application for faculty position in gitam university by dr v s prasanna rajan, hyderabad
DESCRIPTION
Application for faculty positionTRANSCRIPT
Application for Faculty Position in Gitam University
Post Applied for : Assistant Professor
College : Science
Discipline / Branch : Physics
Subject / Specialization
Subject : Physics
Specialization : Computational Electromagnetics
1. Name of the Applicant : Dr. V. S. Prasanna Rajan
2. Father's Name : Shri. T. Sampath
3. Date of Birth : 21-09-1970 Age : 42 Years
4. (a) Address for Communication : 12-13-691-A, G-1, Madhuban, Street 13, Lane 3, Nagarjuna Nagar, Tarnaka, Secunderabad – 500017.
(b) Phone / Mobile Number : +919951109629
Alternative Phone / Mobile Number : 04040274673 (c) Email id : [email protected]
Alternative Email id : [email protected]
5. Category : other
6. Academic Qualifications:
Degree Branch & Specialization
Year of Passing
Class / Grade
% of marks University Studied
Under Graduate
B.Sc ( Mathematics,
Physics, Chemistry )
1992 First Class 70 Sri Sathya Sai Institute of Higher Learning ( Deemed
University )
Post Graduate
M.Sc ( Physics) 1995 First Class 74.1 Pondicherry University
Ph.D Physics ( Computational
Electromagnetics)
2004 University of Hyderabad
7. (a) Teaching Experience
Serial
NumberUniversity / College Position Held From To Total Experience
( in numbers )
Year(s) Month(s)
1 Birla Institute of Technology & Science, Pilani,
Rajasthan
Lecturer 20-09-2005 31-12-2006 1 3
2 Department of Electronics &
Communication Engineering,
Osmania University
Scientist 30-06-2007 30-06-2009 2 0
3 Department of Electronics &
Communication Engineering,
Osmania University
Part Time Lecturer
30-03-2011 05-08-2011 0 5
Total Experience
3 8
(b) Other Experience, if any
(i ) Academic Administration : nil
(ii) Industrial Experience : 5 years 3 months
(iii) Research Experience : 9 years 6 months
8. Area of Research Work : Computational Electromagnetics
9. Research Projects Undertaken : Details given in the resume
10. Consultancy Projects Undertaken : Details given in the resume
11. Details of Research Papers published
(a) No. of papers in national journals : 0
(b) No. of papers in international journals : 0
(c) No. of papers in seminars & conferences : 8
Xerox copies of certain conference papers are sent as annexures with this application
12. Awards / Recognition(s) if any : Awarded Senior Research Fellowship by CSIR, New Delhi.
13. Details of present employment status:
Present Position : Senior Software Development Engineer
Scale of Pay : Rs. 75000/- p.m ( consolidated )
Gross Pay : Rs.75000/- p.m ( consolidated )
Organization where employed : M/s GEOSCAN, Salem, Tamil Nadu.
14. Names & Addresses with telephone numbers and e-mail ID of two references
(a) Dr. A. K. Sinha, Scientist, Microwave Tubes Division, Central Electronics Engineering Research Institute, Pilani, Rajasthan – 333031. Phone: 01596-243189 Email: [email protected]
(b) Prof. P. Anantha Raj, Department of Electronics & Communication Engineering, College of Engineering, Osmania University, Hyderabad – 500007. Phone: 04027098213
15. Ph.D status : Awarded
16. Preference to work : Prepared to work in any of Campuses of the university.
17. Resume along with degree certificates and copies of selected conference papers sent along with this application.
18. Photograph of the applicant:
Declaration: I hereby declare that the information stated in this application is true to the best of my knowledge and belief.
Signature of the applicant
Resume of Dr. V.S. PRASANNA RAJAN________________________________________________________________________12-13-691-A, Mobile: +919951109629G-1, “MADHUBAN”, Email: [email protected] No. 13, Lane No.3, [email protected] Nagarjuna Nagar,Tarnaka, Hyderabad - 500017, India__________________________________________
Gender : Male Date of Birth: 21.09.1970 Nationality: Indian
Marital Status : Married Dependants : Son, Wife
PROFESSIONAL OBJECTIVE
Seeking opportunity in a research and development / teaching environment, that utilizes my research
experience and background in Applied Computational Electromagnetics.
Education
S. No Degree Institution Year of Graduation
CGPA Division
1. Ph.D. (Physics -Applied
Computational Electromagnetics
)
Hyderabad Central
UniversityHyderabad
India.
2004
2. M.Sc (Physics) Pondicherry Central
UniversityPondicherry
India.
19957.41 out of
10 (Maximum attainable
GPA)
I
3. B.Sc (Mathematics,
Physics,Chemistry)
Sri Sathya Sai Institute of
Higher Learning(Deemed
University)Andhra PradeshIndia.
1992 3.5 out of 5 (Maximum attainable
GPA)
I
1
Work Experience: 11 Years 8 Months as on 25.08.2012
(a) Research & Teaching Experience
Designation Name of the University / Institution/
Organization
Period of Service
No of Year(s)
Classes taught / Nature of work
Senior Research
Fellow
University of Hyderabad,Hyderabad – 46,
India.
From 14.02.2000
to28.2.2003
3 Years Research
Lecturer BITS- Pilani,Rajasthan,
India.
From20.09.2005
to31.12.2006
1 Year &3 months
Teaching (for BE /B. Tech students)
Subjects taught: Electronic Devices
&IntegratedCircuits
CommunicationSystems
ElectromagneticFields & Waves
Electrical Sciences-1
Physics -1
ComputationalPhysics
Scientist Centre for Excellence in Microwave Engineering ,
Dept. of ECE,College of Engineering,
Osmania University,Hyderabad -7,
India.
From30.06.2007
to30.06.2009
2 Years Research & Teaching
Subjects taught:a) Electromagnetic Theory
(for BE & ME (ECE) students – for one semester)
b) RF & Microwave Integrated Circuits (for ME
students)
c) Numerical methods in Electromagnetics (for ME –
part time students)
2
(b) Post Doctoral Research Experience
Designation Name of the University / Institution/
Organization
Period of Service
No of Year(s)
Nature of work
Post Doctoral Fellow
Institute for Plasma Research *
Gandhi Nagar,Gujarat,
India
From 17.11.2003
to19.9.2005
1 Year &
9 months
Research ( Grill antenna)
Scientist Fellow
Central Electronics Engineering Research
Institute Pilani,
Rajasthan,India.
