IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 54, NO. 7, JULY 2006 3155

Letters

Comments on “CMOS Low-Noise AmplifierDesign Optimization Techniques”

Jingxue Lu and Fengyi Huang

The above paper [1] analyzes the four low-noise amplifier (LNA)design techniques, i.e.: 1) classical noise matching; 2) simultaneousnoise and input matching (SNIM); 3) power-constrained noise op-timization; and 4) power-constrained simultaneous noise and inputmatching (PCSNIM) based on the noise parameter expressions so asto provide the guideline for LNA designers. Unfortunately, there aresome errors in the derivations of noise parameter expressions for theSNIM, which also applied to the PCSNIM.

In [1, eq. 8], the noise factor F is represented as

F = 1 +1

g2mRs

� gd0 � 1 + s2Cgs(Lg + Ls) 1 + jcj�

�

5

2

�(sCgsRs)2 1 + jcj�

�

5

2

���

5(1� jcj2)gm(sCgs)

2R

2s � sL

2g :

However, it should be

F = 1 +1

g2mRs

� gd0 � 1 + s2Cgs(Lg + Ls) 1 + jcj�

�

5

2

� (sCgsRs)2 1 + jcj�

�

5

2

���

5(1� jcj2)gm(sCgs)

2[R2s � s

2(Lg + Ls)2] :

Therefore, by solving the zero solutions after differentiating the newlyderived noise factor expression with respect toRs andLg , the optimumimpedance Zopt is given by

Zopt =

��

5 (1� jcj2) + j 1 + �jcj

�

5

!Cgs

�2�

5 (1� jcj2) + 1 + �jcj

�

5

2� sLs

Manuscript received February 28, 2006.The authors are with the Institute of RF and Opto-Electronic Integrated Cir-

cuits, Department of Radio Engineering, Southeast University, Nanjing 210096,China (e-mail: jingxuelu@gmail.com).

Digital Object Identifier 10.1109/TMTT.2006.877051

whereas [1, eqs. 10 and 12] expresses it as

Zopt = Z0opt � sLs

where

Z0opt =

1

Y oopt

=

��

5 (1� jcj2)+ j 1 + �jcj

�

5

!Cgs

�2�

5 (1� jcj2)+ 1 + �jcj

�

5

2:

Correspondingly, an approximation of Ls should be revised as shownin [1, eq. 32]

Ls �

��(1� jcj2)

5

!!TCt

:

REFERENCES

[1] T.-K. Nguyen, C.-H. Kim, G.-J. Ihm, M.-S. Yang, and S.-G. Lee,“CMOS low-noise amplifier design optimization techniques,” IEEETrans. Microw. Theory Tech., vol. 52, no. 5, pp. 1433–1442, May2004.

Authors’ Reply

Trung-Kien Nguyen, Chung-Hwam Kim, Gook-Ju Ihm,Moon-Su Yang, and Sang-Gug Lee

The authors of the paper [1] would like to thank Lu and Huang fortheir useful comments on some equations in the original paper [1].

As pointed out by Lu and Huang, [1, eq. (8)] should be replaced by

F = 1 +1

g2mRs

� gd0 � 1 + s2Cgs(Lg + Ls) 1 + jcj�

�

5

2

� (sCgsRs)2 1 + jcj�

�

5

2

���

5(1� jcj2)gm(sCgs)

2[R2s � s

2(Lg + Ls)2] :

Manuscript received March 27, 2006.T.-K. Nguyen, G.-J. Ihm, M.-S. Yang, and S.-G. Lee are with the School of

Engineering, Information and Communications University, Daejeon 305-732,Korea (e-mail: ntkienvn@icu.ac.kr).

