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Topics

1. Background

Leeson’s Phase Noise Model

2. LC Resonators

3. Frequency Control

4. VCO Phase Noise

5. VCO Design

6. Ring Oscillators

7. Top 100 Articles

The Heavenly 75

8. Additional Information

Editors

Editor in Chief

Associate Editors

Voltage-Controlled OscillatorsOscillators are indispensable to electronic systems. They provide carrier signals formodulation/demodulation in wireless communications, and reference timing for bit streamsin a digital system that must be sampled or synchronized with a stable, locally generatedsource.

Literally thousands of papers have been written and published in IEEE journals on thesubject of oscillators over the past 20 years, and the intense interest in building andunderstanding voltage-controlled oscillators (VCOs) is as strong now as it was in the earlydays of RF circuit development in silicon IC technologies. This issue of the RFIC VirtualJournal is centered specifically on LC VCOs, meaning fully monolithic oscillatorsincorporating an on-chip resonant tank in a positive feedback loop with electronicfrequency control. LC VCOs remain the focus of research and commercial interest inoscillator design for communication system applications. However, ring oscillators areutilized in applications such as microprocessors and wireline communication. Therefore abrief overview of the significant publications related to ring oscillators is included tocomplete the picture.

This editorial presents our selection of the top 100 papers written about LC VCOs from theIEEE database of papers published by the IEEE Solid-State Circuits Society, the IEEEMicrowave Theory and Techniques Society, and the IEEE Circuits and Systems Society.Papers published by these three Societies capture a very large share of the circuit designactivity in the RF field, making a useful reference for novice and experienced designers. Itconsists of two parts:

1. The Olympic 25: A description of significant milestones in the development of LCVCOs highlighting contributions from the top 25 papers published in the leading IEEEjournals in the area of RFICs.

Radio Frequency Integrated CircuitsIssue 1•December 2012

John R. LongDelft University of Technology, Delft, TheNetherlands

Earl McCune

Yann Deval

Radio Frequency Integrated Circuits • Issue 1 Current View

Figures Summary References7. Top 100 Articles

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Guest Editors

Frequency ControlFig. 12

BackgroundFig. 1

Leeson’s Phase NoiseModelFig. 5

2. The Heavenly 75: A list of an additional 75 papers of significance, noted for theirinnovations and improvements of significance to the performance, design, andintegration of LC VCOs.

Any list such as this is subjective, but there was surprising agreement between our guesteditors on the papers included in this compendium. It was our intention to highlight thepapers that we felt were noteworthy and that an engineer working in the field should studyto become acquainted with VCO circuits. An engineer could also consult this compendiumas a reference guide when dealing with the design challenges posed by monolithic LC VCOimplementation. For the sake of focus, this selection excludes quadrature topologies andcircuits operating above 10 GHz.

Spotlight On

Howard Luong

Pietro AndreaniLund University, Lund, Sweden

Behzad RazaviUniversity of California, Los Angeles

1. Background

Oscillators are as old as electronics itself, and it is likely that the first oscillator originated (perhapsunintentionally) with the construction of the first vacuum tube amplifier. Numerous well-known oscillatorcircuits have been devised, such as the Colpitts, Hartley, Clapp, Armstrong, and Pierce topologies. Eachvariant is aimed at optimizing some aspect of oscillator performance, and bears the name of its inventor.Interestingly, the circuit most commonly used today is known simply as the cross-coupled differentialoscillator. When tuned electronically by a variable capacitor, it becomes the cross-coupled voltage-controlledoscillator or the cross-coupled VCO.

The cross-coupled VCO is implemented readily using a differential pair (either n- or pMOS) biased by a tail(or top) current source, as shown in Fig. 1(a). Greater transconductance efficiency from the differential gainstage is obtained when nMOS and pMOS are combined, as in the push-pull configuration, as shown in Fig.1(b). More importantly, for a given tail-bias current and differential tank design, the complementarytopology provides twice the output voltage swing, assuming that the supply voltage is large enough.



Fig. 1 Simplified cross-coupled oscillator schematics: (a) NMOS oscillator and (b) push-pull cross-coupled CMOSoscillator (see Andreani 2006).

Oscillators are characterized in the frequency domain by their RF power spectrum, which is typicallysymmetric around the carrier frequency where the output power peaks. Examining one side of this spectrum,the ratio of the single-sideband (SSB) to the carrier power spectral density at a frequency offset ƒ Hz awayfrom the carrier, or L(ƒ ), is the phase noise (see Fig. 2).

Fig. 2 Oscillator power spectrum where the AM noise is insignificant.

The importance of the oscillator phase noise in a wireless transceiver application is illustrated in Fig. 3. Thereceived RF signal strength in the desired channel and the maximum signal strengths in the adjacentchannels are shown in Fig. 3(a). The oscillator spectral characteristics are also shown, where the phase noisedensity of the oscillator must be far below the peak at a frequency offset equal to the channel spacing ƒ .The downconverted spectrum is illustrated in Fig. 3(b). One component is the “desired” block of signals inthe lower part of the diagram, which is downconverted (ideally) by a sinusoidal component at the nominallocal oscillator frequency, f . Interference arises from downconversion of the RF spectrum by a sinusoidalcomponent of the oscillator spectrum that is offset from the main carrier lobe by the channel spacing. Theamplitude of the interference at the IF is directly proportional to the phase noise of the local oscillator andtherefore the level of adjacent channel interference increases as the phase noise of the LO increases. On thetransmit side, on the other hand, the phase noise introduced by the local oscillator used to upconvert thebaseband signal is a potential source of interference to other users in the system.

The channel spacing in many cellular telephone systems is on the order of tens or hundreds of kilohertz, andthe blocking requirements are quite stringent; so the demands on the spectral purity of the oscillator aremuch greater than in systems such as cordless telephones where the channel spacing is on the order of 1MHz and interference specifications are relaxed.

d

d

ch

LO

More on the 1/f Phase NoisePerformance of CMOSDifferential-Pair LC-TankOscillators

Andreani 20062



Fig. 3 Effect of oscillator phase noise in a receiver. (a) RF and LO signals. (b) Resulting baseband output.

1A. Leeson’s Phase Noise Model

Leeson developed the following expression to predict single-sideband oscillator phase noise L(ƒ ) in terms ofcircuit parameters

where Q is the loaded Q-factor of the resonator, ƒ is the frequency of oscillation, ƒ is the flickernoise corner, P is the average power in the output signal, k is Boltzmann’s constant, T is absolutetemperature, and F is the circuit noise factor.

The first term (in square brackets) shows the strong effect of the resonator Q-factor on phase noise. Thesecond term arises from flicker noise sources in active devices, and the last term is the ratio of thermal tosignal noise power. Leeson’s equation predicts the three phase noise regimes shown in Fig. 4: upconverted1/f noise in 1/f regime, a 1/f regime, and the thermal noise floor.

Equation (1) was validated by Leeson experimentally using high-quality microwave sources. However, areliable method of computing the effective noise factor [see F in (1)] for an oscillator was not proposed, sothe equation cannot be used directly for VCO design.

The 1/ƒ regime (see Fig. 4) is of interest to designers because noise at these frequency offsets typically liesoutside the bandwidth of a synthesizer PLL and cannot be suppressed. Cellular mobile system specificationsdefine limits for the phase noise that can be tolerated at specific offsets, which usually lie in the 1/ƒ regime,unless f is very high.L(f ) = 20 log (f /f ) + L(f )

d

(1)

loaded o c

avs

3 2

2

2

c d2 d2 o d1

A simple model of feedbackoscillator noise spectrum

Leeson



Fig. 4 Regimes of single-sideband phase noise in the power spectrum of an LC oscillator.

At offsets in the 1/ƒ regime, the phase noise measured or simulated at offset ƒ and carrier frequency ƒcan be referred to offset ƒ using the equation

Equation (2) is used to compare the performance of oscillators reported in different publications, becauseit allows phase noise measured at various frequency offsets in the 1/ƒ regime to be normalized to the sameoffset for comparison.

A figure of merit (FoM) that is commonly quoted for LC VCOs captures phase noise and power consumption[P in milliwatts (mW)], and is given by

Caution is required when quoting FoM data from different sources, as variations such as the units used forpower consumption in the FoM (e.g., different from mW) can affect fairness of the comparison.

