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OSCILLATORS
Oscillators
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
Oscillators
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.
Oscillators
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.
Oscillators
dc supply
voltage
Oscillator
V out
or
or
Oscillators
Types of oscillators
1. RC oscilators
- Wien Bridge
- Phase Shift
2. LC oscillators
- Hartley
- Colpitts
3. Relaxation oscilators
Oscillators
Basic principles for oscillation
 An oscillator is an amplifier with positive feedback.
Ve
Vs
Ve  Vs  V f (1)
+
Vf
A
Vo
b
V f  βVo (2)
Vo  AVe  AVs  V f   AVs  βVo 
(3)
Oscillators
Vo  AVe
 AVs  V f   AVs  βVo 
Vo  AVs  AbVo
1  Ab Vo  AVs
Oscillators
The closed loop gaind is;
Vo
A
Af 

Vs 1  Aβ 
Ve
Vs
+
Vf
A
b
Vo
Oscillators
In general A and b are functions of frequency and
thus may be written as;
Vo
As 
A f s   s  
Vs
1  As β s 
As βs  is known as loop gain
Oscillators
Writing
T s   As β s  the loop gain becomes;
As 
A f s  
1  T s 
Replacing s with j;
A jω
A f  jω 
1  T  jω
and
T  jω  A jωβ jω
Oscillators
At a specific frequency f0;
T  jω0   A jω0 β  jω0   1
At this frequency, the closed loop gain;
A jω0 
A f  jω0  
1  A jω0 β  jω0 
will be infinite, i.e. the circuit will have finite output
for zero input signal - oscillation
Oscillators
Thus, the condition for sinusoidal oscillation of
frequency f0 is;
A jω0 β  jω0   1
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.
Oscillators
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.
Oscillators
In phase
Vf
Av
Noninverting
amplifier
Feedback
circuit
Vo
Oscillators
Design Criteria for Oscillators
1. The magnitude of the loop gain must be unity
or slightly larger i.e.
Aβ  1
– Barkhaussen criterion
2. Total phase shift, of the loop gain must be 0°
or 360°.
Oscillators
Factors determining 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 sine wave at
frequencies of 100 kHz to 100 MHz.
Crystals generate a square or sine wave over a
wide range,i.e. about 10 kHz to 30 MHz.
Oscillators
1. RC Oscillators
Oscillators
1. 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.
Oscillators – Wien-bridge
It is a low
frequency
oscillator
which ranges
from a few kHz
to 1 MHz.
Structure of
this oscillator
is shown
below;
Oscillators – Wien-bridge
The loop gain for the oscillator is

R2  Z p 

T s   As β s    1 
Z Z 
R
1 
p
s 

where;
R
Zp 
1  sRC
and;
1  sRC
Zs 
sC
Oscillators – Wien-bridge
Hence;


R2 
1

T s    1 

R1  3  sRC  1 /sRC 

Substituting for s;
 R2 

1
T  j   1  

 R1  3  jRC  1/jRC 
Oscillators – Wien-bridge
For oscillation frequency f0;

 R2 
1
T  j0   1  

 R1  3  j0 RC  1/j0 RC 
Since at the frequency of oscillation, T(j) must be
real (for zero phase condition), the imaginary
component must be zero i.e.;
1
j0 RC 
0
j0 RC
Oscillators – Wien-bridge
Which gives us;
1
0 
RC
Oscillators – Wien-bridge
From the previous equation;

