Design of Wide-Tuning-Range Millimeter-Wave CMOS VCO With a Standing-Wave Architecture

1942 IEEE JOURNAL OF SOLID-STATE CIRCUITS, VOL. 42, NO. 9, SEPTEMBER 2007

Design of Wide-Tuning-Range Millimeter-WaveCMOS VCO With a Standing-Wave Architecture

Jun-Chau Chien, Student Member, IEEE, and Liang-Hung Lu, Member, IEEE

Abstract—The design of a wide-tuning-range millimeter-waveCMOS VCO is presented in this paper. In contrast to the conven-tional wideband topologies, a nonuniform standing-wave oscillatorutilizing tapered gain elements, switched transmission lines anddistributed varactors is employed to provide an extended outputrange with the coarse and fine frequency tuning. Due to the useof the transmission line architecture and the position-dependentamplitude of the standing waves, the loading effects of the varac-tors and the MOS switches can be alleviated, enabling the VCOto operate at higher frequencies. Using a 0.18- m CMOS process,a 40-GHz VCO is designed and implemented. Consuming a DCpower of 27 mW from a 1.5-V supply voltage, the fabricated circuitexhibits a frequency tuning range of 7.5 GHz with an output powerlevel ranging from 13.6 to 4 dBm. The measured phase noiseat 1-MHz offset is lower than 96 dBc/Hz within the entire fre-quency range. This work demonstrates the widest tuning range inpercentage among the CMOS VCOs at millimeter-wave frequen-cies.

Index Terms—CMOS millimeter-wave circuits, standing-waveoscillators, switched transmission lines, wide-tuning-range VCOs.

I. INTRODUCTION

WITH recent advances in the semiconductor technologies,implementation of integrated circuits at millimeter-wave

frequencies for both wireless and high-speed communicationsystems becomes feasible by using standard CMOS processes.In such systems, the voltage-controlled oscillator (VCO) is aninevitable building block to provide the required local oscilla-tion and clock signals. Owing to the stringent requirements inthe circuit specifications such as the oscillation frequency, phasenoise, output power and frequency tuning range, tremendousefforts have been made to develop high-performance CMOSVCOs for various application standards. For high-frequencyVCO implementations, the cross-coupled LC-tank topologyis widely used because of its advantages in the phase noiseand power consumption. In the past few years, LC-tank VCOsoperating at frequencies in the tens of gigahertz have beensuccessfully demonstrated using deep-submicron bulk CMOStechnologies [1]–[6]. Due to the limitations on the deviceparasitics and the transistor capability in the millimeter-waveregime, the band-switching techniques [7], [8], which are

Manuscript received September 7, 2006; revised April 12, 2007. This workwas supported in part by the National Science Council under Grant 95-2221-E-002-437 and 95-2220-E-002-018.

The authors are with the Department of Electrical Engineering and GraduateInstitute of Electronics Engineering, National Taiwan University, Taipei 10617,Taiwan, R.O.C. (e-mail: [email protected]).

Digital Object Identifier 10.1109/JSSC.2007.903050

developed to enhance the tuning range and to reduce the tuningsensitivity of the VCOs, are no longer applicable especially foran oscillation frequency beyond 20 GHz. Therefore, most ofthe high-frequency LC-tank VCOs suffer from an inadequatefrequency tuning range, making the circuits vulnerable toprocess variation and unattractive for wideband applications.

