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Letters to the Editor

A Note on the Double Fresnel Integral

L. LEWIN

In a recent paper Penunuri introduces the functions

~ dt and Sii(x) = JO tl/2Cii(x) = ~ t1,2 x Si(t) df

where Ci(x) and Si(x) are the Fresnel integrals. Since a substan-tial Appendix is denoted to the evaluation of these expressions, itappears that the author may have overlooked a simple deriv-ation, obtained by integration by parts, which expresses themdirectly in terms of the Fresnel integrals. The results are

Cii(x) =2x1/2C1(x) (2/7)1/2 sm x (1)Sii(x)=2xi12Sl(x) + (2/7r)1i2[cos x 1] (2)

where, following Penunuri,

JCi(x) =(1/27r)1i2 ~ dt (3)

o t/2

Si(x) = (1/2T)1i2~x~ dt. (4)

Using tabulated values for Ci and Si, (1) and (2) can now bereadily evaluated.

Manmcnpt recewed June 16, 1978.The author n with the Department of Electrical Engmcenng, University of

Colorado, Electromagnetlcs Laboratory, Boulder, CO 803091D. Penunrm, A numencal technique for SAW diffraction simulation,

IEEE Tram. Mzcrowaoe Theory Tech., vol. MTT-26, pp. 288-294, Apr. 1978.

Correction to Sensitivity Analysis of CoupledMlcrostrip Directional Couplers

S. D. SHAMASUNDARA ~ K. C. GUPTA

With reference to the above paper, the following correctionsmay be noted.

1) Equation (13) should read as

S;oy= s;~=;[&][*][m(, -m,(l-c2)],2.2) Values of sensitivity of bandwidth shown in Fig. 1 and

value of bandwidth shown in Fig. 2 are incorrect because of acomputational error. The correct results are given in Figs. 1 and2 of this communication.

3) In Table II Directivity for Ideal coupler should read In-finite.

4) Value of (A C)~,X/ c given in the ninth line of the leftcolumn on page 793 should read 0.061 and not 0.61.

Manuscript rece]ved November 17, 1978.The authors are with the Department of Electrical Engineering, I.I.T.

Kanpur 208016, India.] S. D. Shamasundara and K. C. Gupta, Sensitw]ty analysis of coupled

m]crostnp dmectlonal couplers, IEEE Tram. Microwave Theory Tech., vol.MIT-26, pp. 788794, Oct. 1978.

5-o

4.0 -

3.0 -

m

20 -

W10 - - 01

0 0.2 0. L 06 08 l.o~COupl, ng factor C

I 1 1 1 I

m 20 10 3 Odb+Coupltng in dB

Fig. 1. Sensitivities of couphng and bandwidth with Zoe, ZOO for coupledTEM-hne couplers.

03

- L%J

/ I 0.03~

/ >

./ m

x .y=o 022 2 ,

\ 002 _E

z %=Y = Q~02 ,,- ->, , ~a // . \! oo X=Y .CLoo~\, .1

.

. ---

___ 00 0.2 O.L 0.6 0.8 10+CO.pl, ng factor C

!

m 20 10 3 0db4Co. pl, ng In d.9

Fig. 2. Fractional change m couphng and bandw]dth of coupled TEM-bnecouplers caused by tolerances in ZOe and ZOO.

5) The last line before Section II-D on page 790 (right col-umn) should read as 2 percent for a 2-percent deviation inimpedances.

6) The value of (Al? W)~2X/ BW in the seventh line of SectionII-E on page 790 (right column) should be 0.018 and not 0.011.

Correction to Coupling of Wavegnides ThroughLarge Apertures

V. M. PANDHARIPANDE N B. N. DAS

In the above paper], expression (13) on page 211 should readas

C dB = 20 logl/F

+ 8.686clt,211+j/El

Manuscnpt rece]ved November 17, 1978,The authors are w]th Department of Electronics and Electrical Communi-

cation Engineering. Indian Institute of Technology, Kharagpur 721302, Indm.]V. M. Pandhar]pande and B. N. Das, Courimz of waveeuides throuzh

large apertures: IEEE Trans. Mrcrowaoe The&y ?ech., vol~ MTT26, p~.209-212, Mar. 1978.

0018-9480/79/0200-0208$00.75 01979 IEEE