Not surprisingly, owing to the extensive research by workers in the field, the FoM of LC oscillators hasdramatically improved over the past 20 years. Fig. 5 illustrates this evolution, indicating about 40 dB ofimprovement, which is equivalent to a factor of 10,000 reduction in power consumption.

Fig. 5 Evolution of LC oscillator FoM versus time

Another figure of merit that has become more common recently incorporates the tuning range Δƒ , as well.Such a FoM, often referred to as FoM_T, is obtained by adding 20log [ ΔfT/( 10*f0 ) ] to the above expression.

2d1 o

d2

(2)

2

D

(3)

T



2. LC Resonators

The recent history of monolithic VCOs began with the first circuit integrated on silicon by Nguyen and Meyerin 1992 [Nguyen 1992], and VCO developments over the past two decades have tracked improvements inthe quality factor (Q) of integrated capacitors and inductors that constitute the oscillator’s LC tank. Scalingof CMOS technology from two aluminum interconnect metals on 3 μm of oxide 20 years ago to ten (or more)copper metal layers embedded in 10 μm of insulator for today’s deep submicron processes is clearly drivingthis trend. It also enables the design of integrated VCOs capable of meeting exacting phase noisespecifications, such as the narrowband GSM 900 cellular mobile standard, where the phase noise at 20-MHzoffset from the 900-MHz transmitted carrier must be lower than -162 dBc/Hz at a power consumption ofjust a few milliwatts. Furthermore, RF-CMOS processes provide extra-thick metal layers (e.g., 2-3 μm) foreven higher-Q inductors, and extra-thin dielectric layers for higher Q, higher density metal-insulator-metal(MIM) capacitors. However, these additional features add to the chip cost, so designers continue to deviseclever new ways of extracting higher performance from circuits manufactured in low-cost technologies.

Apart from sheer technological improvements, such as the change from aluminum to copper metals in CMOS,important design innovations are also contributing to improving the LC-tank Q. An early example is thehollow inductor [Caulton 1968]. It is a spiral inductor where the innermost turns are removed, since it wasrecognized that turns at the very center of the spiral contribute little to the inductance value, and highly tothe inductor losses. Today, all inductors are designed hollow, and quite often with a single turn forinductances below 1 nH in value. Initially, differential LC oscillators made use of two identical inductors;however, it was soon recognized [Danesh 1998] that a differentially driven symmetrical inductor layout (witha center-tap for the power-supply connection) produced a higher Q for the same overall inductance value,while consuming less chip area. For these reasons, the symmetrical inductor is used in differential VCOcircuits. Fig. 6 shows an example using a square symmetric inductor. In practice, the inductor is oftenrealized as an octagon to obtain the same inductance but with less wire resistance and greater chip area. Itis also worth mentioning that bond wires proposed as high-Q inductors very early on in the development ofVCOs [Craninckx 1995a] vastly outperformed monolithic inductors. However, with the improvement ofmonolithic inductors, their higher controllability, reliability and insensitivity to stray magnetic fields madethem the solution of choice for mainstream applications. Nonetheless, bond-wire inductors are still used inniche applications requiring extremely low power consumption.

Fig. 6 Simplified LC oscillator using a hollow symmetric inductor.

A second improvement in inductor design makes use of a patterned ground shield between the coil and thesubstrate [Yue 1998] that blocks the electric field from inducing a substrate current and degrading theinductor Q. A low-resistance ground shield intercepts the electric field from the coil (Fig. 7), and improvesthe inductor Q by 10% (or more, according to different experiments). Proximity of the ground shield to thecoil increases the parasitic capacitance to the substrate, so this technique is “not a free lunch, but still a big,free sandwich ”. The ground shield must be perforated or patterned, otherwise it acts as the secondary of a

1

A 1.8 GHz monolithic LC voltage-controlled oscillator

Nguyen 1992

2

Hybrid Integrated Lumped-Element Microwave Amplifiers

Caulton 1968

A Q-factor enhancementtechnique for MMIC inductors

Danesh 1998

Low-noise voltage-controlledoscillators using enhanced LC-tanks

Craninckx 1995a

On-chip Spiral Inductors WithPatterned Ground Shields For Si-based RF IC's

Yue 1998



transformer (the inductor being the primary), with disastrous consequences on the inductor Q. Therefore, theground shield is patterned in a way that does not allow the secondary (eddy) current to flow. However, sincethis current still flows through the substrate, the inductor loss due to the magnetic coupling remains, but itis a small effect in RF-CMOS technologies built on medium resistivity substrates (e.g., 10-20 Ω-cm). A furtherimprovement of this concept is the floating patterned shield for differential inductors, which yields a higher Qand a higher self-resonance, compared to the standard patterned ground shield [Cheung 2006]. Patternedground shields are often generated together with the desired inductor automatically in advanced design kitsfor modern RF IC applications.

Fig. 7 Spiral inductor with patterned ground shield.

Oscillators are notorious for their inclination to be easily disturbed by spurious signals finding their way tothe oscillator core, a phenomenon collectively referred to as pulling. A situation where pulling is a seriousproblem, is when more than one VCO is active at the same time on an IC. For example, the transmitter andreceiver VCOs in a frequency-division duplexed wideband CDMA radio for 3G mobile communication runconcurrently. Since transmit and receive bands usually lie close to each other in frequency, the two VCOs canmodulate or “pull” each other’s frequencies. Even assuming that no disturbances travel on the power supplyand control signals, the magnetic field created by one VCO may couple to the coil of the other VCO (andvice-versa) in a case of mutual pulling. This effect can be mitigated by placing the two VCOs as far awayfrom each other as possible in the chip layout (which may not be possible due to chip area and layoutconsiderations), or the VCO frequencies could be separated by design, which complicates the design of thetransceiver. An alternative, elegant solution is the use of an 8-shaped coil [Itoh 2007], which is insensitiveto common-mode magnetic fields (to the first order) and generates a magnetic field that vanishes far awayfrom the coil. Fig. 8 illustrates the principle: the currents in the two halves produce opposite and equalmagnetic fields along the lines of symmetry passing through P. The 8-shaped coil, which is used in severalcommercial radios, possesses a lower Q-factor than standard coil designs, but high-performance VCOs arestill realizable, especially if thick-metal layers are available [Andreani 2011].

Fig. 8 Inductor with reduced magnetic coupling.

Transformers as a substitute for the LC tank have also been the target of extensive research. A very goodearly example that is especially suited to low power supply voltages is by Kwok and Luong [Kwok 2005],where a (differential) transformer between MOS gate/drain and source of the core transistors allows alltransistor nodes to float, increasing the achievable oscillation amplitude (Fig. 9). Another ingenious use oftransformers in VCOs, devised by Bevilacqua et al. [Bevilacqua 2006], sweeps two separate frequency bandsby driving the transformer (or an auto-transformer [Borremans 2008]) in two different modes employingpairs of core transistors, instead of a single core pair (Fig. 10). This approach is different from short-circuiting a section of an inductor or transformer to change the oscillation frequency using a MOS switch

Shielded passive devices forsilicon-based monolithicmicrowave and millimeter-waveintegrated circuits

Cheung 2006

Twisted Inductor VCO forSupressing On-chip Interferences

Itoh 2007

A TX VCO for WCDMA/EDGE in90 nm RF CMOS

Andreani 2011

Ultra-low-Voltage high-performance CMOS VCOs usingtransformer feedback

Kwok 2005



3. Frequency Control

(e.g., as in [Yim 2006, Kossel 2009]), because loss introduced by a MOS switch that deteriorates the overalltank-Q of the VCO is avoided. The dual-band transformer approach has been improved upon by Li et al. in[Li 2012], where a capacitive-mode switching has been added as well. This enables the realization of a VCOwith a frequency tuning range (TR) in excess of an octave, and very competitive phase-noise performanceand FoM.

Fig. 9 Transformer-based very-low-voltage oscillator: after [Kwok 2005].

Fig. 10 Transformer-based dual-band oscillator: after [Bevilacqua 2006].

VCO frequency tuning is typically performed by changing the bias voltage of a varactor, which is a capacitorwhose value depends on the voltage across its terminals. A reverse-biased diode is traditionally used fordiscrete component varactors, but in CMOS a better solution is the MOS device, in particular, an nMOS-in-N-well varactor, which works in either the depletion or accumulation (AMOS) regimes (Fig. 11).

