Reviews of leeson model of oscillator phase noise

Abstract

Through theoretical deduction, two new explanations of Leeson model are presented: the corner frequency of high Q oscillators in the phase noise curve should be the frequency at the intersection of the f 0 curve segment after adding 3 dB and the f −1 curve segment; f 0 /2Q L of low Q oscillators in the phase noise curve should also be the frequency at the intersection of the f 0 curve segment after adding 3 dB and the f −2 curve segment. Moreover, these two new explanations were verified by the experimental data of a reported 80 MHz high Q quartz crystal oscillator and a reported low Q lithium tantalate (LiTaO 3) oscillator, respectively. The results could help researchers and engineers properly estimate the key parameters of oscillator phase noise.

Phase noise of electrical oscillators due to multi‐Lorentzian noise sources based on the LTV model

“…In region P2, t 2 > t 1 and P (2) = ∫ 0 τ ∫ 0 t 2 e − t 2 − t 1 /τ L dt 2 dt 1 . Due to symmetry, P (1) = P (2) . So…”

“…Due to symmetry of the two regions, P (1) = P (2) and P = 2P (1) = τ 2 + Bτ 2 /2 − Bτ 2 ln τ. Finally, the normalised phase variance of (12) for this noise source will be…”

“…Due to symmetry, P (1) = P (2) and finally, for this noise source when t 1 − t 2 ≤ τ 0 , the normalised phase variance of (12) will be…”

“…From the time that the linear time invariant (LTI) model of the phase noise was introduced by Leeson [1] and developed later [2], up to present, many closed-form and numerical [such as conversion matrix and harmonic balance (HB) methods] models have been introduced to calculate the phase noise ( [3][4][5] and the references in). These models have looked at the phase noise from different points of view.…”