1792 ieee journal of solid-state circuits, vol. 41, no....

1792 IEEE JOURNAL OF SOLID-STATE CIRCUITS, VOL. 41, NO. 8, AUGUST 2006

Tail Current-Shaping to Improve Phase Noisein LC Voltage-Controlled Oscillators

Babak Soltanian, Student Member, IEEE, and Peter R. Kinget, Senior Member, IEEE

Abstract—This paper introduces a tail current-shaping tech-nique in LC-VCOs to increase the amplitude and to reduce thephase noise while keeping the power dissipation constant. The tailcurrent is made large when the oscillator output voltage reachesits maximum or minimum value and when the sensitivity of theoutput phase to injected noise is the smallest; the tail current ismade small during the zero crossings of the output voltage whenthe phase noise sensitivity is large. The phase noise contributionsof the active devices are decreased and the VCO has a largeroscillation amplitude and thus better DC to RF conversion com-pared to a standard VCO with equal power dissipation. A circuitdesign to implement tail current-shaping is presented that does notdissipate any extra power, does not use additional (noisy) activedevices and occupies a small area. The operation and performanceof the presented circuit is extensively analyzed and compared to anideal pulse biased technique. The presented analysis is confirmedby measurement results of two 2-GHz differential nMOS VCOsfabricated in 0.25- m BiCMOS process.

Index Terms—CMOS integrated circuits, LC oscillators, oscilla-tion amplitude, phase noise, radio frequency, tail current-shaping,voltage-controlled oscillators.

I. INTRODUCTION

HIGHLY integrated radio-frequency (RF) integrated trans-ceivers for wireless communications rely on fully inte-

grated oscillator for carrier generation. Transceivers in com-munication applications such as high-speed electrical wired orfiber optic communications require high-quality voltage-con-trolled oscillators (VCOs) to generate local clocks. Differentialcross-coupled LC oscillators have been extensively used thanksto their simplicity, differential operation and relaxed start-upcondition. The spectral purity of the oscillator’s output wave-form or the timing accuracy of its zero crossings depend on thephase noise generated in the oscillator. Extensive research hasbeen done to understand the origins of phase noise and to im-prove the phase noise performance of oscillator designs withoutincreasing their power dissipation.

Fig. 1 depicts an nMOS implementation of a cross-coupleddifferential LC VCO. The main contributors to the phase noiseof this VCO are the cross-coupled switching transistors M1and M2, the tail current source, and the thermal noise associ-ated with the loss in the LC resonator. The resonator’s thermal

Manuscript received December 6, 2005; revised March 14, 2006. Thiswork was supported in part under SRC Sponsored Research Contract No.2004-HJ-1191. Measurement equipment support was provided by NSF MRIGrant ECS-03-20666.

The authors are with the Department of Electrical Engineering, ColumbiaUniversity, New York, NY 10027 USA (e-mail: [email protected];[email protected])

Digital Object Identifier 10.1109/JSSC.2006.877273

Fig. 1. Circuit schematic of a cross-coupled differential nMOS LC-VCO.

noise contribution can be reduced by using inductors, capaci-tors and varactors which have a high quality factor, . How-ever, the maximum achievable for passive components ismainly determined by technology limitations and can only beslightly improved by design or layout techniques. Different fil-tering techniques have been proposed to reduce the contributionof the tail current source to the phase noise [3], [4]. Most oftail current filter techniques are focused on filtering the noiseat the second harmonic and they often consume large areas.AM-to-FM noise conversion by the varactors [1], [5] can makethe oscillator very sensitive to circuit noise. This conversion canbe lowered by reducing the VCO’s tuning gain through the useof discrete tuning, e.g., with a switched capacitor array in theLC resonator [2]. Depending on the oscillator’s state, currentor voltage noise present in the components is converted moreefficiently into phase or into amplitude noise [6], [7]. The sen-sitivity of the VCO’s output phase to current or voltage noiseimpulses is often referred to as the impulse sensitivity function(ISF) [6] and is a periodic function of the VCO’s state or phase.The ISF is typically large when the output voltage is close to thezero-crossing instants and it is typically small when the outputvoltage is close to its maximum or minimum value. To sustainthe oscillations, active devices have to be used to compensatefor the losses in practical resonators, but there is always noiseassociated with the energy injection into the resonator. The as-sociated phase noise in VCOs can be reduced if the energy isinjected at the right moments, i.e., when the ISF is minimum.

