A study of subharmonic injection locking for local oscillators

Zhang, X.; Zhou, Xia; Aliener, B.; Daryoush, A.S.

doi:10.1109/75.124911

Cited by 52 publications

(28 citation statements)

References 7 publications

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“…Due to the difficulties in the analysis of the high-order subharmonic injection-locked regime, approximate oscillator models are used in [5]- [6], [12]- [14], whereas the simulations in [7], [15] rely on the Poincaré-map technique [16]- [18]. This map is applied to the sequence of steady-state solutions obtained through time-domain integration of the differential algebraic equation system when varying a particular analysis parameter, such as the input power or frequency.…”

Section: Introductionmentioning

confidence: 99%

“…However, the case of subharmonic injection-locking of a high order N is particularly demanding. The circuit is in a strongly nonlinear state with respect to the input source, since the oscillation frequency must get locked to a high harmonic N in of the input [12]- [14]. This is different from fundamental and super-harmonic injection, in which synchronized operation bands are obtained from small-signal amplitude of the injection source [21], [31]- [32].…”

Section: Introductionmentioning

confidence: 99%

“…The paper starts with a detailed investigation of subharmonic injection-locking, using both an analytical formulation and numerical techniques. The study will provide insight into the nonlinear mechanisms leading to this regime, as well as its particular characteristics in comparison with the more usual fundamental-and harmonic-injection-locking [12]- [14], [32]. The analysis of the phase sensitivity with respect to the input source will allow an estimation of the input power required to achieve the sub-synchronized state.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Simulation Method for Complex Multivalued Curves in Injection-Locked Oscillators

Hernandez

Pontón

Suárez

2017

IEEE Trans. Microwave Theory Techn.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Simulation Method for Complex Multivalued Curves in Injection-Locked Oscillators

Hernandez

Pontón

Suárez

2017

IEEE Trans. Microwave Theory Techn.

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“…al. [14] presented a computationally complicated method limited to negative feedback oscillators, and provided no insights about multiple lock states for SHIL. To our knowledge, there is no general analysis or theory that provides the correct design intuition and predictive power for SHIL and related phenomena.…”

Section: Introductionmentioning

confidence: 99%

Analysis and design of sub-harmonically injection locked oscillators

Neogy

Roychowdhury

2012

2012 Design, Automation &Amp; Test in Europe Conference &Amp; Exhibition (DATE)

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Abstract-Sub-harmonic injection locking (SHIL) is an interesting phenomenon in nonlinear oscillators that is useful in RF applications, e.g., for frequency division. Existing techniques for analysis and design of SHIL are limited to a few specific circuit topologies. We present a general technique for analysing SHIL that applies uniformly to any kind of oscillator, is highly predictive, and offers novel insights into fundamental properties of SHIL that are useful for design. We demonstrate the power of the technique by applying it to ring and LC oscillators and predicting the presence or absence of SHIL, the number of distinct locks and their stability properties, lock range, etc.. We present comparisons with SPICElevel simulations to validate our method's predictions.is a nonlinear phenomenon in which a self-sustaining oscillator's phase becomes precisely locked (i.e., entrained or synchronized) to that of an externally applied signal. The phenomenon, together with the related effect of injection pulling, has often been regarded as an unwanted disturbance, causing, among other things, malfunction in serial clock/data recovery, increased timing jitter and clock skew, increased BER in communications, etc.. Over the years, however, IL has also been put to good use in electronics -e.g., for quadrature signal generation [4]; for microwave generators in laser optics [5]; for fast, low-power frequency dividers [6]; and in PLLs [7] and wireless sensor networks [8]. Moreover, IL is an important enabling mechanism in biology (e.g., [9], [10]). When an oscillator locks to an external signal whose frequency is close to the oscillator's natural frequency, the phenomenon is termed fundamental harmonic IL. It is also possible, however, for oscillators to phase-lock at a frequency that is an exact integral sub-multiple of the frequency of the externally applied signal; this is termed subharmonic IL (or SHIL, described further in Sec. II-B) and is useful in frequency division applications [6], [7]. Design of circuits exploiting SHIL has tended to rely predominantly on trial-and-error based methodologies, using brute-force transient simulations to assess impact on SHIL-based circuit function. Existing analyses of fundamental and sub-harmonic IL (e.g., [11], [2], [12]) have been limited to very specific circuit topologies (e.g., LC oscillators), while more general analyses [13], that apply to any kind of oscillator, do not consider SHIL. The work of Daryoush et. al. [14] presented a computationally complicated method limited to negative feedback oscillators, and provided no insights about multiple lock states for SHIL. To our knowledge, there is no general analysis or theory that provides the correct design intuition and predictive power for SHIL and related phenomena. In this paper, we develop and validate a general method for analysing and understanding sub-harmonic injection locking. The method applies to any self-sustaining, amplitude-stable oscillator, not only from electronics but also from other domains such as biology. ...

