CENTER FOR COMPUTATIONAL ELECTROMAGNETICS and ELECTROMAGNETICS LABORATORY

ANNUAL PROGRESS REVIEW 2005

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TABLE OF CONTENTS CHAPTER 1. GENERAL INTRODUCTION ......................................................................1 1. Director’s Foreword ........................................................................................................................... 1 2. The Laboratory and Its Staff............................................................................................................... 1 3. Teaching Activities, 2005................................................................................................................... 2 4. Computational Facilities..................................................................................................................... 3 5. Experimental Facilities....................................................................................................................... 3 6. Research Activities............................................................................................................................. 4 7. Financial Support ............................................................................................................................... 5 CHAPTER 2. SAMPLE RESEARCH PROJECTS.......................................................................... 6 Introduction ............................................................................................................................................ 6 Latency Insertion Method with Frequency Dependent Effect................................................................ 7 A Domain Decomposition Scheme to Solve Integral Equations Using Equivalent Surfaces .............. 14 Time-Domain Finite-Element Modeling and Simulation of Broadband Antennas.............................. 19 Comprehensive Electromagnetic Modeling and Transient Analysis of On-Chip Noise Generation and Coupling...................................................................................................................... 23 Antenna and Systems Research in the Electromagnetics Laboratory: Enabling Multifunction Operation in Portable Devices, Sensors, and High Performance Arrays ............................................. 29 CHAPTER 3. PUBLICATIONS LIST AND SEMINAR SERIES....................................37 Journal Publications List, 2005 ............................................................................................................ 37 Electromagnetic Seminar Series, 2005................................................................................................. 40

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CHAPTER 1

GENERAL INTRODUCTION 1. Director’s Foreword In 2005, we did research in various areas in electromagnetics and optoelectronics. In antenna research, progress was made in antenna arrays, antennas for wireless and various sensing applications. Much computational electromagnetics research on antennas and circuits have been performed as a result of demand in the area. Work continues to progress in the optoelectronics area on slow light and quantum cascade lasers. In the same year, Professor Jennifer Bernhard was selected for the U. S. Defense Science Study Group, Sponsored by DARPA, with a tenure from 2006-2007. She has also been selected as UIUC College of Engineering Willett Faculty Scholar for 2005-2008. Professor Shun Lien Chuang continues to serve as the IEEE Lasers and Electro-Optics Society (LEOS) Distinguished Lecturer for 2005-2006. I was selected to serve as the IEEE Antennas and Propagation Society Distinguished Lecturer for 2005-2006, as well as been elected the Y.T. Lo Endowed Chair Professor for the ECE Department.

W.C. Chew 2. The Laboratory and Its Staff Professors:

• Andreas Cangellaris • Weng Cho Chew (Director) • Shun Lien Chuang • Jianming Jin • Eric Michielssen • Jose Schutt-Aine • Paul Klock (Emeritus) • S. W. Lee (Emeritus, Center Scientific Advisor) • Paul Mayes (Emeritus)

Associate Professors:

• Jennifer Bernhard Research Scientists and Visiting Assistant Professors:

• Aosheng Rong Postdoctoral Research Associates: Jin Kyu Byun Ki Hyuk Kim Shu Qing Li Vitaliy Lomakin Rickard Petersson Guoqiang Shen Hui Su Meisong Tong Gong Li Wang Zhiyong Zeng

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Visiting Scholars and Professors: Jinkyu Bang I-Ting Chiang Chia-Hsin Chao Takafumi Fujimoto Levent Gurel Wen Ying Ruan Jukka Sarvas

Research Assistants: Haritha Akkineni Graham Alvey Francesco Andriulli Phillip Atkins Hakan Bagci Joe Banasiak Qin Chen Matt Chuang In Jae (Jason) Chung Joon Chung Dan Connolly Davi Correira Garvin Cung Clayton Paul Davis Zhichao Deng Limin Dong Eric Dunn Matthew Fisher Joshua Fladie Rong Gao Andrew Hesford Erik Hoffman Ran Hu Gregory Huff Jai-Yong Ihm Peilin Jiang Kiersten Kerby Jungho Kim Dmitri Klokotov Varvara Kollia Peter Kondratko Vasileios Kourloulos Samuel Kuo Shih-Hao Lee Maytee Lerttamrab Jian Li Maokun Li Yujia Li Yuan Liu Zheng Lou Meng Lu Mingyu Lu George Manetas Kaiyu Mao Jackie Martin Yidnek Mekonnen Tolga Memioglu Jun Meng Pavle Milosevic Serge Minin Se-Jung Moon Shin Mou Adam Petschke Zhiguo Qian Anand Ramachandran Aravind Ramachandran Morgan Reeder Tyrone Roach Johannes Russer Michael Saville Nicholas Soldner Gregory Sorenson Prasad Sumant Lin Sun Aaron Wallace Rui Wang Anne Woo Hong Wu Jie Xiong Ali Yilmaz Shenghui Zhang Zhuohui Zhang Yu Zhong

Secretarial Staff: Karen Kuhns

3. Teaching Activities, 2005 The teaching obligation of the Laboratory includes: Undergraduate Courses:

• Lines, Fields, and Waves • Automated Microwave Measurements • Electromagnetic Waves and Optics • Antennas • Sensors and Instrumentation

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• Microwave Devices and Circuits Graduate Courses:

• Electromagnetic Waves and Radiating Systems • Analytic Foundations of Electromagnetic Theory • Integrated Optics and Optoelectronics • Theory of Microwave and Optical Waveguides • Waves and Fields in Inhomogeneous Media • Advanced Antenna Theory • Advanced Electromagnetic Diffraction and Radiation • Computational Electromagnetics • Electromagnetic Modeling and Simulation of Electronic Packaging

The undergraduate courses provide a balanced education for undergraduates. The graduate courses are related to the research topics of the professors. Students are often required to do a term project to gain first-hand experience in the field. 4. Computational Facilities The Center for Computational Electromagnetics and Electromagnetics Laboratory is endowed with the following computational resources:

• 1 mini-supercomputer, 16-node Intel cluster with 2 GHz processors, 8 GBytes of memory, 640 GBytes of storage.

• 1 mini-supercomputer cluster with 32 nodes Intel Pentium III processors 850 MHz, 100 Mbps Ethernet (donated by Intel).

