I am just into oscillators where I learned \$AB=1\$ for sustaining oscillations in positive feedback. Since \$A\$ and \$B\$ are both frequency-dependent, \$AB=1\$ is true only for a particular frequency.
What happens to those frequencies for which \$AB>1\$ holds??
Will these frequencies keep on getting amplified until the limiter circuit limits them?
Then why don't we get those frequencies in our output??
Answer
Why do we get only one frequency as output in oscillators?
Oscillators work at one frequency by ensuring two things: -
- The signal fed back to sustain oscillations is exactly in phase with the signal it is trying to sustain. Think about lightly tapping a swinging pendulum at exactly the right place and, in the right direction.
- The loop-gain is slightly more than unity. This ensures that a sinewave is produced without too much distortion and it is "sustained". If the loop-gain were less than 1, then it can't "sustain" an oscillation.
So, if we design a phase-shifting network that has a unique phase-shift for each frequency it handles, we will get an oscillator but, only if the signal fed back is sufficient in amplitude to sustain oscillation.
However, some phase shifting networks can produce a phase shift that is a multiple of the basic oscillation frequency. In other words if 1 MHz produces a phase shift of 360 degrees, maybe some higher-frequency might produce 720 degrees (2 x 360). This could potentially give rise to a sustained oscillation at two frequencies (usually deemed undesireable).
So, we design the phase-shifting network to ensure that the higher-frequency "in-phase" candidate is much lower in amplitude than the "basic" candidate and, given that we only allow the gain to be unity or slightly higher (to accommodate losses in the phase shift network) for the frequency we want, the higher-frequency candidate will not cause oscillation.
The above is also referred to as the Barkhausen criteria.
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