In Section II, we first analyze an LC-VCO biased with an idealperiodic pulsed current source which positions the energy in-jection into the resonator at the most favorable time. We derive

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SOLTANIAN AND KINGET: TAIL CURRENT-SHAPING TO IMPROVE PHASE NOISE IN LC VCOs 1793

the associated oscillation amplitude and phase noise improve-ments compared to a standard VCO biased with a constant cur-rent source and with the same power dissipation. Section III thenintroduces a compact implementation of a tail current-shapingtechnique to bias the VCO with a periodic pulse current wave-form. We analyze the performance of tail current-shaping tech-nique and present experimental results in Section IV. Discussionand conclusions are presented in Sections V and VI.

II. PERIODIC PULSE BIASING FOR LC-VCOS

In this section we study the benefits of pulse biasing in differ-ential cross-coupled LC-VCOs using an ideal pulsed tail currentsource. This allows the calculation of the limits on amplitudeand phase noise improvement under ideal pulse biased opera-tion compared to standard constant bias operation.

The LC resonator in each branch of the differential nMOSLC-VCO in Fig. 1 is composed of an inductor with inductance

and a variable capacitor with capacitance . Loss in the LCresonator is represented by an equivalent parallel resistor . Inthe steady-state, the VCO’s output voltages can be well approx-imated by andwhere and are the single-ended amplitude and the supplyvoltage, and is the oscillator’s phase given by . Theoscillation frequency, , is given by whereis the total single-ended resonator capacitance including andthe capacitive parasitics of L and the active devices. Assuming asufficiently large output swing, the cross-coupled devices (M1and M2) steer the tail current alternatively to one of the differ-ential output nodes.

A. Oscillation Amplitude

Constant Tail Current: The voltage and current waveformsin a VCO biased with a constant tail current source of arepresented in Fig. 2(a), assuming the crossed-coupled devicesM1 and M2 act like ideal switches. The drain currents of M1and M2 are

(1)

(2)

where is a single pulse centered at the origin with unityamplitude and duration of 1:

otherwise.(3)

The DC component, , and the magnitude of the first harmonicat , , of the square currents waveforms in each branch are

and . Given that the resonatorimpedance is low except around , the single-ended oscillationamplitude can be calculated as the product of and [12]:

(4)

Fig. 2. Voltage and current waveforms for the VCO in Fig. 1. (a) Biased witha constant current source. (b) Biased with a periodic pulse current source withperiod T =2.

Pulsed Tail Current: We now assume that the tail current,, in the oscillator of Fig. 1 is a periodic signal with period, where is the period of the output signal, with

amplitude and with pulse duration or conduction angle(in radians) as shown in Fig. 2(b); the pulses are aligned withthe maxima of and which are the least phase sensitiveinstants,1 can be expressed as

(5)

1Although the exact location of the least phase sensitive instants can slightlydeviate from the peaks of the voltage waveform [7], we are making this simpli-fying assumption in our analysis.



and the drain current of M1, , is derived by substitutingfor in (2):

(6)

(7)

The Fourier expansion of can be found using the Fourierexpansion for a pulse train given Appendix I:

(8)

The DC component, , and the magnitude of the first har-monic, , of the drain current now are and

. To keep the power dissipation in thepulse biased VCO equal to the VCO with the constant biascurrent, we assume and thus .The the oscillation amplitude is then

(9)

where .For very narrow tail current pulses, i.e., in the limit when

, the oscillation amplitude becomes whichis times (57%) larger than the oscillation amplitude in thesame VCO with a constant bias current of .

B. Phase Noise Analysis

We now study the phase noise in a standard and a pulsed biasVCO. We first focus on the effect of thermal noise with a whitepower spectral density in the components which leads to phasenoise with a dependency as a function of the frequencyoffset, , from the carrier at . We do a single-ended phasenoise analysis which keeps the equations simpler but the phasenoise in the single-ended and differential signals are identical.The VCO’s phase noise in dBc/Hz at the offset frequencycan be calculated using (10) [6], shown at the bottom of the page,taking into account the three main sources of phase noise, i.e.,loss in the resonator, switching devices, and tail current source.

is the power spectral density of the thermal currentnoise from the resonator’s equivalent parallel resistance and

is the RMS value of its effective ISF; the currentthermal noise power of M1 and the tail source are representedby and ; andare the RMS values of their effective ISF.