Alternatively, wave-based circuit techniques have been com-prehensively studied for the realization of the high-frequencyoscillators. In contrast to the LC-tank VCOs, the operation ofthe wave-based oscillators depends on the behavior of the wavespropagating on the transmission lines. Such circuits can be gen-erally categorized into three distinct groups as the traveling-wave oscillators [9], [10], the rotary traveling-wave oscillators[11], [12], and the standing-wave oscillators (SWOs) [13]–[17],each having its own unique characteristics. Due to the use of dis-tributed architectures in the circuit implementations, the loadingeffect can be effectively alleviated. As a result, the wave-basedoscillators demonstrate great potential for wideband applica-tions at millimeter-wave frequencies. In this paper, the theo-retical analysis and the design considerations of a novel SWO[18] are presented for bandwidth enhancement. By employingtapered gain elements, the switched transmission lines, and thedistributed varactors, the tuning range of the proposed VCOis significantly increased while maintaining remarkable circuitperformance in terms of the output power, close-in phase noiseand power consumption. Using a 0.18- m CMOS process, aVCO prototype operating in the 40-GHz frequency band is im-plemented for demonstration.

This paper is organized as follows. Section II presents the op-eration principles and theoretical analysis of the proposed SWO.The design and the experimental results of the 40-GHz VCO cir-cuit are shown in Section III and IV, respectively. Finally, con-cluding remarks are provided in Section V.

II. THE PROPOSED STANDING-WAVE OSCILLATOR

A. Half-Wavelength Standing-Wave Oscillator

Fig. 1 shows the simplified illustration of a half-wavelengthSWO, where a signal source in the middle of the -resonatorgenerates the forward and reverse traveling wavespropagating toward both ends of the transmission line. Withan ideal electrical short, the incident waves are completely re-flected with an inverted phase, forming a standing wave whichhas a maximum voltage amplitude in the middle and a min-imum voltage swing at the shorted ends. Note that, similarly,full-wavelength [14] or quarter-wavelength standing waves [16]

0018-9200/$25.00 © 2007 IEEE

CHIEN AND LU: DESIGN OF WIDE-TUNING-RANGE MILLIMETER-WAVE CMOS VCO WITH A STANDING-WAVE ARCHITECTURE 1943

Fig. 1. Conceptual illustration of a half-wavelength SWO.

Fig. 2. (a) Typical circuit topology of a half-wavelength SWO. (b) Lumped equivalent circuit of the loaded transmission lines.

can also be formed depending on the boundary conditions. How-ever, this paper will focus primarily on the half-wavelength casefor the demonstration of the wide-tuning-range VCO.

The typical circuit topology of the half-wavelength SWO isillustrated in Fig. 2(a), where a pair of differential transmissionlines with both ends shorted together is utilized as the resonatorto sustain the standing waves. In the circuit implementations,the transmission lines can be realized by various on-chipstructures such as the microstrip lines, coplanar striplines andcoplanar waveguides. With the losses from the conductorsand the substrate, practical transmission lines fabricated inthe CMOS technologies exhibit significant signal attenuation,especially at higher frequencies. Consequently, cross-coupledinverters distributed along the transmission lines are employedto compensate for the losses. Compared with the traveling-waveoscillators where some portion of the energy is absorbed by thetermination resistors, the signal power in the SWOs is entirelyrecycled due to the complete reflection at the short-circuitedends [11], [16]. As a result, the required transconductance ofthe cross-coupled inverters in the SWOs is generally smallerthan that in the traveling-wave oscillators, leading to lowerpower consumption and higher voltage swing for the oscillatordesigns.

B. Oscillation Frequency and Start-Up Conditions

In order to derive the oscillation frequency and the start-upconditions, small-signal analysis is performed on the SWOwhere the loaded transmission lines are modeled by a lumpedequivalent circuit as illustrated in Fig. 2(b). Note that , ,

, and are the equivalent circuit parameters of the unloadedtransmission lines while and represent the equivalenttransconductance and capacitance per unit length contributedby the cross-coupled inverters. By taking into account, thecharacteristic impedance and the propagation constant ofthe loaded transmission lines are given by

(1)

(2)

By applying the low-loss approximation in [20], (1) and (2) canbe expressed as

(3)

(4)


According to the characteristics of the loaded transmission lines,the oscillation frequency of the half-wavelength SWO is givenby

(5)

where is the phase velocity of the traveling waves, is theequivalent wavelength, and is the physical length of the half-wavelength transmission lines.