From02.01.2007
to26.06.2007
6 months Research (High power millimeter wave source - Gyrotron)
(c) Details of Subjects / Courses handled
Details of the courses handled in BITS - Pilani
Courses handled (till 18.5.06)
S. No Course Title Level Name of the book(s) Author(s)1 Electromagnetic Fields
& WavesUG Electromagnetics
(5th Edition)
Finite Elements for Electrical Engineers
(3rd Edition)
J.D. Kraus
P.P. Silvester&
R.L. Ferrari2 Physics -1 UG Fundamentals of
PhysicsResnick
& Halliday
List of courses handled during the semester (from July 2006 to Dec 2006)
S. No Course Title Level Name of the book(s)
Author(s)
1 Electrical Sciences - I UG Fundamentals of Electrical
Engineering
Leonard S. Bobrow
2 Electronic Devices & Integrated Circuits
UG Solid State Electronic
Devices
Ben G. Streetman &
Sanjay Bannerjee
3 Computational Physics PG Computational Physics
Rubin Landau
3
Details of the courses handled in Dept. of ECE, Osmania University from (2007 - 2009) & (2011) (For BE (ECE) & ME – Microwave & Radar Engineering)
S. No Course Title Level Name of the book(s) Author(s)
1Electromagnetic Field
TheoryUG(BE)
Electromagnetic Waves & Radiating
Systems
E.C. Jordan&
K.C. Balmain
2
Electromagnetic Field Theory
PG (ME)
Time Harmonic Electromagnetic
Fields
Field Theory of Guided Waves
Roger. FHarrington
R.E. Collins
3
Microwave Integrated Circuits
PG(ME)
Handbook of Microwave
Integrated Circuits
Advances in Microwaves
Hoffman
Leo, Young & Sobol
4Numerical Methods in
EngineeringPG
(ME)Finite Elements for Electrical Engineers
Silvester & Ferrari
5 Microwave AntennasPG
(ME)Antennas for all
applicationsJohn D Kraus
(d) Work Experience in Commercial Organization
Designation Name of the Organization
Period of Service
No of Year(s)
Nature of work
Scientist Sree Kumaresa Enterprises
From 01.07.2009
to30.04.2011
1 Year&
9 months 29 Days
Computational Electromagnetics Simulation
(e) Thesis Guidance: No. of students guided for their ME thesis: 6
No. Organization Year of completion Title of Thesis Co-guides(if any)1
2.
3.
College of Engineering,Dept. of Electronics &
Communication Engineering,
Osmania University
-do-
-do-
2008
2008
2008
Electromagnetic Simulation and Design of Conical TEM feed
and Dielectric Lens for an Impulse Radiating
Antenna
Design and Development of Band pass filter for Wide
band tuner
Electromagnetic Simulation of Gyrotron
Interaction Cavity
Mr. Venu Gopal, Engineer,
Astra Microwave Products Limited.
4
4.
5.
6.
-do-
-do-
-do-
2008
2009
2010
Finite Element analysis of transmission line
and radiating structures
Design & Simulation of RF MEMS switch
High Power Design of Conical TEM feed for an Impulse Radiating
Antenna(f) Research Projects Carried out
Title of the project Name of the funding agency
DurationFrom To
Role in the project
Electromagnetic Simulation, Design &
Optimization of an Impulse Radiating
Antenna
Research Center Imarat, DRDO, Hyderabad.
01.05.08 31.04.09
1 Year
Investigator
Analysis of Microwave Integrated Circuits &
Very Large Scale Integrated Circuit Interconnects by Computational
Electromagnetic Techniques
Council for Scientific & Industrial Research,
New Delhi.
14.02.00 28.02.03
3 Years
Senior Research Fellow
Salary DetailsName of the Employer Post held /
Currently Holding
Period from Period to Permanent/Temporary
Emolumentsdrawn
Geo Scan Senior Software Development
Engineer
01/09/11 Till Date Contractual Rs. 75000/- per month
Department of Electronics & Communication
Engineering,College of Engineering,
Osmania University
Part time Lecturer 30/03/11 05/08/11 Temporary Rs.280/- per hour of theory class, as per the
University Norms .
Sree Kumaresa Enterprises Scientist 01/07/09 30.04.2011 Contractual appointment
Rs. 45,000/- per month
Astra Microwave Products Limited, Hyderabad
Scientist 30.06.2007 30.06.2009 Contractual appointment
Rs.24235/- per month
CEERI Pilani Scientist Fellow 02.01.2007 20.06.2007 Temporary Rs.18900/- per month
BITS - Pilani Lecturer 20.09.2005 31.12.2006 Temporary Rs. 18400/- per month
Institute for Plasma Research, Gandhinagar,
Gujarat.
Post Doctoral Fellow
17.11.2003 19.09.2005 Temporary Rs.12000/- per month
University of Hyderabad Senior Research Fellow
14.02.2000 28.02.2003 Temporary Rs.9000/- per month
5
Details regarding my research work:
Title of my Ph.D. thesis: “The Theory and Application of a Novel Scaled Boundary Finite Element Method in Computational Electromagnetics”.
A Brief Summary of my Ph.D. work:
The research work is of a theoretical nature, in the area of Applied Computational Electromagnetics, which belongs to the domain of Electrical Engineering. The aim of the work is to develop a semi-analytical methodology to analyze Metallic cavity Structures, Multi-layered and multi conductor micro-strip configurations, Very Large Scale Integrated Circuit Interconnects encountered in multi-layered Printed Circuit Boards and Periodic structures. In this connection, the theory of a novel Scaled Boundary Finite Element Method is reformulated to analyze the above mentioned structures. The research culminated in a general methodology for the development of Electromagnetic Simulation software for analyzing the above mentioned structures.
Summary of the Research work performed after the completion of my Ph.D degree.
I worked as a Post Doctoral Fellow in the Institute for Plasma Research, for 2 years from 2003-2005. The research work then undertaken by me was the development of a novel scaled boundary finite element formulation using the Electromagnetic field theory, for the analysis and design of antenna structures of arbitrary shapes for – (a) Sinusoidal radiation and (b) Pulse radiation.
