Phase noise suppression in LC oscillators: Tutorial

Abstract

This paper presents a comprehensive study of phase noise (PN) suppression in LC-tank oscillators. The goal of this study is to provide designers with the latest techniques for reducing PN in cross-coupled oscillators. To this end, we begin with a discussion of two prevalent PN models in oscillators: Hajimiri and Demir. We prefer the Hajimiri model because it does not involve very complicated math, and it offers engineers better insight into designing low-PN oscillators in the two-PN close-in regions in an oscillator spectrum (1/f 2 and 1/f 3 ). In 1/f 2 region, we show that a need for a large output-voltage swing leads to Class D and B oscillators, and a large output-current swing results in Class C oscillators. Also, reduction of the impulse sensitivity functions (ISFs) of an oscillator core can happen in Class F oscillators. A few solutions are presented for mitigating flicker noise up-conversion, such as adding resistances, controlling the oscillation amplitude, decreasing the conduction angle, guiding the high-frequency harmonics of current, and shifting the phase of V GS against V DS . We also provide a comparison of recent state-of-the-art literature to show what constitutes a good PN in both 1/f 2 and 1/f 3 regions in cross-coupled oscillators. We conclude that a cross-coupled oscillator can reach the best performances in 1/f 3 and 1/f 2 PN regions if the oscillator is designed in Class C with the K block and uses the techniques of narrowing the conduction angle, the tail inductor, and the modified tank simultaneously.

Dynamical behavior analysis of the Van der Pol oscillator with sine nonlinearity subjected to non-sinusoidal periodic excitations by the bifurcation structures

“…( ) E t . Using the same analysis mentioned as for = n 1 the equation ( 4) is described by equation (15). As in the previous cases ( = = n 1 and n 3), equivalence with equation (4) is given by equation (16).…”

“…These oscillators are the starting points for the analysis of non-linear behaviour [6][7][8], since most physical phenomena in life in general and in science in particular are interpreted using non-linear analysis tools [8][9][10]. These non-linear oscillators include the FitzHugh and Nagumo oscillato [11], the Hodgkin-Huxley oscillator [12], the Grudzinski-Zebrowski oscillator [13], the Hartley model [14], the Colpitts model [15], the Tchitnga oscillator [16], etc The results obtained thanks to the richness of their dynamics have contributed to major advances in many areas of research, both fundamental and engineering. [8,[17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32].…”

Investigating the dynamics of Hilfer fractional operator associated with certain electric circuit models

“…Again, w 1 ðtÞ and w 2 ðtÞ are the respective varying currents, and EðtÞ is the source voltage. Additionally, more electric circuit models with both the classical and fractional operators can be seen in the works found in previous studies [30][31][32][33][34][35][36][37][38][39] and the references therewith. More so, the authors of an earlier study 39 tackled certain single electric circuit models of interest via the application of ρ-Laplace transform.…”