In the SWO, the transconductance of the cross-coupled in-verters are utilized to compensate for the losses of the transmis-sion lines. To derive the start-up conditions for the oscillator, theattenuation constant in (4) is modified by introducing a negativeconductance :

(6)

Furthermore, the compensation factor is defined as

(7)

for the evaluation of the oscillation start-up. The line lossescan be fully compensated to initiate the oscillation as long as

is larger than unity. For practical circuit designs, is typ-ically chosen between 3 and 5 to tolerate the process varia-tion. Note that (7) allows the first-order estimation of the re-quired transconductance for the cross-coupled inverters in theSWO. Taking as an example, with mm and

, the required is 12.5 mS/mm. Equation (7) alsoprovides useful design insights for the circuit optimization. It isindicated that reduced power consumption can be achieved byminimizing the series resistance and by maximizing the loadedcharacteristic impedance of the transmission lines.

C. Output Swing and Phase Noise

Another advantage of the SWO is the enhanced voltage swingin the middle of the half-wavelength transmission lines, wherethe output nodes of the oscillator generally locate. Assumingthat the amplitudes of the incident and the reflected wavesare identical in a low-loss transmission media, the maximumvoltage swing of the standing waves is approximately twiceas large as that of the traveling waves. Following the similarderivations in [9], the single-ended oscillation amplitude of thehalf-wavelength SWO with identical cross-coupled invertersis given by

(8)

where is the tail current of the cross-coupled pairs and isthe attenuation constant given in (4).

Due to the inherently low characteristic impedance and highcut-off frequency of the loaded transmission lines, the wave-based oscillators typically demonstrate a steep transition on theoutput voltage waveform at the zero-crossing points [21], whichreduces the noise sensitivity and improves the phase noise per-formance. With the enhanced oscillation amplitude of the SWO,a lower close-in phase noise is expected [11], [16]. Based on thedevice models of a 0.18- m CMOS technology provided by the

Fig. 3. Simulated close-in phase noise of the 40-GHz wave-based oscillatorswith identical stage number and power consumption.

Fig. 4. Simplified circuit model of the SWO to illustrate the proposed fre-quency tuning mechanism.

foundry, the simulated phase noise of two 40-GHz wave-basedoscillators with identical stage number and power consumptionare shown in Fig. 3. It is noted that the SWO demonstrates aphase noise lower than that of the conventional traveling-waveoscillator, making it very attractive for VCO designs at mil-limeter-wave frequencies.

D. Frequency Tuning Mechanism

As indicated in (5), the oscillation frequency of the SWO isdetermined by the effective length and the equivalent capaci-tance of the loaded transmission line. Therefore, the frequencytuning can be achieved by varying the physical length of thetransmission lines with the MOS switches and by modulatingthe wave velocity of the transmission lines with the distributedvaractors. A conceptual illustration of the proposed frequencytuning mechanism is shown in Fig. 4, where the transmissionlines are periodically loaded with identical varactors andequally spaced switches are placed near both ends of the lines.Since the oscillation frequency is inversely proportional to theeffective length of the transmission lines, the total number of thedistinct frequency bands is given by

(9)

By taking the capacitance of the varactors and the cross-coupledinverters into account, the oscillation frequency of the SWOwith cross-coupled inverters and pairs of varactors is ex-pressed as

(10)


where is the shortest electrical length achievable with allswitches turned on, is the spacing between the switches, and

is the number of the additional transmission line sections con-trolled by the switches. Note that and are the capacitancesof the cross-coupled pairs and the varactors, respectively, whilethe parasitic capacitances of the MOS switches are neglected tosimplify the analysis.

Compared with the switched-capacitor topology [5] which iswidely used for the wide-tuning-range LC-tank VCOs, the pro-posed band-switching technique features the advantage in mini-mizing the loading effect of the MOS switches. Due to the natureof the position-dependent amplitude for the standing waves, theswitches, which are placed near both ends of the transmissionlines, experience a reduced voltage swing. Significant degrada-tion in the Q-factor of the resonator is thus prevented. In addi-tion, since the capacitance of the varactors are considered as thecircuit parameters of the artificial transmission lines, higher de-sign flexibility is provided in the proposed SWO architecture.