The structures involved in the radiation of pulsed electromagnetic wave are important in the design of antennas for Ultra Wide Band communication devices and jamming applications.
The currently reported methodology in the literature as well as the commercial software does not simulate the unbounded space exactly. They use the absorbing boundary conditions to truncate the unbounded space at some distance from the source of radiation. This gives rise to approximate results. Moreover, there is ambiguity in the placement of the absorbing boundary so as to get accurate results. Also, the entire three-dimensional problem space is to be discretized for obtaining the solution. This consumes significant time and memory resources of the computer. Hence there is a need for a novel method, which remedies the constraints mentioned above.
This forms the motivation for the development of a novel scaled boundary finite element method for radiation problems.
In my novel formulation, the lacunae mentioned above, are taken care. There is no need for the absorbing boundary condition to be implemented in the problem. The unbounded space is modeled exactly. Only the two-dimensional surface of the source of radiation is discretized. The formulation is applicable for arbitrary three-dimensional radiation structures.
These features of the formulation requires significantly less resource when compared to those required for the conventional approach adopted in the commercial software as well as in the literature.
The development work resulted in a paper entitled “Generalization of the Atkinson-Wilcox Theorem and the Development of a Novel Scaled Boundary Finite Element Formulation for the Numerical Simulation of Electromagnetic Radiation” presented at the International Conference for Antenna Technologies (ICAT-2005) organized by Antenna Systems Group, SAC, ISRO, Ahmedabad, India.
The research work undertaken by me when I was in the RF group of the institute was the “Development of a Novel Scaled Boundary Finite Element formulation for the design of Phased Wave-guide array antenna” which is used to couple 1 MW of RF power from the source to the plasma in the Tokamak. The resulting software code development presently undertaken by myself will be useful to design sophisticated radiating structures.
6
The in house development of the code will result in a better understanding of analysis and design of antennas and will totally eliminate relying on costly commercial soft wares whose accuracy cannot be assured under all circumstances.
Research Interest:
1. Development of a generalized design and analysis methodology using a novel Scaled Boundary Finite Element method for antennas of arbitrary shapes radiating sinusoidal and pulsed electromagnetic waves for their use in Ultra-wide band communication systems.
2. Development of a software code based on the novel Scaled Boundary Finite Element method for the determination of electromagnetic radiation from phased wave-guide arrays.
3. Electromagnetic Simulation of Gyrotron Interaction Cavity.
4. Electromagnetic Simulation & Design of a high power impulse radiating antenna.
5. Electromagnetic Theory, High Power Microwaves, Computational Electromagnetics, Vector Finite Element method.
Awards: Senior Research Fellowship from the Council of Scientific and Industrial Research, Ministry of Human Resource and Development, Govt. of India, for a period of three years from Feb.2000 - Feb. 2003.
Achievements 1. Successfully framed a research project amounting Rs.6 lakhs, during my tenure as a Ph.D student in
the University of Hyderabad. This project was funded by the Council of Scientific and Industrial Research (CSIR), New Delhi. The Title of the project was “Analysis of Microwave Integrated Circuits and Very Large Scale Integrated Circuit Interconnects by Computational Electromagnetic Techniques.”
2. Successfully framed a research project for 4.73 lakhs funded by Research Centre Imarat, DRDO, Hyderabad, during my current tenure as a Scientist in the Dept of ECE Osmania University
Proficiency in the use of Computers:
(a) Familiarity with Operating Systems: Linux (Installation and Maintenance), Windows 95/98/2000, Free BSD.
(b) Proficient in the installation and use of LAPACK, (Linear Algebra Package) (Linux Version) which is a collection of high-performance computing subroutines used in scientific research programs.
(c) Computer Languages Known: Fortran, Basic
Declaration: I hereby declare that the information stated in this resume is true to the best of my knowledge and belief.
(V.S. Prasanna Rajan)
7
List of Publications:
Book Publication: Scaled Boundary Finite Element Method for Electromagnetics – ISBN – 9783639336412 – Published by – M/s VDM Verlag Dr. Muller, Germany. Year: 2011
1. Ravikumar, V.S. Prasanna Rajan, “ Electromagnetic modelling of Gyrotron interaction cavity", Proceedings of 2nd international conference on RF and Signal Processing Systems (RSPS-2010), pp 401- 410, organized by Dept of ECE, Koneru Lakshmaih University, vadeeswaram Guntur (dist) dated 7-9th Jan 2010.
2. V.S. Prasanna Rajan, "Generalization of the Atkinson-Wilcox Theorem and the Development of a novel Scaled Boundary Finite Element method for the numerical Simulation of Electromagnetic Radiation", Proceedings of ICAT-2005, held during Feb.21-24, 2005, organized by SAC, ISRO, Ahmedabad, India.
3. V. S. Prasanna Rajan, K.C. James Raju, “Reformulation of the Novel Scaled Boundary Finite Element Method for Electromagnetics”, accepted for oral presentation in the Sixth World Congress on Computational Mechanics (WCCM VI) in conjunction with the Second Asian-Pacific Congress on Computational Mechanics (APCOM'04), Sept.5-10, 2004, Beijing, China.
4. P. K. Banmeru, V. S. Prasanna Rajan, P.B.Patil, “E Field Finite Element Method with Covariant Projection Elements for Waveguide Analysis”, Proceedings of the National Seminar on Recent Trends in Communication Technology”, Pp.125-128,organized by School of Studies in Physics and Electronics, Jiwaji University, Gwalior, during April – 13-14 ,2002.
5. V.S. Prasanna Rajan, K.C.James Raju, “Transient field analysis of a open microstrip line like structure fed by a pulsed voltage source”, National Conference on Emerging Trends and Advances in Microwave measurements and Techniques, pp.37-38, held during March 2nd – 3rd 2001, Babasaheb Ambedkar Marathwada University, Aurangabad.
