Phase noise analysis in CMOS differential Armstrong oscillator topology

This paper reports a phase noise analysis in a differential Armstrong oscillator circuit topology in CMOS technology. The analytical expressions of phase noise due to flicker and thermal noise sources are derived and validated by the results obtained through SpectreRF simulations for oscillation frequencies of 1, 10, and 100 GHz. The analysis captures well the phase noise of the oscillator topology and shows the impact of flicker noise contribution as the major effect leading to phase noise degradation in nano‐scale CMOS LC oscillators. Copyright © 2016 John Wiley & Sons, Ltd.     

Analyses and techniques for phase noise reduction in CMOS Colpitts oscillator topology

This paper reports the analyses of three techniques for phase noise reduction in the complementary metal‐oxide semiconductor (CMOS) Colpitts oscillator circuit topology. Namely, the three techniques are inductive degeneration, noise filter, and optimum current density. The design of the circuit topology is carried out in 28‐nm bulk CMOS technology. The analytical expression of the oscillation frequency is derived and validated through circuit simulations. Moreover, the theoretical analyses of the three techniques are carried out and verified by means of circuit simulations within a commercial design environment. The results obtained for the inductive degeneration and noise filter show the existence of an optimum inductance for minimum phase noise. The results obtained for the optimum bias current density technique applied to a Colpitts oscillator circuit topology incorporating either inductive degeneration or noise filter show the existence of an optimum bias current density for minimum phase noise. Overall, the analyses show that the adoption of these techniques may lead to a potential phase noise reduction up to 19 dB at a 1‐MHz frequency offset for an oscillation frequency of 10 GHz. © 2015 The Authors International Journal of Circuit Theory and Applications Published by John Wiley & Sons Ltd.     

Memristor‐based voltage‐controlled relaxation oscillators

This paper introduces two voltage‐controlled memristor‐based reactance‐less oscillators with analytical and circuit simulations. Two different topologies which are R‐M and M‐R are discussed as a function of the reference voltage where the generalized formulas of the oscillation frequency and conditions for oscillation for each topology are derived. The effect of the reference voltage on the circuit performance is studied and validated through different examples using PSpice simulations. A memristor‐based voltage‐controlled oscillator (VCO) is introduced as an application for the proposed circuits which is nano‐size and more efficient compared to the conventional VCOs. Copyright © 2013 John Wiley & Sons, Ltd.     

Phase error analysis in CMOS injection‐coupled LC quadrature oscillator (IC‐QO)

This paper presents a novel approach to study the phase error in source injection coupled quadrature oscillators (QOs). Like other LC QOs, the mismatches between LC tanks are the main source of phase error in this oscillator. The QO is analyzed where the phase error and oscillation frequency are derived in terms of circuit parameters. The proposed analysis shows that the output phase error is a function of injection current and the current of source equivalent capacitor. As a result, it is shown that increasing of tail current and LC tank quality factor decreases the phase error. Derived equations show that the phase error can be cancelled and even controlled by adjusting bias currents. To evaluate the proposed analysis and consequent designed QO, a 5.5 GHz CMOS QO is designed and simulated using the practical 0.18 µm TSMC CMOS technology. The experiments show good agreement between analytical equations and simulation results. Copyright © 2013 John Wiley & Sons, Ltd.     

LC‐active VCO for CMOS RF transceivers

A novel fully integrated CMOS LC tank VCO is presented. The LC tanks are implemented by exploiting the active circuit ‘boot‐strapped inductor’ (BSI), which behaves like a high‐quality factor inductor. Particularly, the LC tanks have been implemented by introducing a new version of the CMOS BSI circuit, which provides better versatility and design reliability. In order to verify the effectiveness of such an approach, a case study for 5–6 GHz direct‐conversion multi‐standard WLAN transceivers is presented. The VCO has been designed in a 0.35µm standard CMOS technology. The new BSI exhibits a high‐quality factor (higher than 25 over the all frequency range) and provides a high selectivity without introducing a relevant excess of noise, for a better spectral purity and a lower phase noise (PN) of the VCO. The overall VCO circuit consumes 9 mW. The VCO produces an oscillation in the tuning range from 4.91 to 5.93 GHz (nearly equal to 19%). The circuit exhibits a PN of ?129dBc/Hz at 1 MHz of frequency offset from the central frequency (5.4 GHz) and a FOM equal to 189.5 dBc/Hz at 100 kHz and 194.1 dBc/Hz at 1 MHz of frequency offset, respectively. Copyright © 2009 John Wiley & Sons, Ltd.     