III. DESIGN OF THE 40-GHz WIDE-TUNING-RANGE VCO

The complete schematic of the 40-GHz wide-tuning-rangeVCO based on the proposed SWO topology is illustrated inFig. 5(a), where the differential half-wavelength transmissionlines are loaded with five equally spaced cross-coupled invertersto compensate the losses of the resonator. Four MOS switchesare placed near both ends of the resonator to provide frequencyswitching while three pairs of accumulation-mode MOS varac-tors are distributed along the transmission lines for frequencyfine tuning. In order to achieve the maximum output swing andto drive the external 50- impedance of the test instrument, thedifferential oscillation signals of the VCO are extracted fromthe middle of the half-wavelength resonator through a differen-tial output buffer loaded with transmission-line inductors andon-chip blocking capacitors, as shown in Fig. 5(b). Fig. 5(c)illustrates the six frequency bands by identifying the effectivelength of the transmission lines during the switching. The de-tailed design considerations of the 40-GHz VCO circuit are pre-sented as follows.

A. The Transmission Line Architectures

The circuit design starts with the transmission lines which arerealized by a microstrip line structure. For a standard 0.18- mCMOS process, the signal lines are implemented by the topmetal layer M6 while the bottom metal layer M1 is used as theground plane. Since the signal lines are shielded by the ground,field penetration though the lossy Si substrate is prevented, alle-viating the stringent limitations on the signal attenuation of thetransmission lines at millimeter-wave frequencies. The charac-teristics of the microstrip line are mainly determined by the linewidth for a given technology, which significantly simplifies thedesign and optimization of the VCO circuit. In Appendix A, thedesign procedure for the selection of the signal width is pre-sented. By taking the attenuation constant and the layout sizeinto consideration, a differential microstrip line with a width of5 m and a spacing of 15 m is employed for the circuit im-plementation. Based on the full-wave EM simulation, the char-acteristic impedance, attenuation constant, and quality factor

of the unloaded transmission line in the vicinity of40 GHz are 80.9 , 0.55 dB/mm, and 12.7, respectively.

In the proposed VCO, the bias current for the cross-coupledpairs is provided by a differential short-stub at the center ofthe resonator. Since the short-stub exhibits inductive equiva-lent impedance at the operating frequency, it is also used to tuneout part of the parasitic capacitance, reducing the loading effectin the middle of the resonator. Similar microstrip line structurewith a length of 220 m is employed to realize the short-stub.According to the circuit simulations, a nearly 35% increase inthe oscillation frequency is achieved in the VCO design due tothe use of the short stub. It is worth noting that the proposed bi-asing technique potentially results in multiple oscillation modes.This can be explained by considering the short-stub as anotherquarter-wavelength resonator which resonates with the capaci-tance from the central cross-coupled pair. Nevertheless, the os-cillation frequency of undesirable mode is extremely high inthis particular design such that the transconductance from thecross-coupled inverters is insufficient to compensate the energylosses for a sustained oscillation. Consequently, the output fre-quency is mainly determined by the half-wavelength resonatorin the SWO design.

B. The Cross-Coupled Inverters

Due to the position-dependent voltage amplitude of thestanding waves, the SWO suffers from unequal shunt lossesalong the half-wavelength resonator [16]. The position-depen-dent shunt losses can be simply defined as

(11)

where and are the position-dependent standing-waveamplitude and shunt conductance, respectively. For a given

