CHAPTER 2 - Oscillator.pdf

8/9/2019 CHAPTER 2 - Oscillator.pdf

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EE301 ELECTRONIC CIRCUIT

CHAPTER 2: OSCILLATORS Page 35

Prepared by: NORZILAWATI BINTI ABDULLAH Coordinator: Engr.Muhammad Muizz

Oscillators

2.0 Introduction

An oscillator is an electronic circuit which generates an alternating voltage.

The circuit is supplied energy from D.C source. Oscillator is an electronic device

which generates an ac signal with required frequency, amplitude and wave

shape.

Oscillators have variety of applications. An oscillator generates low

frequency and very high frequencies which may range from few Hz to several

MHz. In radio and television receivers, oscillators are used to generate high

frequency carrier signals. Oscillators are widely used in radars, electronic

equipments and other electronic devices.

Oscillators are broadly classified into two types. They are

i) Sinusoidal oscillators

The sinusoidal oscillators are used for generating only sinusoidal

signals with required frequency and required amplitude.

ii) Non-sinusoidal oscillators (Relaxation oscillators)

The non-sinusoidal oscillators are used for producing non-

sinusoidal signals like square, rectangular, triangular or sawtooth

signals with required amplitude and frequency.

2.1 Understand Sinusoidal Oscillator Circuits And

State Their Characteristics.

The name sinusoidal oscillator itself indicates the meaning that this

oscillator produces sine wave output. For any type of circuit to behave as an

oscillator, first it must satisfy the necessary and sufficient condition which is

mentioned in the previous section. Depending upon the variation in the output

waveform amplitude, there are two types of oscillations.


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1. Damped

Damped oscillations: Oscillations, whose amplitude goes on

decreasing or increasing continuously with time, are called damped

oscillations.

If amplitude of oscillations is decreasing continuously, it is known

as underdamped as shown in figure 1. Where if amplitude of

oscillations is increasing continuously, it is known as overdamped

shown in figure 2.

Figure 2.1: Underdamped Figure 2.2: Overdamped

2. Undamped or (sustained)

Undamped oscillations: Oscillations, whose amplitude remains

constant with time, are called undamped oscillations or sustain

osillations. The figure show in figure 3 below.

Figure 2.3: Undamped


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Practical Oscillators

In practice, to obtain the sustained oscillations at desired frequency

of oscillations, oscillator circuit must satisfy some of the basic

requirements such as,

i) Circuit must have positive feedback

ii) When positive feedback is used in the circuit, the overall circuit

gain is given by,

This equation indicates that if ‘Aβ’ is equal to 1 only then overall

gain becomes infinity. This means, there is output without any external

input. In reality, to get sustained oscillations, at the first time when the

circuit is turned on, the loop gain must be slightly greater than one. This

will ensure that oscillations build up in the circuit. However, once a

suitable level of output voltage is reached, the loop gain must decrease

automatically to unity. Only then the circuit maintains the sustained

oscillation. Otherwise, the circuit operates as over damped. This can be

achieved in the circuit either by decreasing amplifier gain A or decreasing

the feedback gain β.

2.1.1 Draw block diagram of an oscillator.

The basic concept of an oscillator is illustrated in figure 4. Essentially, an

oscillator converts electrical energy in the form of dc to electrical energy in the

form of ac. The difference between positive feedback amplifier and oscillator is

that, in oscillator, there is no need of external input signal. To start the

oscillations, output signal must be fed back in proper magnitude and phase.


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The Barkhausen Criterion states that:

1. The total phase shift around a loop as the signal proceeds

from input through amplifier, feedback network back to

input again, completing a loop is precisely 0° or 360°.

2. The magnitude of the product of the open loop gain of the

amplifier (A) and the magnitude of the feedback factor β is

unity i.e ∣Aβ∣ = 1.

Figure 2.4: Block Diagram of an oscillator

2.1.2 EXPLAIN REQUIREMENTS OF OSCILLATOR CIRCUITS.

Two conditions are required for a sustained state of oscillation:

1. The phase shift around the feedback loop must be 0° (or 360°)

2. The voltage gain Acl, around the closed feedback loop (loop gain)

must equal 1(unity).

