Oscillators

Barkhausen Criteria
Conditions which are required to be satisfied

to operate the circuit as an oscillator are
called as “Barkhausen criterion” for
sustained oscillations.
The Barkhausen criteria should be satisfied

by an amplifier with positive feedback to
ensure the sustained oscillations.
For an oscillation circuit, there is no input

signal “Vs”, hence the feedback signal Vf
itself should be sufficient to maintain the
oscillations.
The Barkhausen criterion states that:

• The loop gain is equal to unity in absolute
magnitude, that is, | β A | = 1 and
• The phase shift around the loop is zero or
an integer multiple of 2π radian (180°) i.e.
<β.A = 0
The product β A is called as the “loop gain”.

Oscillator
oscillator is a mechanical or electronic
device that works on the principles of
oscillation: a periodic fluctuation between
two things based on changes in energy.
Computers, clocks, watches, radios, and
metal detectors are among the many
devices that use oscillators.
Damped Oscillation
whose amplitude reduce with time are
called damped oscillation.
Undamped Oscillation
In oscillation if its
amplitude doesn't change with time then
they are called Undamped oscillation.
Classification of electronic oscillators
1. LC oscillator :-
a. Hartley oscillator
b. Colpitt's oscillator
c. Tuned collector oscillator
2. RC oscillator :-
a. Phase shift oscillator
b. Wien bridge oscillator
3. Crystal oscillator :-
 Crystal oscillator
Crystal oscillators operate on the
principle of inverse piezoelectric
effect in which an alternating voltage
applied across the crystal surfaces
causes it to vibrate at its natural
frequency. It is these vibrations which
eventually get converted into
oscillations. These oscillators are
usually made of Quartz crystal.
Crystal Oscillator Working
The crystal oscillator circuit usually
works on the principle of the inverse
piezoelectric effect. The applied
electric field will produce a
mechanical deformation across some
materials. Thus, it utilizes the
vibrating crystal’s mechanical
resonance, which is made with a
piezoelectric material for generating
an electrical signal of a particular
frequency.
Usually, quartz crystal oscillators are

highly stable, consist of good quality
factor(Q), they are small in size, and
are economically related. Hence,
quartz crystal oscillator circuits are
more superior compared to other
resonators like LC circuits, tuning
forks. Generally in Microprocessors
and Micro controllers we are using an
8MHz crystal oscillator.
The equivalent electrical circuit also

describes the crystal action of the
crystal. Just look at the equivalent
electrical circuit diagram shown in
the above. The basic components
used in the circuit, inductance L
represents crystal mass, capacitance
C2 represents compliance, and C1 is
used to represent the capacitance
that is formed because of crystal’s
mechanical moulding, resistance R
represents the crystal’s internal
structure friction, The quartz crystal
oscillator circuit diagram consists of
two resonances such as series and
parallel resonance, i.e., two resonant
frequencies.
 RC Phase Shift Oscillator
RC phase-shift oscillators use resistor-
capacitor (RC) network (Figure 1) to
provide the phase-shift required by the
feedback signal. They have excellent
frequency stability and can yield a pure
sine wave for a wide range of loads.
Ideally a simple RC network is expected
to have an output which leads the input
by 90°.
However, in reality, the phase-difference
will be less than this as the capacitor
used in the circuit cannot be ideal.
Mathematically the phase angle of the
RC network is expressed as
Where, XC = 1/(2πfC) is the reactance of

the capacitor C and R is the resistor. In
oscillators, these kind of RC phase-shift
networks, each offering a definite phase-
shift can be cascaded so as to satisfy the
phase-shift condition led by the
Barkhausen Criterion.
One such example is the case in which
RC phase-shift oscillator is formed by
cascading three RC phase-shift networks,
each offering a phase-shift of 60°, as
shown by Figure
Here the collector resistor RC limits the
collector current of the transistor,
resistors R1 and R (nearest to the
transistor) form the voltage divider
network while the emitter resistor RE
improves the stability. Next, the
capacitors CE and Co are the emitter by-
pass capacitor and the output DC
decoupling capacitor, respectively.
Further, the circuit also shows three RC
networks employed in the feedback
path.
This arrangement causes the output
waveform to shift by 180o during its
course of travel from output terminal to
the base of the transistor. Next, this
signal will be shifted again by 180° by
the transistor in the circuit due to the
fact that the phase-difference between
the input and the output will be 180° in
the case of common emitter
configuration. This makes the net phase-
difference to be 360°, satisfying the
phase-difference condition.
One more way of satisfying the phase-
difference condition is to use four RC
networks, each offering a phase-shift of
45°. Hence it can be concluded that the
RC phase-shift oscillators can be
designed in many ways as the number of
RC networks in them is not fixed.
However it is to be noted that, although
an increase in the number of stages
increases the frequency stability of the
circuit, it also adversely affects the
output frequency of the oscillator due to
the loading effect.
The generalized expression for the
frequency of oscillations produced by a
RC phase-shift oscillator is given by
Where, N
is the number of RC stages formed by
the resistors R and the capacitors C.

Oscillators

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Barkhausen Criteria

Conditions which are required to be satisfied

The Barkhausen criteria should be satisfied

For an oscillation circuit, there is no input

The Barkhausen criterion states that:

The product β A is called as the “loop gain”.

Usually, quartz crystal oscillators are

The equivalent electrical circuit also

Where, XC = 1/(2πfC) is the reactance of

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