A 3.4-7 GHz Transformer-BasedDual-mode Wideband VCO

Bevilacqua 2006

A 2-GHz low-phase-noiseintegrated LC-VCO set withflicker-noise upconversionminimization

Borremans 2008

Switched resonators and theirapplications in a dual-bandmonolithic CMOS LC-tuned VCO

Yim 2006

LC PLL With 1.2-Octave LockingRange Based on Mutual-Inductance Switching in 45-nmSOI CMOS

Kossel 2009

A Low-Phase-Noise Wide-Tuning-Range Oscillator Based onResonant Mode Switching

Li 2012

Ultra-low-Voltage high-performance CMOS VCOs usingtransformer feedback

Kwok 2005

A 3.4-7 GHz Transformer-BasedDual-mode Wideband VCO

Bevilacqua 2006



Fig. 11 AMOS varactor.

The AMOS varactor is relatively simple to integrate in standard CMOS, and enjoys the full advantage ofchannel length reduction in scaled CMOS processes. A second advantage is that is cannot draw dc current,which is a severe problem with diode varactors in RF applications. Because the AMOS Q-factor is higher thanother varactor types (30-50 at 3 GHz) in modern CMOS processes, its use has become commonplace sinceits first appearance in a VCO [Svelto 2000]. It is worth noting that the AMOS varactor was proposed atalmost the same time in 1998 by at least three independent research teams [Hung 1998, Soorapanth 1998,and Castello 1998], including two back-to-back presentations at the 1998 Symposium on VLSI Circuits.

When a large tuning range (TR) is needed, it is impractical to cover it with a single varactor using analogtuning. A small variation in the varactor control voltage results in a large frequency change for the oscillator(i.e., very large gain constant for the VCO) when a single varactor is used, and the control voltage rangecannot be extended beyond the limits of the power supplies to reduce this sensitivity. As a consequence,disturbances on the VCO control line affect the purity of the oscillation by creating a large amount of phasenoise. The solution proposed by Kral et al. [Kral 1998], and later refined in [Sjöland 2002], is a mix ofdiscrete and continuous tuning. An array of switchable capacitors covers a large TR in discrete steps underthe control of MOS switches, while a varactor sweeps a continuous band large enough to cover a few of thediscrete frequency steps (Fig. 12). In this way, the value of the VCO gain constant is decoupled from the TR,and more noise on the varactor control voltage can be tolerated because the VCO gain can be lower.

Fig. 12 LC oscillator with discrete and continuous tuning [Kral 1998].

This paves the way for complete integration of the phase-locked loop (PLL), and notably of the passive loopfilter. A minor drawback of this approach is that the VCO must be frequency-tuned before the PLLsynthesizer can lock properly, but this is usually not a serious problem to overcome in the design. Thetradeoff between TR and tank Q in a switched-capacitor VCO has been quantitatively treated in [Berny2003], and later improved by [DalToso 2010] and [Sadhu 2010]. In fact, adopting large, low-resistance MOSswitches is definitely good for the tank-Q, but the switch parasitic capacitance reduces both the oscillationfrequency and TR because it is also large. An earlier, and still largely valid VCO design methodology waspresented in [Ham 2001], where optimal design of the tank inductor is studied based on phase noise, powerconsumption and TR requirements (n.b., discrete tuning is not used in this work).

A 1.3 GHz low-phase noise fullytunable CMOS LC VCO

Svelto 2000

High-Q capacitors implementedin a CMOS process for low-powerwireless applications

Hung 1998

Analysis and optimization ofaccumulation-mode varactor forRF ICs

Soorapanth 1998

A ±30% tuning range varactorcompatible with future scaledtechnologies

Castello 1998

RF-CMOS oscillators withswitched tuning

Kral 1998

Improved switched tuning ofdifferential CMOS VCOs

Sjöland 2002

RF-CMOS oscillators withswitched tuning

Kral 1998

A 1.8-GHz LC VCO with 1.3-GHztuning range and digitalamplitude calibration

Berny 2003

DalToso 20102



4. VCO Phase Noise

Discrete tuning may actually come in two flavors, as shown in Fig. 13: either the one just discussed (acapacitor in series with a MOS switch), or using an AMOS varactor switched between its maximum and(near) minimum capacitance value by two discrete tuning voltages [Fong 2003]. Currently, the firstalternative is more popular, although the switched-AMOS is also known to yield excellent performance.However, the AMOS varactor does not have a well-defined minimum capacitance value, and therefore anydisturbance on the control voltage can modulate the VCO causing phase noise degradation.

Finally, an increasingly important class of oscillators disposes of even the small varactor used for continuousfrequency tuning. They are VCOs controlled by digital signals only, or digitally controlled oscillators (DCOs).DCOs find their use in digital PLLs, a research area that has exploded in the last decade after the first DCOwas proposed by Staszewski et al. [Staszewski 2003]. Here, a minimum-size PMOS device was used as thetiniest amount of switchable capacitance, together with high-rate ΔΣ dithering to smear the granularity of theDCO tuning characteristic. One challenge in DCO design is to switch an effective capacitance as small as afew aF - not an easy feat - but still possible even without resorting to ΔΣ dithering (see, e.g., Fanori 2010)to guarantee sufficient dynamic range.

Fig. 13 (Left) Discrete tuning with capacitors and floating MOS switch [Sjöland 2002]. (Right) Discrete tuning withAMOS varactors [Fong 2003].

Parallel to the development of the art of VCO integration on silicon, a deeper understanding of the innerworking of the harmonic oscillator has developed, especially with respect to the generation of phase noise.Analog simulators capable of performing accurate phase noise simulations on time-varying, non-linearcircuits, such as Cadence-SpectreRF™ and Agilent-ADS™, have enabled theoretical studies without resortingto the time and expense of building and characterizing numerous prototypes. It is interesting to note thatthe mathematical framework behind such advanced simulators, developed by Kärtner [Kärtner 1989] (andlater by Demir 2000 and Demir 2002), predates by almost a decade the appearance of the well-knowntheoretical work by Hajimiri and Lee [Hajimiri 1998] on the phase noise in electrical oscillators, which rapidlybecame the most cited oscillator paper in IEEE Xplore™. The reason for this immense popularity lies, we

A 0.06 mm 11 mW LocalOscillator for the GSM Standardin 65 nm CMOS

Capacitor bank design for widetuning range LC VCOs: 850MHz-7.1GHz (157%)

Sadhu 2010

Concepts and methods inoptimization of integrated LCVCOs

Ham 2001

Design of wide-band CMOS VCOfor multiband wireless LANapplications

Fong 2003

A first multigigahertz digitallycontrolled oscillator for wirelessapplications

Staszewski 2003

Capacitive Degeneration in LC-Tank Oscillator for DCO Fine-Frequency Tuning

Fanori 2010

Improved switched tuning ofdifferential CMOS VCOs

Sjöland 2002

Design of wide-band CMOS VCOfor multiband wireless LANapplications

Fong 2003

Determination of the correlationspectrum of oscillators with lownoise

Kärtner 1989



believe, is the rigorous analysis based on the impulse sensitivity function (ISF), which translates noise intophase noise. Technicalities are kept to a bare minimum in this approach, compared to more mathematicaltreatments, making the study of phase noise accessible to working engineers. The lasting lesson of [Hajimiri1998] is that phase noise is generated in a time-variant fashion. The same amount of noise, injected into theLC tank at different times across the oscillation period, results in vastly different phase noise contributions, afact that is accounted for by a non-constant ISF. This effect is illustrated by the SPICE simulation of Fig. 14.The circuit (schematic of Fig. 14a and SPICE netlist of Fig. 14b) applies a start-up current impulse Ι to aparallel LC tank, causing it to resonate at its natural frequency of 1Hz. Current pulse generator Ι isconfigured to apply an additional impulse at different times (td) for 2 of the simulation sweeps plotted in Fig.14c: td=1 s, td=1.75 s, with the resulting green and blue responses, respectively. The reference waveform(in red) shows the unperturbed oscillation (i.e., no second impulse from current generator Ι during thesimulation). The simulation results illustrate that an impulse timed to coincide with the peak of the waveform(td=1 s) causes a large amplitude change but minimal phase shift, while a disturbance at the zero crossing(td=1.75 s) causes a large (in fact, the largest) phase shift of about 33° (the actual amount of phase shift isrelated to the amplitude of the injected current pulse). The phase sensitivity of the oscillating waveform toinjected impulses therefore depends upon the timing of the injected current. Noise injected into an LC-tankhas a similar effect, which is captured by the ISF.

