EDITOR: B. SOMANATHAN NAIR
Oscillators are
electronic circuits that are used to generate waveforms of desired shape and
size. Two principles are mainly used to produce waveforms. One type makes use
of positive feedback for this purpose. The other type makes use of negative
resistance to generate oscillations. In this article, we discuss the principles
of positive feedback oscillators.
1.
PRINCIPLES OF POSITIVE FEEDBACK OSCILLATORS
Figure
1 shows an amplifier A whose output
is connected back to its input through a network called as feedback network B. This network may be constructed using
passive devices (such as resistors, capacitors, and inductors) or active
devices (such as transistors). But the fed-back voltage and the external input
voltage will have the same phase. Then we call this as positive feedback. It
may be noted that B may have value
less than 1, if it is passive. With active feedback, B may be grater than 1. From the figure, we can write the following
relations:
Vo = AVi (1)
Vf = BVo (2)
Vi = Vs + BVo (3)
Av = Vo/Vs
= A/(1‒AB) (4)
Let
us assume that in Eq. (4)
1 - AB = 0
(5)
Then
Av = Vo/0 = ∞ (6)
From
Eq. (6), we observe that when AB = 1,
the gain with feedback becomes infinity. It can be seen that the condition AB = 1 conveys a very important concept
called oscillation, which may be
expressed in the following manner:
An
amplifier with positive feedback produces an output even if its external input is zero. This means
that the circuit is producing an
output on its own. The condition of a circuit producing output signals
on its own (without the aid of any external input) is called oscillation.
From Eq. (5), we find that under the condition of
oscillation the total loop gain
AB = 1Ð0º (7)
Equation
(7) represents two distinct conditions:
·
Magnitude of the total loop gain is unity.
·
Total phase-shift around the loop is 0º
(or 360º).
The conditions given above are
called as the Barkhausen (to be
pronounced as bark-haus-en)
criteria for oscillations.
The first condition suggests that the loss generated in the feedback network B should be counterbalanced exactly by the gain of the amplifier.
Under this condition, the system will produce sinusoidal oscillations. For
example, if B equals 1/3, then A should be 3 to produce sinusoidal
oscillations. If A is far greater
than the required vale (In this case 3) then we get distorted sinusoids.
However, if A< 1 (in this case
<3), then no oscillations will build up in the circuit.
For oscillations to be generated, the following
additional requirements must also be satisfied:
· There must be some kind of input signal to start the
oscillation this can be a noise voltage, the turning on of the power supply switch,
or any other electrical disturbance.
· The gain of the associated amplifier must be very high. This second condition also suggests that
to have high gain, an amplifier must use positive feedback with proper care in
earthing so that the circuit will not go into oscillation, but will act as a high-gain amplifier.
2. GENERAL THEORY OF ELECTRONIC OSCILLATORS
We know that electrons are always in motion in
resistors and other such devices due to the temperature existing in the
atmosphere. These electronic motions can be considered as tiny noise currents
as they are random in nature; they develop tiny noise-voltage drops in
resistors through which they move. These noise voltages are found to exist from
0 Hz (= frequency of DC signals) to about 1013 Hz (frequency of
infrared or thermal radiation).
An amplifier amplifies the noise frequencies
present in its input resistances and applies them to the input of a feedback
network B, which is a frequency-selective
network. The B network will choose only that input noise frequency to
which it resonates to and allows that noise frequency to pass through it
to the input of the amplifier. In this process, the chosen noise frequency may
suffer attenuation if the B
network is made up of passive devices (or may get amplified, if it is an amplifier).
Now, the amplifier amplifies the
fed-back frequency and applies it again to the input of the B network
where, as stated above, it may suffer attenuation (or get amplified further, as
the case may be). But this newly attenuated output of the B network can
be seen to be much more amplified than the original noise input to the
amplifier. This is because the amplification introduced by the amplifier on the
fed-back signal is much more than the loss introduced by the B network on it. The output of the B
network is again applied to the inputs of amplifier and the B network
for still further amplification and attenuation, provided the phase of the
amplified signal and the external input signal are in phase with each other.
Thus we find that the
frequency-selected noise voltage now undergoes continuous amplification by A
and attenuation (or amplification) by B, as it propagates around the
loop, which consists of the amplifier and the attenuator (or second amplifier)
until the noise input and the
fed-back input have the same amplitude and phase. This suggests that the
external input is no longer needed and the system itself is able to produce
signals on its own. Thus sustained oscillation results in the system, provided
the attenuation (or losses in the system) is just counterbalanced by the
amplification (or gain) of the system. This means that, if the total loop gain
is unity and has zero phase-shift, the system will produce sustained harmonic
or sinusoidal oscillations.
The
theory of oscillations discussed above is of a general nature and is not based
on the principle of working of any particular electronic device. Hence this
theory may be used to explain the principle of working of any type of
oscillator that uses positive feedback for its operation.
3. OSCILLATION PROBLEMS IN AUDITORIUMS
Let us consider a practical example concerned with oscillations.
Figure 2 shows an auditorium in which we have a public address (PA) system
being used to amplify speech signals. The PA system consists of a microphone, a
power amplifier, and a loudspeaker, as shown.
Let us now assume that a small sound
is picked up by the microphone, which converts this audio signal into
corresponding electrical signal of 1 μV. Let gain of the amplifier be 1000.
This means that we get an audio output equivalent to 1 mV (=1 μV×1000) from the
loud speaker. This amplified sound gets reflected by the walls of the
auditorium and appears as fedback sound at the microphone input with some
attenuation due to spreading of the reflected sound. Let the fedback sound
after attenuation be as shown in Fig. 2 and let its amplitude be such that the
new value of the microphone output be 100 μV.
The amplifier now amplifies this new signal of 100 μV by a factor of 1000 to yield an output of 100 mV across the loudspeaker. This amplified output signal is again reflected back by the walls and a much higher input than the first input of 1 μV appears at the input of the microphone. This is shown in Fig. 3.
The process of amplification,
feedback through reflection, and further amplification continues until the
microphone input signal and the fed-back signal have the same amplitude and
phase. In this condition, the system does not require any external signal
input; rather, the system starts producing signal on its own. This condition is
known as self-generation or oscillation. This condition is shown in Fig. 4.
The result of
this is that the system starts producing hooting and howling in the auditorium
instead of amplifying the desired microphone input signals. This problem called
as microphonics can be avoided by
reducing the gain of the amplifier as well as changing the position of speaker
and the microphone.
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