Ken Kundert

You are misunderstanding linewidth. In phase noise the total power in the signal is independent of the noise level. The total area under the curve must equal the total power of the signal. If the phase noise increases, the entire curve cannot raise, that would violate the total power constraint. So what happens is the noise at low offset frequencies does not go to infinity, it levels off, and the corner frequency, known as the linewidth, adjusts to keep the total area under the curve constant. The higher the noise level, the higher the linewidth.
To understand this, consider a bicycle wheel. If the wheel rotated a degree or so then a spot on the tire might move by a centimeter or so. The rotation of the wheel corresponds to a shift in phase in the oscillator and the height of the spot corresponds to a variation in voltage in an oscillator. If you then increased the rotation by 10, so the wheel were rotating 1020 degrees, the deviation of the height of the spot would also increase a factor of 10. But now increase by another factor of 10. Now the wheel is going through a half rotation. The deviation in the height of the spot would not go up another factor of 10 because it is constrained by the radius of the wheel. Now increase another factor of 10. Now the wheel would be going through something like 5 complete rotations, but the height of the spot would never increase beyond the radius of the wheel.
The same effect occurs in oscillators. The phase can drift without bound, but the voltage is constrained to fall within the amplitude of the signal. The Q of the oscillator provides inertia which limits the noise at high frequencies, so the largest noise is found at low frequencies. The result is that the amplitude of the noise at low frequencies flattens out as the offset frequency goes to zero.
You can have an infinite variation in phase if you wait forever, but you cannot have an infinite variation in voltage regardless of how long you wait. Thus, as the offset frequency goes to zero, the phase noise increases without bound but the voltage noise always flattens out. The corner frequency is the linewidth. It is adjusts with the noise level to keep the area under the curve equal to the total power of the signal. If you have a different oscillator with higher noise but lower linewidth, then it must have a larger amplitude.
This is why people do not use the absolute noise level of an oscillator as a figure of merit, they always use the relative noise level. It is the relative noise level above the linewidth that reveals the phase noise. However, the linewidth also represents another figure of merit for an oscillator. People designing lasers generally use linewidth as their figure of merit whereas RF designers use normalized noise.
Ken