• 10 SUN Blade 2000 Workstations with 50 GB RAM. • 6 Personal DEC station 500 MHz with 256MB RAM 250 and 3 GB HD. • 4 DEC Alpha station 250 4/266 series Workstations 192 MB RAM, 1.44 MB Floppy, 600 MB

CD-ROM, 1.05 GB SCSI Disk. • 1 SGI Indigo 2 Extreme Workstation, 250 MHz 64 MB RAM, 2 GB Disk. • 2 SGI Indy Workstations, 100 MHz, R4600PC, 32 MB RAM, 535 MB Disk.

In addition, there are numerous SUN workstations, DEC workstations, Apple Macintosh, PC's with Windows 95/NT or LINUX. Furthermore, staff members can access supercomputing facilities at the National Center for Supercomputing Applications (NCSA), as well as the Computational Science and Engineering Program on campus. Students have access to hundreds of engineering workstations in Engineering Workstation Laboratories in the College of Engineering. 5. Experimental Facilities The Electromagnetics Laboratory has several vector network analyzers including a HP 8510D network analyzer (45 MHz-50 GHz) with a Cascade Microtech probe station and an Agilent PNA series network analyzer (E8363GB, 10 MHz-40 GHz). This covers the P, S, X, Ku, K, Ka and Q bands for microwave and millimeter-wave measurements. A small portable anechoic chamber for 26 - 40 GHz uses this network analyzer for high frequency antenna measurements. Through the support of the DURIP program,

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the Laboratory has assembled a state-of-the-art phased array bit error rate (BER) testing system. The system can be configured for either traditional coherent continuous wave antenna testing or for bit error rate testing. The BER testing system can implement a variety of standard or user-defined modulations, noise impairments, and propagation models with the help of specialized software from Agilent. This unique facility will enable us to apply new findings to optimize system behavior and to create entirely new avenues of research into the relationships between antenna and array characteristics, signal processing, and achievable system performance. The BER testing system includes an E4443A PSA series spectrum analyzer, a E4438C ESG vector signal generator, and a E8247C PSG CW signal generator, all from Agilent. The Agilent PNA series network analyzer (E8363GB, 10 MHz-40 GHz) is also used for circuit and automated antenna characterization with the Laboratory's large anechoic chamber. For time-domain measurements, the lab is equipped with a high-bandwidth digitizing scope 50 GHz HP 54750A 2-channel 18 GHz differential time-domain reflectometer HP 54754A. In addition, there are an HP 54120B digitizing oscilloscope, an HP8593E spectrum analyzer, a high-speed Tektronix time-domain reflectometer and digitizing scope, and several high-speed pulse generators for time-domain high-speed digital circuits simulation and broadband radar measurement systems. A T-Tech quick circuit fabrication system enables rapid prototype circuit and planar antenna development. All this equipment is controlled by personal computers, many of them Pentium class PC's, making the collection of measurement data very convenient. In addition, there is an Optoelectronic Laboratory that contains many lasers and optical equipment for optoelectronic device characterization and fiber optical measurements. In particular, there is an HP70951B optical spectrum analyzer, SPEX monochromators, Q-switched YAG laser, HeNe laser, a high resolution Fourier transform infrared spectrometer, as well as photoluminescence systems for spectral measurements. There are high-speed setup for microwave modulation of optical devices and optical power versus current measurement system. The fiber optics facilities consist of a fusion splicer and fiber optics tools, optical power measurement system as well as a nanopositioning system. Other optical equipment includes:

• 1250 SPEX PMT (photon counting) based high resolution optical spectroscopy system (vis-near IR)

• Advantest Q8347 optical spectrum analyzer, high resolution, Michelson-interferometer, (vis-near IR)

• Agilent: 86141B, 70951B optical spectrum analyzer • HP 86120B multi-wavelength meter • 8703A lightwave component analyzer (O/E, E/O, O/O, E/E network analyzer) • 86100A Infiniium DCA with 10GHz optical and 20GHz electrical modules (86106A) • 1300 nm and 1500 nm external cavity tunable wavelength sources • High speed probes for direct semiconductor device modulation • 0-30 GHz high speed optical detectors (600nm-1650nm)

6. Research Activities The research activities in the laboratory can be divided roughly into five categories:

• Computational Electromagnetics and Applications (Chew, Jin, Michielssen) • Electromagnetic Circuits Simulations and Modelling (Cangellaris and Schutt-Aine) • Optics, Photonics and Optoelectronic Devices (Chuang) • Antennas and Wireless Communication (Mayes and Bernhard) • Inverse Scattering, Subsurface Sensing, and Imaging (Chew)

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In addition, Professor Jin has special interest in application of computational electromagnetics to bioelectromagnetics, MRI and antennas. Professor Michielssen investigates the use of genetic algorithms for optimization, as well as the application of computational electromagnetics to micro-electromechanical sensors, circuits and antennas. Professor Chew is interested in computation involving antennas, microstrip antennas and microwave integrated circuits and the related applications. Professor Chuang established an Optoelectronics Laboratory for fiber optical networks and semiconductor quantum optical devices. Professor Mayes researches on broadband antennas. Some sample research projects are described in Chapter 2. 7. Financial Support The University of Illinois at Urbana-Champaign is a state-owned university supported by the state of Illinois. Hence, the academic-year support of the professors in the Laboratory is paid by the state. A large part of the support also comes from U.S. government agencies. For year 2005, the Center for Computational Electromagnetics is partially supported by a grant from the DARPA VET Program, a grant from the AFOSR MURI program. In addition, faculty in the Electromagnetics Laboratory have individual principal investigator grants from the National Science Foundation, NASA, the Office of Naval Research, the Army Research Office, the Army Research Laboratory, Air Force Research Laboratory, DOD High Performance Computing Modernization Program (HPCMP), and Sandia National Lab. There are also contracts, donations and gifts from industry, most notably from General Motors, Texas Instruments, Hewlett Packard, Intel, Mentor, Qualcomm, Northrop Grumman, Lockheed-Martin, Association of American Railroads, Anvik, Ball Aerospace Corp., Amphenol T&M Antennas, Phonak Communications, SRC, Cadence, and SAIC. Many students are also supported by fellowship programs (i.e., Motorola, Vodafone etc.) as well as teaching assistantships from the Department of Electrical and Computer Engineering.

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CHAPTER 2

SAMPLE RESEARCH PROJECTS This Chapter describes sample projects from active researchers in the laboratory. Many of the researchers in the laboratory are involved in a number of projects in addition to those described here. More information about their research can be gleaned from the publications list in the next chapter. Other than the reported research work here, much work is on improving fast algorithms for electromagnetic scattering and simulation. For instance, fast algorithms are applied to integrated circuits and package simulation, novel material, antenna and time-domain computation. Efforts related to the hybridization of finite element, high frequency, and integral equation methods are also ongoing as well as research on inverse scattering, subsurface sensing and nondestructive testing. In addition, we study optical fibers and waveguides and their use in smart structures.