Fig. 14 SPICE simulation of the impulse response sensitivity of an LC tank. (a) Schematic diagram. (b) SPICE netlist.(c) Tank voltage waveforms versus time.

An alternative and equally rigorous approach to the study of phase noise is via the harmonic transferfunction (HTF), pioneered by Samori et al. [Samori 1998]. This work revealed that noise from the tail currentsource biasing the oscillator does contribute to phase noise, contrary to assumptions made previously inlinear time-invariant analysis. This result can be couched in terms of the ISF theory as well [Hajimiri 1999].

The contribution of the core transistors to phase noise in a cross-coupled differential-pair oscillator wasstated in an influential paper by Rael and Abidi [Rael 2000]. This work is also important because it mentionsthe possible importance of the Groszkowski effect (i.e., the slight dependence of the oscillation frequency onthe harmonic content of the current waveform injected by the core transistors into the tank) as a mechanismup-converting flicker noise to phase noise.

Besides the Groszkowski effect, flicker noise can deteriorate the oscillator spectrum via AM-to-FM conversion,in which flicker noise from the bias current source modulates the amplitude of the oscillation waveform,

1

2

2

Phase noise in oscillators: aunifying theory and numericalmethods for characterization

Demir 2000

Phase noise and timing jitter inoscillators with colored-noisesources

Demir 2002

A general theory of phase noisein electrical oscillators

Hajimiri 1998

A general theory of phase noisein electrical oscillators

Hajimiri 1998

Spectrum folding and phasenoise in LC tuned oscillators

Samori 1998

Phase noise to carrier ratio in LCoscillators

Hajimiri 1999

Physical processes of phase noisein differential LC oscillators

Rael 2000



5. VCO Design

which in turn modulates the oscillation frequency by acting across a (large) varactor or the parasitic drain-body depletion diode capacitances of the core transistors [Levantino 2002 and Hegazi 2003]. Thismechanism is especially visible in VCOs with a wide tuning range, where MOS switches used for mixed-modetuning introduce a large and non-linear parasitic capacitance.

The ISF theory made it possible to consider a quantitative revision of Leeson’s famous phase noise equation,which was originally proposed in a heuristic fashion. Eventually, this led to the determination of theoreticalexpressions describing the phase noise behavior of the most important harmonic oscillator topologies, suchas the cross-coupled differential-pair oscillator and Colpitts oscillator [Andreani 2005] (showing that theColpitts is noisier than the cross-coupled oscillator, contrary to what was believed previously), and thedouble differential-pair oscillator [Andreani 2006]. These theoretical advances have had a direct impact onthe practice of LC oscillator design. A very general result for harmonic oscillators where the core transistorsbehave as transconductors reveals [Mazzanti 2008] that the phase noise generated by the core transistors isalways proportional to the phase noise caused by the LC-tank losses, and that the proportionality coefficientdepends on the actual oscillator topology. It is remarkable that the same general result was later derived byMurphy et al. [Murphy 2010] following the HTF approach.

An important issue in the operation of the cross-coupled differential-pair oscillator is the impedance level atthe common source node of the cross-coupled pair. Ideally, it is infinite, but the unavoidable parasiticcapacitances from the cross-coupled pair and current source contribute to lower its level; if this dropssignificantly, the phase noise contribution of the cross-coupled pair increases likewise, both in terms ofthermal noise and flicker noise.

A clever solution to this problem was proposed by Hegazi et al. in [Hegazi 2001], where an LC filter tuned attwice the oscillation frequency is formed between the cross-coupled pair and the current source (Fig. 15a),thus boosting the impedance at the common-source node of the cross-coupled pair by resonating away theparasitic capacitance at that node. At the same time, the high-frequency noise from the tail current source isshunted by a large grounded capacitance providing an RF ground to the tail inductor. Furthermore, thecurrent source can be designed as a long (and correspondingly wide) transistor, because its parasitic drainand gate capacitances are anyway absorbed into the grounded capacitance. This greatly helps reducing theflicker noise from the tail current source.

An alternative approach is to actually exploit the parasitic capacitance at the common source of thedifferential pair, which, possibly augmented by an additional intentional capacitance, turns the typical class-Boperation for this kind of oscillators into class-C [Mazzanti 2008], where current waveforms delivered by thecore transistors are no longer square waves, but rather tall and narrow pulses (Fig. 15b). In this way, theefficiency of the conversion from bias to fundamental oscillation current is increased, resulting in lower powerconsumption for the same phase noise performance. Evolutions of the class-C approach are presented in[Okada 2009, Tohidian 2011, and Chen 2011], but more experiments are needed to assess its actualadvantages on more traditional oscillator designs.

Frequency dependence on biascurrent in 5 GHz CMOS VCOs:impact on tuning range andflicker noise upconversion

Levantino 2002

Varactor characteristics, oscillatortuning curves, and AM-FMconversion

Hegazi 2003

A study of phase noise in colpittsand LC-tank CMOS oscillators

Andreani 2005

More on the 1/f Phase NoisePerformance of CMOSDifferential-Pair LC-TankOscillators

Andreani 20062

Class-C Harmonic CMOS VCOs,With a General Result on PhaseNoise

Mazzanti 2008

Phase Noise in LC Oscillators: APhasor-Based Analysis of aGeneral Result and of Loaded Q

Murphy 2010

A filtering technique to lower LCoscillator phase noise

Hegazi 2001


Mazzanti 2008

A 0.114-mW dual-conductionclass-C CMOS VCO with 0.2-Vpower supply

Okada 2009

High-swing class-C VCOTohidian 2011

A Low Power, Startup Ensuredand Constant Amplitude Class-C

Chen 2011



6. Ring Oscillators

Fig. 15 (a) Noise filter at the tail (after Hegazi 2001) and (b) Class-C oscillator (after Mazzanti 2008).

Although VCOs based on a ring of inverters (either single-ended or differential) are less relevant than LCVCOs to RF communication systems because of their poor phase noise performance for the same powerconsumption, they are the preferred choice in applications where compactness is vital and demands on phasenoise less exacting. As an example, we can mention the ring VCOs used in microprocessors, memories, andsome wireline systems, where PLLs serve to generate and/or multiply clock frequencies.

A limitation on the frequency of a ring oscillator is the propagation delay of the CMOS inverter.Unexpectedly, Maneatis and Horowitz [Maneatis 1993] showed how this seemingly hard constraint can beovercome by coupling ring oscillators to each other in a multidimensional array (Fig. 16), thereby obtaining atime resolution between inverter elements in the array that is well below the single inverter’s. This seminalwork has spawned a number of clever variations on the original theme, as in, e.g., [Park 1999].

VCO in 0.18 μm CMOS

A filtering technique to lower LCoscillator phase noise

Hegazi 2001


Mazzanti 2008

Precise delay generation usingcoupled oscillators

Maneatis 1993

A low-noise 900 MHz VCO in 0.6μm CMOS

Park 1999



7. Top 100 Articles

Fig. 16 Array of ring oscillators (after Maneatis 1993).

As in the case of LC oscillators, the problem of phase noise in ring oscillators has attracted the attention of anumber of researchers. Razavi [Razavi 1996] showed that the definition of Q-factor, which arises naturally inthe context of harmonic oscillators, can be extended to ring oscillators as well. The Q values are not muchlarger than unity, providing an alternative explanation of the poor phase noise performance of ringoscillators. Furthermore, the impact of noise folding on phase noise was recognized explicitly, as well as theup-conversion of low-frequency bias noise to phase noise. These findings were later expressed in thelanguage of the ISF theory by Hajimiri et al. [Hajimiri 1999b], where the following remarkable result wasstated: in single-ended CMOS ring oscillators the phase noise in the 1/ƒ region depends only on theoscillation frequency and power consumption. It is therefore independent of the number of stages in theoscillator. This result was later rediscovered in another closed form by Abidi [Abidi 2006] via a time-domainanalysis reminiscent of McNeill’s [McNeill 1997]. Abidi’s work also provides guidelines for minimizing the up-conversion of flicker noise into phase noise: besides consuming the highest possible amount of power in theoscillator and using the longest practical channel length for the MOS transistors for the inverters in eachstage, the number of stages should be maximized. It is also interesting to learn that the intrinsic MOS-device flicker noise may experience a reduction in ring oscillators, as shown by Gierkink et al. [Gierkink1998]. This is because n- and pMOS transistors are pushed into the off-state periodically by the oscillationtraveling around the ring, with the consequence that their flicker noise is reduced when they reenter the ON-state. It should be noted that this effect is not captured by RF simulators at the present time.