 R2 
1
T  j0   1  

 R1  3  j0 RC  1/j0 RC 
the magnitude condition is;
 R2  1 
1  1   
 R1  3 
or;
R2
2
R1
To ensure oscillation, the ratio R2/R1 must
be slightly greater than 2.
Oscillators – Wien-bridge
With the ratio;
R2
2
R1
then;
R2
K  1
3
R1
K = 3 ensures the loop gain of unity – oscillation.
- K > 3 : growing oscillations
- K < 3 : decreasing oscillations
Oscillators – Wien-bridge
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.
1
fr 
2RC
Oscillators – Wien-bridge
V in
V out
Oscillators – Wien-bridge
Oscillators – Wien-bridge
The lead-lag
circuit is in the
positive
feedback loop of
Wien-bridge
oscillator. The
voltage
divider limits
the gain. The
lead lag circuit
is basically a
band-pass with
a narrow
bandwidth.
Oscillators – Wien-bridge
Since there is a loss of
about 1/3 of the signal
in the positive feedback
loop, the voltagedivider ratio must be
adjusted such that a
positive feedback loop
gain of 1 is produced.
This requires a closedloop gain of 3. The ratio
of R1 and R2 can be set
to achieve this.
Oscillators – Wien-bridge
Oscillators – Wien-bridge
To start the oscillations an initial gain greater
than 1 must be achieved.
Oscillators – Wien-bridge
The back-to-back zener diode
arrangement is one way of
achieving this.
Oscillators – Wien-bridge
D1
R1
D2
R3
+
V out
.

R2
f r Lead-lag
1/3
Oscillators – Wien-bridge
When dc is first applied the zeners
appear as opens. This allows the slight
amount of positive feedback from turn
on noise to pass.
Oscillators – Wien-bridge
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.
Oscillators – Wien-bridge
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.
Oscillators – Wien-bridge
Oscillators – Phase-shift
Rf
0V
R

C
C
C
Vo
.
+
R
R
Oscillators – Phase-shift
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.
1
fr 
2 6 RC
Oscillators – Phase-shift
Rf
0V
R

C
C
C
Vo
.
+
R
R
The transfer function of the RC network is
v in
1
TF 

3
2
v o sRC   5 sRC   6 sRC   1
Oscillators – Phase-shift
If the gain around the loop equals 1, the circuit
oscillates at this frequency. Thus for the oscillations
we want,
K TF   1
or;
sRC 
3
 5 sRC   6 sRC   1 - K  0
2
Oscillators – Phase-shift
Putting s = j and equating the real parts and
imaginary parts, we obtain;
 j RC   j 6RC   0 (Imaginary part)
3
(1)
 5RC   1  K  0 (Real part)
2
(2)
Oscillators – Phase-shift
From equation (1);
 RC   6  0
2
6

RC
Substituting into equation (2);
 6 
2
RC   1  K
 5
2
 RC  
K  29
The gain must be at least 29 to maintain the
oscillations
Oscillators – Phase-shift
Rf
0V
R

C
C
C
Vo
.
+
R
R
The last R has been incorporated into the summing
resistors at the input of the inverting op-amp.
Oscillators – Phase-shift
Rf
0V
R

C
C
C
Vo
.
+
R
1
fr 
2 6 RC
K
R
 Rf
R3
 29
Oscillators
2. LC Oscillators
Oscillators
Oscillators With LC Feedback Circuits
For frequencies above 1 MHz, LC feedback
oscillators are used.
We will discuss the Colpitts, Hartley and
crystal-controlled oscillators.
Transistors are used as the active device in
these types.
Oscillators
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
Oscillators With LC Feedback Circuits
Using the small signal equivalent circuit this becomes;
Oscillators
Oscillators With LC Feedback Circuits
Applying KVL around loop (1), and let
ZT  Z1  Z 2  Z3
we will have;
IZ 3  I  ib Z 2  I  h feib Z1  0
or;
IZ T  ib h fe Z1  Z 2   0
(1)
Oscillators
Oscillators With LC Feedback Circuits
Applying KVL around loop (2);
hieib  I  ib Z 2
Z2I
ib 
hie  Z 2
(2)
Oscillators
Oscillators With LC Feedback Circuits
Substituting (2) into (1);
Oscillators
Oscillators With LC Feedback Circuits
If the Z’s are purely imaginary and hie is real, then;
Substituting (3) into the expression
ZT  Z1  Z 2  Z3  0
Oscillators
Oscillators With LC Feedback Circuits
Z2 and Z1 are the same type of component
Z3 is the opposite type (-ve). If Z2 and Z1 are
inductors, then Z3 is a capacitor and vice versa.
Oscillators
Oscillators With LC Feedback Circuits
Oscillators
Oscillators With LC Feedback Circuits
Oscillators – Colpitts
The Colpitts oscillator utilizes a tank circuit
(LC) in the feedback loop as shown in the
following figure.
Oscillators – Colpitts
Oscillators – Colpitts
The resonant frequency can be determined
by the formula below.
1
fr 
2 LCT
1
1
1