6. V.S. Prasanna Rajan, K.C. James Raju, “Periodic pulse propagation in microstrip line like VLSI interconnects”, Proc. of APSYM – 2000, pp. 170-172, held during Dec. 6-8, 2000, at the Dept of Electronics, Cochin University of Science and Technology,Cochin. 7. V.S. Prasanna Rajan, K.C.James Raju, “Sensitivity Analysis of the cross-talk in microstrip transmission lines”, Proc. of the International Conference on electromagnetic Interference and Compatibility, pp. 129-132, organized by the Society of EMC Engineers (India), held during Dec-6-8, 1999, New-Delhi.
8. V.S. Prasanna Rajan, K.C.James Raju, “Role of the full-wave analysis of a Micro-strip transmission line in the design and fabrication of MIC structures at higher microwave frequencies”, Proc. of APSYM- 1998, pp.280-285, held during Dec.15-16 1998, at the Dept of Electronics, Cochin University of Science and Technology,Cochin.
8
SENSITIVITY ANALYSIS OF THE CROSS-TALK IN MICROSTRIP TRANSMISSION LINES
V.S. PRASANNA RAJAN, K.C. JAMES RAJU
School of Physics, University of Hyderabad, Hyderabad - 500 046
ABSTRACT Z7ik paper concentrates on the phenomena of cross-talk that takes place in the densely packed microstrip transmimion tine like structures encountered in VLSI systems. A sensitivity analpis is performed for the normalized inter-layer unbalanced cross-talk vokage wi!h respect to all the dimensional parameters on which it dependF and the corresponding sensitivity curves plotted Bmed on the calculalions and resuking figures, conclusions are drawn for minimizing the cross- talk. The role of the dielectric constan! of the substrate in the cross-talk is OISo mentioned and the ways to mininrize cross-talk are discussed AU the dimensions are in mils.
Introduction: The interconnects in high speed VLSI systems are analogous. to strip transmission lines employed in microwave integrated circuits. The high-speed electrical interconnections in printed circuit boards are in the form of circuit packs and back-planes. They consist mainly of unbalanced microstrip or strip line transmission lines. The balanced strip-line refers to a configuration in which the sigilal conductors are sandwiched between two ground planes. In a balanced lnicrostrip configuration, there is no upper ground plane. Moreover, in a balanced interconnection, two signal conductors are provided for each signal of interest, since the ground plane do not serve as a return path for the signal. In an unbalanced microstrip confguration, there is no upper ground plane, as well as there is no separate conductor for the return path for the signal. The ground plane below the substrate serves as a return path for the signal.
?le Strip transinission line serves as the m m of propagating high speed digital and analog signals on printed wiring boards and multi-&ip modules. These highdensity interconnections appear as transmission lines, as a result of the
miniaturization in VLSI technology. Under these circumstanccs, the phenomena of cross- talk is a major matter of concern in microelectronics.
Theory: This paper emphasizes the sensitivity of the near-end interlayer unbalanced cross-talk with respect to the dimensional parameters of the unbalanced microstrip geometry given below:
Ground Plans
Unbalanced Microstrip Configuration
Fig( 1 )
The geometry in Fig( I), shows the cross-section of an unbalanced microstrip transmission line like structure. The two signal conductors are placed in an homogenous lossless dielectric substrate above the ground plane. The signal conductors are perpendicular to the plane of the paper. A brief description of the various dimensional parameters denoted in the Fig(1) is given below.
w = Width of the signal line hl= Height of the conductor from the ground plane which carries signal A = Vertical center to center distance between the signal lines r = Horizontal center to center distance between the signal lines to = Thickness of the signal line The general expression for the near end, interlayer unbalanced cross-talk U2UI h l n
layer 1 to layer 2 is given by [ 2],[3],[4],[5]
81-900652-0-3/99 Rs. 40.00 0 1999 SEMCEI 129 INCEMIC-99 : 28.13
Authorized licensed use limited to: OSMANIA UNIVERSITY. Downloaded on January 31, 2009 at 04:54 from IEEE Xplore. Restrictions apply.
Pmceedins of the International Conference on E l e c w g n e t i c Interference and Compatibility '99 . r' + (2h, +A)'
ra+A2 9hl 4111-
w + t ,
In (1) U2UI =
where UZUI = Normalized nearend unh&~~~ced interlayer cross-talk voltage. The sensitivity of a parameter A hith respect to another parameter B is given by
B d A A dB
s,A =--
Based on this definition of sensitivity, the following sensitivity expressions can be imived from the definition given above and by using (1).
r' +A'
s y =
r* +A* W + f ,
9h 1 r 2 + ( 2 4 + A ) 2 I n 2 - --In w +to h, rz + A 2
(4)
SyJ, =: A
In r z +A2
w + to
t0 1 q'"' = -- W + t 0 . 94 In -
w + t ,
(7)
-where S y = sensitivity of U~U, with respect to the horizontal center to center distance between signal lines.
-540
-550
-MO
SY' -570
-580
-590
S? = Sensitiviwof U~U, with respect to the height of the conductor from the ground p l a e which carries signal. S y = Sensitivity of U ~ U I with respect to the vertical center to center distance between signal lines. S y = Sensitivity of u2uI with respect to the width of the signal line. s?' =-Sensitivity of ~ 2 ~ 1 with respect to the thickness of the signal line. From the expression for sruZu1 and sho,o, , it is evident that it is independent of w and L. This implies that and s y are independent of variationsin w and to.
Similarly. for s y ' and ,y,51'"', they are
independent of variations in r and A. Whereas, s?' is dependent on the variation of all the dimensional parameters
Results and Discussion: Based on the expressions for sensitivity, curves are plotted for the variation of the sensitivity with respect to the dimensional parameters.
1 . 10.0 10.2 10.4 10.6 10.8 11.0
Horizontal center to center distance b e h e e n signal lines(r) in mils
Fid2)
In Fig(2), the variation of the sensitivity of U2UI with respect to the horizontal center to center distance bchveen signal lines is plotted. The sensitivity linearly decreases with the increase of the horizontal center to center distance between. signal lines.
-130
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Rajm & Raju : Semitivie Analysis of the Cross-talk ...
