• An amplifier with positive
feedback results in oscillations if the following
conditions are satisfied:
– The loop gain ( product of the
gain of the amplifier and the gain of the
feedback network) is unity
– The total phase shift in the
loop is 0°
• If the output signal is
sinusoidal, such a circuit is referred to as sinusoidal
oscillator.
When the switch at the amplifier
input is open, there are no oscillations. Imagine that a
voltage Vi is fed to the circuit
and the switch is closed. This results in Vo = AV Vi and
bVo = Vf is fed
back to the circuit. If we make Vf = Vi, then even if we remove the input
voltage to the circuit, the
output continues to exist.
Vo = AV Vi
bVo = Vf
b AV Vi = Vf
If Vf has to be same as Vi, then
from the above equation, it is clear that, b AV =1.
Thus in the above block diagram,
by closing the switch and removing the input, we are
able to get the oscillations at
the output if b AV =1, where b AV is called the
Loop gain.
Positive feedback refers to the
fact that the fed back signal is in phase with the input
signal. This means that the
signal experiences 0° phase shift while traveling in the loop.
The above condition along with
the unity loop gain needs to be satisfied to get the
sustained oscillations. These
conditions are referred to as ‘Barkhausen criterion’.
Another way of seeing how the
feedback circuit provides operation as an oscillator is
obtained by noting the
denominator in the basic equation
Af = A / (1+bA).
When bA = -1 or
magnitude 1 at a phase angle of 180°, the denominator becomes 0 and
the gain with feedback Af becomes
infinite.Thus, an infinitesimal signal ( noise voltage)
can provide a measurable output
voltage, and the circuit acts as an oscillator even without
an input signal.
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