C.-H. Kim is with Teltron Inc., Daejeon 350-343, Korea.Digital Object Identifier 10.1109/TMTT.2006.877052

0018-9480/$20.00 © 2006 IEEE

3156 IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 54, NO. 7, JULY 2006

Therefore, [1, eq. (12)] needs to be revised as

Z0opt = 1=Y o

opt =

��

5 (1� jcj2) + j 1 + �jcj

�

5

!Cgs

�2�

5 (1� jcj2) + 1 + �jcj

�

5

2:

By applying the same method, [1, eq. (25)] is now

Zopt =

��

5 (1� jcj2) + j

Ct

Cgs

+ �jcj�

5

!Cgs

�2�

5 (1� jcj2) +

Ct

Cgs

+ �jcj�

5

2:

Accounting for these errors, [1, eqs. (28) and (29)] should be re-placed by

��

5 (1� jcj2)

!Cgs

�2�

5 (1� jcj2) +

Ct

Cgs

+ �jcj�

5

2= Re[Zs]

jCt

Cgs

+ �jcj�

5

!Cgs

�2�

5 (1� jcj2) +

Ct

Cgs

+ �jcj�

5

2� sLs = Im[Zs]:

Correspondinginly, [1, eqs. (32) and (33)] should be revised as

Ls �

��

5 (1� jcj2)

!!TCt

Ls �

��

5 (1� jcj2)

!!TCgs

:

In [1, Appendix, eqs. (A9) and (A14)] should be

F = 1 +1

g2mRs

� gd0 � 1 + s2Cgs(Lg + Ls) 1 + jcj��

5

2

� (sCgsRs)2 1 + jcj�

�

5

2

���

5(1� jcj2)gm(sCgs)

2[R2s � s2(Lg + Ls)

2]

Z0opt = 1=Y o

opt =

��

5 (1� jcj2) + j 1 + �jcj

�

5

!Cgs

�2�

5 (1� jcj2) + 1 + �jcj

�

5

2:

Except for the above noted revisions, the remaining expressions in[1] are correct. The revisions do not affect the general conclusion of[1], although some of the numerical results are modified.

The authors sincerely apologize for any confusion that their errorsmay have caused. The authors are also grateful to Lu and Huang fortheir comments, which gave them an opportunity of reviewing theirwork.

REFERENCES

[1] T.-K. Nguyen, C.-H. Kim, G.-J. Ihm, M.-S. Yang, and S.-G. Lee,“CMOS low-noise amplifier design optimization techniques,” IEEETrans. Microw. Theory Tech., vol. 52, no. 5, pp. 1433–1442, May2004.

Corrections to “Optically Beamformed Beam-SwitchedAdaptive Antennas for Fixed and Mobile Broadband

Wireless Access Networks”

Miguel A. Piqueras, Gerd Grosskopf, Borja Vidal,Javier Herrera, Jose Manual Martínez, Pablo Sanchis,Valentín Polo, Juan L. Corral, Alexandre Marceaux,

Julien Galière, Jérôme Lopez, Alain Enard, Jean-Luc Valard,Olivier Parillaud, Eric Estèbe, Nakita Vodjdani, Moon-Soon Choi,Jan Hendrik den Besten, Francisco M. Soares, Meint K. Smit, and

Javier Marti

With no possible explanation, we forgot to include authorRaymond van Dijk in the byline of the above paper [1]. His com-plete address information is: Raymond van Dijk, TNO Defence,Security and Safety, 2597 AK The Hague, The Netherlands (e-mail:raymond.vandijk@tno.nl). We regret and apologize for this oversight.

REFERENCES

[1] M. A. Piqueras et al., “Optically beamformed beam-switched adaptiveantennas for fixed and mobile broad-band wireless access networks,”IEEE Trans. Microw. Theory Tech., vol. 54, no. 2, pp. 887–899, Feb.2006.

Manuscript received February 27, 2006.M. A. Piqueras, B. Vidal, J. Herrera, J. M. Martínez, P. Sanchis, V. Polo,

J. L. Corral, and J. Martí are with the Nanophotonics Technology Center, Uni-versidad Politécnica de Valencia, 46022 Valencia, Spain (e-mail: vpolor@ntc.upv.es).

G. Grosskopf and M.-S. Choi are with the Fraunhofer-Institute for Telecom-munications, Heinrich-Hertz Institute, 10587 Berlin, Germany.

A. Marceaux, J. Galière, J. Lopez, A. Enard, J.-L. Valard, O. Parillaud,E. Estèbe, and N. Vodjdani are with the Alcatel-Thales III–V Lab, 91460Marcoussis, France.

J. H. den Besten, F. M. Soares, and M. K. Smit are with the COBRA Re-search Institute, Technische Universiteit Eindhoven, 5600 MB Eindhoven, TheNetherlands.

Digital Object Identifier 10.1109/TMTT.2006.877053

0018-9480/$20.00 © 2006 IEEE