0.35
034
O M
'*032
0 3 1
0.30
0.00 2.0 1 .J 3 .O 3.5 4 .O
- - -
- - -
'Vertical Center to cenier distance between the wndudos(h) in mils
Fig(3)
In Fig(3). the variation of the sensitivity with respect to vertical center to center distance between signal lines is plotted. The sensitivity exhibits non-linear decrease upto a value of 3 mils of vertical center to center spacing of signal lines. Then it exhibits a linear behaviour &er 3 mils. In the region of the non-linearity, there is only a slight change in the sensitivity . For a change of 1 mil in the vertical center to center distance between signal lines, the corresponding change in the sensitivity is only around ODl. But in the region of the linear behaviour. the propr&ionate change In sensitivity is observed in the sensitivity of U2UI.
' I
10 15 ao 2s 30 4eight of the signal carrying condudor(h4)from the ground plane in mib
Fid4)
In Fig(4). the variation of sensitivity of U& with respect to the height of the ground plane is plotted. The sensitivity exhibits a very high rate of decrease with respect the variation in the height of the signal carrying conductor fiom the ground plane.
5.0 5.5 6 .O 63 7 .O Width of the signal line (y) in mils
0 2 9 ' . '
Fie ( 5 )
In Fig(5). the variation of the sensitivity of U 2
UI with respect to the width of the signal line is plotted. Linear increase in sensitivity is exhibited in the case of sensitivity variation of U 2 U l with respect to the increase in the width of the signal line -
0.09 - 0.m - 0.01 - O M -
y o . 0 5 : 0.w - 0.03 -
r
01 0.4 0.6 0.8 1.0 11 1.4 1.6 Thidcnes of the signal line 00) in mils
Fig(@
In Fig(6). the variation of the sensitivity of UZUI with respect to the thickness of Ute signal line is plotted. The sensitivity exhibits a lineat increase with respect to the increase in the thickness of the signal line.
Comparing the order of magnitude of the variation of sensitivity of UZU, with respect to various dimensional parameters from all the curves, the magnitude of the sensitivity of UzUl is in huadnds in the case of its variation with respea to the horizontal center to center distance betwee0 signal lines, whenas it is of the order of tenths in the case. of its variation with respect to the height of the signal carrying
131
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Proceedings of the International Conference on Electroms
conductor from the ground plane. The order of magnitude of sensitivity of U2UI is still lower and is of the order of few hundredths in the case of its variation with respect to the tliickncss of the signal line and the vertical center to centcr &stank between signal lines.
Based on these graphical observations, it may be interpreted that, considering the order of magnitude, the sensitivity of U& is more Sensitive to the variation of the horizontal center to center distance between the signal lines followed by its variation with respect to the width of the and height of the signal carrying conductor from the ground plane and finally its variation with respect to vertical center to center distance between signal lines and thickness of the signal line. This fact m y be expressed symbolically as.
Apart from the dimensional parameters discussed above, which influences the unbalanced cross-talk voltage, the material property of the substrate also affects the cross- talk voltage. The material property of the substrate which affects the cross-talk voltage is fhe dielectric constant of the subslrate which contains the signal conductors.
Considering the effect of the dielectric constant on the cross-talk voltage, it is shown in 151 that, reducing the relative dielectric constant for a given characteristic impedance reduces the intra-layer cross-talk. This may be attributed to a lower field concentration in the substrate and in between the signal conductors due to the lowering of the dielectric constant of the substrate. This lower field concentration in between the signal lines, consequently lowers the cross-talk voltage. An analogous situation occurs in the fiill-wave analysis of the microstrip traiisinission line. in which the overall effective dielectric constant of the inhomogenous medium consisting of the center conductor, decreases with the lowering of the dielectric constant of the substrate.
This implies a lower field concentration in the substrate due to the lowering of the dielectric constant of the substrate. Considering the balanced and unbalanced interconnections in a iliicrostrip configuration, it is shown in 151 that balanced interconnections can + 2 used to reduce the cross-talk, radiation, in-rease in noise- immunity, and essentially the ground noise due to the field cancellation resulting from the opposite current froin the other signal conductor of the balanced pair.
rgnetic Interference and Compatibilio '99
Conclusion: The sensitivity analysis of the nonnalized interlayer unbalanced cross-talk voltage (U2UI) indicates that it is most sensitive to tlic horizontal center IO center distance between the signal lines. This puts a practical limit for the horizontal center to center spacing between the signal lines.
In tlie order of the decreasing magnilude of tlie sensitivity, next follows the practical h i t s for the height of tlie signal carrying conductor iron1 the ground plane and the width of the signal line, This is further followed by the limits for the vertical center to center distance bctwecn the signal lines and the tliickncss or the signal line. Furtlicr, tlic lowering of the dielcctric constallt of the substrate also decreases the cross-talk voltage. It was pointed out tliat, the balanced microstrip configuration is more immune to cross-talk when compared to the unbalanced microstrip configuration due to the field canccilation occuring between the signal carrying conductors of tlie balanced pair.
References
[ l 1 A.J.Raina1, "Impedance and' Crosstalk of Stripline and Microstrip Transmission Lines", IEFE Trans. Comp., Packaging, Manufact. Teclinol.. Vol. 20, No.3, pp. 217-224, August, 1997.
. 121 M.S.Lin, A.H.Engvik, and J.S.Loos, "Measureincnts of Crosstalk between closely - ' packcd microstrips on silicon substrates". Electron Lett.. Vol. 26. pp. 714-716, May 24. 1990.
131 J.C.Liao, 0.A.Palusiiiski. and J.L.Priiice. "Conipritntion of transiciits in lossy VLSl packaging intercoiinectious", IEEE Trans. Comp., Hybrids, Manuf. Technof., Vol. 13, pp. 833-838, Dec. 1.990.
14) A.J.Rainal, "Performance limits of electrical interconnections LO a high speed chip", LEEE Trans. Comp.. Hybrids, Manuf. Technol.. Vol. 11, pp. 260-266, Sept. 1988.
IS] A.J.Rainal, "Traiismission Properties of Balanced Interconnections", IEEE Trans. Coinp., Hybrids, Manufact. Technol.. Vol. 16. No.1. February. 1993.