Constant Tail Current ( ; ): We nowderive the appropriate expressions for the RMS values of theISFs for the different noise sources and for their power spectraldensities for substitution into (10). The thermal noise from theresonator’s loss is [8]; isa good approximation for the ISF associated with the [10]and it is easy to calculate that .

The thermal noise power spectral density of M1 iswhen M1 is conducting current

(and in saturation2), and it is close to zero when the transistoris OFF and highly resistive [9]; is the transconductanceof M1 and is a coefficient determined by the used technologyand device size and type. We define asthe transconductance of M1 when operating in saturation witha drain-source current of and is the current gain,defined as where is the mobilityof electrons, is the oxide capacitance, and (W/L) is theaspect ratio [9]. To guarantee oscillation startup, the loop-gaindefined as

(11)

must be larger than one for all process corners. The power spec-tral density of the thermal current noise of M1 can now be ex-pressed as

(12)

The effective ISF of M1 is defined aswhere is the noise modulation wave-

form [6]; for a constant tail bias is a (0,1) square wavewith frequency of as can be concluded from the waveformsin Fig. 2. Given [11], the RMS value of theeffective ISF becomes

(13)

(14)

We assume that the constant tail current is generatedby a MOS device biased in saturation with a drain-sourcecurrent of , so that ;

2We assume the switching devices are in saturation when conducting cur-rent; this assumption is valid as long as the VCO operates in its current-limitedregime, and as long as the output voltage swings are not too large. The devicesin the tail current-shaped VCO we present in Section III, operate under theseconditions since they are required to achieve tail current-shaping.

(10)



is transconductance of the tail MOSdevice. We define as the ratio of the size of the tail deviceand the size of M1 and . The tailcurrent thermal noise power spectral density is then

(15)

When the cross-coupled devices switch quickly, the ISF of thetail node is approximately [10]

forfor

(16)

and the for a constant tail current source ofis calculated as

(17)

We can now substitute the expression for the amplitude (4)and the noise power spectral densities and RMS values of theirrespective ISFs into (10), and obtain the phase noise:

(18)

Pulsed Tail Current Source: We now calculate the phasenoise for a VCO biased with a pulsed tail current source withduration of in radians; as before, the peak value, , is set at

(19)

to keep the average tail current in the pulse biased VCO equalto as in the standard VCO.

The phase noise contribution due to the resonator loss is notaffected by the pulse biasing. However, the noise modulationfunction for the switching devices, , now becomes

as can be shown by evaluating thermalnoise power spectral density of M1 when the device is con-ducting:

(20)

(21)

(22)

Using , as before, the RMS value of the effectiveISF is now (14):

(23)

(24)

We assume that the tail current source is implemented usingan nMOS device (M3) with the appropriate gate-source voltagewaveform to obtain the pulsed bias. Its peak current, , is in-creased by scaling the device aspect ratio while keeping theoverdrive voltage the same when the pulses are made narrower.Under these assumptions, (19) leads to andnow becomes

(25)

When the tail nMOS conducts, its transconductance equalsand thus

(26)

Using (16), the is calculated as

(27)Substituting (9), (11), (22), (24), (26) and (27) in (10), the

phase noise for the pulse biased VCO is

(28)

where and are functions of the conduction angle:

(29)

(30)

Comparison: We expect to obtain an improvement in phasenoise for the pulse biased VCO by making the current pulsesnarrower, i.e., by reducing the conduction angle, . Fig. 3(a)shows the total thermal phase noise reduction for a pulsed biasVCO compared to a constant bias VCO as a function of con-duction angle; the reduction is calculated using (18) and (28)assuming , , and . Lower phase noise isindeed achieved for narrower pulse widths. Three mechanismscontribute to this phase noise reduction: the larger oscillation