The voltage gain around the closed feedback loop (Acl) is the product of

the amplifier gain (Av) and the attenuation (B) of the feedback circuit. Therefore

Acl = (Av)B. For example the amplifier have gain of 100, the feedback circuit

must have an attenuation of 0.01 to make the loop gain equal to 1.


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2.2 Know Types of Sinusoidal Oscillator

There are three basic types of oscillators such as RC oscillator, LC

oscillator and crystal oscillator.

1. RC oscillators:

They use a resistance-Capacitance network to determine the oscillator

frequency. They are suitable for low (audio range) and moderate frequency

applications (5Hz to 1MHz). They are further divided as,

a. RC phase shift oscillator

b. Wien bridge oscillator and

c. Twin-T oscillator

2. LC oscillators:

Here, inductors and capacitors are used either in series or parallel to

determine the frequency. They are more suitable for radio frequency (1 to 500

MHz) and further classified as,

a. Hartley

b. Colpitts

c. Clapp andd. Armstrong oscillators

3. Crystal oscillator :

Like LC oscillators it is suitable for radio frequency applications. But it has

very high degree of stability and accuracy as compared to other oscillators.


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c. Phase Shift (RC) Oscillator

Figure 2.7: Phase Shift (RC) Oscillator

d. Crystal Oscillator


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Figure 2.8: Crystal Oscillator

e. Amstrong

Figure 2.9: Amstrong Oscillator


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2.2.2 Explain the operation of each oscillator.

a. Hartley Oscillator

Hartley Oscillator is a L.C oscillator. It is uses tapped inductor coil.

Circuit diagram of Hartley oscillator using N-P-N transistor is illustrated in

Figure 2.5. This oscillator contains a CE amplifier, feedback network and a

tank circuit made up of L1, L2 and C. The resistor R1 and R2 provide

necessary bias to the amplifier. The capacitor C1 and C0 are used to block

the D.C components. The capacitor CE is a bypass capacitor. The resistor

RE provides negative feedback to the amplifier to improve its stability. The

RF choke (RFC) provides a path for collector bias current but offers high

impedance for oscillating signal.

Principal of operation

When the supply is turned ON, the capac itor ‘C’ is charged. When

this capacitor is fully charged, it discharges through the coils L1 and L2

setting up an oscillation. The output voltage of the amplifier appears

across L1 and the feedback voltage appears across L2. The voltage across

L2 is 180° out of phase with the output voltage. It is the feedback signal. A

phase shift of another 180° is produced by CE amplifier. Hence the total

phase shift between input and output is 180° + 180° = 360°. This results in

positive feedback which makes the oscillation as continuous undamped.

The frequency of the oscillation is given by, f = LeqC 2

1,

where Leq = L1 + L2.

If there exists mutual inductance M between two inductors, it must

be considered while calculating equivalent inductor.

Therefore Leq = L1 + L2 + 2M

Hartley Oscillators are widely used in the radio receivers as local

oscillator.


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LC oscillator using 2 inductors and 1 capacitor in the

tank circuit is called Hartley Oscillator .

The frequency of oscillations is,

f = LeqC 2

1 , where Leq = L1 + L2

If L1 and L2 are wound on same core, mutual inductance M must be

considered. Then,

Leq = L1 + L2 ± 2M

+ve sign is used for series aiding while –ve sign for series opposition

connection of winding

b. Colpitt’s Oscillator

The Colpitts oscillator is same as Hartley oscillator. The circuit

diagram of colpitts oscillator is shown in the Figure 2.6. the major

difference between the two is that the colpitts oscillator uses a tapped

capacitor whereas the Hartley oscillator uses a tapped inductor.

The tank circuit is made up of C1, C2 and L. The resistors R1 and R2

provide proper bias and RE with CE provides stabilization. The RF choke

(RFC) gives high impedance for high frequency oscillating signal.

