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EMT212 – Analog Electronic II
Chapter 4
Oscillator
By
En. Rosemizi Bin Abd Rahim
Objectives
 Describe the basic concept of an oscillator
 Discuss the basic principles of operation of an oscillator
 Analyze the operation of RC, LC and crystal oscillators
 Describe the operation of the basic relaxation oscillator
circuits
Introduction
Oscillators are circuits that produce a continuous
signal of some type without the need of an input.
These signals serve a variety of purposes.
Communications systems, digital systems (including
computers), and test equipment make use of
oscillators.
The Oscillator
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.
Types of Oscillator
1. RC Oscillator - Wien Bridge Oscillator
- Phase Shift Oscillator
2. LC Oscillator - Hartley Oscillator
- Colpitts Oscillator
- Clapp Oscillator
- Crystal Oscillator
3. Relaxation Oscillator
Feedback Oscillator Principles

An oscillator is an amplifier with positive
feedback.
Ve = Vi + Vf
Vo = Ave
Vf = Vo
(1)
(2)
(3)
From (1), (2) and (3), we get
Vo
A

Vi 1  A
Feedback Oscillator Principles




Hence the closed loop gain, Vo/Vi = A/(1 - A)
The closed loop gain can be very large if (1 - A)= 0
A small signal value at the input can produce an
output of reasonable magnitude. Thus the amplifier
will be unstable when (1 - A) = 0, or when the loop
gain A = 1
In polar form, A = 1 0° or 1 360°
Feedback Oscillator Principles
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.
Design Criteria for oscillators
1)
|A| equal to unity or slightly larger at the
desired oscillation frequency.
- Barkhaussen criterion, |A|=1
2)
Total phase shift, of the loop gain must be 0°
or 360°.
Factors that determine the frequency of
oscillation




Oscillators can be classified into many types
depending on the feedback components,
amplifiers and circuit topologies used.
RC components generate a sinusoidal waveform
at a few Hz to kHz range.
LC components generate a sin wave at
frequencies of 100 kHz to 100 MHz.
Crystals generate a square or sin wave over a
wide range,i.e. about 10 kHz to 30 MHz.
1. RC Oscillators
Oscillators With RC Feedback
Circuits
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.
Wien-Bridge Oscillator


It is a low frequency oscillator which ranges from
a few kHz to 1 MHz.
Structure of this oscillator is
Wien-Bridge Oscillator
Wien-Bridge Oscillator
Multiply the top and bottom by jωC1,
we get
V1
jC1 R1

Vo 1  jC1 R1 1  jC2 R2   jC1 R2
Divide the top and bottom by C1 R1 C2 R2
V1

Vo
j


 R1C1  R2C2  R2C1 
1
2

   
R1C2 
 j 

R1C1 R2C2


 R1C1 R2C2

Wien-Bridge Oscillator
Now the amp gives
V0
K
'
V1
Furthermore, for steady state oscillations, we want the feedback
V1 to be exactly equal to the amplifier input, V1’. Thus
'
V1
1 V
  1
Vo K Vo
Wien-Bridge Oscillator
Hence
1

K
j


 R C  R2C2  R2C1 
1
   2 
R1C2 
 j  1 1

R1C1 R2C2


 R1C1 R2C2



 R C  R2C2  R2C1 
1
   2 
jK  R1C2 
 j  1 1

R1C1 R2C2


 R1C1 R2C2

Equating the real parts,
1
2  0
R1C1 R2C2
R1C1  R2C2  R2C1
K
R2C1
Wien-Bridge Oscillator
If R1 = R2 = R and C1 = C2 = C
K 3
1

