Now to have the oscillations,
|𝐴𝛽 | ≥ 1
|𝐴||𝛽 | ≥ 1
1
|𝐴 | ≥ ≥ 29
|𝛽 |
Thus circuit will work as an oscillator which will produce a sinusoidal waveform if the
gain is 29 and total phase shift around a loop is 360°. This satisfies the Barkhausen
criterion for the oscillator. These oscillators are used over the audio frequency range i.e.
about 20 Hz up to 100 kHz.
2. Wien-Bridge Oscillator:
A Wien-Bridge Oscillator is a type of phase-shift oscillator which is based upon a Wien-
Bridge network (Fig-7) comprising of four arms connected in a bridge fashion.
Here two arms are purely resistive while the other two arms are a combination of resistors
and capacitors.In particular, one arm has resistor and capacitor connected in series (R1
and C1) while the other has them in parallel (R2 and C2). This indicates that these two
arms of the network behave identical to that of high pass filter or low pass filter,
mimicking the behaviour of the circuit shown by Fig-8.
Fig-7: Wein-bridge network Fig-8: Two arms of Wein-bridge network
In this circuit, at high frequencies, the reactance of the capacitors C1 and C2 will be much
less due to which the voltage V0 will become zero as R2 will be shorted.
Next, at low frequencies, the reactance of the capacitors C1 and C2 will become very
high. However even in this case, the output voltage V0 will remain at zero only, as the
capacitor C1 would be acting as an open circuit.
This kind of behaviour exhibited by the Wien-Bridge network makes it a lead-lag circuit
in the case of low and high frequencies, respectively.
Amidst two high and low frequencies, there exists a particular frequency at which the
values of the resistance and the capacitive reactance will become equal to each other,
producing the maximum output voltage.
This frequency is referred to as resonant frequency. The resonant frequency for a Wein
Bridge Oscillator is calculated using the following formula:
1
𝑓𝑟 =
2𝜋√𝑅1 𝐶1 𝑅2 𝐶2
If R1=R2=R and C1=C2=C then
22ESC143/243-Intro. to Electronics Engg. notes by Omkar Yatgal 30
𝟏
𝒇𝒓 =
𝟐𝝅𝑹𝑪
Further, at this frequency, the phase-shift between the input and the output will become
zero and the magnitude of the output voltage will become equal to one-third of the input
value. In addition, it is seen that the Wien-Bridge will be balanced only at this particular
frequency.
Wien-bridge oscillators designed using Op-Amps as a part of their amplifier section, is as
shown by Fig-9.
Fig-9: Wein-Bridge Oscillator using Op-amp
However it is to be noted that, here, the Op-Amp is required to act as a non-inverting
amplifier as the Wien-Bridge network offers zero phase-shift. Further, from the circuit, it
is evident that the output voltage is fed back to both inverting and non-inverting input
terminals.
At resonant frequency, the voltages applied to the inverting and non-inverting terminals
will be equal and in-phase with each other.
However, even here, the voltage gain of the amplifier needs to be greater than 3 to start
oscillations and equal to 3 to sustain them. In general, these kind of Op-Amp-based Wien
Bridge Oscillators cannot operate above 1 MHz due to the limitations imposed on them
by their open-loop gain.
Wien-Bridge networks are low frequency oscillators which are used to generate audio and
sub-audio frequencies ranging between 20 Hz to 20 KHz.
Further, they provide stabilized, low distorted sinusoidal output over a wide range of
frequency which can be selected using decade resistance boxes.
In addition, the oscillation frequency in this kind of circuit can be varied quite easily as it
just needs variation of the capacitors C1 and C2.
3. Multivibrators
Multivibrators are a family of oscillator circuits that produce output waveforms consisting
of one or more rectangular pulses. The term ‘multivibrator’ simply originates from the
fact that this type of waveform is rich in harmonics (i.e. ‘multiple vibrations’).
Multivibrators use regenerative (i.e. positive) feedback; the active devices present within
the oscillator circuit being operated as switches, being alternately cut-off and driven into
saturation. The principal types of multivibrator are:
a. Astable multivibrators that provide a continuous train of pulses (these are sometimes
also referred to as free-running multivibrators);
b. Monostable multivibrators that produce a single output pulse (they have one stable
state and are thus sometimes also referred to as‘one-shot’);
c. Bistable multivibrators that have two stable states and require a trigger pulse or
control signal to change from one state to another.
22ESC143/243-Intro. to Electronics Engg. notes by Omkar Yatgal 31