7A. The Olympic 25

THEORY - GENERAL

1. Leeson, D.B. 1966

"A simple model of feedback oscillator noise spectrum,"Proceedings of the IEEE, 1966

2. Kaertner, F.X. 1989

"Determination of the correlation spectrum of oscillators with low noise,"Microwave Theory and Techniques, IEEE Transactions on, 1989

3. Hajimiri, A.; Lee, T.H. 1998

"A general theory of phase noise in electrical oscillators,"

2

Precise delay generation usingcoupled oscillators

Maneatis 1993

A study of phase noise in CMOSoscillators

Razavi 1996

Jitter and phase noise in ringoscillators

Hajimiri 1999b

Phase Noise and Jitter in CMOSRing Oscillators

Abidi 2006

Jitter in ring oscillatorsMcNeill 1997

Reduction of intrinsic 1/f devicenoise in a CMOS ring oscillator

Gierkink 1998

Mathematical, general approach – the subsequent, definitive paper by Kärtner is not on IEEE-Xplore.

http://ieeexplore.ieee.org/xpl/articleDetails.jsp?arnumber=1446612&contentType=Journals+%26+Magazines&source=rfic





Solid-State Circuits, IEEE Journal of, 1998

4. Demir, A.; Mehrotra, A.; Roychowdhury, J. 2000

"Phase noise in oscillators: a unifying theory and numerical methods for characterization,"Circuits and Systems I: Fundamental Theory and Applications, IEEE Transactions on, 2000

LC VCOS - Theory

5. Samori, C.; Lacaita, A.L.; Villa, F.; Zappa, F. 1998

"Spectrum folding and phase noise in LC tuned oscillators,"Circuits and Systems II: Analog and Digital Signal Processing, IEEE Transactions on, 1998

6. Rael, J.J.; Abidi, A.A. 2000

"Physical processes of phase noise in differential LC oscillators,"Custom Integrated Circuits Conference, 2000. CICC. Proceedings of the IEEE 2000, 2000

7. Levantino, S.; Samori, C.; Bonfanti, A.; Gierkink, S.L.J.; Lacaita, A.L.; Boccuzzi, V. 2002

"Frequency dependence on bias current in 5 GHz CMOS VCOs: impact on tuning range and flicker noiseupconversion,"Solid-State Circuits, IEEE Journal of, 2002

8. Andreani, P.; Xiaoyan Wang; Vandi, L.; Fard, A. 2005

"A study of phase noise in colpitts and LC-tank CMOS oscillators,"Solid-State Circuits, IEEE Journal of, 2005

9. Murphy, D.; Rael, J.J.; Abidi, A.A. 2010

"Phase Noise in LC Oscillators: A Phasor-Based Analysis of a General Result and of Loaded Q,"Circuits and Systems I: Regular Papers, IEEE Transactions on, 2010

LC VCOs - Applications

10. Kral, A.; Behbahani, F.; Abidi, A.A. 1998

"RF-CMOS oscillators with switched tuning,"Custom Integrated Circuits Conference, 1998. Proceedings of the IEEE 1998, 1998

11. Svelto, F.; Deantoni, S.; Castello, R. 2000

"A 1.3 GHz low-phase noise fully tunable CMOS LC VCO,"Solid-State Circuits, IEEE Journal of, 2000

12. Ham, D.; Hajimiri, A. 2001

"Concepts and methods in optimization of integrated LC VCOs,"

Most citations of all LC VCO papers in the IEEE database.

Theoretical foundation for phase noise analysis in many commercial RF circuit simulators.

The start of the rigorous phase noise study of the LC oscillator.

First (partially) correct expression of the noise factor in LC cross-coupled oscillators. Major revolution:SpectreRF has arrived.”

Up-conversion of low-frequency noise into phase noise.

First rigorous phase noise analysis of Colpitts and single-switch-pair LC-tank oscillators, based onHajimiri’s theory.

Alternative general analysis – compared to Mazzanti JSSC 2008 – of phase noise in harmonicoscillators, based on a development of Samori’s approach.

Discrete tuning.

AMOS varactor tuning.



http://ieeexplore.ieee.org/xpl/articleDetails.jsp?arnumber=852732&contentType=Conference+Publications&source=rfic












13. Hegazi, E.; Sjoland, H.; Abidi, A.A. 2001

"A filtering technique to lower LC oscillator phase noise,"Solid-State Circuits, IEEE Journal of, 2001

14. Fong, N.H.W.; Plouchart, J.-O.; Zamdmer, N.; Duixian Liu; Wagner, L.F.; Plett, C.; Tarr, N.G. 2003

"Design of wide-band CMOS VCO for multiband wireless LAN applications,"Solid-State Circuits, IEEE Journal of, 2003

15. Staszewski, R.B.; Chih-Ming Hung; Leipold, D.; Balsara, P.T. 2003

"A first multigigahertz digitally controlled oscillator for wireless applications,"Microwave Theory and Techniques, IEEE Transactions on, 2003

16. Berny, A.D.; Niknejad, A.M.; Meyer, R.G. 2005

"A 1.8-GHz LC VCO with 1.3-GHz tuning range and digital amplitude calibration,"Solid-State Circuits, IEEE Journal of, 2005

17. Kwok, K.; Luong, H.C. 2005

"Ultra-low-Voltage high-performance CMOS VCOs using transformer feedback,"Solid-State Circuits, IEEE Journal of, 2005

18. Bevilacqua A.; Federico P.; Sandner C.; Gerosa A.; Neviani A. 2006

"A 3.4-7 GHz Transformer-Based Dual-mode Wideband VCO,"Solid-State Circuits Conference, 2006. ESSCIRC 2006. Proceedings of the 32nd European, 2006

19. Mazzanti, A.; Andreani, P. 2008

"Class-C Harmonic CMOS VCOs, With a General Result on Phase Noise,"Solid-State Circuits, IEEE Journal of, 2008

20. Guansheng Li; Li Liu; Yiwu Tang; Afshari, E. 2012

"A Low-Phase-Noise Wide-Tuning-Range Oscillator Based on Resonant Mode Switching,"Solid-State Circuits, IEEE Journal of, 2012

Ring

21. Maneatis, J.G.; Horowitz, M.A. 1993

"Precise delay generation using coupled oscillators,"Solid-State Circuits Conference, 1993. Digest of Technical Papers. 40th ISSCC., 1993 IEEE International,1993

A first, partially still valid approach to a rigorous VCO design.

Tail noise filter.

Discrete tuning with AMOS.

First digitally controlled oscillator.

VCO design taking tuning range into account.

Early example of transformer-coupled VCO with very low Vdd.

Dual-band operation without inductor switching.

New class-C oscillator; general phase noise theory of harmonic oscillators.

Evolution of Bevilacqua’s approach, very large tuning range at high FoM.

Beyond the plain ring oscillator.












22. Razavi, B. 1996

"A study of phase noise in CMOS oscillators,"Solid-State Circuits, IEEE Journal of, 1996

23. Gierkink, S.L.J.; Klumperink, E.A.M.; Ikkink, T.J.; van Tuijl, A.J.M. 1998

"Reduction of intrinsic 1/f device noise in a CMOS ring oscillator,"Solid-State Circuits Conference, 1998. ESSCIRC '98. Proceedings of the 24th European, 1998

24. Hajimiri, A.; Limotyrakis, S.; Lee, T.H. 1999

"Jitter and phase noise in ring oscillators,"Solid-State Circuits, IEEE Journal of, 1999

25. Abidi, A.A. 2006

"Phase Noise and Jitter in CMOS Ring Oscillators,"Solid-State Circuits, IEEE Journal of, 2006

7B. The Heavenly 75

Theoretical Analyses

26. Weigandt, T.C.; Beomsup Kim; Gray, P.R. 1994

"Analysis of timing jitter in CMOS ring oscillators,"Circuits and Systems, 1994. ISCAS '94., 1994 IEEE International Symposium on, 1994

27. Craninckx, J.; Steyaert, M. 1995

"Low-noise voltage-controlled oscillators using enhanced LC-tanks,"Circuits and Systems II: Analog and Digital Signal Processing, IEEE Transactions on, 1995

28. McNeill, J.A. 1997

"Jitter in ring oscillators,"Solid-State Circuits, IEEE Journal of, 1997

29. Hajimiri, A.; Lee, T.H. 1999

"Design issues in CMOS differential LC oscillators,"Solid-State Circuits, IEEE Journal of, 1999

30. Huang, Q. 2000

"Phase noise to carrier ratio in LC oscillators,"Circuits and Systems I: Fundamental Theory and Applications, IEEE Transactions on, 2000

Early theory, noise folding.

