provides positive feedback.
Department of Electronics and Communication Engineering, KUET 12
o In order to produce continuous undamped oscillations at the
output of an amplifier, the positive feedback should maintain
the following criterion, it is called Barkhausen criterion:
mv Av = 1
here, mv is the feedback fraction and Av is the gain of amplifier
Mathematical Explanation: The voltage gain of a positive feedback amplifier is given by;
If mvAv = 1, then Avf → ∞.
• Thus once the circuit receives the input trigger, it would
become an oscillator, generating oscillations with no external
signal source.
Barkhausen Criterion
vv
vvf
Am
AA
−=
1
Department of Electronics and Communication Engineering, KUET 13
Different Types of Transistor Oscillators
A transistor can work as a oscillator to produce continuous undammed oscillations of any desired frequency if tank and feedback circuits are properly connected to it.
The commonly used transistor oscillator circuits are :
1. Tuned collector oscillator
2. Colpitt’s oscillator
3. Hartley oscillator
4. Phase shift oscillator
5. Wien bridge oscillator
6. Crystal oscillator
Department of Electronics and Communication Engineering, KUET 14
1. Tuned Collector Oscillator• It contains tuned circuit L1
and C1 in the collector
• Frequency of oscillation depends on the values of L1
and C1 :
• The coil L2 acts as feedback circuit
The capacitor C connected in the base circuit provides low reactance path to the oscillations
When switch S is closed, collector current starts increasing and
charges the capacitor C1. After full charge of C1. It discharges
through coil L1 and create an oscillation.
These oscillation induce some voltage in the coil L2 by mutual
induction.
Department of Electronics and Communication Engineering, KUET 15
2. Colpitt’s Oscillator (1/2) In Colpitt’s oscillator the tank
circuit is made up of C1, C2 and
L. The frequency of oscillation
is given by
TLCf
2
1=
21
21Where,CC
CCCT
+=
Circuit Operation:o When the circuit is turned on, the capacitors C1 and C2 are
charged.
o The capacitors discharge through L, setting up oscillations of
frequency determined by the above expression.
o The output voltage of the amplifier appears across C1 and
feedback voltage is developed across C2.
Department of Electronics and Communication Engineering, KUET L5, 16
2. Colpitt’s Oscillator (2/2)
o The voltage across C1 is 1800 out of phase and feedback voltage across C2 provides +ve voltage to the transistor.
Feed back fraction mv:
The amount of feedback voltage in Colpitt’soscillator depends upon the feedback fraction mv
of the circuit.
2
1
1
2
C
C
x
x
v
vm
C
C
out
f
v ===
Department of Electronics and Communication Engineering, KUET 17
Example / ProblemPb# What is the frequency of oscillation in following Fig.? What is
the feedback fraction? How much voltage gain does the circuit need to start oscillating?
Soln: Here, we know
21
21
CC
CCCT
+
=
66
66
1001.010001.0
)1001.0)(10001.0(−−
−−
+
=TC
pF909=TC
MHz36.1)10909)(1015(2
1
126=
=
−−rf
1.001.0
001.0==vm 10
001.0
01.0(min) ==vA
Department of Electronics and Communication Engineering, KUET 18
3. Hartley Oscillator (1/2)
It is similar to the Colpitt’s oscillator with minor modification.
It uses two inductors L1 and L2 instead of using two capacitors C1 and C2.
The tank circuit is made up of L1, L2, and C.
Frequency of oscillation:
where, LT = L1+L2+2M
M = Mutual inductance between L1
and L2
TCLf
2
1=
Department of Electronics and Communication Engineering, KUET 19
3. Hartley Oscillator (2/2) Circuit Operation:
o When circuit is ‘on’ capacitor C is charged and it discharged through L1 and L2.
o Output voltage appears across L1.
o Feedback voltage appears across L2.
o Voltage across L2 is 1800 out of phase with voltage across L1.
o A phase shift of 1800 is produced by transistor and another 1800 phase shift is produced by L1 & L2 voltage divider.
o Finally, positive feedback is produced and make undamped
oscillations.
