By substitute small signal high frequency equivalent circuit into the circuit and then derived transfer function in frequency domain and use inverse Laplace's transform to plot amplitude of oscillation in time domain. You will see that at some range of current consumption the amplitude of oscillation will be distorted considerably. From my experience phase noise is not related with noise source of MOSFET but it is related with supply voltage ripple which might not be dc.
The phase noise inside the devices is due to random movement of electrons and the random movement estimation in a semiconductor may be done using Einstein-Boltzman equation (you may refer to "Electronics circuit & device" by Millman & Halkias)
Dear Kittipong,
Your question is interesting as it is about one of the important subjects concerning the oscillator performance. Your question about the phase noise. By definition the phase noise is random or statistical variations of the oscillation frequency. Instead to be a pure sinusoidal with frequency wo say, the output wave form will be a sine wave, which is phase modulated by a random signal. Mathematically, vo= V sin wot+ phi (t),
Differentiating the argument of the sine we get the instantaneous frequency w= wo + dw(t) where dw is the instantaneous frequency deviation. This waveform when transformed to the frequency domain by Fourier transform we get the oscillation at wo surrounded by two sidebands. quantitatively, the phase noise is measured by the ratio a signal amplitude at certain frequency deviation dw to the amplitude at wo in dBs scale and its unit is dBc/Hz.
The statistical phase noise is due to noise generated inside the the oscillator circuit including flicker, shot and thermal noise. This noise signal causes short term statistical variations in cycle time of the oscillator
In voltage and current controlled oscillators, there is an additional phase noise because the noise signal superimposed on the controlling voltage leading to statistical variations of the oscillator frequency.
Ripples in power supply are residual harmonics of the rectification process and can lead also to variation in the oscillator frequency but their nature is not random and can be filtered out to eliminate their effect on the oscillator. It is well known that one have to use filtered and regulated power supplies.
For the derivation of the phase noise and its origins please see the useful link:
http://www.ieee.li/pdf/essay/phase_noise_basics.pdf
I hope i precised some concepts concerning the phase noise.
wish you success.
But do you known even regulated supply voltage , there are some minimum ripple may be 1-100pV in the form of sawtooth waveform? Doesn't it expand into many terms in sinusoidal waveform infinite series? After that, it will be mixing with pure sinusoidal of cross couple oscillator which is exactly sinusoidal waveform?
Yes Kittipong. This what i said in my previous answer to your question. I said:The Ripples in power supply are residual harmonics of the rectification process and can lead also to variation in the oscillator frequency but their nature is not random and can be filtered out to eliminate their effect on the oscillator.
To be more obvious, the power supply ripples that couple directly to the output of the oscillator or indirectly to the control input of the voltage controlled oscillator frequency modulate its frequency and appears as spread spectrum signal as the the phase noise appearance. Both will be create unwanted frequency component around the wanted carrier in the frequency spectrum of the output oscillator signal. But while the noise has smeared frequency spectrum , the ripples has discreet discrete frequency components around the main oscillator signal. This is because the ripples are periodic as you stated above.
Wish you success.
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