The frequency of the oscillation is given by f = LCeq2

1

Where Ceq =21

2.1

C C

C C


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When the supply is turned ON, the capacitor C1 and C2 are

charged. Then these capacitors discharged through the coil ‘L’. So

oscillations are produced. The oscillations across C2 are applied to the

input of the CE amplifier. The amplified output is available at the collector

terminal of the transistor.

The amount of feedback depends upon the capacitance values of

C1 and C2. The capacitor feedback circuit provides 180° phase shift. The

transistor amplifier (CE) provides another 180° phase shift, which provides

positive feedback. Therefore continuous undamped oscillation is

produced.

The Colpitts oscillator is very commonly used as local oscillator in

superheterodyne radio receiver.

c. Phase Shift (RC) Oscillator

The RC oscillators produce good frequency stability signal ang also

operate at very low frequencies. The circuit diagram of RC phase shift

oscillator is shown in Figure 2.7. The oscillator consists of three stages of

RC networks (R1C1, R2C2 and R3C3). The resistor R5 provides bias and RE

with CE provides stabilization.

LC oscillator using C1, C2 and L in the tank circuit is

called Colpitts oscillator.

The frequency of oscillations is,


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The frequency of the oscillation is given by

f =62

1

RC


When the supply is ON, the random variations of base current

caused by noise variations in the transistor and voltage variations in the

power source produce oscillation. The variation is amplified by the CE

amplifier.The feedback network consists of three stages of RC networks.

The three stages are identical. The feedback section provides 180° phase

shift because each RC network provides 60° phase shift (3 x 60° = 180°).

The CE amplifier provides another 180° phase shift. Hence the total phase

shift is 360°, which provides positive feedback. Therefore continous

undamped oscillation is produced.

R-C Oscillators are used for low frequency range called audio

frequency range.

It uses op-amp in inverting mode which introduces 180°

phase shift between input and output.

The feedback network has 3 R-C sections, each adjusted for

60° phase shift. Hence total phase shift due to feedback

network is 180°.

Hence total phase shift around a loop is 180° + 180° = 360°

To satisfy Aβ ≥ 1, the gain of op-amp circuit ∣A∣≥ 29

The frequency oscillation is given by


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d. Crystal Oscillator


The circuit diagram of crystal oscillator is illustrated in Figure 2.8.

The natural frequency of the LC circuit is made nearly equal to the natural

frequency of the crystal. When the supply is switched ON, the capacitor C1

is going to charged. When the capacitor C1 is fully charged, it discharges

through crystal which produces oscillation.

The frequency of the oscillation depends upon the values of C1,

C2, and the RLC equivalent values of crystal. If the frequency of the

oscillationis equal to its crystal resonant frequency, the circuit producesmore stable oscillation. The crystal frequency is independent of

temperature.

The C2 feedback network provides 180° phase shift, and alsi the

CE amplifier provides another 180°phase shift. Hence the total phase shift

is 360°, which provides positive feedback. Therefore continous undamped

oscillation is produced. A crystal oscillator always generates high

frequency oscillations range from 20KHz to 20MHz.


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e. Amstrong Oscillator

The armstrong oscillator is used to produce a sine-wave output of

constant amplitude and of fairly constant frequency within the RF range. It

is generally used as a local oscillator in receivers, as a source in signal

generators, and as a radio-frequency oscillator in the medium- and high-

frequency range.

The identifying characteristics of the Armstrong oscillator are that:

a. It uses an LC tuned circuit to establish the frequency of

oscillation,b. Feedback is accomplished by mutual inductive coupling

between the tickler coil and the LC tuned circuit.

c. It uses a class C amplifier with self-bias. Its frequency is

fairly stable, and the output amplitude is relatively constant.

The armstrong oscillator uses transformer coupling for the feedback

signal. The secondary winding is also called tickler coil, because it

feedbacks the signal that sustains the oscillations. The LC tank circuit is

driven by the collector. The feedback signal is taken from the small

secondary winding and feedback to the base. There is a phase shift of

180° in the transformer. If the loading effect of the base is ignored, the

feedback fraction is β = L

M , where M is the mutual inductance and L is

the inductance of the primary winding. Here the voltage gain must be

greater than

1 for starting the oscillations.


