Automated Design and Optimization of Low-Noise Oscillators

Vytyaz, Igor; Lee, D.C.; Hanumolu, Pavan Kumar; Moon, Un-Ku; Mayaram, K.

doi:10.1109/tcad.2009.2014808

Cited by 7 publications

(8 citation statements)

References 26 publications

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“…Mathematically, the perturbation projection vector is identical to the infinitesimal phase-response curve. It is used as a reduction tool to study oscillators and to design electronic circuits [80].…”

Section: Phase-response Curves In Engineeringmentioning

confidence: 99%

Sensitivity Analysis of Oscillator Models in the Space of Phase-Response Curves: Oscillators As Open Systems

Sacré

Sepulchre

2014

IEEE Control Syst.

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O scillator models-whose steady-state behavior is periodic rather than constant-are fundamental to rhythmic modeling, and they appear in many areas of engineering, physics, chemistry, and biology [1]- [6]. Many oscillators are, by nature, open dynamical systems in that they interact with their environment [7]. Whether functioning as clocks, information transmitters, or rhythm generators, these oscillators have the robust ability to respond to a particular input (entrainment) and to behave collectively in a network (synchronization or clustering).

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Section: Phase-response Curves In Engineeringmentioning

confidence: 99%

Sensitivity Analysis of Oscillator Models in the Space of Phase-Response Curves: Oscillators As Open Systems

Sacré

Sepulchre

2014

IEEE Control Syst.

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“…Furthermore, it can be shown that defining amplitude perturbations in this fashion ensures that Δ v 29 Demir [167] presented numerically efficient and accurate procedures to compute K ICO (analogous to the oscillator perturbation projection vector in [167]), which enforce the condition K ! Similarly, Vytyaz employed phasenoise sensitivity analysis using Floquet vectors to create an automated oscillator optimization algorithm [144]. ss t ð ÞÞ=d 2pf osc t ð Þ¼1 by construction.…”

Section: Procedure/examplementioning

confidence: 99%

“…Maffezzoni also presented a nonlinear Floquet-analysis-based technique to obtain period and amplitude perturbations caused by either a small constant shift in circuit parameters or a small signal injection into a circuit node-the latter could also be adapted to infer the oscillator K ICO or perturbation projection vector [168]. Similarly, Vytyaz employed phasenoise sensitivity analysis using Floquet vectors to create an automated oscillator optimization algorithm [144]. 30 For the Floquet eigenvector to be computed, most tools require that state variables (capacitor voltages/inductor currents) be continuous functions of those state variables.…”

Section: Procedure/examplementioning

confidence: 99%

Survey of integrated‐circuit‐oscillator phase‐noise analysis

Pankratz

Sánchez-Sinencio

2013

Circuit Theory & Apps

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This tutorial distills the salient phase-noise analysis concepts and key equations developed over the last 75 years relevant to integrated circuit oscillators. Oscillator phase and amplitude fluctuations have been studied since at least 1938 when Berstein solved the Fokker-Planck equations for the phase/amplitude distributions of a resonant oscillator.The principal contribution of this work is the organized, unified presentation of eclectic phase-noise analysis techniques, facilitating their application to integrated circuit oscillator design. Furthermore, we demonstrate that all these methods boil down to obtaining three things: (1) noise modulation function; (2) noise transfer function; and (3) current-controlled oscillator gain. For each method, this paper provides a short background explanation of the technique, a step-by-step procedure of how to apply the method to hand calculation/computer simulation, and a worked example to demonstrate how to analyze a practical oscillator circuit with that method.This survey article chiefly deals with phase-noise analysis methods, so to restrict its scope, we limit our discussion to the following: (1) analyzing integrated circuit metal-oxide-semiconductor/bipolar junction transistor-based LC, delay, and ring oscillator topologies; (2) considering a few oscillator harmonics in our analysis; (3) analyzing thermal/flicker intrinsic device-noise sources rather than environmental/parametric noise/ wander; (4) providing mainly qualitative amplitude-noise discussions; and (5) omitting measurement methods/phase-noise reduction techniques.We categorize oscillators into one of three varieties, as illustrated in Figure 3: resonant, delay line, or relaxation. First, the resonant oscillator consists of a nonlinear amplifier and a lumped frequencyselective network or resonator, which typically has a band-pass frequency response with a single magnitude peak as indicated conceptually in the figure. This resonator can take the form of an LC tank circuit, dielectric puck, quartz crystal, SAW or bulk acoustic wave transducer, yttrium iron garnet resonator, or ceramic disk resonator to name a few [43,147,148]. IC resonant oscillators typically use LC tanks, although they are often designed to work in concert with an external 874 E. PANKRATZ AND E. SÁNCHEZ-SINENCIO ! ss t ð Þ correspond to the roughly circular trajectory in the figure called a limit cycle [150].Figure 4. Optoelectronic delay-line oscillator. 876 E. PANKRATZ AND E. SÁNCHEZ-SINENCIO For some subtleties of amplitude-noise behavior, see [50,143], where [50] also points out effects of not employing Floquet normalization (cf. Section 4.7).½ =fVoigt ð Þ 2(Gaussian) at small offsets [78,151,152,154]. Chorti also observed that, in general, noise processes with long correlation times tend to create such 'Gaussian' voltage spectra for small frequency offsets f m [151,152]. 4 Note well that, technically, defining spectra for f proves problematic, as it is not stationary and, what is worse, not bounded. This is in fact one reason why the ...

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“…Previous works have been done in the field of analog design automation to enable fast design at the block level. Different strategies and approaches have been proposed during the evolution of analog design automation, such as simulation-based optimization [5,9,17], symbolic simulation [10], artificial intelligence [6], manually derived design equations [4,21], hierarchy and topology selection [11], geometric programming [12,16] and memetic algorithms [15]. The main difficulty encountered for wide spread usage of these tools is that they require appropriate modeling of both devices (technology dependent) and circuit topologies in order to achieve the design objectives in a reasonable processing time.…”

Section: Introductionmentioning

confidence: 99%