A Nonlinear Transient Analysis of Regenerative Frequency Dividers

Sengupta, Kaushik; Bhattacharyya, Tarun Kanti; Hashemi, Hossein

doi:10.1109/tcsi.2007.906067

Cited by 13 publications

(7 citation statements)

References 6 publications

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“…It is interesting to observe that, even if the system (27) can be practically handled, only if the assumptions in (29) are made, the results are sufficiently accurate, as shown in Figure 4, where analytical results are compared with numerical results obtained by SPICE simulation of the circuit in Figure 1. From the aforementioned analysis, we conclude that the approach in [12] allows us not only to obtain the same results as in [10,11] for the LR, but it allows us also to obtain closed form solutions for the amplitude and phase as well as for the stability analysis [13] and the transient behaviour using firstorder dynamical equations.…”

Section: Polynomial-likementioning

confidence: 75%

“…Polynomial nonlinearity is also used in [11]. The equivalent circuit shown in Figure 1 with a cubic feedback nonlinearity models an ILFD based on a mixer, wherein the fed-back output signal does feedthrough to the output of the mixer.…”

Section: Polynomial-like Nonlinearitymentioning

confidence: 99%

“…This phenomenon has recently been considered in a number of papers aimed at obtaining useful design guidelines for analog integrated dividers based on the injection locking of LC differential oscillators in MOS technology [3][4][5][6][7][8][9][10][11][12][13]. An ILFD operates properly as a frequency divider only if the basic LC oscillator tracks the input signal, and this occurs over a limited range of frequency, called locking range (LR); its prediction is the main issue of investigation.…”

Section: Introductionmentioning

confidence: 99%

“…Starting from the equivalent circuit usually employed for describing the LC frequency dividers and the classical result by Adler concerning injection-locked oscillators, we present the models of ILFDs with saturation-like nonlinearities and with polynomiallike nonlinearities. Then, we show the potential of the perturbation approach in [12], which provides analytical results more complete than those in [5][6][7][8][9][10][11], as it results from an analytical and numerical comparison. The perturbation 2 Journal of Electrical and Computer Engineering approach allows us to determine not only the amplitude and phase of the locked oscillation and the locking range, but also the stability of the oscillation and its envelope in transient.…”

Section: Introductionmentioning

confidence: 99%

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Investigation on Locking and Pulling Modes in Analog Frequency Dividers

Buonomo

Schiavo

2013

Journal of Electrical and Computer Engineering

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We compare the main analytical results available to estimate the locking range, which is the key figure-of-merit of LC frequency dividers based on the injection locking phenomenon. Starting from the classical result by Adler concerning injection-locked oscillators, we elucidate the merits and the shortcomings of the different approaches to study injection-locked frequency dividers, with particular emphasis on divider-by-2. In particular, we show the potential of a perturbation approach which enables a more complete analysis of frequency dividers, making it possible to calculate not only the amplitude and the phase of the locked oscillation, but also the region where it exists and is stable, which defines the locking region. Finally, we analyze the dynamical behaviour of the dividers in the vicinity of the boundary of the locking region, showing that there exists a border region where the occurrence of the locking or the pulling operation mode is possible, depending on the initial conditions of the system.

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Section: Polynomial-likementioning

confidence: 75%

Section: Polynomial-like Nonlinearitymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Investigation on Locking and Pulling Modes in Analog Frequency Dividers

Buonomo

Schiavo

2013

Journal of Electrical and Computer Engineering

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“…The expressed in (5) injection-locks the oscillator to frequency . The magnitude of this injection current in terms of can be expressed as (7) These expressions are valid for differential oscillators where the injection signal is applied to the gate of the tail current source.…”

Section: Stability Analysis Of Injection-locked Regenerative Freqmentioning

confidence: 99%

Stability and Operation of Injection-Locked Regenerative Frequency Dividers

Farazian

Gudem

Larson

2010

IEEE Trans. Circuits Syst. I

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Injection-locked regenerative frequency dividers can achieve a fractional division ratio similar to regenerative frequency dividers and can provide quadrature output phases. An analysis of the steady-state operation, stability, and phase noise of injection-locked regenerative frequency dividers is presented. In addition, two-stage ring oscillators (based on negative-resistance delay cells) are studied, and their steady-state free-running operation and injection-locked behavior are investigated. Simulation results based on the equations derived in this paper are compared with circuit simulations to examine the accuracy of our analysis, which is quantified in different parts of this paper.Index Terms-Fractional frequency divider, inductorless design methodology, injection-locked frequency divider (ILFD), injection-locking, locking range, polyphase filter, regenerative frequency divider, ring oscillator, self-resonance frequency (SRF), single-sideband (SSB) mixer .

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