Fig. 3. Comparison of the phase noise analysis results for a VCO biased witha periodic rectangular pulse current source to a reference VCO biased with aconstant current source. The results are plotted for different current pulse widthsin radians (conduction angels, 2�). (a) shows total phase noise reduction w.r.t�. (b) shows phase noise reduction breakdown into the contributions from theactive devices throughF (�)+E(�) and the oscillation amplitude; it is assumed = 2=3, � = 2, and � = 3:2.

amplitude [see (9)], smaller cross-coupled device noise up-con-version (smaller ), and less tail current noise upconversion(smaller ). The breakdown of these contributions is plottedin Fig. 3(b). The phase noise improvement at the limit when

, is about 9.1 dB [Fig. 3(a)] where 3.9 dB is from largeroscillation amplitude and 5.2 dB is from eliminating phase noisecontributions of the cross-coupled and the tail current sourcenMOS devices.

Flicker Noise: So far we have investigated the phasenoise due to thermal noise in the circuit elements. Herewe show pulse biasing also reduces the DC component ofthe effective ISF for both M1 and M3 which translates toless conversion of flicker noise in the circuit componentsto phase noise with a dependence in the oscil-lator [6]. If we decompose each ISF into AC and DC parts,

, the corresponding effective ISFiswhere is the noise modulation function. The forM1 and M3 are usually odd functions of and their productwith the noise modulation function of doesn’tcreate any significant DC component; the DC componentof becomes smaller for narrower pulses(smaller ) and as a result the has a smaller DCcomponent and smaller flicker noise upconversion in the pulsedbias VCO. In the limit when the phase noise in the

region can be made very small whereas thephase noise cannot be reduced below the contribution fromthe loss in the resonator. We thus expect a more significantreduction of the phase noise in the region comparedto the region and as a result the phase noise corner

frequency is expected to move to lower frequencies by makingsmaller.

III. TAIL CURRENT-SHAPING

The implementation of the periodic pulse current sourceusing active devices requires extra power and can introduceadditional noise. The creation of narrow current pulses and theirsynchronization with the VCO’s output is challenging sincethe associated circuits need to operate at the second and higherorder harmonics of the output frequency. However, as tech-nology scaling continues an active approach may become morefeasible in the future. We now introduce a tail current-shapingcircuit technique with an inherent synchronization mechanismrequiring only one passive element.

Fig. 4 shows the schematic of the VCO with the tail cur-rent-shaping technique; we will refer to it as VCO2. The ca-pacitor parallel to the tail current source M3 is carefullydesigned to shape the effective tail current . An identicaloscillator, VCO1, but without is used as our reference os-cillator to evaluate the effectiveness of tail current-shaping. Thecircuit is biased and the devices are sized such that the VCOoperates in the current limited regime such that M1 and M2 donot enter the deep triode region. The voltage at the tail node

is then approximately a sinusoid with frequency :, where is its amplitude and is its phase

delay compared to the output voltage.3 This frequency doublingis the characteristic of a nonlinear circuit and linear analysisis not generally applicable here, but we show that resorting tothe linear circuit analysis during half a cycle provides useful in-sight and design guidelines that are presented in Section III-C.In each half cycle, e.g., when M1 is on and M2 is off, the cir-cuit is similar to a source follower [8] with its simplified smallsignal equivalent circuit shown in Fig. 5. Assuming that theoutput resistance of the tail current source is much larger thanthe impedance of at , is calculated using phasor anal-ysis from

(31)

with the gate-source capacitance and the transconduc-tance of M1 or M2. and are phasors of the commonsource node and single-ended output voltages. From (31) theamplitude and phase delay are obtained:

(32)

(33)

Given this , the current through , , is now. The tail current injected into VCO2,

, is where is the DC current through M3.Through appropriate circuit sizing we can set the amplitude of

3If the VCO operates in the voltage-limited regime, the voltage at the tail node(V ) is not a second harmonic sinusoid and contains strong higher harmonicsas well.



Fig. 4. Schematic of the fabricated VCO2 core and auxiliary measurement circuits including differential bipolar peak detector and output buffer.