1/f noise reduction in switched CMOS devices in ring oscillators.

Application of ISF theory to the analysis of phase noise in ring oscillators.

State-of-the-art, partially based on McNeill (see Heavenly 75 list for reference).

A theoretical analysis of jitter in a CMOS ring oscillator (source-coupled, resistor-loaded differentialdelay cells) is validated by Monte Carlo simulations.

Early effort to develop a formula predicting oscillator phase noise based on an effective resistanceand capacitance approximation illustrating trade-off between phase noise and power consumption.

Early theoretical description and calculation of timing jitter in ring oscillators with experimentalverification.

Application of ISF theory to the analysis of phase noise in the differential cross-coupled CMOS LCoscillator.

A theoretical analysis of the Colpitts oscillator.












31. Samori, C.; Lacaita, A.L.; Zanchi, A.; Levantino, S.; Cali, G. 2000

"Phase noise degradation at high oscillation amplitudes in LC-tuned VCO's,"Solid-State Circuits, IEEE Journal of, 2000

32. Demir, A. 2002

"Phase noise and timing jitter in oscillators with colored-noise sources,"Circuits and Systems I: Fundamental Theory and Applications, IEEE Transactions on, 2002

33. Levantino, S.; Samori, C.; Zanchi, A.; Lacaita, A.L. 2002

"AM-to-PM conversion in varactor-tuned oscillators,"Circuits and Systems II: Analog and Digital Signal Processing, IEEE Transactions on, 2002

34. Hegazi, E.; Abidi, A.A. 2003

"Varactor characteristics, oscillator tuning curves, and AM-FM conversion,"Solid-State Circuits, IEEE Journal of, 2003

35. Razavi, B. 2004

"A study of injection locking and pulling in oscillators,"Solid-State Circuits, IEEE Journal of, 2004

36. Navid, R.; Lee, T.H.; Dutton, R.W. 2005

"Minimum achievable phase noise of RC oscillators,"Solid-State Circuits, IEEE Journal of, 2005

37. Andreani, P.; Fard, A. 2006

"More on the 1/f Phase Noise Performance of CMOS Differential-Pair LC-Tank Oscillators,"Solid-State Circuits, IEEE Journal of, 2006

38. Bonfanti, A.; Levantino, S.; Samori, C.; Lacaita, A.L. 2006

"A varactor configuration minimizing the amplitude-to-phase noise conversion in VCOs,"Circuits and Systems I: Regular Papers, IEEE Transactions on, 2006

39. Mirzaei, A.; Abidi, A.A. 2010

"The Spectrum of a Noisy Free-Running Oscillator Explained by Random Frequency Pulling,"Circuits and Systems I: Regular Papers, IEEE Transactions on, 2010

40. Takinami, K.; Walsworth, R.; Osman, S.; Beccue, S. 2010

"Phase-Noise Analysis in Rotary Traveling-Wave Oscillators Using Simple Physical Model,"

Analysis of phase noise dependence on oscillation amplitude for LC VCOs, highlighting phase noisedue to the bias current source.

Theory and practical characterization of phase noise in oscillators due to colored (as opposed towhite) noise sources

AM-to-PM noise conversion due to varactors and nonlinear capacitances in LC VCOs.

Non-linear analysis relates the small-signal specification of the varactor capacitance to the VCOtuning curve.

Theoretical derivation of injection locking characteristics of oscillators and a graphical analysis offrequency pulling.

Time-domain phase noise analysis used to define a theoretical (lower) bound for relaxation and ringoscillator phase noise.

2

Rigorous phase noise analysis of double-switch-pair LC-tank oscillators.

Rigorous analysis of amplitude-to-phase noise conversion of the varactor in the LC tank

Rigorous theoretical analysis of phase noise from the frequency domain perspective.

















Microwave Theory and Techniques, IEEE Transactions on, 2010

LC VCO Design Techniques

41. Nguyen, N.M.; Meyer, R.G. 1992

"A 1.8 GHz monolithic LC voltage-controlled oscillator,"Solid-State Circuits Conference, 1992. Digest of Technical Papers. 39th ISSCC, 1992 IEEE International,1992

42. Craninckx, J.; Steyaert, M.S.J. 1997

"A 1.8-GHz low-phase-noise CMOS VCO using optimized hollow spiral inductors,"Solid-State Circuits, IEEE Journal of, 1997

43. Razavi, B. 1997

"A 1.8 GHz CMOS voltage-controlled oscillator,"Solid-State Circuits Conference, 1997. Digest of Technical Papers. 43rd ISSCC., 1997 IEEE International,1997

44. Margarit, M.A.; Joo Leong Tham; Meyer, R.G.; Deen, M.J. 1999

"A low-noise, low-power VCO with automatic amplitude control for wireless applications,"Solid-State Circuits, IEEE Journal of, 1999

45. Chan-Hong Park; Beomsup Kim 1998

"A low-noise 900 MHz VCO in 0.6 μm CMOS,"VLSI Circuits, 1998. Digest of Technical Papers. 1998 Symposium on, 1998

46. De Muer, B.; Borremans, M.; Steyaert, M.; Li Puma, G. 2000

"A 2-GHz low-phase-noise integrated LC-VCO set with flicker-noise upconversion minimization,"Solid-State Circuits, IEEE Journal of, 2000

47. Hui Wu; Hajimiri, A. 2001

"Silicon-based distributed voltage-controlled oscillators,"Solid-State Circuits, IEEE Journal of, 2001

48. Troedsson, N.; Sjoland, H. 2002

"An ultra low voltage 2.4GHz CMOS VCO,"Radio and Wireless Conference, 2002. RAWCON 2002. IEEE, 2002

49. Ismail, A.; Abidi, A.A. 2003

"CMOS differential LC oscillator with suppressed up-converted flicker noise,"Solid-State Circuits Conference, 2003. Digest of Technical Papers. ISSCC. 2003 IEEE International, 2003

Simplified phase noise analysis validated by simulation and measurement.

The first fully-integrated voltage-controlled oscillator (including resonator) on a silicon IC.

Integrated 18.Hz VCO in standard CMOS.

VCO with wide tuning range using series connected, stacked metal inductors in the LC-tank.

Demonstration of automatic amplitude control in a monolithic bipolar LC VCO.

Voltage-controlled CMOS ring oscillator using a dual delay path to realize both high frequency ofoscillation (750MHz-1.2GHz) and 50% tuning range.

LC VCO design with very low flicker noise upconversion.

Distributed amplifier in positive feedback realizes a distributed oscillator for high frequency (12GHz)signal generation.

Low supply voltage LC VCO substitutes an inductor for the tail current source.












50. Taeksang Song; Sangsoo Ko; Dae-Hyung Cho; Han-Su Oh; Chulho Chung; Euisik Yoon 2004

"A 5 GHz transformer-coupled shifting CMOS VCO using bias-level technique,"Radio Frequency Integrated Circuits (RFIC) Symposium, 2004. Digest of Papers. 2004 IEEE, 2004

51. Staszewski, R.B.; Fernando, C.; Balsara, P.T. 2005

"Event-driven Simulation and modeling of phase noise of an RF oscillator,"Circuits and Systems I: Regular Papers, IEEE Transactions on, 2005

52. Staszewski, R.B.; Chih-Ming Hung; Barton, N.; Meng-Chang Lee; Leipold, D. 2005

"A digitally controlled oscillator in a 90 nm digital CMOS process for mobile phones,"Solid-State Circuits, IEEE Journal of, 2005

53. Tasic, A.; Serdijn, W.A.; Long, J.R. 2005

"Design of multistandard adaptive voltage-controlled oscillators,"Microwave Theory and Techniques, IEEE Transactions on, 2005

54. Soltanian, B.; Kinget, P.R. 2006

"Tail Current-Shaping to Improve Phase Noise in LC Voltage-Controlled Oscillators,"Solid-State Circuits, IEEE Journal of, 2006

55. Huijung Kim; Seonghan Ryu; Yujin Chung; Jinsung Choi; Bumman Kim 2006

"A low phase-noise CMOS VCO with harmonic tuned LC tank,"Microwave Theory and Techniques, IEEE Transactions on, 2006