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“…Adler [1] took an engineering approach and introduced the locking range gure of merit for an oscillator locked to the fundamental frequency of an incident signal. Others ( [2], [4]) followed Adler's work and showed how a n oscillator can be locked to a harmonic of an incident signal in what is conventionally called subharmonic locking.…”

Section: Introductionmentioning

confidence: 99%

Superharmonic injection locked oscillators as low power frequency dividers

Rategh

Lee

1998 Symposium on VLSI Circuits. Digest of Technical Papers (Cat. No.98CH36215)

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I. AbstractSuperharmonic injection locking is investigated in a new theoretical approach. Low p o w er frequency dividers are designed using injection locked oscillators with cascode transistors. The Rockwell 0:5m CMOS process is used to design a 3mW injection locked frequency divider in the 1800M H z frequency range. A 200M H z maximum locking range is achieved in simulations. 2SC3302 TOSHIBA NPN transistors are also used to build a 1:75mW injection locked frequency divider in the 800M H z frequency range to verify the theory. II. IntroductionForced oscillations in nonlinear oscillators were rst analyzed by van der Pol [3] in a purely theoretical investigation. Adler [1] took an engineering approach and introduced the locking range gure of merit for an oscillator locked to the fundamental frequency of an incident signal. Others ([2],[4]) followed Adler's work and showed how a n oscillator can be locked to a harmonic of an incident signal in what is conventionally called subharmonic locking.In this work we show how an oscillator can be locked to an incident signal whose fundamental frequency equals a harmonic of the oscillator frequency in superharmonic locking, so that the oscillation frequency is an integer fraction of the fundamental frequency of the incident signal. We present a new method to calculate the locking range of an injection locked oscillator both for sub-and superharmonic locking. We also present a n o v el oscillator which is locked to half of the incident signal frequency. III. Injection LockingAn LC oscillator can be modeled as a non-linear system f(x), followed by a frequency selective system (e.g., RLC tank), H(!), in a positive feedback loop. The nonlinear system includes all nonlinear elements plus any nonlinear amplitude limiting mechanism. The same model can be used for an injection locked oscillator with an external input (i.e., incident signal) as shown in g. 1. To i n v estigate the locking phenomenon in an injection locked oscillator, dene the input, output, intermediate signal, and H(!) as:where, i (t) is the incident signal, o (t) is the output signal, is the phase dierence between the two signals, ! r and Q are the resonant frequency and quality factor of the RLC tank respectively. The output of the nonlinear element, u(t), may h a v e all the harmonics and intermodulation terms of i (t) and o (t), and can be written as: (5) is an intermodulation coecient dened as:whereWe assume that all components of u(t) far from the resonant frequency of the tank are ltered out and the output

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A study of subharmonic injection locking for local oscillators

Cited by 52 publications

References 7 publications

Simulation Method for Complex Multivalued Curves in Injection-Locked Oscillators

Simulation Method for Complex Multivalued Curves in Injection-Locked Oscillators

Analysis and design of sub-harmonically injection locked oscillators

Superharmonic injection locked oscillators as low power frequency dividers

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