A numerical model for the oscillation frequency,the amplitude and the phase‐noise of MOS‐current‐mode‐logic ring oscillators

This paper presents a new model for the frequency of oscillation, the oscillation amplitude and the phase‐noise of ring oscillators consisting of MOS‐current‐mode‐logic delay cells. The numerical model has been validated through circuit simulations of oscillators designed with a typical 130 nm CMOS technology. A design flow based on the proposed model and on circuit simulations is presented and applied to cells with active loads. The choice of the cell parameters that minimize phase‐noise and power consumption is addressed. Copyright © 2009 John Wiley & Sons, Ltd.     

Analysis and modeling of LC oscillator reliability

In this paper, MOS device degradations due to hot carrier and gate oxide breakdown are shown experimentally, and their effects on the NMOS LC oscillator have been evaluated analytically and through SpectreRF simulation. The reduction in transconductance of the differential pair transistors may cause the oscillation to cease. The amplitude of oscillation reduces as the equivalent tank resistance decreases due to the breakdown effect on the MOS varactor. The reduction of amplitude reduces the tank capacitances, and therefore shifts the frequency of oscillation and increases the oscillator phase noise. The tank amplitude of the oscillator is derived analytically. A closed-form expression for the average capacitance of the varactor that accounts for large-signal effects is presented. Finally, a set of guidelines to design an LC oscillator in reliability is presented.     

Survey of integrated‐circuit‐oscillator phase‐noise analysis

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. Copyright © 2013 John Wiley & Sons, Ltd.     

Design and implementation of switched coil LC‐VCOs in the GHz range using the self‐inductance technique

This paper presents the design and implementation of dual‐band LC‐VCOs in the GHz‐range featuring a switched coil LC‐tank. The proposed design exploits the self‐inductance technique. The design of the coil starts from simple considerations and back‐of‐the‐envelope calculations, then electromagnetic simulations are used to optimize the coil layout. The sizing of the switch and its impact on the VCO performance are addressed as well. The VCOs have been implemented in 65 nm CMOS technology. Good correlation between simulated and measured tuning range and phase noise is obtained for all designs, thus confirming the validity and robustness of the design methodology and coil models. Copyright © 2013 John Wiley & Sons, Ltd.     

A study of amplitude‐to‐phase noise conversion in planar oscillators

This paper explores the many interesting implications for oscillator design, with optimized phase‐noise performance, deriving from a newly proposed model based on the concept of oscillator conjugacy. For the case of 2‐D (planar) oscillators, the model prominently predicts that only circuits producing a perfectly symmetric steady‐state can have zero amplitude‐to‐phase (AM‐PM) noise conversion, a so‐called zero‐state. Simulations on standard industry oscillator circuits verify all model predictions and, however, also show that these circuit classes cannot attain zero‐states except in special limit‐cases which are not practically relevant. Guided by the newly acquired design rules, we describe the synthesis of a novel 2‐D reduced‐order LC oscillator circuit which achieves several zero‐states while operating at realistic output power levels. The potential future application of this developed theoretical framework for implementation of numerical algorithms aimed at optimizing oscillator phase‐noise performance is briefly discussed.     

67 GHz three‐spiral transformer CMOS oscillator

This paper presents a 67GHz LC oscillator exploiting a three‐spiral transformer and implemented in 65nm bulk complementary metal–oxide–semiconductor technology by STMicroelectronics. The three‐spiral transformer allows operating with a lower voltage supply, still obtaining good phase noise performance, and achieving a compact design. Measured performances when supplied with 1.2 V are: oscillation frequency of 67 GHz, phase noise (PN) equal to ?96 dBc/Hz at 1 MHz frequency offset from the carrier, power consumption (P_C) equal to 19.2 mW and figure of merit (FOM) equal to ?179.7 dB/Hz. Measured performances when supplied with 0.6 V are: oscillation frequency of 67 GHz; PN equal to ?88.7 dBc/Hz at a 1 MHz frequency offset from the carrier; P_C equal to 3.6 mW and FOM equal to ?179.7 dB/Hz. Copyright © 2016 John Wiley & Sons, Ltd.     