RC
1
fr 
2RC
- Gain > 3 : growing oscillations
- Gain < 3 : decreasing oscillations
Wien-Bridge Oscillator
The lead-lag circuit of a Wien-bridge oscillator reduces
the input signal by 1/3 and yields a response curve as
shown. The frequency of resonance can be determined
by the formula below.
fr = 1/2RC
Wien-Bridge Oscillator
The lead-lag circuit is in the
positive feedback loop of
Wien-bridge oscillator. The
voltage divider limits gain.
The lead lag circuit is
basically a band-pass with a
narrow bandwidth.
Wien-Bridge Oscillator
Since there is a loss of about 1/3 of the signal in the positive
feedback loop, the voltage-divider ratio must be adjusted
such that a positive feedback loop gain of 1 is produced. This
requires a closed-loop gain of 3. The ratio of R1 and R2 can
be set to achieve this.
Wien-Bridge Oscillator
To start the oscillations an initial gain greater than 1 must be
achieved. The back-to-back zener diode arrangement is one way of
achieving this. When dc is first applied the zeners appear as opens.
This allows the slight amount of positive feedback from turn on
noise to pass.
Wien-Bridge Oscillator
The lead-lag circuit narrows the feedback to allow just the
desired frequency of these turn transients to pass. The higher
gain allows reinforcement until the breakover voltage for the
zeners is reached.
Wien-Bridge Oscillator
Automatic gain control is necessary to maintain a gain of exact
unity. The zener arrangement for gain control is simple but produces
distortion because of the nonlinearity of zener diodes. A JFET in the
negative feedback loop can be used to precisely control the gain. After
the initial startup and the output signal increases the JFET is biased
such that the negative feedback keeps the gain at precisely 1.
Phase Shift Oscillator
The phase shift oscillator utilizes three RC circuits to provide
180º phase shift that when coupled with the 180º of the opamp 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.
fr = 1/26RC
Phase Shift Oscillator
The transfer function of the RC network is
Phase Shift Oscillator
If the gain around the loop equals 1, the circuit oscillates at this
frequency. Thus for the oscillations we want,
Putting s=jω and equating the real parts and imaginary parts,
we obtain
Phase Shift Oscillator
From equation (1) ;
Substituting into equation (2) ;
# The gain must be at least 29 to maintain the oscillations.
Phase Shift Oscillator – Practical
The last R has been incorporated into the summing resistors
at the input of the inverting op-amp.
fr 
1
2 6 RC
K
 Rf
R3
 29
2. LC Oscillators
Oscillators With LC Feedback
Circuits
For frequencies above 1 MHz, LC feedback oscillators
are used.
We will discuss the Colpitts, Hartley and crystalcontrolled oscillators.
Transistors are used as the active device in these types.
Oscillators With LC Feedback
Circuits
Employs BJTs (or FETs) instead of op-amps and are
therefore useful at high frequencies.
Consider the general BJT circuit:
Oscillators With LC Feedback
Circuits
Using the small signal equivalent circuit this becomes
Applying KVL around loop (1), and let ZT = Z1 + Z2 + Z3
Oscillators With LC Feedback
Circuits
Using KVL in loop (2) ;
Substituting (2) into (1) ;
Oscillators With LC Feedback
Circuits
If the Z’s are purely imaginary and hie is real, then
Substituting (3) into the expression ZT = Z1 + Z2 + Z3 = 0 ;
Z2 and Z1 are the same type of component
Oscillators With LC Feedback
Circuits
Z3 is the opposite type (-ve)
if Z2 and Z1 are inductors, then Z3 is a capacitor and vice
versa.
Oscillators With LC Feedback
Circuits
Colpitts Oscillators
The Colpitts oscillator utilizes a tank circuit (LC) in the feedback
loop. The resonant frequency can be determined by the formula
below.
1
fr 
2 LCT
1
1
1


CT C1 C2
Colpitts Oscillators
Conditions for oscillation and start up

Vf
Vout
Av 

1

Av 
C1
C2
IX c1 C2

IX c 2 C1
Hartley Oscillators
The Hartley oscillator is similar to the Colpitts. The tank circuit
has two inductors and one capacitor. The calculation of the
resonant frequency is the same.
fr 
1
2 LT C
LT  L1  L2

Av 
L1
L2
1


L2
L1
Crystal Oscillators
The crystal-controlled oscillator is the most stable and
accurate of all oscillators. A crystal has a natural frequency
of resonance. Quartz material can be cut or shaped to have
a certain frequency. We can better understand the use of a
crystal in the operation of an oscillator by viewing its
electrical equivalent.
Oscillators With LC Feedback
Circuits
Since crystal has natural
resonant frequencies of 20
MHz or less, generation of
higher frequencies is
attained by operating the
crystal in what is called the
overtone mode.
3. Relaxation Oscillators
Relaxation Oscillators
Relaxation oscillators make use of an RC timing and a device
that changes states to generate a periodic waveform (nonsinusoidal).
1.
Triangular-wave
2.
Square-wave
3.
Sawtooth
Triangular-wave Oscillator
Triangular-wave oscillator circuit is a combination of a
comparator and integrator circuit.
fr 
1  R2 
 
