Waveform symmetry properties and phase noise inoscillators

A 2-GHz low-phase-noise integrated LC-VCO set with flicker-noise upconversion minimization

“…The relation between noise upconversion and symmetry is confirmed by [9], which state that flicker-noise upconversion is minimal for waveforms with half-wave symmetry with the waveform period), i.e., for waveforms with no even harmonics.…”

A 1/f Noise Upconversion Reduction Technique for Voltage-Biased RF CMOS Oscillators

“…Hajimiri and Lee [12] have shown that the upconversion of any flicker noise source depends on the dc value of the related effective ISF, which can be significantly reduced if the waveform has certain symmetry properties [12], [13]. Another explanation was offered in [14] and [15], suggesting that if the 1/f noise current of a switching MOS transistor is to be modeled by a product of stationary noise and a periodic function w(t), then this noise can upconvert to PN if w(t) is asymmetric.…”

Low-frequency noise in downscaled silicon transistors: Trends, theory and practice

“…thermal noise or shot noise due to quiescent current) by the term (c o )²∑S RF (kf s ) in the bottom line of the equation. As shown in [321], ISF dc is minimized when having particular symmetry in the waveforms of the oscillator, either even periodic waveforms f(t)=f(−t±nT), or half-wave symmetric waveforms f(t)=−f(t+T/2±nT). From practical point of view, both symmetries put requirements for identical transitions in oscillator waveform.…”