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Resonator or Oscillator?

The words resonator and oscillator are very commonly interchangeably used, especially for physicists. But from engineering point of view, these are two drastically different concepts. In short, a resonator is a passive element whereas an oscillator is an active element.

A resonator need external drive: its responses has the same frequency as the external drive. If the drive only contains a single frequency component, then the resonator will be oscillating at the same frequency, with certain amplitude. If the drive frequency coincides with the resonant frequency of the resonator, then the resonator will give the strongest response (largest amplitude). In this sense, a resonator can be considered as a linear system (i.e., does not create new frequency component).

An oscillator, on the other hand, also requires some drive, but as DC input. It then outputs a signal with predetermined frequency. Most commonly, an oscillator can be thought of a resonator plus a feedback mechanism (doesn't need to be electrical feedback circuit, if we are talking outside the scope of electronic implementation). At the beginning of the time, the resonator will experience white noise from the environment, which can be thought of drives with all frequency components of equal power density. Given the virtue of the resonator, it will respond most strongly at its resonant frequency. Then this response is picked up by the feedback mechanism, which amplifies the signal, and then feed the amplified signal back to drive the resonator. Now the frequency power spectrum of the drive is no longer flat, but peaks at the resonant frequency. Therefore, the positive feedback loop starts, and the resonator "vibrates" with larger and larger "amplitude" as time goes. When does it stop growing? Well, some nonlinear effect must take place to limit the amplitude, and the most common place for this nonlinearity happens in the feedback mechanism: as the response from the resonator (which can be considered as the input of the feedback mechanism) gets larger and larger, the amplification gain (the ratio between the output and input of the feedback) will reduce, until the response of the resonator does not increase (effective total gain of 1), therefore the resonator reaches a fixed output. This is also known as Barkhausen Criterion. If the feedback gain, hence the response of the resonator keeps dropping below unity, the gain of the feedback will increase accordingly, to boost the response of the resonator in the next iteration. Note that, the Barkhausen Criterion (effective total gain of 1) only ensures the instance of the oscillation, but not stability of the oscillation - the stability of the oscillation is ensured by the nonlinearity. Therefore, an oscillator, as a whole, needs to be considered as a nonlinear system. In an electronic feedback implementation, this nonlinearity is usually takes form as amplifier saturation, or automatic gain control. Of course, there are many other ways to ensure the required nonlinearity, as we have just recently shown.

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