132
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1COMPUTATIONAL MECHANICSWCCM VI in conjunction with APCOM’04, Sept. 5-10, 2004, Beijing, China 2004 Tsinghua University Press & Springer-Verlag
Reformulation of the Novel Scaled Boundary FiniteElement Method for ElectromagneticsV. S. Prasanna Rajan 1*, K. C. James Raju 2
1 Post Doctoral Fellow, Institute for Plasma Research, BHAT, Gandhi Nagar, 382428, India2 School of Physics, University of Hyderabad, Hyderabad, 500 046, Indiae-mail: [email protected], [email protected]
AbstractThe scaled boundary finite-element method is a novel semi-analytical method jointlydeveloped by Song and Wolf to solve problems in Elastodynamics and allied problemsin civil engineering. The scaled boundary transformations are quite general, and theycan be applied to differential equations governing the phenomena in any discipline.This novel method is reformulated recently for solving problems in electromagnetics.The class of problems for which the scaled boundary finite element method ispresently reformulated in electromagnetics are: 1) Eigen values of metallic cavitystructures, 2) Shielded Micro-strip transmission line structures, Very Large ScaleIntegrated Circuit (VLSI) Interconnects, and periodic structures. In this paper, thereformulation of the novel method for the case of metallic cavity structures isexplained.
Keywords: Computational Electromagnetics, Scaled Boundary Finite Element method, Cavity Structures.
1. Introduction: The Scaled Boundary Finite Element method is a novel semi-analytical method, jointly developed by Chongmin Song and John. P. Wolf [1,2] of theInstitute of Hydraulics and Civil Engineering, Swiss Federal Institute of Technology. Itwas successfully used to solve Elastodynamic and allied problems of Civil Engineeringand Soil structure interaction. The initial development of the novel method was basedon an approach, using the concept of assemblage and similarity familiar to engineers.The method was then called as the Consistent Infinitesimal Finite-Element Cell method,[3] reflecting its derivation. Successive developments of the method led to itsreformulation based on the scaled boundary transformation. In this approach, thegoverning differential equations are transformed using a Galerkin weighted residualtechnique. This results in the scaled boundary finite-element equation of the problem[1,2]. This method is called the Scaled Boundary Finite Element method. This methodis reformulated in this paper, making it suitable for electromagnetics. The reformulationis done specifically for determining the eigen values of metallic cavity structures.
2 The Scaled Boundary finite-element method, is based entirely on finite elements,but with a discretization only on the boundary. Unlike the boundary element method,this method doesn’t require any fundamental solution to be known in advance. Thescaled boundary finite-element method combines the advantages of both the finite andboundary element methods. This novel semi-analytical method is analytical in itsapproach in the radial direction with respect to an origin. It implements the finiteelement method in the circumferential direction. As a prelude to the reformulation of the scaled boundary finite- element method forelectromagnetics, the concept of the scaled boundary transformation and the equationsassociated with such a transformation are explained in detail in the forthcomingsection.2. Concept of the Scaled Boundary Transformation: In order to apply this novelmethod, a scaling center is first chosen in such a way that the total boundary underconsideration is visible from it [1,2]. In case of geometries where it is not possible tofind such a scaling center, the entire geometry is sub-structured [4]. In eachsubstructure, the scaling center can be chosen and the scaled boundary finite elementmethod is applied to each substructure independently. Each such substructure iscombined together so that in effect, the whole geometry is analyzed. The concept of the scaled boundary transformation is that, by scaling the boundaryin the radial direction with respect to a scaling center O, with a scaling factor smallerthan 1, the whole domain is covered. For bounded domains, the upper and lowerbounds of the scaling factor are 1 and 0 respectively. For the problems dealing withunbounded domains, the corresponding lower and upper bounds of the scaling factorare 1 and ∞ . The Figure (2a) and (2b) shown below, illustrate the concept of the scaledboundary transformation.
Fig.(2a) Unbounded Medium with Fig.(2b) Scaled Boundary(Section). Scaling center inside the medium (section).
3 The scaling applies to each surface finite element. Its discretized surface on theboundary is denoted as Se (superscript e for element). Continuous scaling of theelement yields a pyramid with volume Ve. The scaling center O is at its apex. The baseof the pyramid is the surface finite element. The sides of the pyramid forming theboundary Ae follow from connecting the curved edge of the surface finite element tothe scaling center by straight lines. No discretization of Ae occurs. Assembling all thepyramids by connecting their sides, corresponds to enforcing compatibility andequilibrium conditions. This results in the total medium with volume V and the closedboundary S. No boundaries Ae passing through the scaling center remain.Mathematically, the scaling corresponds to a transformation of the coordinates for eachfinite element. This results in two local curvilinear coordinates along thecircumferential directions and one dimensionless radial coordinate representing thescaling factor. This transformation is unique due to the choice of the scaling centerfrom which the total boundary of the geometry is visible [1,2].The key advantages of this novel method [1,2] are:a) Reduction of the spatial dimension by one, reducing the discretization effort.b) No fundamental solution required which permits general anisotropic material to be
addressed and eliminates singular integrals.c) The method being analytical in the radial direction, permits the radiation condition
at infinity, to be satisfied exactly for unbounded media.d) No discretization on that part of the boundary and interfaces between different
materials passing through the scaling center.e) Converges to the exact solution in the finite-element sense in the circumferential
directions.f) Tangential continuity conditions at the interfaces of different elements are
automatically satisfied.
The scaled boundary transformation is basically a relation between the derivativesin the cartesian coordinates and the derivatives expressed in the scaled boundaryvariables. [1,2]
3. The scaled boundary finite element method in electromagnetics:
The scaled boundary transformation equations [1,2] are quite general, and it can beapplied to differential equations governing the phenomena in any discipline. Thisfeature of the scaled boundary transformations is used in the reformulation of the novelmethod for electromagnetics [5]. However, the actual formulation of the scaledboundary finite-element equation depends upon the additional constraints that arespecific to the discipline, which are to be satisfied. This approach ensures that, thescaled boundary finite-element equation thus framed, takes into account, the specificfeatures of that discipline. Hence, a closest possible representation of the system,represented by the original differential equations along with the constraints in the formof boundary conditions, is achieved.
