Design and Simulation Model for Compensated and Optimized T junctions in Microstrip Line

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Abstract— Advances in microwave solid state devices have simulated interest in the integration of the microwave circuits. Microstrip lines are being considered as viable candidates for microwave communication and other applications. Microstrip due to its various design advantages is particularly very attractive. This creates the need for accurate modeling and simulation of microstrip transmission lines. Virtually all practical distributed circuits must contain discontinuities as straight uninterrupted lines would be of little engineering use. Microstrip discontinuities such as crossings, T-junctions, bends and impedance steps are elements of many complex microstrip circuits like filters, power dividers, ring couplers, and impedance transformers. Therefore knowledge of exact reflection and transmission properties in dependence on frequency is of great importance. A simulation model is presented here for analyzing the T-junctions in microstrip lines through Sonnet Software at low frequencies (below 10 GHz). The parameters of microstrip lines are determined from the empirical formulae which are based on full wave analysis. The simulation work has been performed on Alumina substrate. The T-junctions are simulated and S-parameters hence calculated show the transmission properties of the discontinuity and their frequency dependency. The T-junction is also compensated to get better transmission properties, and optimized which gives important results for designing desired frequency microwave circuits.

Index Terms— Full wave analysis, Microstrip line, Microstrip discontinuities, T-junctions, Steps in width, Sonnet Software, Substrate permittivity and S-parameters.

I. INTRODUCTION

In Microwave integrated circuits (MICs), the transmission structure should be planar in configuration i.e. the characteristics of the element can be determined by the dimensions in a single plane. As for example, in a microstrip line on a dielectric substrate the width can be adjusted to control its impedance. The commonly used different types of printed transmission lines for MICs are microstrip line, strip line, suspended strip line, slot line, coplanar waveguide and fin line, as shown in Fig. 1. Microstrip line is one of the most popular lines in a transmission structure, mainly due to the fact that the mode of propagation in a microstrip is almost TEM [1]. The physical structure of a microstrip is shown in the Fig. 2.

Manuscript received Dec,2014

Dr. Alok Kumar Rastogi, Department of Physics & Electronics, Institute for Excellence in Higher Education, Bhopal, India, 9425004984.

Munira Bano, Department of Physics & Electronics, Institute for Excellence in Higher Education, Bhopal, India, 9893320310.

Shanu Sharma, Department of Physics & Electronics, Institute for Excellence in Higher Education, Bhopal, India, 9893809894.

Fig.1. Various Planar Transmission Line Structures

Fig.2. Physical & Constructional view of Microstrip line

A.Microstrip Discontinuities

All practical distributed circuits, whether in waveguides, coaxial lines or any other propagation structure, must inherently contain discontinuities. A straight uninterrupted length of transmission structure would be of little engineering use, and in any case junctions are essential. Although such discontinuities give rise to only very small capacitances and inductances (often <0.1pF and <0.1nH) the reactance of these become particularly significant at the high microwave and millimeter wave frequencies. Many circuits such as filters, mixers and oscillators involve several discontinuities. All technologies whether based on hybrid MICs or MMICs (Monolithic Microwave Integrated Circuits) inherently involves transmission discontinuities [2]. Discontinuity modeling is based upon equivalent capacitances and

Design and Simulation Model for Compensated

and Optimized T-junctions in Microstrip Line

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Volume 3 Issue 12, December 2014

inductances. The following are several forms of discontinuities emerging from circuit requirements:

a) Open circuits b) Series coupling gaps

c) Short circuits through to the ground plane d) Step width changes

e) T & cross junctions

[image:2.595.61.268.221.338.2]

The T-junctions is perhaps the most important discontinuity in a microstrip as it is found in most circuits such as impedance networks, stub filters and branch line couplers. A microstrip T-junction and its equivalent circuit are shown in the Fig.3.

Fig. 3. Microstrip T-junction and its Equivalent Circuit

The T-junction discontinuity compensation is much more difficult than right angled bends and steps in width discontinuity compensation techniques. The T-junctions can be compensated by adjusting the lengths of the three microstrip lines forming the junction.

Various approaches have been made to calculate the equivalent circuits for discontinuities. Oliner [3] used Babinet‘s principle to describe stripline discontinuities, Silvester and Benedek [4]-[6], and Stouten [7] calculated the capacitances of microstrip discontinuities, and Gopinath and Silvester [8], Gopinath and Easter [9], and Thomson and Gopinath [10] computed the inductive elements of the equivalent circuits. All the methods described in these papers are based on static approximations, and therefore are valid with sufficient accuracy only for low frequencies.

II. MICROSTRIPSYNTHESIS

In actual design of microstrip, one wishes to determine the width ‗w‘ required to obtain specified characteristic impedance ‗Z0‘ on a substrate of known permittivity ‗εr‘ and thickness ‗h‘. This operation is called synthesis. Various researchers have reported formulas for microstrip calculations [11], [12]. Owens [13] carefully investigated the ranges of applicability of many of the expressions given by Wheeler, comparing calculated results with numerical computations. The closed formulas are highly desirable as they are accurate and fast. CAD algorithms can be implemented with these formulas of Edward & Steer [14].

