Tip of the Week: Please explain in more practical (less theoretical) terms the concept of "oscillator line width."

Question:
From spectre -h pnoise. I find the definition for oscillator linewidth:
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" In a phase noise analysis for an oscillator, the line width, which is also known as the corner frequency, is defined as either the full width at half maximum (FWHM), or as twice the half power (-3dB) width (HW). In the absence of 1/f noise and ignoring any noise floor, the phase noise spectrum satisfies the Lorentzian equation:
L(f) = (1/pi) * [ pi * c * fosc^2 ] / [(pi * c * fosc^2)^2 + f^2],
where 'c' is a constant that defines the phase noise characteristics of the oscillator, 'fosc' is the fundamental frequency of the oscillator, and 'f' is the offset frequency of the oscillator. Therefore,
line width := FWHM = 2* HW = 2 * pi * c * fosc^2. "
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Please explain from a more practical (less theoretical) viewpoint the term "oscillator line width."

Answer:
In less theoretical (more practical) terms, here is what "oscillator line width" means:
When a oscillator oscillates, because of the noise in the circuit the frequency wanders a little bit. Usually, it's pretty close to the oscillation frequency, but occasionally (because of a spike in the noise), it generates frequencies that are farther away from the center frequency. In the frequency domain, what you want is a perfect spike at the center frequency.  What actually happens is the frequency spreads a little. Pnoise is designed to calculate the frequency response of the oscillator.

Here comes the caveat.... Pnoise is a small-signal analysis. When pnoise runs, it doesn't know about physical limitations of the circuit. For frequencies that are very close to the center (oscillation) frequency, it can calculate a large-signal response. It's wrong because when a small-signal approach used is for a large-signal system, it's nonsensical. (An analogy is in AC analysis. When you specify the input to be 1KV, the output might be 10KV. In the real world it would never occur, but because the system is assumed to be small-signal, 10KV out is OK.)

In the physical world, when you look at a real oscillator and you visualize what really happens, the frequencies that are produced are pretty level when near the oscillation frequency. As you go farther away, the frequency response drops off. When you look at an actual measurement (using test equipment that measures the oscillator output), instead of seeing a perfectly narrow spike, you see a curve with a finite width. Oscillator line width is the width of this line to the point where the power drops 3dB. The way we report it, we show the frequency from the center to the frequency above the center frequency where the power drops 3dB. The width from the lower frequency point to the upper frequency point is double what we report.

"Many thanks to colleague and fellow blogger Rich Davis for his insight on this topic."