Fig. 5. Simplified small signal equivalent circuit for M1, M2 and M3 fromFig. 4 when M1 is in saturation and M2 is off.

equal to the DC current so that , and weobtain

(34)

Fig. 6 shows the simulated voltage and current waveforms inthe VCO2. is a sinusoidal waveform with a peak-to-peakamplitude of . If we size the devices so that is set toapproximately , the tail current peaks align with the peaksof the output voltage:

(35)

A. Oscillation Amplitude

The single-ended oscillation amplitude, , for VCO2 isagain calculated by multiplying and the Fourier seriescoefficient for the first harmonic, , of the current going intothe resonator. Assuming M1 and M2 act as ideal switches, andusing the tail current waveform in (35), ,and

(36)

Based on (4) and (36), VCO2 is expected to have a 33% largeramplitude than VCO1 for the same DC bias current. The actualimprovement in the oscillation amplitude is somewhat lower be-cause the cross-coupled transistors are not ideal switches. Fig. 7shows the simulated waveforms in VCO1 and VCO2. Table I

Fig. 6. Simulated voltage and current waveforms of VCO2 with the tail current-shaping technique.

summarizes the simulation results for different process corners;the measured amplitude improvement in VCO2 compared toVCO1 is about 20%.

B. Phase Noise Analysis

To calculate the phase noise using (10), we assume that thecross-coupled transistors switch fast and steer to differentbranches in each half cycle. The drain current of M1 is obtainedfrom when M1 is on

, and when M1 is off ( and). The VCOs are designed to operate in the current-limited

regime. To keep M1 and M2 in saturation when they are ONtheir maximum , which is equal to the differential oscillation



Fig. 7. Simulated output voltage and drain current waveforms in (a) VCO1 (notail current-shaping) and (b) VCO2 (with tail current-shaping) for the nominalC = 8 pF and �25% tolerance.

amplitude, needs to be kept below the threshold voltage. In theused technology the threshold voltage of the nMOS transistors isabout 0.7 V. The simulated single-ended output voltages (

TABLE IOSCILLATION AMPLITUDE INCREASE IN VCO2 COMPARED TO VCO1

and ) in VCO1 and VCO2 are shown in Fig. 7 and theiramplitude is indeed less than 0.7 V. When the transistor M1 ison and steers tail current into the resonator, the noise currentpower density of M1 is then

(37)

(38)

(39)

(40)

Again after [11] we assume the ISF of M1 isand from (40) the noise modulation function is

, so the RMS value of the effective ISF isobtained from

(41)

(42)

(43)

(44)

Comparing (44) with (14) shows that the mean-square valueof the effective ISF of M1 in VCO2 is about 15% smaller thanfor VCO1 which translates to smaller phase noise contributionfrom the cross-coupled devices in the tail-current-shaping VCO.The simulated4 ISFs and their effective waveforms for VCO1and VCO2 are presented in Fig. 8; the simulated mean-squarevalue of the effective ISF for M1 is about 5% smaller in VCO2than in VCO1. The difference with the calculated values is at-tributed to the fact that the cross-coupled devices do not actas ideal switches. Additionally, the drain current reported bythe simulator includes drain-source channel currents as well the

4ISF is simulated by injecting a very narrow current pulse at the desired nodefor different VCO states. This technique is described in [6].



Fig. 8. Simulated V , I , � , and � for VCO1 and VCO2 at carrierfrequency of 1.75 GHz.

capacitive charging and discharging currents for the parasiticssuch as , , , and etc.; only the channel current needsto be taken into account in the noise estimation because only thedrain-source current generates device noise. With the availablemodels these currents could not be separated.

By placing parallel to the tail current source transistor M3,the high frequency noise of M3 is filtered so that the phase noisecontribution of M3 is reduced [3], [4]. This phase noise reduc-tion can be captured in a parameter defined as the ratio ofthe effective tail current ISF in VCO2 compared to VCO1:

(45)

The simulated tail ISFs for the VCO1 and VCO2 are presentedin Fig. 9 and is obtained at GHz.We now have all necessary terms to calculate the phase noisein the region for VCO2 by substitutingfrom (44), from (40), and the oscillation amplitude

from (36) into (10):

(46)

whereas the phase noise for VCO1 is obtained from (18). Using, , , and to compare the

phase noise of VCO1 and VCO2 given by (18) and (46), we find

Fig. 9. Simulated ISF of the tail node for VCO1 and VCO2 at carrier frequencyof 1.75 GHz.