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Latency Insertion Method with Frequency Dependent Effect

Z. Deng and J. Schutt-Ainé

1. Introduction The frequency-dependent behavior of circuit element is a critical parameter in the simulation of integrated circuits. With higher processing speeds, digital signals have spectrum components that easily extend into the GHz range. The simulation of such circuits can be prohibitive and often times requires several days of CPU time on a traditional workstation. The latency insertion method was recently developed to simulate the high-frequency response of large networks in the time domain [1]. The method makes use or introduces reactive latency in all branches and nodes of a circuit to generate update algorithms for the voltage and current quantities. The updating of branch currents and node voltages is performed in a leapfrog manner similar to the Yee algorithm used in the finite-difference time-domain (FDTD) method [7]. As a result, LIM has linear computational complexity and is thus substantially faster than the traditional matrix-vector product based methods such as SPICE. In order to handle the skin effect of the conductors, a simple formulation is derived and verified by the measurement result. The paper is organized as follows. In Section 2, we review the basic formulation of the LIM method. Next, in Section 3, a formulation is derived to model the skin effect. In Section 4, a simulation example is performed and compared with measurements. 2. Basic Formulation of LIM In the LIM algorithm [1], the linear elements in a branch linked to a node (Fig. 1.) are discretized according to the following relations.

1

1 / 2 1 / 2 1 / 2n nij ij n n n n

ij i j ij ij ijI I

L V V R I Et

++ + +⎛ ⎞−

= − − +⎜ ⎟⎜ ⎟∆⎝ ⎠ (1)

1 / 2 1 / 2

1 / 2 1 / 2

1

in n Mi i n n n

i ij i i ik

V VC I G V Ht

+ −+ +

=

⎛ ⎞−= − − +⎜ ⎟∆⎝ ⎠∑ (2)

The nonlinear elements of a branch linked to a node (Fig. 2) are discretized as below:

( )1

1 / 2 1 / 2 1 1 / 2 1 1n nij ij n n n n n

ij i j ij ij ij ijI I

L V V R I E f It

++ + + + − +⎛ ⎞−

= − − + −⎜ ⎟⎜ ⎟∆⎝ ⎠ (3)

1 / 2 1 / 2

1 / 2 1 / 2 1 / 2

1

( )in n M

i i n n n ni ij i i i i

k

V VC I G V H f Vt

+ −+ + +

=

⎛ ⎞−= − − + −⎜ ⎟∆⎝ ⎠∑ (4)

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Figure 1: Linear branch and node

Figure 2: Nonlinear branch and node

3. Skin Effect Implementation The generalized branch and nodes LIM equations showing space dependence can be written in the S domain as below:

( ) , ( ) ( ) ( )VZ s I Z s R s sL sx

∂= − = +

∂ (5)

( ) IsC G Vx∂

+ =∂

(6)

In this paper, the frequency dependent effects of dielectric loss (G) and capacitance (C) are ignored. It means that C and G are independent of frequency. When the frequency dependent losses of the conductor are taken into account, the resistance R and the inductance L vary with frequency. This dependence can be analytically described using various methods. In particular, a rational function expansion can be used to model the frequency-dependent of conductors as can be observed in [4]-[5]. This expansion could be used to model the frequency dependent C and G.

01

( )Q

qe

qq

RZ s R sL

s P== + +

−∑ (7)

For modeling skin effect, the above formulation is replaced by a simpler and more efficient approximation used in [2] in which the frequency dependences of the resistance R and inductance L are shown as in (8)-(11).

( ) ( ) ( )Z s R s L s= + (8)

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0( ) , ( ) ( )s i eR s R R s L s L s L+ + (9)

In the above equations, 0R is the constant dc resistance per unit length (p.u.l.); eL is the constant external

inductance p.u.l. and iL is the internal inductance p.u.l., which decrease with s . The skin effect can then be represented by ( )iZ s , which is defined as in (10)-(11).

( ) ( )i eZ s Z s sL= + (10)

( ) ( ) ( )i iZ s R s sL s+ (11)

Then the frequency-domain representation is given by

0( ) ( ) ( )i s iZ s R R s sL s= + + (12)

Since 1/iL s∝ , the frequency dependent impedance can be expressed as in [2]

( )iZ s A B s= + (13)

0 , ( ) , ( ) / 2s iA R R f B f L f B fπ π= = = (14)

Equations (5) and (6) are transformed to yield

( )( ) ( ) ( )e i

V ssL I s Z s I sx

∂+ = −

∂ (15)

( )( ) ( ) I ssCV s GV sx

∂+ =

∂ (16)

The term ( ) ( )iZ s I s translates to a convolution in the time domain because 11

s tπ↔

( ) ( ) ( ) ( )iBZ s I s AI s sI ss

= + (17)

0

1 ( )( ) * ( ) ( )( )

ti

B I tZ t I t AI t dt

τ ττπ τ

∂ −⇒ = +

∂ −∫ (18)

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The integral in (18) can be evaluated using piecewise constant convolution techniques such as in [3], which have second-order accuracy.

( 3/ 2)1/ 2 1

100 ( 1/ 2)

1 1( ) * ( )mn

ni t n t

t n t n mm m

B t I IZ t I t AI d dt t

τ τπ τ τ

+−

= ∆= = − −= +

⎡ ⎤∆ ∂ ∂⎢ ⎥≅ + +∂ ∂⎢ ⎥⎣ ⎦

∑∫ ∫ (19)

After substitution of (19) into (15) and discretization, the branch current update equation takes the form

( )

11/ 21/ 2 0

1/ 20 1/ 2 1 1/ 2

/ 2

1 / 2

n ek

n n n nek k k k

L BI At tL B BA I V V

t xt t

π

π π

−++

−+ + +

⎛ ⎞= + + Ψ⎜ ⎟∆ ∆⎝ ⎠⎡ ⎤⎛ ⎞

− + Ψ + − − Ψ⎢ ⎥⎜ ⎟∆ ∆∆ ∆⎝ ⎠⎣ ⎦

(20)

where the variables 0Ψ and 1/ 2

nk+Ψ are defined as

( )( 3/ 2)1/ 2 1

1/ 2 3/ 20 1/ 2 1/ 2 1/ 2

00 ( 1/ 2)

1 1, mn

n n m n mk k k

m m

d I I dτ ττ τ

+−− − − −

+ + += +

Ψ Ψ −∑∫ ∫ (21)

We next transform the integral into a recursive convolution form. This is done by approximating with a series of exponentials [4].