56. Soltanian, B.; Ainspan, H.; Woogeun Rhee; Friedman, D.; Kinget, P. 2006

"An Ultra Compact Differentially Tuned 6 GHz CMOS LC VCO with Dynamic Common-Mode Feedback,"Custom Integrated Circuits Conference, 2006. CICC '06. IEEE, 2006

57. Hauspie, D.; Eun-chul Park; Craninckx, J.; Come, B. 2006

"Wideband VCO with Simultaneous Switching of Frequency Band, Active Core and Varactor Size,"Solid-State Circuits Conference, 2006. ESSCIRC 2006. Proceedings of the 32nd European, 2006

58. Hsieh-Hung Hsieh; Liang-Hung Lu 2007

"A High-Performance CMOS Voltage-Controlled Oscillator for Ultra-Low-Voltage Operations,"Microwave Theory and Techniques, IEEE Transactions on, 2007

59. McCorquodale, M. S.; O'Day, J. D.; Pernia, S. M.; Carichner, G. A.; Kubba, S.; Brown, R. B. 2007

"A Monolithic and Self-Referenced RF LC Clock Generator Compliant With USB 2.0,"

Current tuning of a VCO via switchable resistors replacing the more common MOS current source.

Voltage-level shift and transformer coupling to reduce phase noise.

Event-driven VHDL simulator to model phase noise behavior of an RF oscillator for wirelessapplications.

First digitally-controlled oscillator (DCO) for cellular mobile communications.

Adjusting VCO bias to optimize performance of a single oscillator for multiple wireless standards.

Tailoring the shape of the tail (bias) current in a cross-coupled CMOS VCO to optimize phase noise.

Harmonic tuning to increase the steepness of the oscillation across the LC tank to reduce phasenoise.

Differentially-tuned, area-compact (0.24mm ) LC VCO with wide tuning range.2

Adapting size of the core transistors and the varactor to widen tuning range.

Capacitive feedback and forward-bias of the MOS body to reduced supply voltage and powerconsumption.
















60. Okada, Kenichi; Nomiyama, You; Murakami, Rui; Matsuzawa, Akira 2009

"A 0.114-mW dual-conduction class-C CMOS VCO with 0.2-V power supply,"VLSI Circuits, 2009 Symposium on, 2009

61. Shih-An Yu; Kinget, P.R. 2009

"Scaling LC Oscillators in Nanometer CMOS Technologies to a Smaller Area But With ConstantPerformance,"Circuits and Systems II: Express Briefs, IEEE Transactions on, 2009

62. Toso, S.D.; Bevilacqua, A.; Tiebout, M.; Da Dalt, N.; Gerosa, A.; Neviani, A. 2010

"A 0.06 mm 11 mW Local Oscillator for the GSM Standard in 65 nm CMOS,"Solid-State Circuits, IEEE Journal of, 2010

63. Razavi, B. 2010

"Cognitive Radio Design Challenges and Techniques,"Solid-State Circuits, IEEE Journal of, 2010

64. Fanori, L.; Liscidini, A.; Castello, R. 2010

"Capacitive Degeneration in LC-Tank Oscillator for DCO Fine-Frequency Tuning,"Solid-State Circuits, IEEE Journal of, 2010

65. Levantino, S.; Zanuso, M.; Samori, C.; Lacaita, A. 2010

"Suppression of flicker noise upconversion in a 65nm CMOS VCO in the 3.0-to-3.6GHz band,"Solid-State Circuits Conference Digest of Technical Papers (ISSCC), 2010 IEEE International, 2010

66. Andreani, P.; Kozmin, K.; Sandrup, P.; Nilsson, M.; Mattsson, T. 2011

"A TX VCO for WCDMA/EDGE in 90 nm RF CMOS,"Solid-State Circuits, IEEE Journal of, 2011

67. Jian Chen; Jonsson, F.; Carlsson, M.; Hedenas, C.; Li-Rong Zheng 2011

"A Low Power, Startup Ensured and Constant Amplitude Class-C VCO in 0.18 μm CMOS,"Microwave and Wireless Components Letters, IEEE, 2011

68. Tohidian, M.; Fotowat-Ahmadi, A.; Kamarei, M.; Ndagijimana, F. 2011

"High-swing class-C VCO,"ESSCIRC (ESSCIRC), 2011 Proceedings of the, 2011

A 1.536 GHz temperature-compensated LC reference oscillator

Class-C VCO implemented using dual cores operated a different bias points.

Operating oscillators at higher frequency to reduce chip area.

2

Oscillator/divider combination to reduce chip area of a VCO for cellular mobile applications.

Analysis and design of dual-mode oscillators.

Extremely fine frequency tuning of a DCO via degeneration of the core using switched capacitors.

Insertion of resistors in series with the drains of the core FETs to suppress flicker (1/f) noiseupconversion.

All currently operational WCDMA/EDGE TX bands synthesized by a single VCO working at double orquadruple of the desired frequency band.

Class-C VCO with automatic start-up circuit and digital amplitude control loop.

Transformer feedback decouples bias control of the core transistors in a class-C oscillator to maximizetank swing.

















Switched inductors and higher-order LC tanks

69. Herzel, F.; Erzgraber, H.; Ilkov, N. 2000

"A new approach to fully integrated CMOS LC-oscillators with a very large tuning range,"Custom Integrated Circuits Conference, 2000. CICC. Proceedings of the IEEE 2000, 2000

70. Zhenbiao Li; O, K.K. 2005

"A low-phase-noise and low-power multiband CMOS voltage-controlled oscillator,"Solid-State Circuits, IEEE Journal of, 2005

71. Seong-Mo Yim; O, K.K. 2006

"Switched resonators and their applications in a dual-band monolithic CMOS LC-tuned VCO,"Microwave Theory and Techniques, IEEE Transactions on, 2006

72. Goel, A.; Hashemi, H. 2007

"Frequency Switching in Dual-Resonance Oscillators,"Solid-State Circuits, IEEE Journal of, 2007

73. Da Dalt, N.; Thaller, E.; Gregorius, P.; Gazsi, L. 2005

"A compact triple-band low-jitter digital LC PLL with programmable coil in 130-nm CMOS,"Solid-State Circuits, IEEE Journal of, 2005

74. Tchamov, N.T.; Broussev, S.S.; Uzunov, I.S.; Rantala, K.K. 2007

"Dual-Band LC VCO Architecture With a Fourth-Order Resonator,"Circuits and Systems II: Express Briefs, IEEE Transactions on, 2007

75. Demirkan, M.; Bruss, S.P.; Spencer, R.R. 2008

"Design of Wide Tuning-Range CMOS VCOs Using Switched Coupled-Inductors,"Solid-State Circuits, IEEE Journal of, 2008

76. Borremans, J.; Bevilacqua, A.; Bronckers, S.; Dehan, M.; Kuijk, M.; Wambacq, P.; Craninckx, J. 2008

"A Compact Wideband Front-End Using a Single-Inductor Dual-Band VCO in 90 nm Digital CMOS,"Solid-State Circuits, IEEE Journal of, 2008

77. Kossel, M.; Morf, T.; Weiss, J.; Buchmann, P.; Menolfi, C.; Toifl, T.; Schmatz, M.L. 2009

"LC PLL With 1.2-Octave Locking Range Based on Mutual-Inductance Switching in 45-nm SOI CMOS,"Solid-State Circuits, IEEE Journal of, 2009

78. Safarian, Z.; Hashemi, H. 2009

"Wideband Multi-Mode CMOS VCO Design Using Coupled Inductors,"Circuits and Systems I: Regular Papers, IEEE Transactions on, 2009

Using MOS switches to widen VCO tuning range by switching tank inductors.

Inductor and capacitor switching using MOS switches to realize a VCO operating in multiple bands(2.4, 2.5, 4.7, and 5GHz).

MOS device used to switch the tank inductor to realize a multi-band VCO.

Selecting one of 2 stable modes in a fourth-order LC oscillator using MOS switched-capacitors.

MOS switched-inductor enables triple-band operation at 2.2, 3.4, and 4.6 GHz in 0.21mm area.2

Dual-band LC VCO realized using a fourth-order resonator fed by dual cores.

Mutually-coupled inductors are MOS switched to widen the tuning range of an LC VCO.

4-port inductor realizes oscillation in 2 widely separated bands (3.5GHz and 10GHz).