, a larger voltage swing corresponds to higher energylosses. In order to improve the compensation efficiency, anonuniform architecture is introduced in the proposed SWOby designing the transconductance of the central cross-coupledstage larger than that of the stages near the boundaries [19].This concept is analogue to the technique presented in [16]where a loss-reducing tapered coplanar stripline is utilized toenhance the Q-factor of the quarter-wavelength resonator. Bytapering the transconductance of the cross-coupled invertersinstead of the transmission lines, the design procedure is thussimplified while a more compact chip layout can be realized.However, care should be taken to minimize the impedancemismatching of the loaded transmission lines, preventing localreflections such that the desirable standing-wave characteristicscan be maintained. In this design, a transconductance twiceas large as that of the other four stages is employed for thecentral cross-coupled pair. With a fixed oscillation frequencyand output amplitude, circuit simulation indicates that a currentsaving up to 30% is achieved in the nonuniform SWO com-pared with the one with a uniform architecture. A more detaileddesign consideration is given in Appendix B.

C. The MOS Switches

For switched-capacitor VCO designs within 10 GHz, thesize of the MOS switches is mainly determined based on the


Fig. 5. (a) Circuit schematic of the proposed wide-tuning-range VCO. (b) Circuit schematic of the differential output buffer. (c) Proposed band-switching mech-anism for the circuit implementation.

trade-off between the on-resistance and the parasitic capaci-tance. However, as the oscillation frequency increases, specialcares are required to ensure the operations of the switches.Fig. 6 illustrates simplified models of the MOS switches oper-ating in the “on” and “off” state. For the standing-wave VCOwith the switched transmission lines, it is desirable to minimizethe on-resistance of the switches by increasing the aspectratio of the MOS devices. However, if the device size is exces-sively large, the parasitic capacitances act as low-impedancesignal paths even the switches are in the “off” state such thatthe VCO fails to perform the band switching. Hence, a designtrade-off between the effective band switching and the Q-factor

of the resonator should be taken into account in the selectionof the MOS switches. In order to provide a useful designguideline, simulated equivalent impedances of the switches at40 GHz are plotted in Fig. 7 for various device sizes. Basedon the simulation results, a MOSFET with a channel widthlarger than 480 m generally fails to function as a switch at thedesirable frequency bands. Therefore, a gate width of 320 mis adopted for the MOS switches in the circuit design to providesufficient safe margin, resulting in an on-impedance of 2 andan off-impedance of 21 . In the circuit layout, each one of theswitches is separated into four identical cells surrounded bywide guard rings to minimize the substrate resistance [8].


Fig. 6. Equivalent circuit models of the MOS switches in (a) the “off” and(b) the “on” state.

Fig. 7. Simulated impedance of the MOS switches at 40 GHz.

D. Band Switching and Frequency Tuning

In the proposed circuit topology, the overall frequency tuningrange is determined by the ratio of the maximum to the min-imum length of the transmission lines, while the frequency finetuning depends on the design of the varactors. With a specifiedtuning range of the VCO circuit, the varactor sizes can be tradedfor the number of frequency bands. In order to achieve an opti-mized SWO design, the losses of the half-wavelength resonatorresulted from the series resistance is investigated and can be ex-pressed as

(12)

where and represent the position-dependent currentamplitude of the standing waves and the series resistance ofthe resonator, respectively. In contrast to the voltage ampli-tude, has a maximum swing at the boundaries of thehalf-wavelength resonator, imposing stringent limitations onthe equivalent impedance of the switches. As large varactorsare employed in the design, the frequency range of the indi-vidual bands increases accordingly, allowing less frequencybands and fewer MOS switches along the transmission lines.It is beneficial to the VCO performance in consideration ofthe series losses. However, the excessive capacitance from thevaractors results in heavy loading on the transmission lines. Inorder to achieve the desirable loaded characteristic impedance,a reduced line width has to be used for the microstrip structures,leading to a possible decrease in the unloaded Q-factor of theresonator due to the higher conductor losses. In this design,the frequency tuning scheme and the SWO architecture are

Fig. 8. Simulated output voltage swing as a function of the tail current for var-ious frequency bands.

selected to maximize the Q-factor of the resonator such thatenhanced VCO performance in terms of phase noise and powerconsumption can be achieved. Based on the design criteria,four switches are employed at the ends of the half-wavelengthresonator while the three distributed varactors are designed toprovide sufficient frequency overlapping between the adjacentfrequency bands.