A. Synthesis Formula

For given Z0 and frequency: In case of narrow strips i.e. when Z0 > (44 - εr) Ω

1 ' '

exp

4

1

8

exp



















H

h

w

…… (1) where











































4

ln

1

2

ln

1

2

1

9

.

119

)

1

(

2

0 ' r r r r

Z

H

…… (2) and 2 '

4

ln

1

2

ln

1

2

1

2

1

























































r r r r eff

H

(3) …… (3) where

H

'is given by equation (2) or alternatively as a

function of

h

w

from equation (1)

               

ln 4 16 2

2 ' w h w h H …… (4) For microstrip line on Alumina, this expression appears to be accurate to 0.2 % over the impedance range





50

8

Z

₀

when h w_and

r



are given:

                

 ln 4 16 2

) 1 ( 2 9 . 119 2 0 _w h w h Z r  …… (5) III. SIMULATION

Sonnet Software [15] is commercial Software which provides solutions for high frequency electromagnetic analysis. This Em simulation software is used for design and analysis for high frequency microstrip circuits. The analysis engine of Sonnet Suite®_,_Em_{is appropriate for a wide range} of 3D planar structures. Via capabilities allow the analysis of air bridges, wire bonds, spiral inductors, wafer probes, and internal ports as well as for simple grounding.

IV. RESULTS AND DISCUSSION

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The T-junction is chamfered in different ways in order to compensate the excess reactance. The compensated models are shown in the fig. 5 and 7 along with their three dimensional models shown in figures 6 and 8 resp.

Fig. 5 Compensated T-junction with Triangular Groove and increased width

[image:3.595.50.290.50.213.2]

Fig. 6 Three Dimensional View of the compensated T-junction

Fig.7 T -junction compensated by making grooves in the main arm

Fig. 8 3D view of the compensated T-junction

[image:3.595.308.545.50.210.2]

The results are shown in the Fig. 9 and 10 through graphs of the reflection and transmission coefficients which are analyzed up to the frequency 10 GHz (below X-band).

Fig 9 shows that when the T-junction is compensated the return loss or the reflection coefficient [S11] decreases which is much better in both the ways of compensation rather than the symmetrical T-junction.

Fig. 10 shows that the transmission along the T-junction is also increased by compensating it in either of the ways which is shown by the magnitude of [S12].

[image:3.595.308.544.251.423.2] [image:3.595.50.289.311.475.2] [image:3.595.50.286.352.678.2] [image:3.595.50.284.516.682.2]

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Volume 3 Issue 12, December 2014

Fig 9 Reflection Coefficient Vs Frequency for Microstrip T-junction and its compensated models

Fig 10 Transmission Coefficient Vs Frequency for Microstrip T-junction and its compensated models

Fig. 11 Current Density of the compensated T-junction along with scale depicting the value

The compensated T-junction is then optimized in order to get better results as shown in Fig. 12. The optimization tool in Sonnet is used to see the variation in return loss when the width of the T-junction is varied. The results of optimization are shown in the Fig. 13. As it can be seen from the figure that the minimum return loss is obtained when the compensated

width of the line is 0.9 mm. If the width is changed from this value (either increased or decreased), the reflection increases hence increasing the return loss. Thus the graph here supports our calculations as well as simulation. Thus after optimizing we can fix the width of the T-junction to make our return loss minimum and proper transmission of waves.

Fig. 12 The compensated model used for optimization with width as the variable

Fig. 13 Results of Optimizing the T-junction

V. CONCLUSION

As soon as a transmission line is used in practical circuits, there will be no longer a continuous cross-section geometry, but there will be changes brought about by the joining together of lines, the changing of characteristic impedance or propagation direction and the connection to various loads.

A method is described for calculating the dynamical properties of various microstrip T-junctions. The elements of scattering matrix (i.e. reflection and transmission coefficients) give important results for lower frequencies. CAD models are used to compensate the T-junctions for better efficiency at low frequencies. Sonnet Software is used to optimize the width of the compensated T-junction which gives a way to lower the return loss in the circuit.

[image:4.595.50.289.54.238.2] [image:4.595.308.544.144.318.2] [image:4.595.49.289.282.455.2] [image:4.595.309.543.363.537.2] [image:4.595.50.288.504.679.2]

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REFERENCES

[1] K. C. Gupta, Ramesh Garg, I. J. Bahl, ―Microstrip Lines and Slot Lines‖, Artech House Inc. Washington, 1979.

[2] Wheeler, H.A., ―Transmission Line Properties of a Strip on a Dielectric Sheet on a plane‖, IEEE Trans. Vol. MTT-25, 1977, pp 631-647. [3] A. A. Oliner, ―Equivalent circuits for discontinuities in balanced strip

transmission line‖, IEEE Trans. Microwave Theory Tech. (Special Issue on Symp. On Microwave Strip Circuits), Vol. MTT-3, pp. 134-143, Nov. 1955.