A 3.6‐mW 6‐GHz current‐reuse VCO‐buffer with improved load drivability in 65‐nm CMOS

A new current‐reuse voltage‐controlled oscillator (VCO)‐buffer with enhanced load drivability is proposed. It incorporates a PMOS‐based source follower stacked atop a NMOS‐based LC VCO to share the bias current, while preventing the voltage stress at any oscillation node from exceeding the 1.2‐V technology voltage limit. Also, ac‐coupling networks are avoided between the VCO and buffer, improving the Q of the LC tank while minimizing parasitics. With internal buffering, the VCO can directly drive up a 50‐Ω load for testing, or to withstand a large capacitive load in on‐chip local oscillator distribution, particularly suitable for multi‐band MIMO WLAN radios . The fabricated VCO‐buffer in 65‐nm CMOS measures 13.8% tuning range from 5.64 to 6.4 GHz, consumes 3.6 mW at 1.2 V and exhibits ?108.84 dBc/Hz phase noise at 1‐MHz offset. Copyright © 2013 John Wiley & Sons, Ltd.     

Analysis and design of LC oscillators associated with frequency multipliers: a phase noise perspective

When a local oscillator signal generation system is based on an LC oscillator and a frequency multiplier, the question of determining the optimal multiplication factor is a key issue. In this paper, the problem is addressed in order to minimize the 1/f ² phase noise within a tuning range constraint. The analysis, with a practical graphical representation, reveals the oscillator phase noise dependence on the oscillating frequency in the transition from two different regimes, named the inductor‐limited quality factor and the capacitor‐limited quality factor. The results obtained enable the evaluation of the phase noise performance of systems based on a sub‐harmonic and super‐harmonic oscillators and how they compare with an oscillator in the fundamental mode. Crucial questions like the phase noise improvement that these systems can achieve are analytically answered. A design methodology is thus proposed and verified through measurements on a frequency source at 31 GHz, composed by a sub‐harmonic voltage‐controlled oscillator followed by an injection‐locked frequency tripler, dedicated to backhauling applications, designed on a BiCMOS process technology. The tuning range is 10%, and the phase noise at a 1‐MHz offset is −112 dBc/Hz. Copyright © 2017 John Wiley & Sons, Ltd.     

A 4.8–6.8 GHz low phase noise LC VCO in 0.13‐µm CMOS technology

This letter presents a novel LC voltage controlled oscillator (VCO) supporting the high‐speed serial transmission standard of RapidIO in 0.13‐µm complementary metal‐oxide semiconductor technology. The low phase noise is achieved through several techniques including current source switching, parallel coupled negative transconductance cell, and varactor bias combination scheme. Measured results of proposed circuit show a low phase noise of ?120 dBc/Hz at 1 MHz offset from 6.25 GHz carrier and tuning range of 4.8 ~ 6.8 GHz (34.48%) while consuming 7.4 mW under the supply voltage of 1.2 V. Copyright © 2015 John Wiley & Sons, Ltd.     

Increasing power efficiency in the design of a low power and low phase noise CMOS LC oscillator

This study developed a local oscillator (LO) with low phase noise and low power consumption. The proposed oscillator core comprises a pair of cross‐coupled transistors, which are fed by another pair of transistors that injects current at moments close to the peak of output voltage. The position of the current injection transistors, which are inserted in series with the cross‐coupled transistors, affects the waveform of current injected into an inductive–capacitive (LC) tank. Installing a capacitor on the source node of the cross‐coupled transistors increases the current injected into the LC tank and thereby augments the output voltage amplitude and power efficiency of the LO. The resonator phase shift and Q can be corrected by adjusting the source capacitance, which filters noise. These changes reduce the phase noise to ?123.4 dBc/Hz at a frequency offset of 1 MHz and improve oscillator performance with a figure of merit equal to ?193.5 dBc/Hz. To evaluate the LC tank, a 5 GHz LO was simulated at 1.8 V power supply and 2.5 mW power consumption. The simulation was conducted using a practical 0.18 complementary metal–oxide–semiconductor model manufactured by the Taiwan Semiconductor Manufacturing Company. The simulation results confirmed the analytical findings.     