Feedback Fraction mv:
1
2
1
2
L
L
x
x
v
vm
L
L
out
f
v ===
Department of Electronics and Communication Engineering, KUET 20
In this oscillator resistive and capacitive elements are used to obtain good frequency stability and waveform.
The RC or phase shift oscillators have the additional advantages that they can be used for very low frequencies.
Phase Shift Circuit:
A phase shift circuit essentially consists of an R-C network
Principle of Phase Shift Oscillators (1/2)
From the elemental theory of electrical
engineering we can say the voltage across R
leads the applied voltage v1 by φ0.
The value of φ depends on R and C, if R is
varied the value of φ also change. If R is
reduced to zero then φ = 900 .
But R = 0 is impracticable because it would
lead to no voltage across R.
1v
Department of Electronics and Communication Engineering, KUET 21
In practice, R is varied to such a value that makes to lead v1
by 600.
To obtain 1800 phase shift three R-C networks should be
connected in series.
In above Fig., each section produces a phase shift of 600.
Consequently a total phase shift of 1800 is produced. i.e., voltage
v2 leads the voltage v1 by 1800.
1v
Principle of Phase Shift Oscillators (1/2)
Department of Electronics and Communication Engineering, KUET 22
4. Phase Shift Oscillator (1/2)
If R1=R2=R3=R and C1=C2=C3=C then frequency of
oscillations is:
or
where, N= No. of stages
62
1
RCfo
=
NRCfo
22
1
=
Department of Electronics and Communication Engineering, KUET 23
Circuit Operation:
The output Eo of the amplifier is feedback to RC feedback
network. This network produces a phase shift of 1800 and a
voltage Ei is applied to the transistor amplifier.
The feedback fraction m = Ei /Eo
Total phase shift is 3600. Because phase shift produced by RC
network = 1800 and phase shift produced by transistor = 1800.
Advantages:
(i) it does not require transformers
(ii) it can be used to produce very low frequency
(iii) the circuit provides good frequency stability
Disadvantages:
(i) it is difficult for the circuit to start oscillations as the feedback is
generally small.
(ii) the circuit gives small output.
4. Phase Shift Oscillator (2/2)
Department of Electronics and Communication Engineering, KUET 24
Example/ Problem
Pb: In the phase shift oscillator shown in Fig. below, R1 = R2
= R3 = 1 MΩ and C1 = C2 = C3 = 68 pF. At what frequency
does the circuit oscillate ?
Ans: R1 = R2 = R3 = R = 1 MΩ = 106 Ω
C1 = C2 = C3 = C = 68 pF = 68 × 10−12 F
Frequency of oscillations is
= 954 Hz
Department of Electronics and Communication Engineering, KUET 25
Example/ Problem
Pb: A phase shift oscillator uses 5 pF capacitors. Find the
value of R to produce a frequency of 800 kHz. Ans: we know:
Department of Electronics and Communication Engineering, KUET 26
5. Wien Bridge Oscillator (1/3)
It is used to produce oscillation in the range of 10 Hz
to about 1 MHz frequencies.
It is most widely used audio oscillator as the output is
free from circuit fluctuations and ambient
temperature.
Department of Electronics and Communication Engineering, KUET 27
The bridge circuit has the arms R1C1, R3, R2C2 and tungsten
lamp Lp.
Resistance R3 and Lp are used to stabilize the amplitude of the
output.
The transistor T1 serves as an oscillator and amplifier.
While the transistor T2 serves as an inverter.
The frequency of oscillation is determined by the series element
R1C1 and parallel element R2C2 of the bridge.
If R1 = R2 = R and C1 = C2 = C, then
5. Wien Bridge Oscillator (2/3)
Department of Electronics and Communication Engineering, KUET 28
5. Wien Bridge Oscillator (3/3)
The two transistors produce a total phase shift of 3600 so that
proper positive feedback is ensured.
The positive feedback in the circuit ensures constant output.
Advantages:
a) It gives constant output.
b) The circuit works quite easily.
c) The overall gain is high because of two transistors.
d) The frequency of oscillations can be easily changed by using
a potentiometer.
Disadvantages:
a) The circuit requires two transistors and large number of
components.
b) It can not generate very high frequencies.
Department of Electronics and Communication Engineering, KUET 29
Example/ Problem
Pb: In the Wien bridge oscillator shown in following Fig., R1 = R2
= 220 kΩ and C1 = C2 = 250 pF. Determine the frequency of
oscillations.
Soln: Here,
R1 = R2 = R = 220 KΩ
C1 = C2 = C = 250 pF
We know, frequency of
oscillation:
Department of Electronics and Communication Engineering, KUET 30
Limitations of LC and RC Oscillators The major problem in the LC and RC oscillators is that their
operating frequency does not remain strictly constant. There
are two principal reasons for it,
1. As the circuit operates, it will warm up. Consequently, the
values of resistors and inductors, will change with
temperature. This causes the change in frequency of the
oscillator.
2. If any component in the feedback network is changed, it will
shift the frequency of oscillation.
Solution: In order to maintain constant frequency,
1. Piezoelectric crystals are used in place of LC or RC circuits.
2. Oscillators of this type are called crystal oscillators.
3. The frequency of a crystal oscillator changes by less than
0.1% due to temperature and other changes.
Department of Electronics and Communication Engineering, KUET 31
Crystal Oscillators (1/4) In order to maintain constant frequency Piezoelectric crystals
are used in place of LC and RC circuits. This type of oscillators
are called crystal oscillators.
Piezoelectric Crystals:
o Rochelle salt, quartz, and tourmaline are piezoelectric
crystals.
o This crystal vibrates at the frequency of applied voltage. In
contrast, when they placed under mechanical stain to vibrate,
they produce an ac voltage.
Frequency of Crystal:
Each crystal has a natural frequency like a pendulum.
f = K/t
where, K is a constant and t is the thickness.
Department of Electronics and Communication Engineering, KUET 32
Crystal Oscillators (2/4)
Equivalent Circuit of Crystal:
(i)
• When the crystal is not vibrating, it is equivalent
to capacitance Cm because it has two metal plates
separated by a dielectric.
• This capacitance is known as mounting
capacitance.
(ii)
• When a crystal vibrates, it is equivalent to
R – L – C series circuit.
• So, the equivalent circuit of a vibrating
crystal is R – L – C series circuit shunted by
the mounting capacitance Cm.
Department of Electronics and Communication Engineering, KUET 33
Crystal Oscillators (3/4) Frequency Response of Crystal:
If the crystal is vibrating the frequency
response is shown in the figure.
(i) At low frequencies: The crystal
impedance is controlled by extremely
high values of Xcm and Xc. So, at low
frequencies the impedance of the
network is high.
(ii) When the frequency is increased: At this stage, the R-L-C
branch approaches its resonant frequency. At fs, the XL will be
equal to XC. The frequency at which the vibrating crystal
behaves as a series resonant circuit is called series resonant
frequency fs.
LCfs
2
1=
Department of Electronics and Communication Engineering, KUET 34
Crystal Oscillators (4/4)
(iii) At a slightly higher frequency: At this stage, The R-L-C
branch becomes inductive and equal to XCm. The crystal acts
as a parallel-resonant circuit. The frequency at which crystal
acts as a parallel-resonant circuit is called parallel-resonant
frequency fp.
(iv) At frequencies greater than fp: The value of XCm drops and
the crystal acts as a short circuit.
m
mT
T
pCC
CCC
LCf
+
== ,where
2
1
Department of Electronics and Communication Engineering, KUET 35
Example Question: The ac equivalent circuit of a crystal has the values: L =
3H, Cs = 0.05 pF, R = 2 KΩ, and Cm = 10pF. Determine the series and
parallel resonant frequencies of the crystal.
Sol:
The fo is between 411 kHz and 412 kHz.
Department of Electronics and Communication Engineering, KUET 36
Crystal Stability
The frequency of any oscillator tends to change
slightly with time.
This drift is produced by -
Temperature
Aging and
Other causes
In crystal oscillator, frequency drift is very small-
typically less than 1 part in 106 per day.
