Title of Presentation - KUET · (ii) Undamped Oscillations (i) Damped Oscillations: The electrical oscillations whose amplitude goes on decreasing with time are called damped oscillations

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


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.


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.


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


(ii) Undamped Oscillations

The electrical oscillations whose amplitude and

frequency remain constant with time are called

undamped oscillations.

Types of Sinusoidal Oscillations (2/2)


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


(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


(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:


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.


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


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


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.


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 ===


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


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=


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 ===


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


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)


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

=


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)


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


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:


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.


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




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.


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:


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.


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.


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.


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=


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


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.


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.


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.


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.


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


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


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.


Physical structure

Unijunction Transistor (UJT)


UJT Relaxation Oscillator


Negative Resistance in Oscillator

(UJT)


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:



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.



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;




Thanks for Your Kind

Attention

Department of Electronics and Communication Engineering, KUET

Documents

Title of Presentation - KUET · (ii) Undamped Oscillations (i) Damped Oscillations: The electrical oscillations whose amplitude goes on decreasing with time are called damped oscillations