( )( 3/ 2) 1/ 2

01 1( 1/ 2) 0

1 1exp( ), m P P

i i ii im

Pz m d a b m d aτ ττ τ

+

= =+

≅ Ψ = ≅∑ ∑∫ ∫ (22)

By substituting (22) into (21), we have a recursive convolution updating equation

( )

( )

1 1/ 2 1/ 21/ 2, 1/ 2 1/ 2

01/ 2 1/ 2

1/ 2, 1/ 2 1/ 2

exp( )

exp( ) , 1, ,

nn n m n mk i k k ii

mn n nk i i i k k

I I b ma

b a I I i P

+ + − − −+ + +

=

+ −+ + +

Φ = −

= Φ + − =

∑ (23)

and 0 1

1/ 2, 1/ 2, 0k i k i+ +Φ = Φ = for any i and k. This process discretizes equation (16), which then provides final LIM update equations implementing the skin effect. The branch currents and node voltages are updated by using

11

( )

11/ 21/ 2 0

1/ 20 1/ 2 1 1/ 2,

1

/ 2

1/ 2

n ek

Pn n n nek k k k i

i

L BI At t

L B BA I V Vt xt t

π

π π

−++

−+ + +

=

⎛ ⎞= + + Ψ⎜ ⎟∆ ∆⎝ ⎠

⎡ ⎤⎛ ⎞− + Ψ + − − Φ⎢ ⎥⎜ ⎟∆ ∆∆ ∆⎝ ⎠⎣ ⎦

∑ (24)

( )1 1 1/ 2 1/ 21/ 2 1/ 2

1( ) ( )2 2

n n n nk k k k

C G C GV V I It t x

+ − + ++ −

⎡ ⎤= + − + −⎢ ⎥∆ ∆ ∆⎣ ⎦ (25)

where ( )1 1/ 2 1/ 2

1/ 2, 1/ 2, 1/ 2 1/ 2exp( ) , 1, ,n n n nk i k i i i k kb a I I i P+ + −+ + + +Φ = Φ + − = .

Using the above updating equations, LIM can handle conductors with skin effect efficiently.

4. Simulation Example To validate the above general formulation for skin effect in LIM, we use an example in [6], in which a 100-meter twisted-pair cable is considered with the parameters shown in Table 1.

0Z ( )Ω

eL ( / )nH m

C ( / )nF m

relativev ( / )m ns

0R ( / )mΩ

SR

( / - )m GHz ρΩ ρ maxf

( )GHz100 476.19047619 0.047619048 0.7 0 16 0.5 0.2

The circuit configuration is shown in Fig. 3. The cable in Fig.3 is a 100-meter twisted-pair cable with far end open circuited. The magnitude of the excitation pulse is 2.7 V, the rise and fall times are 1 ns, the pulse width is 80 ns. The cable is modeled using 1000 RLC blocks, as shown in Fig. 4. The simulation results using our formulation and the measurement results from [6] are shown in Fig. 5 and Fig. 6. 5. Summary

This paper extends the capability of the LIM algorithm to frequency-dependent conductors. A straightforward formulation for handling the skin effect within the LIM algorithm was derived and validated through measurements.

V1

Vs

Zs=50 OhmCable

Near end Far end

Lij(f) Vj

Vi

Rij(f)

Iij

Ci Gi

Table 1: Twisted-pair cable parameters

Figure 3: Transmission line configuration for both simulation and

measurement Figure 4: One segment of the cable

model

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0 500 1000 1500 2000-1

0

1

2

3

Time (ns)

Vol

tage

(vol

t)

Input pulseNear End

0 500 1000 1500 2000-1

0

1

2

3

Time (ns)

Vol

tage

(vol

t)

Far End

References [1] José E. Schutt-Ainé, “Latency insertion method (LIM) for the fast transient simulation of large

networks,” IEEE Trans. Circuits Syst., vol. 48, pp. 81-89 Jan. 2001. [2] N. S. Nahman, and D. R. Holt, “Transient analysis of coaxial cables using the skin effect

approximation A + B s ,” IEEE Trans. circuit theory, vol. 19, no. 5, pp. 443-451, Sept. 1972. [3] J.W. Schuster, and R.J. Luebbers, “An accurate FDTD algorithm for dispersive media using a

piecewise constant recursive convolution technique,” Proc. IEEE Int. Symposium AP-S, vol. 4, pp. 2018 – 2021, June 21-26 1998.

[4] J. H. Beggs, R. J. Luebbers, K. S. Yee, and K. S. Kunz, “Finite-difference time-domain implementation of surface impedance boundary conditions,” IEEE Trans. Antennas Propagat., vol. 40, no. 1, pp. 49-56, Jan. 1992.

[5] K.M. Coperich, J. Morsey, V.I. Okhmatovski, A.C. Cangellaris, and A.E. Ruehli, “Systematic development of transmission-line models for interconnects with frequency-dependent losses,” IEEE Trans. MTT, vol. 49, no. 10, part 1, pp. 1677 – 1685, Oct. 2001.

Figure 5: Simulation results using LIM

skin-effect formulations Figure 6: Measurement result

(a) near end (b) far end

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[6] José E. Schutt-Ainé, “High-Frequency Characterization of Twisted-Pair Cables,” IEEE Trans. Communications, vol. 49, no. 4, pp. 598-601, April 2001.

[7] K. S. Yee, “Numerical solution of initial boundary value problems involving Maxwell’s equation in isotropic media”, IEEE Trans. Antennas Propagat., vol. AP-14, pp. 302-307. May 1966.