[4] P. Silvester and P. Benedek, ―Equivalent capacitances of microstrip open circuits‖, IEEE Trans. Microwave Theory Tech., Vol. MTT-20, pp. 511-516, Aug. 1972.

[5] P. Benedek and P. Silvester, ―Equivalent capacitances of microstrip gaps and steps‘, IEEE Trans. Microwave Theory Tech., Vol. MTT-20, pp. 729-733, Aug. 1972.

[6] P. Silvester and P. Benedek, ―Microstrip Discontinuity capacitances for right angled bends, T-junctions and crossings‖ IEEE Trans. Microwave Theory Tech., Vol. MTT-21, pp. 341-346, May 1973. [7] P. Stouten, ―Equivalent Capacitances on T-junctions‖, Electron. Lett.,

vol. 9, pp. 552-553, Nov. 1973.

[8] A. Gopinath and P. Silvester, ―Calculation of inductance of finite length strips and its variation with frequency‖, IEEE Trans. Microwave Theory Tech., Vol. MTT-21, pp. 380-386, June 1973. [9] A. Gopinath and B. Easter, ―Moment method of calculating

discontinuity inductance of microstrip right angled bends‖, IEEE Trans. Microwave Theory Tech.(Short Papers), Vol. MTT-22, pp. 880-883, Oct. 1974.

[10] A. Thompson and A. Gopinath, ―Calculation of microstrip discontinuity inductance‖, IEEE Trans. Microwave Theory Tech., Vol. MTT-23, pp. 648-655, Aug. 1975.

[11] Wheeler, H. A., ―Transmission-line properties of parallel wide strips by a conformal mapping approximation,‖ IEEE Trans. Microwave Theory and Tech.,Vol. 12, May 1964.

[12] Wheeler, H. A., ―Transmission-line properties of parallel strips separated by a dielectric sheet,‖ IEEE Trans. Microwave Theory and Techn.,Vo1.13, , Mar. 1965, pp. 172-185.

[13] Owens, R. P., ―Accurate analytical determination of quasi-static microstrip line parameters,‖ The Radio and Electronic Engineer, 46, No. 7, July 1976, pp. 360-364.

[14] T.C. Edwards, M.B. Steer, ―Foundations of Inter connect and Microstrip Design‖, John Wiley & Sons Ltd.

[15] High Frequency Electromagnetic Software SONNET-13.56 User guide.

Dr. Alok Kumar Rastogi Presently Dr. Alok Kumar Rastogi is Professor & Head, Department of Physics & Electronics at Institute for Excellence in Higher Education Bhopal. He did M.Phil (Physics) from the Department of Physics & Astrophysics, University of Delhi in 1984 and completed his Ph.D. Degree in Electronics Engineering from Bhopal University, Bhopal in the year 1990. He received Young Scientist Award for his excellent research work in the field of Microwave Communication in the year 1987. He received EC Post doctoral “Marie Curie” Fellowship, awarded by European Commission, Brussels, Belgium and Ministry of Science and Technology, DST, New Delhi to carry out research work in University of Bradford, England (U.K.) in the year 1995.

Indo-Russian Long Term Project (ILTP) was awarded to him in 1996 by Russian Academy of Science, Moscow and DST, New Delhi for the period of three years. He completed various Major and Minor Research Projects awarded by UGC, New Delhi. UGC New Delhi awarded him several research projects to carry out research work in the field of microwave communication. He is having professional affiliation with various national organizations. He is Fellow ofIETE and life member of IE, IAPT, ISCA, ISTE, PSSI etc. Seven Ph.D. have been awarded under his supervision in the field of microwave communication and five candidates are perusing research work for their Ph.D. degree under his guidance. About 100 research papers have been published in the reputed International and National Journals. More than 20 International conferences attended and visited many countries (U.S.A., U.K., Belgium, Holland, Luxemburg, Germany, Japan

and France) to present research papers in the International Conferences. In the year 2009 UGC, New Delhi nominated Dr. Rastogi to visit Mauritius under IVth UGC – TEC consortium agreement to deliver series of lectures at University of Mauritius for the period of three months. Dr. Rastogi established “Microwave and Optical Fiber communication Study and Research Laboratory” in the Institute for Excellence in Higher Education, Bhopal under Mission Excellence Scheme of MPCST, Bhopal in the year 2011.

Ms. Munira Bano she is currently undertaking research in microwave communication at Institute for Excellence in Higher Education, Bhopal under the guidance of Dr. Alok Kumar Rastogi. She was awarded M.Phil (Physics) in 2007 by Barkatullah University, Bhopal. She is a Senior Research Fellow under the Maulana Azad National Fellowship Programme of UGC. She has published many research papers in various scientific journals. She has also participated in numerous national and international conferences. She has been awarded best research paper at International Conference on Interdisciplinary Research in Engineering, Management, Pharmacy and Sciences held at Sagar Institute of Research & Technology Bhopal from 20th_-23rd_{Feb. 2014.}