4
In this context, when the scaled boundary is reformulated in electromagnetics in Hformulation, it is necessary that apart from satisfying the essential boundaryconditions, the fields should satisfy the solenoidality property of the magnetic field [5].This condition should be necessarily incorporated while formulating the scaledboundary finite-element equation in electromagnetics [5]. This is necessary so that nospurious solutions occur as eigen solutions of the boundary value problem [5]. The distinct feature of the scaled boundary finite element method when formulatedin electromagnetics is that, the accuracy of the eigen solutions depend upon thenumber of terms included in the radial expansion of the field. This is apart fromdepending on the conventional factors like the choice of the interpolation functions,size of the element, accuracy of the Jacobian transformation, etc, as observed in thetraditional vector finite-element method [5]. This fact is demonstrated numerically insection 3.3.1 The Scaled Boundary Finite Element Formulation for Cavity Structures: The boundary value problem representing the cavity structures form a separateclass. The ideal metallic cavity structures represent the total confinement of theelectromagnetic field in a volume of space bounded externally by metallic surfaces.The eigen-modes of the cavity structures are in fact the standing wave field patternscorresponding to various eigen values. The tangential component of the electric fieldand the normal component of the magnetic field vanish at the boundary comprising themetallic surfaces. It is assumed that, the metallic surface is a perfect conductor. In this section, the scaled boundary finite-element equation is developed for ageneral metallic cavity structure, and a numerical implementation is illustrated for thecase of a spherical metallic cavity.
3.1.1 Theory: The vector helmholtz equation in H formulation [6] is given by
where εr and µr are the local material properties corresponding to the relativepermittivity and relative permeability of the medium respectively. The associatednatural boundary condition [6] is given by
The natural boundary condition implies that the magnetic field is purely tangential tothe bounding metallic surface. The natural boundary condition implies that themagnetic field is purely tangential to the bounding metallic surface. 1n denotes unitnormal to the surface under consideration.
(1a) 021 =−×∇×∇ − HH rr k µε
(1b) 0=×∇⋅ H1 n
5
The associated variational form of Eq.(1) is given by, [6]
In the above expression, Ω denotes the domain under consideration.The variational functional given in (2) is made stationary, with respect to the unknowncoefficients in the expansion of H, which corresponds to the solution of the vectorhelmholtz equation. Expanding the i, j, k components of H in terms of thevariables (ξ,η,ς) as [5]
The functions f1(ξ), f2(ξ) and f3(ξ) in the form of the power series expansion in ξ as [5]
The form of the functions h(η) and h(ζ) are given in [7].
( ) ( )( ) )2( d k-21 21 Ω⋅×∇⋅×∇= ∫
Ω
− HHHH rrF µε
theare )(h ),(h and ts,
radial on the depending
ii η
(3.7c)
(3.3a) (3a) )(h)(hh)(f),,(H0 0
1^ ζηξζηξji
m
i
n
jiij)(i,ii
^^^∑∑= =
=
(3b) )(h)(hh)(f),,(H0 0
2^ ζηξζηξjj
m
i
n
jijj)(i,jj
^^^∑∑= =
=
(3c) )(h)(hh)(f),,(H0 0
3^ ζηξζηξjk
m
i
n
jikj)(i,kk
^^^∑∑= =
=
theare )(h ),(h and ts,coefficienunknown are h h h and , coordinate
radial on the depending functions radialunknown are f ,f ,f functions thewhere 321
iij)(i,kj)(i,jj)(i,i
^^^ η
0.n and 0m and ly respective and in s variation thengrepresenti , of functions variablesingle
≠≠ζηζη
(4a) a)(f kk1 ξξ =
(4b) b)(f kk2 ξξ =
(4c) c)(f kk3 ξξ =
6The solenoidality condition for the magnetic field is given by,
where µ is the permeability of the medium.
When µ is a non-zero scalar constant,
Rewriting the Eq.(5b) in terms of scaled boundary transformation in 3-D [1 ] andusing the expressions given in (3) & (4), and equating the coefficients of the likepowers of ξ, the relationship between the unknown coefficients of the power series ofthe radial variable ξ is given as [5]
…(6)
In Eq. (6) N1, N2, N3 correspond respectively to the double summation part of the i, j,and k cartesian components in the expansion for H given in Eq.(3) . The expression forck is substituted in the variational functional written in terms of the scaled boundaryvariables. The radial coordinate ξ is independent of the two circumferentialcoordinates η and ς. Integrating the fnctional with respect to ξ with its lower andupper limits being 0 and 1, makes Eq.(3.20) entirely in terms of the circumferentialvariables η and ς. The functional entirely expressed in terms of the surface integralswill be of the form [5]
where the letters with a prime denote the terms after the integration with the radialvariable ξ. An important observation that is to be noted is that, the terms in (7)contains only the surface discretization parameter |J| in the finite-element integrals,even for general 3-D structures [5] unlike the conventional finite-element method.
(5a) 0).( =∇ Hµ
(5b) 0. =∇ Hµ
++
+++
++
=
ζη
ζηζη
ζζ
ηη
ξξ
ζζ
ηη
ξξ
ζζ
ηη
ξξ
ddN
n|J|
gd
dNn
|J|g
kNn|J|
g
ddN
n|J|
gd
dNn
|J|g
kNn|J|
gb
ddN
n|J|
gd
dNn
|J|g
kNn|J|
ga-
c33
3
222k
111k
k
zzz
yyyxxx
. 0kfor valid ≥
[ ] (7) d d VUTkSRQ
PNMLKJIHGFEDCBA21
'''r
20
'''
''''''''''''''
),(
'
ζηζη
++−++
+++++++++++++++∫
7The expression given in (7) is evaluated for every surface element characterized by thecircumferential variables η and ς. The normal continuity of the fields between theelements along the radial direction, wherever applicable is enforced. The variation withrespect to each undetermined coefficient is set to zero. This process leads to a set oflinear equations of the form
The Eq.(8) is a standard form of the matrix eigen value equation which can be solvednumerically for the unknowns contained in h .
3.1.2 Numerical Implementation: The theoretical formulation is implementednumerically for the case of a spherical metallic cavity, with air being the dielectricmedium. The spherical metallic cavity considered for the numerical implementation isshown in Fig.(3a). For the finite element discretization of the surface, an eight nodecurvilinear quadrilateral elements were used with the mesh of one octant consisting ofthree finite elements. The discretized boundary of the solid sphere of one octant isshown in Fig.(3b) in the following page. The integration involving the scaled boundaryvariables were done numerically using 5 point gaussian quadrature. The eigen valueequation resulting from assembling the element matrices were solved by using thestandard LAPACK [8] collection of Fortran subroutines. The number of terms wereused in the radial expansion of the fields were five. [5]
Fig.(3a) Spherical metallic Cavity
(8) 0 Y W 20 =+ hh k
8
Fig.(3b) Finite Element mesh of one octant of boundary of solid sphere.
