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Active and Passive Elec. Comp., 1996, Vol. 19, pp. 171-176Reprints available directly from the publisherPhotocopying permitted by license only

(C) 1996 OPA (Overseas Publishers Association)Amsterdam B.V. Published in The Netherlands under license by

Gordon and Breach Science Publishers SAPrinted in Malaysia

OPEN-CIRCUIT END EFFECT OF MICROSTRIPLINE CONFIGURATION IN PLASMA MEDIUM

PREM BHUSHAN MITAL,Fellow, IETE

Department of Electronics & Communication Engineering, C R State College of Engineering, Murthal(Sonepat) Pin 131039 (INDIA)

(Received August 31, 1995; in final form January 25, 1996)

The extension in length for open microstrip configuration in plasma media is determined using spectraldomain technique under quasi static approach [1, 2]. The results were verified by modifying Hammer-stad equation for plasma media. Good agreement is found between the two results.

INTRODUCTION

The ideal field patterns of a open-circuited microstrip line are distorted withfringing electric fields. The fringing fields and the increase in electrostatic energy asa result of the extra stored energy is modeled by a capacitive termination CF. Thefringing capacitance at the termination of the line is equivalent to extending line byA/ as given by the expression

1A/? tan- (Zo to Cv) (1)

where [3 propagation constant on the line

Z0 characteristic impedence of the lineto angular frequency

FORMULATION

The microstrip in plasma medium is shown in Fig. 1 where ep is the dielectricconstant of plasma medium defined as

ep A2= 1 mp (2)

where A is the plasma parameter

If (x, y) static potential distribution in microstrip structure

171

172 P. MITAL

y y= oo

(R) P,o,n’,o @media

I

y=o

MICROSTRIP IN PLASMA MEDIUMFIGURE 1

then (13, y) Fourier transform of +(x, y)

j (x, y) dx dx

Assuming in media (1) + Acy + Be-y (3)

& in media (2) Ce-y + Dey (4)

In Fourier transform domain, the boundary conditions are

at y 0 (13, 0) 0 (5)

y oo (13, o) 0 (6)

At interface

$(13, h + O) $(13, h O) (7)

d$ dand el: (13, h + O) 1 y $(, h O) (13) (8)

Taking f(x) as the change distribution on the strip conductor, total charge on stripconductor

Q f: f(x) dx

Hence

MICROSTRIP LINE 173

f(13) f(x) ejinx dx (9)

Solving the above, we have

(x, h) Ce-Ih f()(1 coth [3h + ep)

Hence the fourier transform of potential distribution is given as:

(10)

(13, h)[(1 coth [3h + ep)

Line capacitance C is obtained using symmetry as

(11)

1 1 fo [(13)}2xr Q2 {ep + 1 coth 13h} [3h

d(13h) (12)

Taking approximately trial function for f(x) Ixl which gives capacitance asmaximum

f(x) ={ -t/2 -< x -< t/2elsewhere

Q

2 sin sin

If [3h x, then d[3h dx.

Hence

1 ro Q

dx[ep + er coth x]x

(14)

or

174 P. MITAL

1.9

Zo

L)

I--

UJ

1.1

RT DUROID (r 2.

--- A =0.5

--’" A 0.9A= 1-0

0-2 10- 100

wlh

FIGURE 2

Cx o.)) x(t)

sin sin

x(.o x(.o

2h 4h

(ep + er coth x)x

dx

The effective permittivity of microstrip is given by

0.5

0.4

0.3

0.2

I0-2 10- 100 10wlh

FIGURE 3

MICROSTRIP LINE 175

Ceef C-- (16)

where C and Co are the capacitances per unit length of line with and withoutdielectric. The effective dielectric constant is also given as

r + P r- P 1 to+ >- 1 (17)eeff-- 2 2 / 12h h

1+

And line extension A/? as given by Hammerstad is [3]:

+ 0.262e + 0.3 h

0.412 (18)e 0.258 to

+ 0.813h

NUMERICAL RESULTS

The results were obtained solving equations 15, 16, 17, and 18 numerically and areplotted in Fig. 2 to 5.

zou

11.0

10.0

9.0

8.0

7.0

10-2

-.A-, 1.0

10-1 100 i0w/h

FIGURE 4

176 E MITAL

0.4

0.3

0.2

10- 100 10wlh

FIGURE 5

CONCLUSIONS

Calculations of length extension (A?) in plasma medium for various plasmaparameter values (A .1,.3,.5,.7,.9) in an open microstrip configuration areobtained using spectral domain technique under quasi static approach [4,5] and bymodifying Hammerstad equation for plasma media. Good agreement is foundbetween the two results.

ACKNOWLEDGEMENT

The author is indebted to Prof. B. Bhat and Prof. S.K. Koul, Centre for AppliedResearch in Electronics, I.I.T. New Delhi for providing research facilities.

REFERENCES

1. E. Yamashita "Variational method for the analysis of Microstrip-like transmission lines", IEEEtrans. Microwave theory and techniques, Vol. MTT-16, pp. 529-535, August 1968.

2. B. Bhat & S.K. Koul "Lumped Capacitance, Open circuit end effects and edge capacitance ofmicrostrip-like transmission lines for microwave and millimeter wave applications", IEEE trans.,Microwave theory and techniques, Vol. MTT-32, No. 4, pp. 433-439, April 1984.

3. E.O. Hammerstad "Equations for Microstrip Circuit design", 5th European MW conference, pp.268-272, 1975.

4. E Silvester and E Benedek, "Equivalent capacitance of Microstrip Open Circuits", IEEE trans.MTT-20, pp. 511-516.

5. B. Bhat & S.K. Koul, "Strip line-like transmission lines for Microwave Integrated Circuits", WilleyEastern Ltd.

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