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A Domain Decomposition Scheme to Solve Integral Equations Using Equivalent Surfaces

Mao-Kun Li, Weng Cho Chew and Lijun Jiang

1. Introduction The domain decomposition method has been used in many electromagnetic solvers to accelerate computations and provide a natural interface to parallel computing [1]. The finite element (FEM) and finite difference (FD) methods have been used as the solvers of each subdomain [2, 3]. In this paper, a domain decomposition scheme based on the equivalence theorem and the method of moments (MOM) is introduced. The unknowns on every subscatterer are transferred to the unknowns on its surrounding equivalent surface [4, 5]. With this scheme, both the number of unknowns and the memory usage are reduced. 2. Formulations A. Equivalence Theorem The equivalence theorem, also known as Huygens' theorem, was conjectured by Huygens and made rigorous by other scientists [6] that the field off a closed surface can be determined by the tangential components of the fields on the surface. This may be derived from Maxwell's equations. The electric field may be written [7]

( ) ( ) ( ) ( ) ( ) ( ) ( )

( ) ( ) ( ) ( )

1

, , ,

S S

S SEM S EJ S

dS g dS giωε

′ ′ ′ ′ ′ ′ ′ ′= ∇× − × − ∇×∇× − ×

′ ′ ′ ′= +

∫ ∫S SE r r r n r E r r r n r H r

r r M r r r J rK L (1) where S S= ×J n H , S S= − ×M n E and ( )g ′−r r is the Green’s function in the embedding medium. The formula for magnetic fields can be derived from (1) using duality principle:

( ) ( ) ( ) ( ) ( ) ( ) ( )

( ) ( ) ( ) ( )

1

, , ,

S SS S

S SHJ S HM S

dS g dS giωµ

′ ′ ′ ′ ′ ′ ′ ′= ∇× − × + ∇×∇× − ×

′ ′ ′ ′= − +

∫ ∫H r r r n r H r r r n r E r

r r J r r r M rK L (2) Eqs. (1) and (2) provide a way to decompose the whole solution domain into several subdomains using the equivalent current on the surface of the subdomains. B. Electric Field Integral Equation The electric field integral equation (EFIE) can be used to solve for the electric current distribution on a perfect electric conductor (PEC). It can be derived from the equivalence theorem,

.inc S

EJ S− ⋅ = ⋅ ⋅E Jt t L (3)

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Using subdomain methods such as FEM or MOM, we can derive the matrix equation [ ]S inc

EE S⎡ ⎤ ⎡ ⎤⋅ = −⎣ ⎦ ⎣ ⎦Z J E . The current coefficient on each basis function can be solved from this equation.

Once the surface current is known, the scattered field can be computed as

.sca SEJ S= ⋅E JL

(4) C. Using Equivalent Surfaces to Solve the One-Object Scattering Problem The procedure of solving the one object problem can be divided into three steps: outside-in propagation, solving for the current on the object and inside-out propagation as shown in (b), (c) and (d) in Fig. 1. The incident electric and magnetic currents on the equivalence surface are first computed from incE and incH . Substituting the incident field with the incident currents will generate the same incident field inside the surface by

inc S inc S incEM S EJ S= +E M JK L (5)

and null field outside. Since the currents generate field only propagating inside, this step is called outside-in propagation. In the next step, the electric currents on the object are solved given the incident wave on its surface. Once this current on the object is known, the equivalent electric and magnetic currents on the surface can be computed, which will generate null field inside and the scattered field outside. Therefore, we call these currents scattered currents and this step is defined as inside-out propagation. These three steps can be written in matrix form as the following

1ˆˆ

sca S inc incS S SS EJ S SEE EM EJsca S inc inc

S HJ S SCurrentSolver Outside In

Inside Out

−

−−

⎡ ⎤ ⎡ ⎤ ⎡ ⎤ ⎡ ⎤− ×⎡ ⎤ ⎡ ⎤ ⎡ ⎤= ⋅ ⋅ ⋅ = ⋅⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥⎣ ⎦⎣ ⎦ ⎣ ⎦×⎣ ⎦ ⎣ ⎦ ⎣ ⎦ ⎣ ⎦

M n L M MZ K L S

J n K J J

(6)

Scatterer

incEn

( )a

Scatterer

incEn

scaJ

( )c

nscaJ scaM

0

scaE

( )d

incM

ScattererincE

nincJ

0

( )b

Figure 1: An example of using equivalence surface: plane wave scattered by a PEC object

16

With the above equation, the scattered currents were computed given the incident currents on the equivalent surface. Hence, we call S matrix the scattering matrix. It is also seen that the unknowns on the scatterer are transferred to the unknowns on the equivalent surface with the information of the scatterer embedded in the S matrix. To compute the field outside, we only need to know the scattered current on the surface. This method has advantages in analyzing scatterers with fine structures, which have to be modeled with many unknowns. Because these fine structures mainly contribute to near-field interactions, but are not important for the far field, the unknown density on the equivalent surface can be much smaller than the one on the scatterer without losing accuracy. D. Solving Multi-Object Scattering Problems with Equivalent Surfaces. This equivalent surface scheme shows its advantages especially in solving the multi-object scattering problem. By representing the scatterers with equivalent surfaces, interactions between two objects are substituted with interactions between two equivalent surfaces. The translation operator is used to compute this interaction [7]. For simplicity, the equation for three scatterers is shown below, in which scatterers 2 and 3 are enclosed with equivalent surfaces:

3211 1 12 13 1

32

32 222 21 1 22 23 22

32 2

33 31

scascaS S PH PH inc

scasca

scasca incHP S HH

scasca inc

HP

⎡ ⎤⎡ ⎤⎡ ⎤ ⎡ ⎤ ⎡ ⎤ ⎡ ⎤ ⎡ ⎤⋅ + ⋅ + ⋅ = −⎢ ⎥⎢ ⎥⎣ ⎦ ⎣ ⎦ ⎣ ⎦ ⎣ ⎦ ⎣ ⎦

⎣ ⎦ ⎣ ⎦⎡ ⎤⎡ ⎤ ⎡ ⎤

⎡ ⎤ ⎡ ⎤ ⎡ ⎤ ⎡ ⎤⎡ ⎤ ⎡ ⎤− ⋅ ⋅ + − ⋅ ⋅ = ⋅⎢ ⎥⎢ ⎥ ⎢ ⎥⎣ ⎦ ⎣ ⎦⎣ ⎦ ⎣ ⎦ ⎣ ⎦ ⎣ ⎦⎣ ⎦ ⎣ ⎦⎣ ⎦