The resonant frequencies of TM 011 mode for the spherical cavity were computed byvarying the radius of the spherical cavity, and the numerically obtained results showclose agreement to the values obtained by a field theoretical analysis [9], and is shownbelow in Table .(3c) . By theoretical modal field analysis, the resonant frequency fr fora spherical cavity of radius 3 cms for TM (even) (011) = TM (even) (111) = TM(odd) (111)and it is equal to 4.367 x 10 9 Hz [9] . Accordingly, the resonant frequency obtainedthrough the scaled boundary formulation for the spherical cavity of radius 3cms for theabove mentioned modes were also constant with a value of 4.3668 x 109 Hz [5].Another important feature of the scaled boundary finite-element formulation, is theeffect of the number of terms in the radial expansion of the field variable on theaccuracy of the eigen values.
Table (3c) showing the agreement between the theoretical and the numerical values of theresonant frequency of TM (011) mode.
S.No Radius of the sphericalmetallic cavity.
a (in cms)
Resonant frequency computedfor the TM011 mode by theory.
fr (10 9 Hz)
Resonant frequencycomputed by scaled
boundaryFinite element method.
Fr (10 9 Hz)1 3 4.369 4.3684
2 4 3.277 3.278
3 5 2.622 2.6215
4 6 2.185 2.1848
9Table (3d), shown below, shows the effect of increase in the number of terms in theradial expansion of the field variable, on the accuracy of the resonant frequency.
Table (3d) showing the effect of increase in the number of terms in the radial expansion of the fieldvariable, on the resonant frequency of TM (011) mode. [5]
No. of terms inthe radial
expansion of thefield variable
Radius of thesphericalmetalliccavity.
a (in cms)
Resonant frequencycomputed for the TM011 mode
by theory.fr (10 9 Hz)
Resonant frequencycomputed by scaled
boundaryFinite element method.
Fr (10 9 Hz)
5 3 4.369 4.3684
6 3 4.369 4.3687
7 3 4.369 4.3689
8 3 4.369 4.3690
From Table (3d), it can be inferred that, the number of terms in the radial expansion ofthe field variable, has a marked influence on the accuracy of the resonant frequency. Itis observed from the above table that, the increase in the number of terms in the radialexpansion of the field variable, is accompanied by the corresponding increase in theaccuracy of the eigen values [5]. A close agreement is observed between thetheoretical values of the resonant frequency and those calculated by the scaledboundary finite element formulation for cavity structures [5]. The scaled boundaryfinite element formulation developed in this section, for cavity structures, isindependent of the geometry. Also, this method involves only the surfacediscretization unlike the finite element method which involves discretization in threedimensions.
4. Conclusion: The scaled boundary finite element method is a novel semi analyticalmethod based on finite elements, originally developed in the field of civil engineeringto study problems pertaining to elastodynamics and Soil structure interaction. Thisnovel method, based on the weighted residual approach, is reformulated to suitproblems in electromagnetics. The scaled boundary finite element method isformulated to analyze cavity structures. The closeness of the numerical resultsobtained from the scaled boundary finite element method to those obtained fromanalytical approach, proves the validity of the novel method. An important consequence of the method being semi-analytical is that, the accuracyof the numerical values depend not only on the element size as in the conventionalfinite element method, but also on the number of terms that are used in the radialseries expansion of the fields.
10This enables to get accurate numerical results even by increasing the number of termsin the radial expansion of the fields without tampering with the element size. Thescaled boundary finite element formulation in electromagnetics is further developed toanalyze wave-guides, VLSI interconnects, and periodic structures.
Acknowledgements: The first author thank Prof. John. P. Wolf, Institute of Hydraulicsand Civil Engineering, Swiss Federal Institute of Technology, Lausanne, Switzerland,and Dr. Chongmin Song, Department of Environmental and Civil Engineering,University of New South Wales, Australia, for their valuable suggestions andproviding their research articles on Scaled Boundary Finite Element Method. Theauthors thank the Council for Scientific and Industrial Research (CSIR), New Delhi,for its financial support for the research project.
References:
[1] Chongmin Song and John P. Wolf, “The Scaled boundary finite-element method- alias Consistent infinitesimal finite-element cell method – for elastodynamics”,Computer Methods in applied mechanics and engineering, (1997), No.147 , pp.329-355.
[2] John. P. Wolf and Chongmin Song, “The scaled boundary finite element method – a primer : derivations”, Computers and Structures , 78, pp.191-210, 2000.
[3] Chongmin Song and John P. Wolf, “Consistent Infinitesimal Finite-Element Cell Method: Three-Dimensional Vector Wave Equation”, International Journal for Numerical Methods in Engg, (1996), Vol.39, pp.2189-2208.
[4] Andrew J. Deeks, John P. Wolf, “An h- hierarchical adaptive procedure for the scaled boundary finite-element method- for elastodynamics”, Int. J. Numer. Meth. Engng, (2002), 54, pp.585-605.
[5] V.S. Prasanna Rajan, “The Theory and application of a Novel Scaled Boundary Finite element method in computational electromagnetics”, Ph.D thesis, submitted to the school of Physics, University of Hyderabad, India, on Dec.2002.
[6] P.P. Silvester , R.L. Ferrari, “Finite elements for Electrical Engineers”, 3rd Ed, Cambridge University Press, (1996), pp.96-99.
[7] Ibid., pp.308.
[8] LAPACK users guide, 3rd Ed, SIAM, Philadelphia.
[9] C.A. Balanis, “Advanced Engineering Electromagnetics”, pp.560-562.
This is to certify that Dr. V. S. Prasanna Rajan, worked in this organization from 1 st
July 2009 to 30th April 2011 as a Consultant, on a consolidated salary of Rs.
30,000/- per month ( Rupees Thirty Thousand only).