To ensure stable oscillation signals, the loading effect of theswitches and the varactors on the transmission lines must becarefully examined for each one of the frequency bands. Due tothe imbalance switching at both sides of the resonator, ,

, and exhibit asymmetric property for the standingwaves. As a result, the maximum voltage swing takes place ata point departing from where the output buffer locates, leadingto a variation in the output swing among the frequency bands.In addition, the attenuation of the transmission line varies fromone band to another due to an unequal number of the “off”switches. The equivalent impedance of the switches and thevaractors also change significantly during the band switching,which further complicates the analysis of the loading effect.Nevertheless, the line attenuation at each band can still be eval-uated by the required transconductance to satisfy the start-upconditions. Fig. 8 plots the simulated output voltage swing withrespect to the tail current for the individual bands. Based onthe simulation results, exhibits the smallest output swingwhile suffers from the most severe attenuation. More-over, gives the largest oscillation amplitude due to theabsence of the on-switches, leading to smaller losses and supe-rior phase noise performance.

By taking the practical considerations as described above intoaccount, the proposed wide-tuning-range VCO is implementedat the 40-GHz frequency band. The circuit parameters in thisparticular design are summarized in Table I.

IV. EXPERIMENTAL RESULTS

Using a standard one-poly six-metal (1P6M) 0.18- m CMOSprocess, the 40-GHz wide-tuning-range VCO is implementedfor demonstration. Fig. 9 shows the microphotograph of the fab-ricated circuit with a chip area of 1.25 0.5 mm includingpads. The single-ended output spectrum and the close-in phasenoise of the VCO were measured by Agilent E4407B spectrumanalyzer and 11970Q harmonic mixer equipped with a phase


TABLE ICIRCUIT PARAMETERS OF THE VCO

Fig. 9. Microphotograph of the fabricated 40-GHz wide-tuning-range VCO.

noise measurement system. To characterize the intrinsic perfor-mance of the proposed circuit, on-wafer probing was performedwhile the losses from the measurement setup were calibrated at40 GHz and de-embedded in the experimental results.

Operated at a supply voltage of 1.5 V, the current consump-tions of the VCO core and the output buffer are 18 and 10 mA,respectively. The VCO circuit provides six overlapping fre-quency bands by the switches – while the controlledvoltage of the varactors is utilized for frequency finetuning. Fig. 10 shows the measured output tuning characteris-tics of the VCO, indicating an achievable output frequency from34.4 to 41.9 GHz and a tuning range of 20%. Note that the con-trolled voltage ranges from 0.5 to 2.5 V in this particular designsince the center of the tuning range occurs around zero gate biasof the accumulation-mode MOS varactors. Alternatively, theSWO can be modified by employing a top-biased scheme witha pMOS current source to confine the controlled voltage withinthe supply voltage. From the measured tuning characteristics, itis also observed that the tuning range of each individual bandsdecreases from to . This is primarily due to theincreasing effective length of the transmission lines and theadditional capacitive loading as more switches are turned off.

The measured output power and phase noise of the VCO aredepicted in Fig. 11 and 12, respectively. The VCO delivers an

Fig. 10. Measured output tuning characteristics of the proposed VCO.

Fig. 11. Measured output power of the VCO for various frequency bands.

Fig. 12. Measured phase noise of the VCO at 1-MHz offset frequency.

output power ranging from 13.6 to 4 dBm while the phasenoise at 1-MHz offset is lower than 96 dBc/Hz within the en-tire frequency range. The worst performance in terms of theoutput power and phase noise is observed at due to theexcess attenuation of the resonator. Operating at the lowest fre-quency band with an oscillation frequency of 34.4 GHz, themeasured output spectrum of the VCO are shown in Fig. 13,indicating a calibrated output power of 5.3 dBm and a phasenoise of 107.5 dBc/Hz at 1-MHz offset. Fig. 14 shows themeasured output spectrum of the VCO at the highest frequency


Fig. 13. VCO output spectrum at an oscillation frequency of 34.4 GHz.

band. With an output frequency of 40 GHz, the calibrated outputpower and phase noise are 9.1 dBm and 100.2 dBc/Hz, re-spectively.

