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A New Extraction Method for the Characteristic Impedance and

Effective Dielectric Constant of Transmission Line with DGS

Minwoo Kang1, Sunju Park1, Kwisoo Kim1, Sang-Min Han1, Jongsik Lim1, Kwansun Choi1 andDal Ahn1

1Department of Electrical Communication System Engineering, Soonchunhyang University, Asan,

Chungcheongnam-do, 336-745, Republic Of Korea

Email: elano@ramrec.sch.ac.kr

Abstract In this paper, we propose a new extractionmethod for the characteristic impedance and effectivedielectric constant of a microstrip line. It extracts thecharacteristic impedance and effective dielectric constant of amicrostrip line that uses the results of S Parametersthrough the EM Simulation. And it also extracts thecharacteristic impedance and effective dielectric constant ofmicrostrip line with DGS and compare the variation offrequency response. We simulate a microstrip line which hasa dumbbell type DGS, and extract the electrical length,characteristic impedance and effective dielectric constantaccording to the DGSs size and the number of DGS. Fromthese results, we analyze how DGS influence the variation ofthe transmission line characteristics such as the characteristicimpedance and effective dielectric constant of a microstripline.

Index Terms Microstrip line, S Parameter, electricallength, characteristic impedance, effective dielectric constant,DGS (Defected Ground Structure)

I. INTRODUCTION

The demand for communication devices has been

growing rapidly due to the development of the wireless

communication system market. Also, because of the

increase in the clock speed of digital communication

circuits, many circuits have EMI and crosstalk problems.

Because the connection lines in digital circuits act as

transmission lines in a high speed clock system. [1][2]

Transmission lines are basic elements in a circuit and

because they are used widely, it is very important to

extract their characteristic parameters to design better

performing circuits.

In this paper, we propose a new extraction method for

the characteristic parameters of microstrip transmission

lines with DGS. [3]

Furthermore, we extract the characteristic impedance and

effective dielectric constant of a transmission line,

according to the changes of the size and number of DGS.

So, we compare and analyze the dielectric constants and

the characteristic impedances.

II. ANALYZE AND AEXTRACTION METHOD

Fig. 1 represents a transmission line expressing reflected

and transmitted waves. And the transmission line can be

expressed ABCD Parameter as Eq. (1).

In Eq. (1), the Zoc and Yoc are the characteristic

impedance and admittance of the transmission line,respectively, in Fig. 1.

0

0

cos sin

sin cos

C

C

jZA B

jYC D

=

(1)

The ABCD Parameter can be calculated by using the

conversion formula between the S Parameter and the

ABCD - Parameter as in Eq. (2). [4]

( ) ( )

( )( )

( )( )

( )( )

11 22 12 21

21

11 22 12 21

0

21

11 22 12 21

0

21

11 22 12 21

21

1 1

2

1 1

2

1 1

2

1 1

2

C

C

S S S S

A S

S S S S B Z

S

S S S S C Y

S

S S S S D

S

+ +

=

+ + =

=

+ =

(2)

Fig. 1. A transmission line expressing reflected andtransmitted waves.

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2009 IEEE International Symposium on Radio-Frequency Integration Technology

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Using Eq. (1) and Eq. (2), the electrical length of

transmission line can be calculated as Eq. (3).

180

[deg]effl

C

= (3)

Eq. (4) represents the effective dielectric constant of the

transmission line and it can be calculated by using Eq. (3).

2

1coseffC

Al

=

(4)

Microstrip line having 50 characteristic impedance at

2GHz center frequency was simulated to prove the validity

of this extraction method in extracting the characteristicimpedance and effective dielectric constant of a

transmission line. Fig. 2. shows the microstrip line of

1.85mm in line width(a) and 22.53mm in line length(b) at

2GHz center frequency.

Fig. 3 (a) and (b) represent the frequency response of

the electric length and effective dielectric constant of Fig.

2, which were obtained by using EM Simulation result

(HFSS Ver. 11.1.1 of Ansoft Co.).