MOS-switched, mutually-coupled inductors extend the tuning range of an LC VCO.

Sixth-order resonator using 3 coupled inductors driven by separate cores activated by bias current
















79. Catli, B.; Hella, M.M. 2009

"A 1.94 to 2.55 GHz, 3.6 to 4.77 GHz Tunable CMOS VCO Based on Double-Tuned, Double-Driven CoupledResonators,"Solid-State Circuits, IEEE Journal of, 2009

80. Ghosh, D.; Taylor, S.S.; Yulin Tan; Gharpurey, R. 2010

"A 10 GHz low phase noise VCO employing current reuse and capacitive power combining,"Custom Integrated Circuits Conference (CICC), 2010 IEEE, 2010

81. Wei Deng; Okada, K.; Matsuzawa, A. 2011

"A 25MHz–6.44GHz LC-VCO using a 5-port inductor for multi-band frequency generation,"Radio Frequency Integrated Circuits Symposium (RFIC), 2011 IEEE, 2011

Inductors and Varactors

82. Caulton, M.; Knight, S.P.; Daly, D.A. 1968

"Hybrid Integrated Lumped-Element Microwave Amplifiers,"Solid-State Circuits, IEEE Journal of, 1968

83. Craninckx, J.; Steyaert, M.S.J. 1995

"A 1.8-GHz CMOS low-phase-noise voltage-controlled oscillator with prescaler,"Solid-State Circuits, IEEE Journal of, 1995

84. Long, J.R.; Copeland, M.A. 1997

"The modeling, characterization, and design of monolithic inductors for silicon RF IC's,"Solid-State Circuits, IEEE Journal of, 1997

85. Danesh, M.; Long, J.R.; Hadaway, R.A.; Harame, D.L. 1998

"A Q-factor enhancement technique for MMIC inductors,"Radio Frequency Integrated Circuits (RFIC) Symposium, 1998 IEEE, 1998

86. Hung, C.-M.; Ho, Y.-C.; Wu, I.-C.; O, K. 1998

"High-Q capacitors implemented in a CMOS process for low-power wireless applications,"Microwave Theory and Techniques, IEEE Transactions on, 1998

86-a. Castello, R.; Erratico, P.; Manzini, S.; Sveito, F. 1998

"A ±30% tuning range varactor compatible with future scaled technologies,"VLSI Circuits, 1998. Digest of Technical Papers. 1998 Symposium on, 1998

switching.

Multi-band VCO realized by switching current in a multi-winding tuned transformer resonator.

Power combining of multiple LC VCOs to reduce phase noise and current reuse to conserve powerconsumption.

Dual-mode LC VCO implemented using a 5-port inductor realizes 25MHz-to-6.44GHz of continuoustuning.

Early design guidelines for hollow spiral inductors fabricated on insulating substrates.

A VCO using bondwire inductors for the LC resonator instead of an on-chip coil to reduce powerconsumption.

Circuit simulation models and design guidelines for on-chip inductors.

The differentially-driven symmetric inductor.

CMOS accumulation mode varactors to control the frequency of a VCO. Reported in the same yearby: Castello 1998 and Soorapanth 1998

Reported in the same year as Hung, et al. 1998 (CMOS accumulation mode varactors).













86-b. Soorapanth, T.; Yue, C.P.; Shaeffer, D.K.; Lee, T.I.; Wong, S.S. 1998

"Analysis and optimization of accumulation-mode varactor for RF ICs,"VLSI Circuits, 1998. Digest of Technical Papers. 1998 Symposium on, 1998

87. Yue, C.P.; Wong, S.S. 1997

"On-chip Spiral Inductors With Patterned Ground Shields For Si-based RF IC's,"VLSI Circuits, 1997. Digest of Technical Papers., 1997 Symposium on, 1997

88. Andreani, P.; Mattisson, S. 2000

"On the use of MOS varactors in RF VCOs,"Solid-State Circuits, IEEE Journal of, 2000

89. Porret, A.-S.; Melly, T.; Enz, C.C.; Vittoz, E.A. 2000

"Design of high-Q varactors for low-power wireless applications using a standard CMOS process,"Solid-State Circuits, IEEE Journal of, 2000

90. Kleveland, B.; Diaz, C.H.; Vook, D.; Madden, L.; Lee, T.H.; Wong, S.S. 2001

"Exploiting CMOS reverse interconnect scaling in multigigahertz amplifier and oscillator design,"Solid-State Circuits, IEEE Journal of, 2001

91. Wood, J.; Edwards, T.C.; Lipa, S. 2001

"Rotary traveling-wave oscillator arrays: a new clock technology,"Solid-State Circuits, IEEE Journal of, 2001

92. Zolfaghari, A.; Chan, A.; Razavi, B. 2001

"Stacked inductors and transformers in CMOS technology,"Solid-State Circuits, IEEE Journal of, 2001

93. Rogers, J.E.; Long, J.R. 2002

"A 10-Gb/s CDR/DEMUX with LC delay line VCO in 0.18-μm CMOS,"Solid-State Circuits, IEEE Journal of, 2002

94. Sjoland, H. 2002

"Improved switched tuning of differential CMOS VCOs,"Circuits and Systems II: Analog and Digital Signal Processing, IEEE Transactions on, 2002

95. Mira, J.; Divel, T.; Ramet, S.; Begueret, J.-B.; Deval, Y. 2004

"Distributed MOS varactor biasing for VCO gain equalization in 0.13 μm CMOS technology,"Radio Frequency Integrated Circuits (RFIC) Symposium, 2004. Digest of Papers. 2004 IEEE, 2004

Reported in the same year as Hung, et al. 1998 (CMOS accumulation mode varactors).

Patterned ground shield for spiral inductors.

A benchmarking comparison of 1.8GHz CMOS VCOs using PN-junction, I-MOS and A-MOS varactorsfor tuning.

Design of low loss varactors driven differentially.

Demonstration of coplanar waveguide to implement inductors on-chip for very high frequency (>10GHz), wideband oscillators (and amplifiers).

Traveling-wave ring oscillator using an on-chip differential transmission line for high frequency(2.5GHz) generation.

Series connection of stacked coils to realize inductors and transformes using less chip area.

Delay line, (quadrature) LC VCO implemented using compact, differential spiral delay lines.

Differential MOS switches to improve the Q-factor in switched-capacitor tuning.













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8. Additional Information

96. Andress, W.F.; Ham, D. 2005

"Standing wave oscillators utilizing wave-adaptive tapered transmission lines,"Solid-State Circuits, IEEE Journal of, 2005

97. Cheung, T.S.D.; Long, J.R. 2006

"Shielded passive devices for silicon-based monolithic microwave and millimeter-wave integrated circuits,"Solid-State Circuits, IEEE Journal of, 2006

98. Itoh, N.; Hideaki; Masuoka; Fukase, S.-i.; Hirashiki, K.-i.; Nagata, M. 2007

"Twisted Inductor VCO for Supressing On-chip Interferences,"Microwave Conference, 2007. APMC 2007. Asia-Pacific, 2007

99. Toso, S.D.; Bevilacqua, A.; Gerosa, A.; Neviani, A. 2010

"A thorough analysis of the tank quality factor in LC oscillators with switched capacitor banks,"Circuits and Systems (ISCAS), Proceedings of 2010 IEEE International Symposium on, 2010

100. Sadhu, B.; Harjani, R. 2010

"Capacitor bank design for wide tuning range LC VCOs: 850MHz-7.1GHz (157%),"Circuits and Systems (ISCAS), Proceedings of 2010 IEEE International Symposium on, 2010

LTSpice IV is a free-to-download mixed-signal circuit simulator from Linear Technology Inc. Download a copyfrom the URL: http://www.linear.com/designtools/software. A User's Guide and other useful documentation isavailable on the same webpage.

NGSPICE is a mixed-level/mixed-signal circuit simulator which is the open-source successor of Spice3f5. Theofficial website is at: http://ngspice.sourceforge.net.

Linearization of the MOS varactor to realize a consistent VCO gain constant.

Tapered transmission lines optimize the Q-factor of a quarter-wave resonator.

Substrate shielding of differential passive components using floating shield metal and electricinduction.

Inductor layout designed to cancel the effect of external interference on signal current in an on-chipLC tank.

Analysis of the contribution of the switched capacitances in the off state on tank quality factor in LCVCOs.

Optimal sizing of switches in the capacitor array for an LC VCO with wide tuning range.

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