Fig. 10. Simulated phase noise of the VCOs with SpectreRF at carrier fre-quency of 1.75 GHz; VCO2 has tail current-shaping and VCO1 is a referenceVCO with a constant tail current source.

a 5.6 dB phase noise improvement in the tail current-shapingVCO for the region. This improvement is composed of2.5 dB due to the larger oscillation amplitude and about 3.1 dBfrom a reduced phase noise contribution of the active devices.Phase noise simulations using SpectreRF presented in Fig. 10show about 3 dB improvement in the phase noise of VCO2 at anoffset frequency of 600 kHz from a 1.75-GHz carrier by imple-menting tail-current-shaping technique. The discrepancy withthe calculated value can probably be attributed to the non-idealswitching in the cross-coupled devices.

This analysis proves that tail current-shaping techniqueimproves the phase noise through three different mechanisms.First, the increased oscillation amplitude reduces thephase noise. Second, the narrower drain current pulses reducethe RMS value of the effective ISF of M1, . Acomparison of the simulated drain current waveforms ( and

) in VCO1 [Fig. 7(a)] and in VCO2 [Fig. 7(b)] shows thatthe drain currents in VCO2 are narrower pulses and inject more



current when the output is close to its peak. Third, the capacitoris a noise filter for the tail current source and reduces its

contribution in the phase noise similar to [3].Flicker noise: can be associated with the fact that

the parallel capacitor attenuates the higher frequency compo-nents of the noise of the tail current source M3 [4]. Simulationsfurther show a reduction in the phase noise contribution of M3in the region. The harmonic analysis of the simulatedISFs in Fig. 9 reveals that the DC component of isabout 12% less than the DC component of the . As aresult M3’s flicker noise upconversion is smaller in VCO2 com-pared to VCO1. This effect is not observed for a tail capacitorthat acts only as a high frequency noise filter.

The analysis and simulation of flicker noise upconversion ofM1 and M2 are very complex because the cross-coupled devicesoperate in different regions of operation. Additionally, the effectof switching on the flicker noise power spectral density [13] isnot captured by the simulator.

The contribution of the resonator loss in the thermal phasenoise is not reduced and this noise contribution sets the lowerlimit in the region. We expect the phase noisecorner to move towards lower frequencies when the reductionin the flicker phase noise is larger than the total reduction inthe thermal noise. Analysis in Section II showed thatnoise corner frequency becomes smaller for a VCO biased witha periodic narrow pulse current source. Circuit simulation inFig. 10 shows that for the VCO with tail current-shaping the

phase noise corner located at a lower frequency (about80 kHz) compared to the standard VCO (about 140 kHz).

C. Circuit Design

The presented guidelines along with other VCO design con-siderations such as startup loop gain, tuning range, power dis-sipation, signal level and phase noise were used to optimize thecomponent sizing. The circuit design starts with calculating the

, from the loss in the resonator and the required loopgain. The bias current, , is selected to keep the differen-tial oscillation amplitude close to the device threshold voltagesto make sure M1 and M2 stay in saturation. Next, the aspectratio of the active devices is derived from and .Then the parallel tail capacitor, , is selected such that thephase delay, , in (33) becomes close to which implies

. A good approximation to start withis . From here the circuit design becomesan iterative process to optimize the circuit for different processcorners and operating frequencies.

We extensively used transient and phase noise simulationsto verify circuit operation over different process corners andtemperatures and to verify robustness of the design. For example,after sizing, we simulated the VCO’s performance for differentvalues of . Fig. 7(b) shows the results for the nominalvalue of pF and 25% variations. The resultingvariation in the output voltage amplitude is small and theshape of drain currents does not change considerably. Thesimulated phase noise variations are within a 1.2 dB range.This demonstrates that tail current-shaping is robust in thepresence of process variations.

Fig. 11. Die photograph of the reference oscillator (VCO1) and the oscillatorwith tail current-shaping technique (VCO2).

Fig. 12. Measured phase noise of the VCOs; VCO2 has tail current-shapingand VCO1 is a reference VCO without tail current-shaping.