To evaluate the overall performance of the VCO, a figure ofmerit including the frequency tuning range [22] is em-ployed. It is defined as

(13)

where is the phase noise at an offset frequency fromthe carrier frequency , is VCO power consumption inmilliwatts and stands for frequency tuning range in per-centage. Based on the measurement results, the fabricated VCOexhibits a of 183.9 dBc/Hz. The performance of theproposed circuit along with results from the state-of-the-art mil-limeter-wave CMOS VCOs are summarized in Table II.

V. CONCLUSION

A wideband circuit topology for CMOS VCOs operating atmillimeter-wave frequencies is presented in this paper. By in-corporating the switched transmission lines and the distributedvaractors in the nonuniform half-wavelength SWO, the outputfrequency range is significantly enhanced. With the theoreticalanalysis and design considerations for practical circuit imple-mentations, a wide-tuning-range VCO is realized in a 0.18- m

Fig. 14. VCO output spectrum at an oscillation frequency of 40 GHz.

CMOS technology, demonstrating a frequency tuning range of20% in the vicinity of 40 GHz.

APPENDIX

A. Optimization of the Microstrip Line Geometry in the SWO

A simplified design procedure for the microstrip line in theproposed VCO is demonstrated. Considering a half-wavelengthSWO loaded with cross-coupled pairs, the design goal is to op-timize the width of the signal lines for maximum compensationefficiency. Hence, the required transconductance of the cross-coupled inverters to meet the start-up conditions can be mini-mized, leading to reduced power consumption in the VCO de-sign. The procedure starts with the parameter extraction. Basedon the full-wave EM simulations, the circuit parameters of theunloaded microstrip including , , , and are extracted [23]for various line widths as shown in Fig. 15. For a given transcon-ductance and capacitance of the cross-coupled pairs,the physical length of the loaded microstrip lines can be derivedfrom (5) with and is expressed as

(14)

The calculated microstrip lengths with various numbers of thecross-coupled stages are depicted in Fig. 16. With ,the compensation efficiency which can be estimated by (7) is


TABLE IIPERFORMANCE COMPARISON OF CMOS MILLIMETER-WAVE OSCILLATORS

at 10-MHz offset FOM = PN+ 20 logf

�f� 10 log

P

1mWFOM = PN+ 20 log

f

�f�

FTR

10%� 10 log

P

1mW

Fig. 15. Unloaded circuit parameters extracted from full-wave EM simulationsof the microstrip lines.

shown in Fig. 17. It is noted that the compensation efficiencyreaches its maximum values for a line width ranging from 5to 10 m. For a signal line wider than 10 m, the associatedlength increases accordingly, resulting in a lower efficiency dueto the reduced value of . For a stage number of 5 in the SWO

Fig. 16. Required length of the microstrip lines for various stage numbers ofthe cross-coupled inverters with g = 5 mS and c = 50 fF each.

Fig. 17. Simulated compensation efficiency of the SWO as a function ofmicrostrip line width for various stage numbers of the cross-coupled inverters.

design, a microstrip width of 5 m is adopted for the circuitimplementation. In addition to the line width, another importantdesign parameter to be determined is the spacing between thedifferential signal lines. In consideration of the of the circuit


Fig. 18. Simplified circuit model for the analysis of the local reflection due to the tapered gain cells. (a) Incident waves. (b) Reflected waves.

layout and the series losses due to the proximity effect [24], aline spacing of 15 m is employed in this particular design.