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2.2.3 Determine the oscillation frequency by using the formula:

a. Hartley Oscillator

Example 1:

Calculate the frequency of oscillations of a Hartley oscillator having

L1=0.5mH, L2 = 1mH and C = 0.2µF

Solution:

The given values are,

L1 = 0.5mH, L2 = 1mH, C = 0.2µF

Formula : f = LeqC 2

1

where Leq = L1 + L2 = 0.5m + 1m = 1.5mH

Therefore f =63

102.0105.12

1

x x x = 9.19 kHz

Example 2:

In a transistorized Hartley oscillator the two inductances are 2mH and

20µH while the frequency is to be change 950 kHz to 2050 kHz. Calculate

the range over which the capacitor is to be varied.

Solution:

The frequency is given by,


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f = LeqC 2

1

where Leq = L1 + L2 = 2m + 20µ = 0.00202

For f = fmax = 2050kHz

2050x103 = xC 00202.02

1

Therefore C = 2.98pF

For f = fmin = 950kHz

950x103 = xC 00202.02

1

Therefore C = 13.89pF

Hence C must be varied from 2.98pF to 13.89pF, to get the required

frequency variation.

Self Review Questions

1. With a neat circuit diagram, explain the operation of Hartley Oscillator.

2. A Hartley oscillator circuit has L1 =L2 =100µH. The frequency ofoscillations required is 50kHz. Calculate value of the capacitance required.

( Ans: 0.0507µF)

3. Find the operating frequency of a Hartley oscillator if L1=0.1mH, L2=1mH

and C=200pF.

( Ans: 339.32kHz)

4. Calculate the frequency of oscillations of Hartley oscillator having

L1=0.5m, L2=1mH and C=0.22µF. ( Ans: 8.761kHz)


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b. Colpitt’s

Example 1:

By referring to the Colpitts oscillator circuit shown in the figure 3 below:

i. What is approximate frequency?

ii. What will be the new frequency if the value of L is doubled?

Solution:

i.

f =CeqL 2

1

where Ceq =21

21

C C

xC C

= C1= C2 = 0.001µF

Ceq = 66

66

10001.010001.0

10001.010001.0

x x

x x x= 5 x 10-10F

L = 5µF


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Therefore f = 51052

1

10 x x = 3.183MHz

ii. Now L is double, therefore L = 10µH

f = 101052

1

10 x x = 2.25MHz

New frequency = 2 x 3.183 = 6.366MHz

6.366x106 = xL x 101052

1

Therefore L = 1.25H

Example 2:

Design the value of an inductor to be used in Colpitts oscillator to generate

a frequency of 10 MHz. The circuit is used a value of C1 = 100 pF and C2

= 50 pF.

Solution:Given, C1 = 100 pF, C2 = 50pF, f = 10MHz, L =?

Ceq =21

21

C C

xC C

=

p p

p px

50100

50100

= 33.33pF

f =CeqL 2

1

10M = pxL33.332

1

Therefore L = 7.6µH


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Example 2:

Design R-C phase shift oscillator using op-amp for frequency of 900 kHz.

Solution:

f = 900 kHz

Let C = 1pF

Therefore f = RC 62

1

900k = p Rx162

1

Therefore R = 72.194 kΩ

The gain of op-amp must be 29.

291

R

Rf

Therefore Rf = 29 R1

By choosing R1= 1kΩ

Rf = 29 kΩ

Hence the designed circuit is shown in the figure 4 below.

Figure 4: Designed circuit.


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Example 3:

Estimate the values of R and C for an output frequency of 1kHz in a RC

phase shift oscillator.

Solution:

Given: f = 1kHz

Now f = RC 62

1

Choose C = 0.1µF

Therefore 1k =u Rx 1.062

1

R = 649.747 Ω ≈ 680Ω

Example 4:

In R-C phase shift oscillator R = 5000Ω and C = 0.1µF. Calculate the

frequency of oscillations.

