272 mm TRANSACTIONS ON MfCROWAVS THRORY AND Tf3CHN3QUf3S,VOL, m-28, NO. 3, MARCH 1980

Letters

CM Design of (h@ed Mkrostrip Lines

J. H. HINTON

~hfwet-w SYIItkdS alpP2WCb by .’ikbtarza@ ROWf30th~ sod

.JOM [1] for eoqkd mkmatrip lines shows close agreement with theBryant &mdWeim KS&S [2] exeept for smafl W/H where tbe deviation fsabout M percent in computing Z@. It is shown that the apfmmeb in [1] wiff

producx cke sgreement with [2] for aff W/H when Wheeler’s formula [4]for siagfe mkrmtrip tine fs incorporated in the synthesis procedme.

Coupling between parallel microstrip lines has been synthe-

sized by Akhtarxad, Rowbotham, and Jones [1] which facilitates

the determination of the geometry of a devise when the even-

and odd-mode characteristic impedances (Zw and Z@) are

known. The procedure involves computing single-line W/H),e

and W/H),O ratios for ZM/2 and ZW/2, respectively, by exist-

ing formulations. These ratios serve as references for W/H).e

and W/H)=O computed using S/H and W/H in relations (2)

and (3) of [1] derived for conformal mapping.

As indicated in Table 1 of [1] close agreement between the

results of [1] and those of Bryant and Weiss [2] occurs except

when W/H is small. For small W/H and S/H the deviation is

about 14 percent for Z~ and this deviation was attributed to the

Bryant and Weiss data.

The significant differences in Z& at small W/H k a result of

the choice of the formulation used to compute the reference

single-line W/E& and W/H),O in the synthesis. The formula

used in [1] is

( W/K-J).= :(d- 1) - :h2(2d- 1)

q-l+—

[

ln(d– 1) +0.293 – ~m, 1

(1),

where

d= 60w2/ZOl& , ZoHZW/2, and Zm/2.

‘Ms is Wheeler’s formula [3] modified for balanced stripline and

is valid only for large W/H. Wheeler’s updated formula [4] for

single microstriphne,

#

8V’[(. )]exp &* -1 *+*

w/H), =

[(. )]exp &fi -1

(2)

k valid for a wider range of W/H. In the synthesis for coupled

lines this formula may be used instead of (1) to determine the

referense W/H).e and W/H),. using RwZm/2 and ZW/2.

A program for the synthesis relations [1] was written for the

HP65 incorporating (2) and exercised in an analysis manner to

compute Z~ and Zw for several S/H and W/H. As shown in

Table I the results are in good agreement with [1] for W/H>

Manuscript received August 27, 1979; October 23, 1979.The author is with E-Systems, Inc., Dallas TX 75266.

TABLE I

~y—1,1.1.2.2.2,2.5,5.5.5

1.01,01,01.0

~~.1,5

1.02.0

.1

.51.02.0

.1,5

1.02.0

.1,5

1,02.0

mparl sonBryant

IzOe*

164.196.266,541.7

156.092.264,541,0

138.484.560.539.4

126.077.456,537,6

_Ielss

ZOO*

55.434.527.821.666.139.931.623.783.549.738.127,496.657.743.230.1

S1 Resu~

~141.7

92.165,041.3

136.089.063.440,7

125.282.259.739.2

116.476.156.237.6

~zad

&53, s35.229.022.764.641.133.125.180.950.839.528.792,558 344.331.2

Usin<in I

20e164,3

95.866.041.5

154,291.764.240.7

137.284,360.339.2

125.077 756,737.7

——

*Scaled by Wr

0.5 and for all W/H shown with Bryant and Weiss.

[1]

[2]

[3]

[4]

73—

.~54.335.328.822.765.741.233.125.183,251.039.528,796,158.844.431,2

S. Akhtarzad, T. R. Rowbotharn, and E’. B. Jones, “TIM dwigu ofcoupled microstrip lines,” IEEE Tram. Microwaoe T?teory Tech., VOL

MTT-23, pp. 486-492, June 1975.T. G. Bryant and J. A. Weiss, “Parameters of microstrip transmissionlines and of coupled pairs of rnicrostrip finesfl IEEE Trans. hficrowaoe

i%eory Tech., vol. MTT-16, pp. 1021–1027, Dee. 1968.H. A. Wheeler, “Transmission-line propartics of parallel strips separatedby a dielectric sheet: IEEE Trans. Microwatx Themy Tech., vol. MTT-13, pp. 172– 185, Mar. 1965.—, “Transmission fine properties of a strip on a dielectric sheet on aplane: IEEE Trans. Microrvavs Theory Tech., vol. WIT-25, pp.631–647, Aug. 1977.

Correction to “Characteristics of Coqded

Mlcmstriplines”

RAMESH GARG ANO L J. B~L

In the above paper*, the following typographical errors should

be corrected.

On page 701, (7a) should read

K(k’)c— k=

s/h

‘“= ‘0 K(k) ‘ S/h+2W/h ‘~’.~

On the same page the left-hand side of (7b) should read

K(k’)/K(k) and the right-hand side of (!J) should read

[cm ]-’.

Manuscript recenwd October 10, 1979.R. Garg is with the Advanced Clmtre for Electronic Systems, Department

of Electrical Engineering, Indian Institute of Technology, Kanpur 208016,

India.

I. J. Bafd is with the Department of Electrical Engineering, University of

Ottawa, Ottawa, Canada.

] R. Garg and 1. J. Bald, IEEE Trans. Microwarx Theoiy Tech., vol. fvlTT-

27, pp. 700-705, hfy 1979.

0018-9480/80/0300-0272$00.75 @1980 IEEE