B. Design Consideration of the Tapered Gain Distribution

In [19], a standing-wave oscillator with a tapered gain cells isintroduced with the respective gain being amplitude-dependentto save power. The advantage of tapering seems straightforward;nevertheless, attention must be paid to the influence of the localreflection caused by impedance mismatch.

By analyzing the SWO as a distributed oscillator [9], onecan derive the start-up requirement including the effect ofimpedance mismatch along the propagation media. Fig. 18(a)shows a simplified model of the SWO with five equally spacedtapered gain stages. Starting from the center of the SWO(node ), the forward wave travels toward the right end isamplified by the gain stages. Due to the tapering of the gainstages, the equivalent characteristic impedance and propagationconstant of the transmission line section is scaled, resultingin local reflections at the discontinuities. Assuming that thetransmission media is lossless and the multiple reflections areneglected, the amplitude of the incident wave near the shorttermination (node ) is given by

(15)where is the tapering factor and is the transmission coef-ficient at the discontinuity toward the short-circuit termination.With an ideal short circuit, the incident wave is completely

reflected, denoted as . Again, the reflected wavetravels along the transmission line while being amplified by thegain stages. As the wave components add up at node as shownin Fig. 18(b), the amplitude of the traveling wave is

(16)where is the transmission coefficient at the discontinuity withthe opposite direction to . By substituting (15) into (16), andsetting , the required normalized gain to sustain theoscillation is

(17)Note that the term stands for the effect of the localreflection. Larger impedance mismatch associated with theincreasing tapering factor results in smaller . However,since the transconductance is tapered as well, the requiredoverall gain reduces as increases.

With the presence of impedance mismatch in the transmis-sion line, the maximum amplitude of the standing-wave wouldbe theoretically smaller compared with the case where theimpedance is matched. However, since the bias current in themiddle stage of the SWO is scaled up with a factor of , thereduction in the maximum voltage amplitude of the standingwaves is not significant. In this design, a tapering factor of2 is chosen. Moreover, in order to compensate the additional


losses from the switches for band selection, the gain of the twoamplifiers located near the boundaries is enlarged, leading tothe proposed circuit architecture as in Fig. 5(a).

ACKNOWLEDGMENT

The authors would like to thank Yu-Hsun Peng of ADSI Laband Chihun Lee of ECL Lab, Graduate Institute of ElectronicsEngineering, National Taiwan University, Taipei, Taiwan, formeasurement supports, and National Chip ImplementationCenter, Hsinchu, Taiwan, for chip fabrication.

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Jun-Chau Chien (S’05) received the B.S. and M.S.degrees in electronics engineering from NationalTaiwan University, Taipei, Taiwan, R.O.C., in 2004and 2006, respectively.

His research interests focus on integrated circuitdesigns for high-speed communication systems.

Mr. Chien was a recipient of the 2007 IEEEISSCC Silkroad Award, the 2006 OutstandingResearch Award and Annual Best Thesis Awardof Graduate Institute of Electronics Engineering,National Taiwan University.

Liang-Hung Lu (M’02) received the B.S. and M.S.degrees in electronics engineering from NationalChiao-Tung University, Hsinchu, Taiwan, R.O.C., in1991 and 1993, respectively, and the Ph.D. degreein electrical engineering from the University ofMichigan, Ann Arbor, MI, in 2001. During hisgraduate study, he was involved in SiGe HBT tech-nology and monolithic microwave integrated circuit(MMIC) designs.

From 2001 to 2002, he was with IBM T. J. WatsonResearch Center, Yorktown Heights, New York,

working on low-power and RF integrated circuits for silicon-on-insulator (SOI)technology. In August 2002, he joined the faculty of the Graduate Instituteof Electronics Engineering and the Department of Electrical Engineering,National Taiwan University, Taipei, Taiwan, where he is currently an AssociateProfessor. His research interests include CMOS/BiCMOS RF and mixed-signalintegrated circuit designs.

Design of Wide-Tuning-Range Millimeter-Wave CMOS VCO With a Standing-Wave Architecture

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