7. R.A. Bhatti, Y.T. Im, N.N. Anh, and S.O. Park, Multiband internal

monopole antenna for mobile phones, Microwave Opt Technol Lett

51 (2009), 739–742.

8. C.T. Lee and K.L. Wong, Uniplanar coupled-fed printed PIFA for

WWAN/WLAN operation in the mobile phone, Microwave Opt

Technol Lett 51 (2009), 1250–1257.

9. C.C. Chen, C.Y.D. Sim, and F.S. Chen, Novel compact quad-band

narrow strip-loaded printed monopole antenna, IEEE Antennas

Wireless Propag Lett 8 (2009), 974–976.

10. K.S. Yoon, S. B. Park, S. Min Kim, and W.G. Yang, Penta-band

internal antenna for mobile handset applications using

parasitic element, Microwave Opt Technol Lett 50 (2008), 3045–3048.

11. P. Ciais, R. Staraj, G. Kossiavas, and C. Luxey, Design of an inter-

nal quad-band antenna for mobile phones, IEEE Microwave Wire-

less Compon Lett 14 (2004), 148–150.

12. C.I. Lin and K.L. Wong, Internal hybrid antenna for multiband operation

in the mobile phone, Microwave Opt Technol Lett 50 (2008), 38–42.

13. C.H. Wu and K.L. Wong, Internal hybrid loop/monopole slot

antenna for quad-band operation in the mobile phone, Microwave

Opt Technol Lett 50 (2008), 795–801.

14. C.Y.D. Sim, P.C. Cheng, and C.H. Lee, Low-profile multiband pla-

nar hybrid antenna design for mobile handset applications, Micro-

wave Opt Technol Lett 53 (2011), 910–915.

VC 2012 Wiley Periodicals, Inc.

COMMENTS ON ‘‘A TRIANGULARDIELECTRIC RESONATOR ANTENNAEXCITED BY A COAXIAL PROBE’’

Sudipta Maity and Bhaskar GuptaDepartment of Electronics and Tele-Communication Engineering,Jadavpur University, Kolkata 700032, India

Received 19 September 2011

ABSTRACT: Original article published Microwave Opt Technol Lett

30:340–341, 2001. VC 2012 Wiley Periodicals, Inc. Microwave Opt

Technol Lett 54:1548, 2012; View this article online at

wileyonlinelibrary.com. DOI 10.1002/mop.26808

Key words: dielectric resonator antenna; transcendental equation

In the above communication [1], Ahmed A. Kishk has given

an approximate expression to compute the resonant frequency of

an equilateral triangular dielectric resonator antenna (DRA) with

height h and an equi-triangular uniform cross section with a side

length Ld, placed on a ground plane. He has given a transcen-

dental equation for computing the wave number kz in the zdirection as given below:

kz tan kzh� p=2ð Þ ¼ er � 1ð Þ � kz½ �1=2 (1)

where er is the relative permittivity of DRA. Hence, the reso-

nance frequency can be found by using the following expres-

sion:

fmn ¼ c

2pffiffiffiffier

p 4p3Ld

� �2

m2 þ mnþ n2� �þ k2z

" #1=2

(2)

where c is the velocity of light in free space. He has used the

resonance frequency index mn instead of mnl because

l ¼ mþ nð Þ (3)

But by applying image theory to remove the ground plane at

z ¼ 0 and enforcing continuity of tangential field to the surface

of dielectric resonator at z ¼ 6h, for TM to z mode, the follow-

ing transcendental equation will result

kz tan kzh� p=2ð Þ ¼ er � 1ð Þk20 � k2z� �1=2

(4)

where k0 denotes the free-space wave number corresponding to

the resonant frequency. Equation (4) satisfies all the data of col-

umn 2 of Table 1 in that communication [1]. It might have been

a typographical error. Hence, Eq. (1) of the above-mentioned ar-

ticle [1] must be corrected or replaced by Eq. (4).

Now, the DRA has triangular cross section. Hence, we need

triangular co-ordinate of a point which can be found by trilinear

transformation. For equilateral triangular cross section, we have

to use homogeneous trilinear coordinates [2] which satisfy the

relation:

lþ mþ n ¼ 0 (5)

Hence,

l ¼ � mþ nð Þ (6)

Similarly, the expression for third index (l) in that article [1]

must be corrected or replaced by Eq. (6).

REFERENCES

1. A.A. Kishk, Microwave Opt Technol Lett 30 (2001), 340–341.

2. S.A. Schelkunoff, Electromagnetic waves, Van Nostrand, New

York, 1943, pp. 393–396.

VC 2012 Wiley Periodicals, Inc.

1548 MICROWAVE AND OPTICAL TECHNOLOGY LETTERS / Vol. 54, No. 6, June 2012 DOI 10.1002/mop