And Eq. (5) is the characteristic impedance of themicrostrip line, and it can be calculated by using Eq. (2).

Fig. 4. shows the frequency response of the characteristic

impedance of the microstrip line.

Data in Fig. 4. represents the characteristic impedance of

Fig. 2. at about 48.6 on center frequency.

02

Im[ ]

1

BZ

A=

(5)

Fig. 2. A microstrip transmission line (fc = 2GHz )

(a)

(b)

Fig. 3. Extracted parameters of transmission line(a) Electrical length (b) Effective dielectric constant

Fig. 4. Extracted characteristic impedance oftransmission line

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III. THE CHARACTERISTIC IMPEDANCE AND EFFECTIVE

DIELECTRIC CONSTANT OF TRANSMISSION LINE WITH DGS

Fig. 5. shows the microstrip line inserted with a

dumbbell type DGS in ground plane. We simulate this

line to extract the electrical length, characteristicimpedance and effective dielectric constant.

Fig. 6 shows the frequency responses of the electrical

length, effective dielectric constant and characteristic

impedance of a microstrip line having one dumbbell type

DGS. We can see that the slope of the electrical length

of the microstrip line becomes steeper when the size of

the DGS increases (d is 2mm to 4mm, g = 0.4mm). And

the characteristic impedance and effective dielectric

constant increase when the size of the DGS increases, as

well.Fig. 7. represents the variation of parameters of the

microstrip according to the change in number of the

DGS (the number of DGS is changed 1 to 3). The result

shows a similar trend as those of the previous cases.

Fig. 5. A microstrip transmission line withdumbbell type DGS

(a)

(c)

Fig. 6. The variation of characteristic parameters when DGSssize is changed.(a) Electrical length (b) Effective dielectric constant (c)Characteristic impedance

(b)

(a)

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But the slope of the frequency response of the electrical

length of the microstrip line having two dumbbell type

DGSs ( Its size is 4 4 mm2

) is the steepest.

Therefore, the proposed extraction method of the

characteristic impedance and effective dielectric constant

by using S Parameters is simpler than the establishedextraction method. [3] At the same time, this method has

other merits : the variations of electrical length, effective

dielectric constant and characteristic impedance

according to frequency can be obtained.

IV. CONCLUSION

This paper proposed a new extraction method for the

characteristic impedance and effective dielectric constant

of a microstrip line. The characteristic impedance and

effective dielectric constant of microstrip lines were

extracted by using S Parameters. Furthermore, the

variations of parameters according to the changes of the

size and number of the DGS were obtained.

This extraction method of the characteristic impedanceis simpler than the established extraction method and it

can calculate the values of effective dielectric constant and

electrical length. In addition the frequency responses of

the desired parameters can be obtained with this method.

This extraction method is more analytical than the

established method (example : the trial and error method )

and it is very useful for analyzing transmission lines of

digital circuits with EMI and crosstalk due to higher

frequencies.

REFERENCES[1] J. P. Simpson, R. R. Goulette, and G. I. Costache,

Radiation from microstrip transmission lines, in Proc.IEEE Int. Symp., pp. 340-343, Aug. 1988.

[2] W. T. Huang, C. H. Chen, C. H. Lu, S. Y. Tan, A NovelDesign to prevent crosstalk,IEEE, TENCON 2007 2007IEEE Region 10 Conference, pp. 1-4, Oct. 30 2007-Nov. 22007.

[3] C. S. Kim, J. S. Park, J. B. Lim and D. Ahn, A Novel 1-DPeriodic Defected Ground Structure for Planar Circuits,IEEE, Microwave and Guided Wave Letters, vol 10, No. 4,pp. 131-133, April 2000.

[4] David M. Pozar, Microwave Engineering 3rd ed., MA JohnWiley & Sons, Inc., pp. 174-178, 2005.

(b)

Fig. 7. The variation of characteristic parameters whenchange number of DGS

(a) Electrical length (b) Effective permittivity (c)Characteristic impedance

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