CT C1 C2
Oscillators – Colpitts
Conditions for oscillation and start up
b
Vf
Vout
Av 
1
b
C1
Av 
C2
IX c1 C2


IX c 2 C1
Oscillators – Hartley
The Hartley
oscillator is similar
to the Colpitts.
The tank circuit
has two inductors
and one capacitor
Oscillators – Hartley
The calculation of the resonant frequency is the same.
1
fr 
2 LT C
LT  L1  L2
L1
b
L2
1
L2
Av  
b L1
Oscillators – Crystal
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 – Crystal
Oscillators – Crystal
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
Oscillators
3. Relaxation Oscillators
Oscillators – Relaxation
Relaxation oscillators make use of an RC timing
and a device that changes states to generate a
periodic waveform (non-sinusoidal).
1. Triangular-wave
2. Square-wave
3. Sawtooth
Oscillators – Relaxation
Triangular-wave oscillator
Triangular-wave oscillator circuit is a combination
of a comparator and integrator circuit.
Oscillators – Relaxation
Triangular-wave oscillator
Oscillators – Relaxation
Triangular-wave oscillator
1  R2 
 
fr 
4CR1  R3 
VUTP
 R3 
 Vmax  
 R2 
VLTP
 R3 
 Vmax  
 R2 
Oscillators – Square-wave
A square wave relaxation oscillator is like the
Schmitt trigger or Comparator circuit.
The charging and discharging of the capacitor
cause the op-amp to switch states rapidly and
produce a square wave.
The RC time constant determines the frequency.
Oscillators – Square-wave
Oscillators – Square-wave
Oscillators – Sawtooth voltage controlled
oscillator (VCO)
Sawtooth VCO circuit
is a combination of a
Programmable
Unijunction Transistor
(PUT) and integrator
circuit.
Oscillators – Sawtooth 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.
Oscillators – Sawtooth VCO
OPERATION
Oscillators – Sawtooth VCO
OPERATION
When Vout = VP
•
•
•
Vanode > VG , PUT turns ‘ON’
The capacitor rapidly
discharges.
Vout drop until Vout = VF.
• Vanode < VG , PUT turns ‘OFF’
VP – maximum peak value
VF – minimum peak value
Oscillators – Sawtooth VCO
OPERATION
Oscillation frequency
VIN  1 


f 
Ri C  VP  VF 
Oscillators – Sawtooth VCO
EXAMPLE
In the following circuit, let VF = 1V.
a) Find;
(i) amplitude;
(ii) amplitude;
b) Sketch the output waveform
Oscillators – Sawtooth VCO
EXAMPLE (cont’d)
Oscillators – Sawtooth VCO
EXAMPLE – Solution
a) (i) Amplitude
R4
10
 V  
15  7.5 V
VG 
R3  R4
10  10
VP  VG  7.5 V
and
So, the peak-to-peak amplitude is;
VP  VF  7.5 1  6.5 V
VF  1 V
Oscillators – Sawtooth VCO
EXAMPLE – Solution
a) (ii) Frequency
VIN  1

f 
Ri C  VP  VF



R2
 V   1.92 V
VIN 
R1  R2
Oscillators – Sawtooth VCO
EXAMPLE – Solution
a) (ii) Frequency
1.92
1


f 


100k 0.0047μ   7.5V  1V 
 628 Hz
Oscillators – Sawtooth VCO
EXAMPLE – Solution
b) Output waveform
1
1
T 
 2 ms
f 628
7.5 V
V out
1V
2 ms
t
Oscillators
The 555 timer
as an oscillator
Oscillators
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
Oscillators
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 %
 R1  R2 
100%
Duty cycle  
 R1  2 R2 
Oscillators
The 555 Timer As An Oscillator
Duty Cycle < 50 %
 R1 
100%
Duty cycle  
 R1  R2 
Oscillators
The 555 Timer As An Oscillator
Oscillators
The 555 Timer As An Oscillator
The 555 timer
may be
operated as a
VCO with a
control voltage
applied to the
CONT input
(pin 5).
Oscillators
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.
Oscillators
Summary (cont’d)
 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.