IV. EXPERIMENTAL RESULTS

Fig. 11 shows the microphotograph of the two differentialnMOS VCOs fabricated in a 0.25- m BiCMOS process. Theelectromagnetic simulator EMX was used to design a differen-tial octagonal inductor with differential inductance of nHand a of about 12 at 2 GHz. Inversion-mode MOS varactorsare used to tune the VCO from 1.755 GHz to 2.123 GHz by ad-justing from 0 to 1.5 V. The VCOs both operate from a1.5-V supply voltage and both draw 1.5 mA bias current. A RFbipolar peak detector [14] and a MOS open drain output bufferare also included on chip to facilitate the measurements (Fig. 4).The peak detector enables accurate on chip oscillator amplitudemeasurements independent of the output buffer attenuation.5

Four sets of circuits were measured on a Cascade RF probe-sta-tion with an Agilent Technologies E4446A spectrum analyzerequipped with phase noise measurement software. The mea-sured data was very consistent and the results of a typical set arepresented here. Fig. 12 shows overlaid phase noise plot versusthe offset frequency from a 1.755-GHz carrier for both VCOs.VCO2, with the tail current-shaping technique, demonstrates5 dB and 4.4 dB improvements in the phase noise at 100 kHzand 600 kHz offset frequencies, respectively, compared to thereference VCO1. The VCOs dissipate 2.25 mW, and VCO2 hasa measured phase noise at 600 kHz offset from 1.755-GHz and

5To accurately measure the oscillation amplitude, the differential bipolar peakdetector is first calibrated [14] by applying V to its inputs via the differentialinductor of the VCO while the bias current of the VCO is turned off to preventthe circuit from oscillating.



2.123-GHz carriers of 120 dBc/Hz and 117.5 dBc/Hz, re-spectively. As we expected from analysis and simulations, theoscillation amplitude is larger for the tail current-shaping VCO(Table I) because of the narrower current pulses going into theresonator in each cycle.

V. DISCUSSION

The analysis in Section II-B shows the phase noise improve-ment trend in a VCO biased with a periodic pulse current sourcecomparing to a standard VCO reaches 9.1 dB in the limit (for

, , and ), where the tail current waveformisan impulse train .This idealcaseshowsthe trendof im-proving thermalphase noise in adifferential VCO with pulsed tailbiasing. Despite challenges in implementation of a narrow pulsegeneration circuit with active devices, the presented technique inSection III shows promising results. The analysis promised 5.6dB thermal phase noise improvement over a standard VCO and4.4dBimprovementat600kHzoffset frequencyfroma1.75-GHzcarrier was recorded in the measurements.

To compare the performance of the introduced pulse biasedVCO to the state of the art, we use the following figure of merit(FoM)6 [12]:

(47)

where is the phase noise at the offset from the car-rier, and is the VCO’s core power dissipation in mW. TheFoM for VCO2 is 185.8 at 1.755 GHz and 185 at 2.123 GHz.In [3], a 2.1-GHz differential LC-VCO with noise filter con-sumes 4 mA from a 2.7-V supply, uses a differential inductorwith , and has a measured phase noise of 134 dBc/Hzat 3 MHz offset resulting in a FoM of 180.6. The noise-shiftingdifferential Colpitts 1.8-GHz VCO in [15] has a phase noise of

139 dBc/Hz at 3 MHz offset for a 10 mW power dissipation,and has an inductor with ; its FoM is 184.6. The 1.9-GHzLC CMOS VCO using a bondwire inductor with (min-imum of the resonator is about 14) in [16] dissipates 2 mW,and has a measured phase noise of 120.5 dBc/Hz at 600 kHzoffset frequency resulting in a FoM of 187.5. The FoM is 185.7for a 2.5-GHz CMOS VCO using helical inductors [17]. Theperformance of the reported VCO2 with tail current-shapingcompares favorably with these high-performance designs whichdemonstrates the effectiveness of the proposed solution.

VI. CONCLUSIONS

Tail current-shaping technique is presented to improve thephase noise in LC-VCOs. Narrow current pulses deliver energyto the resonator at the less phase sensitive instances and the ac-tive devices are turned off at the most sensitive instances, i.e.,zero-crossings. It is shown that larger phase noise improvementsare obtained by making the current pulses narrower but main-taining the same average value. In the limit, the phase noise con-

6Ideally the FoM should account for the difference in resonator Q betweendifferent oscillator designs which strongly affects the oscillator performance.However, a widely accepted FoM incorporating the effect of Q is not availableso we are using the standard FoM definition.

tributions of the active devices vanish when the VCO is drivenby an impulse train.

