Rotary Traveling-Wave Oscillators, Analysis and Simulation

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 ...

Section: Delay-line Oscillator Examplementioning

confidence: 99%

“…A slightly different technique in[26,30,32,74]. For instance, the entry Z p,k (f m ) in the matrix indicates the gain 14 cf.…”

mentioning

confidence: 99%

Survey of integrated‐circuit‐oscillator phase‐noise analysis

Pankratz

Sánchez-Sinencio

2013

“…These lead to the degradation of the phase noise formulas accuracy. Also, the phase noise formulas extracted in Chen and Pedrotti are not in the closed forms, which weaken formulas usefulness…”

Section: Introductionmentioning

confidence: 98%

“…Also, it is essential for integrated phase arrays, clock and data recovery circuits, noninteger dividers, and high‐frequency doublers . Moreover, the distributed structure of the RTWO alleviates the limitations imposed on the LC oscillator at high frequencies such as degradation of quality factor and phase noise . Despite the mentioned advantages, there are some deficiencies in the field of the RTWO analysis.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Thermal and flicker phase noise analysis in rotary traveling‐wave oscillator

Abbasalizadeh

Javadi

Naimi

2019

Summary This paper analyzes the thermally induced phase noise and the up‐conversion of flicker noise into phase noise of rotary traveling‐wave oscillator (RTWO). Based on the analyses, this paper extracts the closed‐form formulas for the thermal and flicker phase noise of the RTWO. This paper compares the theoretical results with appropriate simulations to evaluate the accuracy of the derived closed‐form formulas. Comparisons confirm the accuracy of the extracted phase noise formulas. By using the presented straightforward approach along with accurate phase noise formulas, the designers can understand the RTWO's design tradeoffs. Also, they can design the RTWO for a specific phase noise without needing lengthy simulations.

Automatic phase error compensation of rotary traveling wave oscillator: Analysis and design

Fallahtabar

Abbasalizadeh

Naimi

2023

A new rotary traveling wave oscillator (RTWO) with automatic phase error compensation feedback is proposed in this paper. By introducing a new negative transconductor (ÀG m cell) circuit, the currents in four ÀG m cells adjust differently to cancel the phase errors. To better understand the new RTWO phase error compensation technique and design procedure of the whole system, the system analysis for describing the phase error compensation technique is provided. The design considerations of each block of the new RTWO at the circuit level are clarified. Besides, the stability of the whole system is analyzed. Appropriate simulations have been done in 0.18 μm CMOS technology with a 1.8 V supply voltage to evaluate the new RTWO performance and its accuracy. The evaluations verify the capability of the new RTWO to cancel the phase error.