Sinusoidal shaping of the ISF in LC oscillators

A new method to decrease the phase noise of the sinusoidal oscillators is proposed. The proposed method is based on using a dynamic transistor biasing in a typical oscillator topology. This method uses the oscillator impulse sensitivity function (ISF) shaping to reduce the sensitivity of the oscillator to the transistor noise and as a result reducing the oscillator phase noise. A 1.8 GHz, 1.8 V designed oscillator based on the proposed method shows a phase noise of ?130.3dBc/Hz at 1 MHz offset frequency, thereby showing about 6 dB phase noise decreasing in comparison with the typical constant bias topology. This result is obtained from the simulation based on 0.18u CMOS technology and on‐chip spiral inductor with a quality factor equal to 8. Copyright © 2007 John Wiley & Sons, Ltd.     

Time‐domain analysis of phase‐noise and jitter in oscillators due to white and colored noise sources

This paper presents an original time‐domain analysis of the phase‐diffusion process, which occurs in oscillators due to the presence of white and colored noise sources. It is shown that the method supplies realistic quantitative predictions of phase‐noise and jitter and provides useful design‐oriented closed‐form expressions of such phenomena. Analytical expressions and numerical simulations are verified through measurements performed on a relaxation oscillator whose behavior is perturbed by externally controlled noise sources. Copyright © 2011 John Wiley & Sons, Ltd.     

Nonlinear dynamics of divide‐by‐two injection‐locked frequency dividers in locked operation mode

A method for analyzing the nonlinear dynamics of the injection‐locked frequency dividers in synchronized operation mode is presented, including the stability analysis of locked states. We use a specific divide‐by‐two circuit, namely a differential LC CMOS divider with a complementary topology, as a guideline for presentation, showing that the sizing of the devices significantly affects the synchronization mechanism of the divider, which exhibits a very rich dynamical behavior. We provide closed‐form expressions to determine the amplitude and the phase in the locked state, as well as the locking range, leading to accurate results, which are validated by numerical simulations. The presented analysis of the frequency divider dynamics enables us to establish that stable locked oscillations occur on the whole locking range predicted by the well‐known Adler's equation and that these are possible also beyond that range. Copyright © 2013 John Wiley & Sons, Ltd.     

A systematic method for the development of a three‐phase transformer non‐linear model

In this work, a novel three‐phase transformer non‐linear model is developed. The proposed model takes into account the magnetic core topology and the windings connections. The non‐linear characteristic curve of the core material is introduced by its magnetization curve or by its hysteresis loop using the mathematical hysteresis model proposed by Tellinen or the macroscopic hysteresis model proposed by Jiles–Atherton. The eddy currents effects are included through non‐linear resistors using Bertotti's work. The proposed model presents several advantages. An incremental linear circuit, having the same topology with the magnetic circuit of the core, is used in order to directly write the differential equations of the magnetic part of the transformer. The matrix L _d that describes the coupling between the windings of the transformer is systematically derived. The electrical equations of the transformer can be easily written for any possible connection of the primary and secondary windings using the unconnected windings equations and transformation matrices. The proposed methods for the calculation of the coupling between the windings, the representation of the eddy currents and the inclusion of the core material characteristic curve can be used to develop a transformer model appropriate for the EMTP/ATP‐type programs. Copyright © 2009 John Wiley & Sons, Ltd.     

Short‐term stability in the intermediate region between quartz crystal oscillation and LC oscillation

In a quartz crystal oscillator circuit, an LC resonance circuit was inserted that enabled major enlargement of the variable range of frequency compared with the conventional Colpitts or Pierce quartz crystal oscillator. The short‐term stability of the oscillation was measured with Allan variance in the intermediate region between the quartz resonance and LC resonance, showing higher stability compared with the common LC oscillator. The analytical result is presented showing continuous transition from the quartz resonance to the LC resonance. © 2012 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc.