REFERENCES

1. W.L. Ko and R. Mittra, A combination of FDTD and Prony’s methodsfor analyzing microwave integrated circuits, IEEE Trans MicrowaveTheory Tech (1991), 2176–2181.

2. Y. Hua and T.K. Sarkar, Matrix pencil method for estimating parame-ters of exponentially damped/undamped sinusoids in noise, IEEE TransAcoustics Speech Signal Process 38 (1990), 814–824.

3. V.N. Vapnik, Statistical learning theory, Springer, New York, 1998.4. J.A.K. Suykens, L. Lukas, P. Van Dooren, B. DeMoor, and J. Vande-

walle, Least squares support vector machine classifiers: A large-scalealgorithm, ECCTD’99 Euro Conf Circ Theory Design 1999, pp. 839–842.

5. J.A.K. Suykens, Least-squares support vector machines for classifica-tion and nonlinear modeling, Neural Network World 10 (2000), 29–48.

6. A. Smola and B. Scholkopf, On a kernel-based method for patternrecognition, regression, approximation and operator inversion, Algo-rithmic 22 (1998), 211–231.

7. A. Taflove, Advances in computational electrodynamics: The finite-difference time-domain method, Artech House, Boston, 1998.

8. R.S. Chen, D.X. Wang, E.K.N. Yung, and J.M. Jin, Application of themultifrontal method to the vector FEM for analysis of microwave filters,Microwave Opt Technol Lett 31 (2001), 465–470.

© 2005 Wiley Periodicals, Inc.

1.8-V 3.1–10.6-GHz CMOS LOW-NOISEAMPLIFIER FOR ULTRA-WIDEBANDAPPLICATIONS

Yang Lu, Kiat Seng Yeo, Jian Guo Ma, Manh Anh Do, andZhenghao LuDivision of Circuits and SystemsSchool of Electrical and Electronic EngineeringNanyang Technological University, Singapore

Received 1 July 2004

ABSTRACT: A novel CMOS low-noise amplifier (LNA) for 3.1–10.6-GHzultra-wideband (UWB) applications is presented in this paper. As opposedto most of the previously reported UWB LNAs, which are based on SiGetechnology, the proposed UWB LNA is designed based on chartered semi-conductor manufacturing (CSM) 0.18-�m 1.8-V standard RFCMOS tech-nology. The prelayout and post-layout circuit simulation results show thatlow noise figure, good input and output matching, a relatively flat gain inthe 3.1–10.6-GHz UWB band, and low power consumption features are allachieved in the proposed CMOS UWB LNA. © 2005 Wiley Periodicals,Inc. Microwave Opt Technol Lett 44: 299–302, 2005; Published online inWiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.20616

Key words: low-noise amplifier; ultra-wideband; RFCMOS

1. INTRODUCTION

The 7500 MHz of spectrum from 3.1 to 10.6 GHz has beenallocated for the unlicensed use of ultra-wideband (UWB) devicesby the Federal Communications Commission (FCC) since Febru-ary 14, 2002 [1]. According to the FCC, an UWB signal is definedas any signal that occupies more than 500 MHz within the 3.1G–10.6-GHz UWB band and meets the UWB effective isotropicradiated power (EIRP) emission level limitation. Because of thevast available spectrum and the EIRP emission level limitation, anUWB communication system exhibits much better performance inshort-range wireless communication applications compared withother wireless solutions. The main advantages of UWB transmis-

sion are listed as follows: high channel data-rate capacity, highsecurity level, low power dissipation, and low cost.

Under the FCC’s definition of the UWB signal, the UWBspectrum can be utilized either with an impulse that occupies thewhole band or with narrower bandwidth (� 500 MHz) impulsesthat divide the whole band into multisubbands. However, in bothcases, the UWB receiver front-end generally requires a low-noiseamplifier that provides a relatively flat gain from 3.1 to 10.6 GHzwith a low noise figure [2, 3]. To meet the requirement for lowpower dissipation and low cost in UWB applications, a CMOSUWB LNA that provides a lower-power and lower-cost solution aswell as better integration feasibility compared with other technol-ogies is highly desired. Generally, most research works on CMOSLNAs reported to date are mainly on narrowband LNAs andwideband LNAs with sub-1-GHz bandwidth. The methodologiesfor designing narrowband CMOS LNAs [4] and sub-1-GHz band-width wideband CMOS LNAs [5, 6] have been well established.However, few CMOS LNAs with a bandwidth of several GHz,acceptable input and output matching, and low noise performancehave been reported [7]. Moreover, to the best of the authors’knowledge, no work has reported the successful design of a high-performance full-UWB band LNA using a standard RFCMOSprocess operating at a low voltage of 1.8 V up to now.

In this paper, a CMOS UWB LNA with good input and outputmatching and a relatively flat gain in the 3.1–10.6-GHz band aswell as low-noise performance is presented. Section 2 analyzes thecircuit operation and the noise performance of the proposed LNA.In section 3, the prelayout and post-layout circuit simulation re-sults as well as gain-flatness optimization technique are given. Acomparison between the reported UWB LNAs and the CMOSUWB LNA proposed in this paper is also made in section 3.Finally, section 4 is the conclusion of this work.

2. CIRCUIT OPERATION AND NOISE ANALYSIS

The schematic diagram of the proposed CMOS UWB LNA designis illustrated in Figure 1. In this LNA design, all the MOS tran-sistors use a minimum gate length of 0.18 �m. The LNA employsa common-gate stage and a source follower as the input buffer andoutput buffer respectively, which can provide 50� input andoutput matching over the 3.1–10.6-GHz band. A current mirrorbiases both the common-gate stage and the source follower with alarge AC grounding capacitor Cg that bypasses noise current anda large resistor R3 that ensures good reverse isolation. Two cas-code stages with current mirror biasing are added for sufficientgain as well as better gain flatness. As shown in Figure 1, the three

Figure 1 Schematic of the proposed UWB LNA

MICROWAVE AND OPTICAL TECHNOLOGY LETTERS / Vol. 44, No. 3, February 5 2005 299

inductive loads (L1, L2, and L3) of the common-gate stage andtwo cascode stages form three output tune circuits, together withthe total capacitance at the drains of M2, M5, and M7, respec-tively. With proper selection of L1, L2, and L3, the three tunedloads peak the gain of the UWB LNA at three frequencies withinthe 3.1–10.6-GHz band. However, the gain of the LNA tends tovary greatly over the whole band, which is not acceptable forUWB applications. A feedback technique is introduced to circum-vent this problem. The feedback path formed by Rf and Cf betweenthe drains of M5 and M6 influences the gain-curve frequencydependency, which helps to achieve reasonable gain flatness.

By employing a common-gate input stage, wideband inputmatching is achieved at the cost of higher minimum achievablenoise figure, compared with narrowband input-matching architec-tures such as source-inductive degeneration. Meanwhile, the noisefrom the following stages contributes more to the overall noisefigure due to the relatively low gain of the common-gate stage. Thenoise factor of the common-gate stage, taking into considerationthe channel thermal noise in,d

2 , the gate induced noise in, g2 and the

correlation between the two noise sources can be given by

F �in, o, Rs

2 � in, o, g2 � in, o, d

2 � in, o, corr2

in, o, Rs

2, (1)

where in, o, RS

2 ,in, o, g2 ,in, o, d

2 , and in, o, corr2 denote the equivalent output

noise current contributed by the source impedance Rs, the gateinduced noise in, g

2 , the channel thermal noise in, d2 , and the correla-

tion of in, g2 and in, d

2 , respectively. Hence the noise factor is derivedand given by

F � 1 ��

�gmRs�

��Rs�2Cgs

2

5gm�

�Rs

�gm�Z0�2 �2j�c�Rs�Cgs

gmZo���

5,

(2)

where � is the angular operating frequency, Cgs and gm are thegate-to-source capacitance and the transconductance of M2, re-spectively, Z0 is the impedance of the LC tank formed by Ls andCgs, �, �, and � are the transconductance to zero-bias drainconductance ratio of M2, coefficients of channel thermal noise,and induced gate noise, respectively.

In Eq. (2), it can be seen that the noise figure can be suppressedby increasing gm and �Z0�. The input impedance of the common-gate stage is given by

Zin �1

� gm � Z0�1�

, (3)

from which we can determine that gm should be kept around 20 mSfor best input matching. However, as increasing gm helps tosuppress the noise of the common-gate stage and the noise con-tribution of the following stages substantially, while an S11 around�10 dB is already acceptable for input matching, gm is increasedin the proposed LNA design in order to optimize the common-gatestage noise-performance while keeping the input matching withinan acceptable range. Additionally, it also can be seen in Eq. (2) thatby selecting proper Cgs (that is, proper channel width of M2) andLs with a relatively high Q factor, Cgs and Ls are tuned out at thecenter of the 3.1–10.6-GHz band, thus providing a high �Z0� value,which further suppresses the average noise figure of the proposedLNA. By applying the two methods for noise suppressing, acommon-gate CMOS LNA for UWB applications with good inputmatching and noise performance is achieved.

3. GAIN-FLATNESS OPTIMIZATION AND SIMULATIONRESULTS

The novel 1.8-V 3.1G–10.6-GHz UWB LNA is designed based onCSM 0.18-�m standard RFCMOS technology. The prelayout andpost-layout circuit simulation is performed using CadenceSpectreRF with model files derived from actual devices fabricatedwith the CSM 0.18-�m standard RFCMOS process. The first

Figure 2 First prelayout simulation result of S11, S12, S21, and S22

Figure 3 First prelayout simulation result of noise figure

Figure 4 Prelayout, post-layout simulation results of S21 after gainflatness optimization and estimated measured S21: a S21 of prelayoutsimulation; — — — b S21 of extracted simulation; – – – c estimated mea-sured S21

300 MICROWAVE AND OPTICAL TECHNOLOGY LETTERS / Vol. 44, No. 3, February 5 2005

prelayout simulation is performed to testify the possibility ofachieving a flat power gain from 3.1 to 10.6 GHz and its results forthe S-parameters and the noise figure are given in Figures 2 and 3,respectively. In Figure 2, it can be seen that after carefully select-ing the values for L1, L2, and L3 and adjusting the values of Rf andCf, a relatively flat gain (S21) of 18.1 dB � 1.7 dB is achieved. S11

and S22 are below �10 dB over the 3.1–10.6-GHz band because ofthe common-gate stage serving as the input buffer and the source-follower serving as the output buffer. S12 is very low because ofthe employment of two cascode stages. In Figure 3, it can be seenthat the noise figure is kept below 4.0 dB over the whole band withan average value of only 3.0 dB. In this case, the total powerdissipation is 22.1 mW, including input and output buffers. Thefirst prelayout simulation justifies the possibility of realizing alow-noise amplifier with a relatively flat gain, good input andoutput matching, and low noise figure simultaneously in the 3.1–10.6-GHz UWB band using standard RFCMOS technology. How-ever, the gain should be adjusted to optimize its flatness afterfabrication. Generally, the gain of a fabricated CMOS LNA islower than the gain indicated in simulation, most probably due tothe lossy silicon substrate which can be observed in many works(typically in [7]), and this effect is even more serious as thefrequency increases. Considering this, it is desired that the simu-lated gain will increase reasonably with frequency in order tocounteract this effect. The reasonable increasing tendency of the

simulated gain curve can be achieved by adjusting L1, L2, and L3.The prelayout, post-layout simulation gain curves and the esti-mated measured gain curve of the proposed LNA are given inFigure 4. The estimation is based on the assumption that this effectcauses 1-dB loss at 3.1 GHz and 5-dB loss at 10.6 GHz with theloss increasing linearly with the frequency [7]. It can be seen thatthe estimated gain is within the 16.4 � 1.8-dB range. Figure 5shows the noise-figure curves for the prelayout and post-layoutsimulations. The extracted simulation shows that the noise figure isbelow 5.8 dB in the whole UWB band with an average value of 4.0dB. In Figure 6, S11, S12, and S22 in both prelayout and post-layout simulations are shown. S11, S12, and S22 degrade a little inthe extracted simulation; however, all are still within an acceptablerange. The layout of the CMOS UWB LNA is shown in Figure 7with a total chip area of 0.57 mm2. The final power dissipationafter optimization is 25.8 mW.

The comparison of the proposed CMOS UWB LNA and otherrecently reported UWB LNAs are shown in Table 1. The first LNAis a current-mode LNA realized using 0.35-�m SiGe BiCMOStechnology from ST Microelectronics [8], the second is one com-ponent of the Trinity chipset announced by XtremeSpectrum [9],and the third was reported in a thesis dissertation [10]. It is shownthat the proposed CMOS UWB LNA possesses similar perfor-mance to its counterparts based on the SiGe process. With a carefulstudy of all the design trade-offs, the CMOS UWB LNA is

Figure 5 Prelayout and post-layout simulation results of noise figureafter gain flatness optimization: ____________ a noise figure of prelayoutsimulation; ------------ b noise figure of extracted simulation

Figure 6 Pre-layout and post-layout simulation results of S11, S12, andS22 after gain flatness optimization: a S11 of prelayout simulation; b S11 ofpost-layout simulation; c S22 of post-layout simulation; d S22 of prelayoutsimulation; e S12 of post-layout simulation; f S12 of prelayout simulation

Figure 7 Layout of the proposed UWB LNA

TABLE 1 Comparison of the Proposed CMOS UWB LNA withOther Recently Reported UWB LNAs

LNA [8] LNA [9] LNA [10] This Work

Technology [�m] SiGe SiGe 0.18 SiGe 0.5 CMOS 0.180.35

Bandwidth [GHz] 0–10 3.1–10.6 0.8–1.6 3.1–10.6Noise Figure [dB] 2.7–5.5 5.6 (high-gain

mode)3.0 2.9–5.8

(average 4.0)Power Gain [dB] 0–29 Two modes:

0 (low gain)20 (high gain)

8.4 � 0.1 14.6–18.2

Supply Voltage[V]

1.5 3.3 3.3 1.8

Power Dissipation[mW]

7 (max) 200 (module) 23.1 25.8

MICROWAVE AND OPTICAL TECHNOLOGY LETTERS / Vol. 44, No. 3, February 5 2005 301

achieved with good input and output matching, a low noise figure,a relatively flat gain, and low power dissipation.

4. CONCLUSION

This paper has presented a novel low-noise amplifier for ultra-wideband applications based on the CSM 0.18-�m standardRFCMOS process. According to the post-layout simulation results,the performance of the proposed CMOS UWB LNA is comparablewith the previously reported UWB LNAs realized using SiGetechnology. The realization of a CMOS UWB LNA contributes tothe implementation of an UWB receiver front-end using standardRFCMOS technology, which will lead to the high level of inte-gration and low level of cost for an ultra-wideband communicationsystem.

REFERENCES

1. Federal Communications Commission, In the matter of Revision ofpart 15 of the Commission’s Rules Regarding Ultra-Wideband Trans-mission Systems, FCC, 2002, available at www.uwb.org/files/new/FCC_RandO.pdf.

2. G.R. Aiello, Challenges for ultra-wideband (UWB) CMOS integration,IEEE Radio Freq Integrated Circ (RFIC) Symp, Philadelphia, PA,2003, pp. 497–500.

3. D. Barras, F. Ellinger, and H. Jackel, A comparison between ultra-wideband and narrowband transceivers, TRLabs/IEEE Wireless 2002,Calgary, 2002, pp. 211–214.

4. D.K. Shaeffer, and T.H. Lee, A 1.5-V, 1.5-GHz CMOS low-noiseamplifier, IEEE Solid-State Circ 32 (1997), 745–759.

5. J. Janssens, M. Steyaert, and H. Miyakawa, A 2.7-volt CMOS broad-band low-noise amplifier, VLSI Circuits Symp, 1997, pp. 87–88.

6. F. Bruccoleri, E.A.M. Klumperink, and B. Nauta, Generating alltwo-MOS-transistor amplifiers leads to new wide-band LNAs, IEEE JSolid-State Circ 36 (2001), 1032–1040.

7. S. Andersson, C. Svensson, and O. Drugge, Wideband LNA for amultistandard wireless receiver in 0.18-�m CMOS, Proc ESSCIRC2003 Conf, Estoril, Portugal, (2003), pp. 655–658.

8. S. Dia, B. Godara, F. Alicalapa, and A. Fabre, Ultra wide-band: Stateof the art and implementation of a performance-controllable low-noiseamplifier, Int Conf Electrical and Electronics Eng (ELECO 2003),Bursa, Turkey, 2003.

9. XtremeSpectrum TRINITY chipset, TRINITY for media-rich wireless appli-cations, XtremeSpectrum, 2002, available at www.xtremespectrum.com/PDF/xsi_trinity_brief.pdf.

10. S. Lee, Design and analysis of ultra-wide bandwidth impulse radioreceiver, Ph.D. dissertation, University of Southern California, 2002.

© 2005 Wiley Periodicals, Inc.

REMARKS ON “GROUP VELOCITY,NEGATIVE AND ULTRA-HIGH INDEX OFREFRACTION IN PHOTONIC BAND GAPMATERIALS”

Alvaro Gomez, Angel Vegas, and Miguel A. SolanoUniversity of CantabriaDpto. De Ingenierıa de ComunicacionesAvda. de los Castros s/n39005 Santander, Spain

Received 10 June 2004

ABSTRACT: In the paper of Ojha et al. (Microwave Opt Technol Lett42 (2004), 82–87), an erroneous definition of the effective refractiveindex neff in a photonic band gap (PBG) structure is used. The effectiverefractive index neff is defined as a function of the group velocity; this

suffers from two main errors: firstly, the concept of group velocity is notuseful in regions of anomalous dispersion, and this is just the region ofinterest for the calculus in Ojha et al. (Microwave Opt Technol Lett 42(2004), 82–87) of neff of the PBG structure, and secondly, in any casethe refractive index has to be defined in terms of the phase velocity.© 2005 Wiley Periodicals, Inc. Microwave Opt Technol Lett 44:302–303, 2005; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.20617

Key words: photonic band gap structures; effective refractive index

In [1], the authors investigate some optical properties of a photonicband gap (PBG) structure; especially, they compute an effectiverefractive index neff of the PBG that verifies the Scully’s prediction[2]: an exceptionally high values of effective refractive index inthe photonic band edge have to be found. The authors use thegroup velocity to define neff instead of the phase velocity. In [3] (aswell as in [1]), using the correct definition of the refractive indexas [4]

n �c

p, (1)

where c is the velocity of light in the vacuum and p is the phasevelocity, these exceptionally high values were not found. Then, analternative definition is used in [1]:

neff �c

g, (2)

where g is the group velocity. Thus, these high values are ob-tained.

Obviously, “effective” quantities can be defined convenientlybecause they are introduced in order to characterize a globalresponse of a structure using a concept which cannot be directlyapplied to that structure. But, as we will show, in [1] the groupvelocity is used in a frequency range where it does not have acorrect physical insight. The PBG analyzed in [1] has a dispersivebehavior because the phase velocity is a function of the frequency.Consequently, the phase velocity and the group velocity are dif-ferent; in fact, the relationship between them is

g �p

1 �

p

dp

d�

, (3)

which indicates that in a dispersive medium both velocities aredifferent. If dp/d� � 0 (or dk/d� � 0), the medium has normaldispersion, g � p, and the velocity of energy flow is less thanthe phase velocity. However, in the regions where dp/d� � 0 (ordk/d� � 0), the medium has an anomalous dispersion behavior.Then, the group velocity can be greater than c or even negative [5];but in this case, group velocity is generally not a useful concept [5]because a rapid variation of p with � occurs and the assumptionfor obtaining g, which is a slow variation of k with the frequency� in such a form that a linear equation relating them can be used,is no longer valid. This is just the situation in [1]. Inspecting Figure2 of [1], we can see a frequency region where dk/d� � 0 (with avery rapid variation). Then, this region corresponds to an anoma-lous-dispersion behavior of the Bloch wavenumber k, given by Eq.(10) of [1] and, consequently, the concept of group velocity cannotbe appropriately used.

302 MICROWAVE AND OPTICAL TECHNOLOGY LETTERS / Vol. 44, No. 3, February 5 2005