A circuit implementation of the tail current-shaping tech-nique incorporating a parallel tail capacitor is proposed. Thesizes of the cross-coupled MOS devices and the size of aparallel tail capacitance are optimized to generate a periodictail current waveform that is better adapted to the periodicnature of the ISF. It is shown that the parallel tail capacitoroperates in large signal mode and its role is more than a simplenoise filter because there is larger DC-to-RF conversion, lowerthermal phase noise contribution from the switching devices,and lower noise upconversion of the tail device, wherenone of these effects are observed for a noise filter capacitor.The phase noise analysis is presented and effectiveness of thissolution is verified by simulation and measurement results fora 2-GHz differential nMOS LC-VCO fabricated in 0.25- mBiCMOS technology. The measurement results are comparedwith a reference standard VCO; the tail current-shaping tech-nique improves the phase noise by more than 3 dB at the600 kHz offset frequency, for 1.75-GHz and 2.12-GHz outputcarriers. The VCO draws 1.5 mA from a 1.5-V supply. TheVCO’s FoM compares favorably with the state of the art. Thepresented technique does not require extra power dissipationand consumes only a small silicon area. The presented circuittechniques can be applied for other VCOs as well.

APPENDIX IFOURIER SERIES OF A PULSE TRAIN

If is a periodic pulse train with period and pulsewidthof W

(48)

then its Fourier series expansion is

(49)

where

(50)

(51)

(52)

ACKNOWLEDGMENT

The authors would like to thank Philips Semiconductors forchip fabrication, and S. Kapur and D. Long of Integrand Soft-ware for the use of the EMX simulation tool.



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Babak Soltanian received the B.Sc. and M.Sc. de-grees in electrical engineering from Sharif Universityof Technology, Tehran, Iran, in 1992 and 1995, re-spectively, and the Licentiate in Technology in com-munications engineering from Tampere University ofTechnology, Tampere, Finland, in 2004. He is cur-rently working toward the Ph.D. degree at ColumbiaUniversity, New York, NY.

During summer 2004, he was with IBM T. J.Watson Research Center and designed high-fre-quency CMOS integrated circuits for high-speed

serial link applications. He was a Research Staff Member at the Department ofMicrowave and Signal Processing, NEC Laboratories America, Princeton, NJ,from 2001 to 2002, where he designed analog circuits for a direct conversionWCDMA RFIC using SiGe BiCMOS technology. From 1999 to 2001, he was aResearcher at the Institute of Communications Engineering, Tampere, Finland,developing low-complexity baseband receivers for CDMA systems. His currentresearch includes analog and RF integrated circuits, communication systems,and signal processing.

Peter R. Kinget received the engineering degree(summa cum laude) in electrical and mechanicalengineering and the Ph.D. degree (summa cumlaude) in electrical engineering from the KatholiekeUniversiteit Leuven, Belgium, in 1990 and 1996,respectively.

From 1991 to 1995, he received a graduate fellow-ship from the Belgian National Fund for ScientificResearch (NFWO) to work as a Research Assistantat the ESAT-MICAS Laboratory of the KatholiekeUniversiteit Leuven. From 1996 to 1999, he was at

Bell Laboratories, Lucent Technologies, Murray Hill, NJ, as a Member of Tech-nical Staff in the Design Principles Department. From 1999 to 2002, he heldvarious technical and management positions in IC design and development atBroadcom, CeLight, and MultiLink. In the summer of 2002, he joined the fac-ulty of the Department of Electrical Engineering, Columbia University, NewYork, NY. His research interests are in analog and RF integrated circuits andsignal processing. He has published over 50 papers in journals and conferencesand holds three U.S. patents with several applications under review. His researchgroup has received funding from the National Science Foundation, the Semicon-ductor Research Corporation, an IBM Faculty Award and from several grantsfrom semiconductor companies.

Dr. Kinget has served on the Technical Program Committee of the IEEECustom Integrated Circuits Conference (CICC) and currently serves on theTechnical Program Committee of the IEEE Symposium on VLSI Circuits,the European Solid-State Circuits Conference, and the IEEE InternationalSolid-State Circuits Conference. He has been an Associate Editor for theJOURNAL OF SOLID-STATE CIRCUITS since 2003.


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