Clock uses quartz crystal oscillator as the basic
timing device. A clock with this drift will take 300
years to gain or lose 1s.
Department of Electronics and Communication Engineering, KUET 37
6. Transistor Crystal Oscillator (1/2) It is a colpitt’s oscillator modified to act as a crystal oscillator.
Only a crystal is added in the feedback network and it will act
as a parallel-tuned circuit.
Here, L is replaced by the crystal Y and resonance is formed
by the (C1 + C2)
Feedback is positive. 1800 phase shift is produced by the
transistor and another 1800 phase shift is produced by the
capacitor voltage divider.
This oscillator will oscillate only at fp.
Department of Electronics and Communication Engineering, KUET 38
6. Transistor Crystal Oscillator (2/2)
Advantages:
1. They have a high order of frequency stability.
2. The quality factor of the crystal is very high.
Disadvantages:
1. They are fragile and consequently can be used in
low power circuit.
2. The frequency of oscillations can not be changed
appreciably.
Department of Electronics and Communication Engineering, KUET 39
Example/ Problem
Pb: The ac equivalent circuit of a crystal has these values: L = 1
H, C = 0.01 pF, R = 1000 Ω and Cm = 20 pF. Calculate fs and
fp of the crystal.
Soln: we know:
Hz101590
1099.912
1
1099.92001.0
2001.0,where
2
1 and
Hz101589
1001.012
1
2
1
3
15
3
3
12
=
=
=+
=
+
==
=
==
−
−
−
p
m
mT
T
p
s
f
pFCC
CCC
LCf
LCf
Frequency of oscillation of
this crystal will be between
1589 KHz and 1590 KHz
Department of Electronics and Communication Engineering, KUET 40
Assignment
Pb#: A crystal has these values: L= 3 H, C = 0.05 pF, R = 2 KΩ,
and Cm = 10 pF. What are the series and parallel resonant
frequencies of the crystal?
Pb#: A crystal oscillator has the value of inductance L = 2 H, and
the frequency of oscillation is between 1223 KHz and 1225
KHz. Calculate the values of capacitances C and Cm.
Pb#: A Hartley oscillator has the values of L1 = 1000 μH, L2 =
100 μH and C = 20 pF, find the (i) operating frequency and
(ii) feedback fraction.
Self Study: All the examples of VK Mehta
Department of Electronics and Communication Engineering, KUET 41
Unijunction Transistor (UJT)
Physical structure:
• One lightly-doped (high resistivity) silicon slab.
• Two base contacts (B1 and B2) at both end
of the slab.
• The p-n junction is form by alloying an aluminum rod to the slab.
• The aluminum rod is closer to B2 contact than B1 contact.
• B2 is made positive with respect to B1.
Department of Electronics and Communication Engineering, KUET 42
Physical structure
Unijunction Transistor (UJT)
Department of Electronics and Communication Engineering, KUET 43
UJT Relaxation Oscillator
Department of Electronics and Communication Engineering, KUET 44
Negative Resistance in Oscillator
(UJT)
Department of Electronics and Communication Engineering, KUET 45
Assume that the initial
capacitor voltage, VC is
zero.
When the supply voltage
VBB is first applied, the
UJT is in the OFF state.
IE is zero and C charges
exponentially through R1
towards VBB.
The operation:
UJT Relaxation Oscillator
Department of Electronics and Communication Engineering, KUET 46
When the supply
voltage VC (= VE)
reaches the firing
potential, VP, the UJT
fires and C discharges
exponentially through
R2 until VE reaches the
valley potential VV.
UJT Relaxation Oscillator
Department of Electronics and Communication Engineering, KUET 47
When VE reaches the
valley potential VV the
UJT turns OFF, IE goes
to zero and the capacitor
is recharged.
This process repeats itself
to produce the
waveforms for vC and vR2
as shown below;
UJT Relaxation Oscillator
Department of Electronics and Communication Engineering, KUET 48
UJT Relaxation Oscillator
Thanks for Your Kind
Attention
Department of Electronics and Communication Engineering, KUET