Solution:

f = RC 62

1

=

1.0500062

1

x x=129.949 Hz


1. With a neat circuit diagram, explain the operation of RC phase shift.

2. What is the expression for the frequency of a RC phase shift oscillator?

State the op-amp gain required for the oscillations.


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d. Crystal

Example 1:

A crystal has L =0.1 H, C = 0.01 pF, R = 10kΩ and CM=1pF. Find the

series resonance and Q factor.

Solution:

fs = LC 2

1=

121001.01.02

1

x x = 5.032 MHz

Q = 22.3161010

1.010032.522

3

6

x

x x x

R

fsL

R

sL

Example 2:

A crystal has the following parameters:

L = 0.5H, Cs = 0.06pF, Cp=1pF and R=5kΩ. Find the series and parallel

resonant frequencies and Q-factor of the crystal.

Solution:

a) The series resonant frequency of the crystal is

fs = 121006.05.02

1

2

1

x x LCs = 918.9kHz

Q-factor of the crystal at

fs = 577105

5.0109.91822

3

3

x

x x x

R

fsL

R

sL


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b) The parallel resonant frequencu of the crystal is

fr = kHz

x x x x

x

LCsCp

CpCs946

1011006.05.0

1006.1

2

1

2

1

1212

12

Q-factor of the crystal at fp = 594105

5.01094622

3

3

x

x x x

R

fpL

R

pL

2.2.3 Determine The Effect Of Varying The Values Of The L And C To

The Oscillation Frequency.

Effect of Frequency on Inductive Reactance

In an a.c. circuit, an inductor produces inductive reactance which causes

the current to lag the voltage by 90 degrees. Because the inductor "reacts" to a

changing current, it is known as a reactive component. The opposition that an

inductor presents to a.c. is called inductive reactance (XL). This opposition is

caused by the inductor "reacting" to the changing current of the a.c. source. Both

the inductance and the frequency determine the magnitude of this reactance.

This relationship is stated by the formula:

As shown in the equation, any increase in frequency, or "f," will cause a

corresponding increase of inductive reactance, or "XL." Therefore, the

INDUCTIVE REACTANCE VARIES DIRECTLY WITH THE FREQUENCY. As


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you can see, the higher the frequency, the greater the inductive reactance; the

lower the frequency, the less the inductive reactance for a given inductor. This

relationship is illustrated in figure 5. Increasing values of XL are plotted in terms

of increasing frequency. Starting at the lower left corner with zero frequency, the

inductive reactance is zero.

As the frequency is increased (reading to the right), the inductive

reactance is shown to increase in direct proportion.

.

Figure 5 - Effect of frequency on inductive reactance

Effect of Frequency on Capacitive Reactance

In an a.c. circuit, a capacitor produces a reactance which causes the

current to lead the voltage by 90 degrees. Because the capacitor "reacts" to a

changing voltage, it is known as a reactive component. The opposition a

capacitor presents to a.c. is called capacitive reactance (XC). The opposition iscaused by the capacitor "reacting" to the changing voltage of the a.c. source. The

formula for capacitive reactance is:


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In contrast to the inductive reactance, this equation indicates that the

CAPACITIVE REACTANCE VARIES INVERSELY WITH THE FREQUENCY.

When f = 0, XC is infinite and decreases as frequency increases. That is, thelower the frequency, the greater the capacitive reactance; the higher the

frequency, the less the reactance for a given capacitor.

As shown in figure 6, the effect of capacitance is opposite to that of

inductance. Remember, capacitance causes the current to lead the voltage by 90

degrees, while inductance causes the current to lag the voltage by 90 degrees.

Figure 6 - Effect of frequency on capacitive reactance


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di h d i

Extra notes:

Compare RC phase shift and crystal oscillator.

Answer:


1. Compare The Performance Of The Oscillators In Section 2.2.1

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CHAPTER 2 - Oscillator.pdf