4CR1  R3 
R 
VUTP  Vmax  3 
 R2 
R 
VLTP  Vmax  3 
 R2 
Square-wave Oscillator
A square wave relaxation oscillator is like the Schmitt trigger or
Comparator circuit.
The charging and discharging of the capacitor cause the opamp to switch states rapidly and produce a square wave.
The RC time constant determines the frequency.
Sawtooth Voltage-Controlled Oscillator
(VCO)
Sawtooth VCO circuit is a combination of a Programmable
Unijunction Transistor (PUT) and integrator circuit.
Sawtooth Voltage-Controlled Oscillator
(VCO)
Operation
Initially, dc input = -VIN
•
Vout = 0V, Vanode < VG
•
The circuit is like an integrator.
•
Capacitor is charging.
•
Output is increasing positive going
ramp.
Sawtooth Voltage-Controlled Oscillator
(VCO)
Operation
When Vout = VP
•
Vanode > VG , PUT turn ‘ON’
•
The capacitor rapidly discharges.
•
Vout drop until Vout = VF.
•
Vanode < VG , PUT turn ‘OFF’
VP-maximum peak value
VF-minimum peak value
Sawtooth Voltage-Controlled Oscillator (VCO)
Oscillation frequency is
VIN  1

f 
Ri C  VP  VF



Sawtooth Voltage-Controlled Oscillator
(VCO)
Example
Let VF = 1V, find
i)
Amplitude
ii) Frequency
iii) Sketch the output
waveform
Sawtooth Voltage-Controlled Oscillator
(VCO)
Solution
i)
Amplitude
R4
 V 
VG 
R3  R4
10k
15  7.5V
VG 
20k
V p  VG  7.5V
VF  1V
So, peak – to- peak Amplitude is
V p  VF  6.5V
Sawtooth Voltage-Controlled Oscillator
(VCO)
ii) Frequency
V  1
f  IN 
Ri C  VP  VF



R2
 V   1.92V
VIN 
R1  R2
1.92
1


f 

  628Hz
100k 0.0047    7.5V  1V 
Sawtooth Voltage-Controlled Oscillator
(VCO)
iii) Output Waveform
1
1
T 
2ms
f 628
The 555 Timer As An Oscillator
The 555 timer is an
integrated circuit that can be
used in many applications.
The frequency of output is
determined by the external
components R1, R2, and C.
The formula below shows the
relationship.
144
fr 
R1  2 R2 Cext
The 555 Timer As An Oscillator
Duty cycles can be adjusted by values of R1 and R2. The
duty cycle is limited to 50% with this arrangement. To have
duty cycles less than 50%, a diode is placed across R2. The
two formulas show the relationship.
Duty Cycle >50 %
 R  R2 
100%
DutyCycle   1
 R1  2 R2 
Duty Cycle <50 %
 R1 
100%
DutyCycle  
 R1  R2 
The 555 Timer As An Oscillator
The 555 Timer As An Oscillator
The 555 timer by be operated as a VCO with a control
voltage applied to the CONT input (pin 5).
Summary
 Sinusoidal oscillators operate with positive feedback.
 Two conditions for oscillation are 0º feedback phase
shift and feedback loop gain of 1.
 The initial startup requires the gain to be momentarily
greater than 1.
 RC oscillators include the Wien-bridge, phase shift,
and twin-T.
 LC oscillators include the Colpitts, Clapp, Hartley,
Armstrong, and crystal.
Summary
 The crystal actually uses a crystal as the LC tank circuit
and is very stable and accurate.
 A voltage controlled oscillator’s (VCO) frequency is
controlled by a dc control voltage.
 A 555 timer is a versatile integrated circuit that can
be used as a square wave oscillator or pulse generator.