A Deep Investigation of the Synchronization Mechanisms in LC-CMOS Frequency Dividers

Journal of Electrical and Computer Engineering

2013

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An analytical model and a methodology are presented for the analysis of CMOS injection-locked frequency dividers with direct injection, which are used in modern wireless communication systems. The amplitude and phase of the oscillation in the synchronous operation mode, as well as the locking range, are found in explicit form. The width of the locking range is determined by the condition of the existence and stability of synchronous oscillations. The accuracy of the model and of the presented formulas is validated through a comparison with experimental results, which are in good agreement with the analytical ones.

Section: Resultsmentioning

confidence: 84%

Modeling, Analysis, and Experimental Validation of Frequency Dividers with Direct Injection

Buonomo¹,

Journal of Electrical and Computer Engineering

2013

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“…To determine these modes, let us consider the circuit in Fig. 2 where the nonlinearity of the active part of the circuit is carefully approximated through the third-degree polynomial , where is the differential trans-conductance of MOS devices at the quiescent point, and [24]- [27]. Consequently, we get , .…”

Section: B Amplitudes Of Oscillationmentioning

confidence: 99%

Analysis and Design of Dual-Mode CMOS LC-VCOs

Buonomo¹,

IEEE Trans. Circuits Syst. I

2015

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We present a nonlinear analysis of the basic circuit of a dual-band voltage controlled oscillator (VCO), composed by an active one-port and by a double-tuned LC circuit. Both the frequencies and the amplitudes of the two modes of sinusoidal oscillation are calculated by closed-form expressions by which a detailed analysis of the steady-state and dynamical behavior of circuit is performed, including the stability analysis of the modes. We show the appearance of the phenomenon of the frequency hysteresis allowing us to explain the mechanism of the switching between modes and predict the VCOs performance over the whole operation range. The theoretical results, validated by Spice simulations of a VCO realized in 0.13 m MOS technology and by measurements on a circuit prototype, provide useful design insights.Index Terms-Analog integrated circuits, dual-band voltagecontrolled oscillators (VCO), microwave oscillators, multiband VCOs, nonlinear systems. 1549-8328

“…According to this method, the amplitude and phase of the first harmonic of v are considered slowly varying quantities, that is, v ( t ) t = w ( t ) + h ( t ), where w ( t ) = W ( t )cos[ ωt + θ ( t )] denotes the first harmonic of v and h ( t ) the sum of the remaining harmonics. Thus, by using the averaging method, equation is reduced to a system of first‐order equations for the amplitude and the phase of w ( t ), which take the form (Appendix)

\overset{W}{true} ((), t) = prefix- \frac{1}{2 R C} W - \frac{1}{2 C} I^{c}

\overset{θ}{true} ((), t) = ((), ω_{0} - ω) + \frac{1}{2 C W} I^{s}

where the dot denotes the time derivative, and I c and I s denote the cosine and sine coefficients of the fundamental harmonic of i ( w + h , v in ), respectively. The quantity h is given by the solution of the linear equation

\frac{d^{2} h}{d t^{2}} + \frac{1}{R C} \frac{d h}{d t} + ω_{0}^{2} h = prefix- \frac{1}{C} \frac{d}{d t} i_{h} ((),, w, v_{italicin})

where i h ( w , v in ) denotes the harmonics of i ( v , v in ) that we assume to be slightly dependent on the harmonics of v , so that i h ( w + h , v in ) ≈ i h ( w , v in ).…”

Section: Model Of Driven Oscillators Under Weak Injectionmentioning

confidence: 99%

Evaluating the spectrum of periodic pulling in subharmonic resonant LC circuits

Buonomo¹,

2014

Circuit Theory & Apps

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SUMMARYWe analyze the features of the oscillations arising in forced inductor-capacitor (LC) oscillators when they operate in the periodic pulling mode, under the action of a weak injection signal. In radio frequency integrated circuits, both voltage-controlled oscillators subject to undesired couplings and injection-locked frequency dividers behave like forced LC oscillators. These are modeled as second-order driven oscillators working in the subharmonic (secondary) resonance regime. The analysis is based on the generalized Adler's equation, which we introduce to describe the phase dynamics of dividers of any division ratio and to derive closed-form expressions for the spectrum components of the system's oscillatory response. We show that the spectrum is double-sided and asymmetric, unlike the single-sided spectrum of systems with primary resonance. Numerical and experimental results are given to validate the presented results, which significantly generalize those available in the literature.