⎡ ⎤ ⎡− ⋅⎣ ⎦ ⎣

JJL J T T E

MM

JJ JS T J S T S

MM M

S T 3 321 33 32 33

3 32

,sca incsca

S HHsca incsca

⎡ ⎤ ⎡ ⎤⎡ ⎤⎤ ⎡ ⎤ ⎡ ⎤⎡ ⎤ ⎡ ⎤⋅ − ⋅ ⋅ + = ⋅⎢ ⎥ ⎢ ⎥⎢ ⎥⎣ ⎦ ⎣ ⎦⎦ ⎣ ⎦ ⎣ ⎦

⎣ ⎦ ⎣ ⎦ ⎣ ⎦

J JJJ S T S

M MM (7)

where HH

ijT is the translation matrix between equivalent surfaces and HPijT is the translation matrix from

scatterer j to equivalent surface i . Similar equations can be derived for more than three objects. Furthermore, if the same subdomain exists repeatedly in the simulation, only one scattering matrix needs to be stored in the memory for these repeated elements. Hence, memory usage is greatly reduced. 3. Numerical Examples The numerical example shown here is a 2 2× array of XM antennas. To reduce the size of this antenna, it was designed as a microstrip patch antenna with substrate permittivity above 20. This leads to a very dense mesh to model the XM antenna. The volume-surface integral equation with RWG basis and multiple delta gap excitations are used in the simulation. The total number of unknowns is 7780 4× , the unknown density is over 150 per free-space wavelength. Four equivalent surfaces are used to enclose each antenna, with only 1536 unknowns on each. The reduction of the number of unknowns is 80%. Moreover, only one S matrix needs to be stored due to the symmetry of the structure. Therefore, this 2 2× antenna array can be simulated with the memory requirement of only one element. The electric and magnetic current distributions on the equivalent surfaces along with the radiation pattern are shown in Fig. 2. 4. Conclusion A domain decomposition scheme based on the equivalence theorem is introduced in this paper. The unknowns on the scatterers are transferred to unknowns on equivalence surfaces. This leads to a reduction in the number of unknowns and memory requirements.

17

Figure 2: An example of simulating a 2 x 2 XM antenna array

18

References [1] B. Butrylo, F. Musy, L. Nicolas, R. Perrussel, R. Scorretti, and C. Vollaire, "A Survey of Parallel

Solvers for the Finite Element Method in Computational Electromagnetics," COMPEL, vol. 23, pp. 531-546, 2004.

[2] S. Lee, M. Vouvakis, and H. Lee, "A Non-overlapping Domain Decomposition Method with Non-matching Grids for Modeling Large Finite Antenna Arrays," J Comput Phys, vol. 203, pp. 1-21, 2005.

[3] F. Xu and W. Hong, "Domain Decomposition FDTD Algorithm for the Analysis of a New Type of E-plane Sectorial Horn with Aperture Field Distribution Optimization," IEEE Trans Antenn Propag, vol. 52, pp. 426-434, 2004.

[4] W. C. Chew and C. C. Lu, "The Use of Huygens Equivalence Principle for Solving the Volume Integral-Equation of Scattering," IEEE Trans Antenn Propag, vol. 41, pp. 897-904, 1993.

[5] C. C. Lu and W. C. Chew, "The Use of Huygens Equivalence Principle for Solving 3-D Volume Integral-Equation of Scattering," IEEE Trans Antenn Propag., vol. 43, pp. 500-507, 1995.

[6] J. A. Stratton, Electromagnetic Theory, 1st ed. New York, London,: McGraw-Hill book company, inc., 1941.

[7] W. C. Chew, Waves and Fields in Inhomogeneous Media. New York: IEEE Press, 1995.

19

Time-Domain Finite-Element Modeling and Simulation of Broadband Antennas

Zheng Lou and Jian-Ming Jin

1. Introduction Typical broadband antennas have very complex structures to achieve a desired bandwidth with a compact design. Frequency-domain CAD tools employing techniques such as the finite element method (FEM) and the method of moments (MoM) have the capability of modeling complex shapes and materials, but they are often very time consuming for broadband applications. On the other hand, typical time-domain techniques, such as the finite-difference time-domain (FDTD) method, can model the entire frequency band of interest with a single pass; however, the FDTD is less efficient and accurate with the modeling of complex structures and materials. This is especially true when the complex structures involve very small details that have to be modeled and resolved in the numerical simulation. Recently, the time-domain finite element method (TDFEM) has been proposed as a potentially better alternative to the FDTD and the frequency-domain FEM and MoM for modeling and simulation of complex broadband antenna designs. In this paper, we discuss the numerical issues of applying the TDFEM to the modeling and simulation of broadband antennas and demonstrate its application and capability through several numerical examples. Two critical simulation components, namely the truncation of the open free space and the modeling of antenna feeds, are discussed. The implementation of perfectly matched layers (PML) is briefly described for the truncation of the TDFEM computational domain. An accurate waveguide port boundary condition (WPBC) is employed to model the commonly used coaxial feeds as well as other waveguide feeding structures. In addition, an improvement to the simplified probe feed model is developed. Numerical examples are presented to demonstrate the modeling and simulation of typical broadband antennas, which include a pyramidal horn antenna and a logarithmic spiral antenna. 2. Perfectly Matched Layers We treat the PML as artificial anisotropic material layers [1, 2], where the permittivity and permeability of the material are represented as space- and frequency-dependent diagonal tensors. The inverse Laplace transform of the second-order wave equation yields its time-domain counterpart. Next, we apply Gakerkin's method and Newmark-beta method for spatial and temporal discretization, respectively. Finally, we arrive at a complicated time-marching system which involves convolutions of solutions of past time steps. From our numerical experience, we found that the convolutions may potentially destroy the unconditional stability of the TDFEM system. However, we also found that the PML is able to produce stable results when typical time step sizes are used. The thickness L and conductivity of the PML are the parameters that can be optimized to achieve the best tradeoff between absorbing performance and numerical efficiency. In our PML implementation, these parameters are determined by 22

01 Lrrm // ξξεµσσξ −= where zyx ,,=ξ , m = 0.02, and L = 4h where h is the element size in the PML region. This specific PML is able to achieve a reflection level less than -40 dB at normal incidence. A better performance, if desirable, can be obtained by increaseing L in terms of the number of elements and adjusting m accordingly.

20

3. Waveguide Port Boundary Condition To model a coaxial and waveguide feed, the FEM mesh is terminated at the coax or waveguide opening (with no need to mesh inside the coax or waveguide) and a boundary condition of the third kind is then enforced for the electric field at the opening or the port:

( ) incUEPE =+×∇×n

This boundary condition is referred to as the WPBC, which has been used successfully in the FEM analysis of a variety of waveguide devices in the frequency domain [3] and recently extended to the time domain [4]. The boundary condition is based on modal expansion in the waveguide. All TEM, TE and TM modes are included in the boundary condition in a unified formulation. Since all higher-order waveguide modes are properly modeled, the WPBC can be placed very close to the antenna or the waveguide discontinuity. Using the WPBC, excitation to the FEM system with arbitrary modes also becomes possible. 4. Simplified Feed Model Simplified feed models, such as the commonly used electric probe model, are sometimes advantageous because they allow using less dense discretizations in the feed region. In the electric probe model, a short current probe is inserted between two terminals of the antenna to model the current flow. The voltage across the antenna terminals is then evaluated from the FEM field solution and the input impedance of the antenna can be calculated accordingly. The electric probe model is useful for predicting the far-field behaviors such as radiation patterns. For calculating input impedance, the accuracy is usually insufficient. One intrinsic drawback of this model is that no radius is specified for the probe and the electromagnetic field is singular in the vicinity of the probe. To overcome this problem, we introduce several observation probes in addition to the source probe. The observation probes are placed at some distances away from the source probe to avoid field singularity. We then calculate the voltage across the terminals using the averaged fields on the observation probes. Numerical results show that the improved probe feed model agrees much better with the accurate coaxial feed model. 5. Numerical Examples We first consider a pyramidal horn antenna fed by a 2.29 cm by 1.02 cm rectangular waveguide with TE10 incident mode. The size of the open aperture is 6.75 cm by 4.95 cm and the length of the horn measured from the waveguide/horn juncture to the open aperture is 13.87 cm. The inclusion of higher modes in the WPBC allows the truncation of the waveguide very close the horn (1.3 cm away from the juncture). The horn antenna is tightly enclosed by a 1 cm-thick PML. The far field radiated by the antenna is computed by a time-domain near-to-far field transformation and the E- and H-plane antenna gain patterns at 10 GHz are shown in Figs. 1(a) and 1(b), respectively. The TDFEM results are found to agree well with the MoM results published in [5]. The difference occurred at larger angles in the H-plane pattern is probably due to different modeling of the exterior surfaces.

21

(a) (b)

Figure 1: Radiation pattern for a 15-dB standard pyramidal gain horn at 10 GHz.

(a) E-plane pattern. (b) H-plane pattern. We then consider a logarithmic spiral antenna that consists of two free-standing conducting arms, as shown in Fig. 2(a). The centerline of the arms is prescribed by πϕτ 2

0/rr = where the scale factor is

chosen to be 1.588. The inner and outer radii of the spiral are 0.22 cm and 3.5 cm, respectively. In this example, we apply our improved probe feed model to compute the input impedance over a wide frequency range. The feed region of the spiral antenna is shown in Fig. 2(b). A 0.56 mm-long source probe is inserted between the two conducting fins at the center of the antenna. Two observation probes are placed symmetrically around the central probe with a separation distance of 0.28 mm. The calculated input resistance (solid line) and reactance (dashed line) versus frequency are shown in Fig. 3. The curves exhibit a transition from the resonant region to the broadband region as the frequency increases. We also note that the calculated input impedance converges ) for a self-complementing structure [6]to the theoretical impedance (188.5 at the higher frequency end.

(a) (b)

Figure 2: Two-arm logarithmic spiral antenna. (a) Geometry of the arms. (b) Enlarged feed region.

22

Figure 3: Input impedance for the logarithmic spiral antenna. 6. Conclusion This paper presented the TDFEM for the modeling and simulation of complex broadband and UWB antennas. Two critical components related to the modeling of antenna feeds and the truncation of infinite free space were discussed in detail. The PML was implemented for the truncation of the TDFEM computational domain and an accurate WPBC was employed to model the antenna feeds. An improvement to the simplified probe feed model was also presented. Numerical examples were presented to demonstrate the modeling and simulation of typical broadband and UWB antennas, which included a pyramidal horn antenna and a logarithmic spiral antenna. References [1] Z. Sacks, D. Kingsland, R. Lee, and J. Lee, “A perfectly matched anisotropic absorber for use as an

absorbing boundary condition,” IEEE Trans. Antennas Propagat., vol. 43, no. 12, pp. 1460-1463, Dec. 1995.

[2] S. Gedney, “An anisotropic perfectly matched layer absorbing media for the truncation of FDTD lattices,” IEEE Trans. Antennas Propagat., vol. 44, no. 12, pp. 1630-1639, Dec. 1996.

[3] J. Liu, J. M. Jin, E. K. N. Yung, and R. S. Chen, “A fast, higer order three-dimensional finite-element analysis of microwave waveguide devices,” Microwave Opt. Tech. Lett., vol. 32, no. 5, pp. 344-352, Mar. 2002.

[4] Z. Lou and J. M. Jin, “An accurate waveguide port boundary condition for the time-domain finite-element method,” IEEE Trans. Microwave Theory Tech., vol. 53, pp. 3014-3023, Sept. 2005.

[5] K. Liu, C. Balanis, C. Birtcher, and G. Barber, “Analysis of pyramidal horn antennas using moment methods,” IEEE Trans. Antennas Propagat., vol. 41, no. 10, pp. 1379-1388, Oct. 1993.

[6] G. Deschamps, “Impedance properties of complementary multiterminal planar structures,” IRE Trans. Antennas Propagat., vol. AP-7, no. 8, pp. S371-S379, Dec. 1959.

23

Comprehensive Electromagnetic Modeling and Transient Analysis of On-Chip Noise Generation and Coupling

J.-Y. Ihm, I. J. Chung, G. Manetas and A. C. Cangellaris 1. Introduction Noise-aware signal distribution and power delivery are imperative requirements for ensuring the functionality of state-of-the-art and future integrated circuits (ICs). With device feature sizes shrinking well below 100 nm, switching speeds in the order of a few picoseconds call for predictive electrical performance analysis of the signal and power distribution networks over a bandwidth ranging from dc to several tens of GHz. With the speed of light in SiO2 approximately equal to 15 cm/ns, the wavelength at 25 GHz is 6 mm. Thus, the electrical area of the footprint of a 3-cm square silicon die is 25 square wavelengths at 25 GHz (a frequency equal to the 5th harmonic of a 5-GHz clock frequency), and 100 square wavelengths at 50 GHz (a frequency equal to the 5th harmonic of a 10-GHz clock frequency). The above considerations make evident the need for electromagnetic accuracy in the development of models for signal and power integrity analysis. In addition to electromagnetic retardation, the model must be capable of comprehending the impact of interconnect loss on signal attenuation, delay and distortion. Considering the transmission line interconnect formed by a 1-mm square Cu wire cross section along with its (ground wire) return path of the same cross section, its per-unit-length dc resistance, R, is approximately 350 Ohm/cm. Assuming a distance between the wires such that the per-unit-length inductance, L, of the transmission line is 10 nH/cm, a rough estimate of the frequency bandwidth, RCf , over which signal transmission delay is RC limited is obtained by setting 4(2 ).RCR f Lπ= This yields

1.4RCf ≈ GHz, implying that, despite the large value of the per-unit-length resistance for on-chip wiring, electromagnetic retardation is a dominant contributor to interconnect delay over most of the bandwidth of the transmitted signal, and must be taken into account for accurate assessment of interconnect-induced delay in on-chip multi-GHz bandwidth signal transmission. Furthermore, the impact of frequency-dependent ohmic loss (the skin depth in Cu is 0.66 mm at 10 GHz) on signal degradation becomes an issue when dealing with pulse rise and fall times of the order of a few picoseconds. In addition to on-chip interconnect-induced delay and signal degradation, on-chip noise generation and coupling mechanisms need to be re-examined and analyzed with enhanced accuracy at the higher end of the switching signal spectrum. In particular, in addition to the well-understood interconnect-induced crosstalk, noise coupling through the power grid and the semiconductor substrate are becoming important for noise-aware design, especially for the case of mixed-signal ICs. Furthermore, accurate prediction of any (undesirable) resonance behavior during switching requires both the on-chip and the package portions of the power grid and the associated decoupling capacitances to be taken into account in the model and the transient simulation. To address the aforementioned electromagnetic modeling and simulation needs, a comprehensive methodology was proposed in [1]-[3]. The proposed methodology is founded on a discrete electromagnetic model for the on-chip power grid directly from the physical geometry. This is complemented by a) a distributed model for the semiconductor substrate-induced noise coupling; b) transmission-line models for the interconnects; c) behavioral models for the drivers and receivers; d) and lumped-circuit models for any on-chip decoupling capacitance and any other lumped elements that must be taken into account. Finally, a multi-port network interface is provided for the concurrent simulation of the electromagnetic response of the die model and a multi-port model for the package power distribution network.

24

In this paper some of the attributes of this modeling methodology are demonstrated through its application to the transient simulation of noise coupling and the prediction of power grid fluctuations during switching. Prior to presenting the sample case study, an overview of the modeling methodology is provided, with emphasis placed on the justification of the methodology used for modeling of on-chip interconnects and the semiconductor substrate-induced noise coupling. 2. The Electromagnetic Model 2.1 On-Chip Power Grid We begin by reviewing briefly the discrete electromagnetic model used for the on-chip power grid. Figure 1 provides a graphical illustration of the multi-layered on-chip metallization. Geometry information for this structure is provided in [1]. The finite difference approximation of Maxwell’s curl equations, in the spirit of the popular FDTD method, is used for the development of the discrete electromagnetic model for the grid. It should be noted that only the power grid wire structure is discretized in the development of the finite difference model. Any signal wiring that must be included in the model for noise coupling related studies, is represented in terms of distributed lumped element models as discussed in more detail later in Section 2.3. The finite conductivity of the wires is taken into account in the development of the discrete model. The result of this discretization is a state-space system of equations, with unknowns the discrete values of the electric and magnetic field vectors throughout the power grid metallization volume. In matrix form, the system is written as follows,

Figure 1: Schematic of a multi-layered on-chip power grid. “Mx” denotes metallization layer x, while “Vy” denotes via layer “y.”

h S

e S

d

dt+ =

⎡ ⎤ ⎡ ⎤⎡ ⎤ ⎡ ⎤ ⎡ ⎤⎢ ⎥ ⎢ ⎥⎢ ⎥ ⎢ ⎥ ⎢ ⎥⎣ ⎦ ⎣ ⎦ ⎣ ⎦⎣ ⎦ ⎣ ⎦

G D ie C 0 e

D R vh 0 L h (1)

The vectors of state variables e and h contain the discrete unknown electric and magnetic fields, respectively, while the matrices, G, R, L, and C, capture the electromagnetic properties of the insulating medium and the metallization. Finally, the matrices, Dh, and De, are very sparse matrices describing the way the circulation of the electric and magnetic fields is approximated in the discrete model. The source vectors, iS and vS, describe any voltage and current sources, respectively, that are connected to the grid.

25

One advantage of (1) is its seamless compatibility with the Modified Nodal Analysis (MNA) formalism used by most SPICE-like circuit simulators. Consequently, any SPICE netlist can be interfaced with the discrete model of (1). For example, any lumped elements associated with on-chip decoupling capacitance, and the circuit description of the on-chip sources and drivers, can be embedded in (1) in a straightforward fashion making use of the fact that the currents and voltages in the I-V relationships of lumped elements are readily expressed in terms of line integrals of the discretized electric and magnetic field, respectively. Accurate modeling of skin-effect ohmic loss would require a very fine discretization of the wire cross section and would result in an undesirable increase in the dimension of (1). To avoid this computational complexity without penalizing model accuracy the following modeling strategy is adopted. Recognizing that the impact of skin effect loss is most critical to the prediction of signal degradation, accurate modeling of the skin effect-induced loss is performed during the development of the distributed lumped circuit models for the interconnects (see Section 2.3). As far as the power grid modeling is concerned, the finite-difference grid size used is dictated by the dimensions of the wire cross section and interlayer dielectrics [1]. Even in this case, the large ratio of transverse die dimensions to wiring feature size (O(103)) results in a discrete model of dimension in the order of tens to hundreds of millions. Therefore, any means for reducing model order complexity need to be exploited, especially when the simulation objective is full-chip power grid modeling. 2.2 Semiconductor Substrate Due to the inherent inductance of the power delivery system, the supply transient currents originated from the switching activity of digital circuits give rise to voltage fluctuations at the power and ground contacts that bias the logic drivers and the substrate. Spurious currents may then be injected into the substrate from the ground contacts, through their low ohmic junction with the substrate, and from VDD contacts through the depleted capacitance between the N-wells and the substrate. Noise injection takes place also through the depleted capacitances of the junctions of switching devices with the substrate and through the impact ionization mechanism. The flow of these spurious currents in the silicon wafer results in voltage drops that may inadvertently influence sensitive analog devices sharing the silicon substrate in mixed-signal circuits. An analog device senses substrate noise either through its capacitive junctions with the substrate or through a power supply that has been contaminated with substrate noise. Furthermore, the signal in an analog NMOS device can be modulated due to substrate voltage variations through the body effect. From an electrical modeling point of view, the interaction areas between supply contacts and devices with the underlying substrate constitute the terminals in the electrical network that is developed to model substrate noise coupling. A rigorous electromagnetic model for the semiconductor substrate could, in principle, be developed through the discretization of Maxwell’s equations over the Si volume. However, considering that the Si substrate is an order of magnitude thicker than the SiO2 substrate, it is immediately evident that such a model would lead to a computationally undesirable (if not prohibitive) increase in the dimension of the discrete model. Thus, an alternative approach is adopted, where substrate noise coupling between neighboring contacts is represented in terms of a multi-terminal quasi-static, RC network, which is extracted as described in [4]. The quasi-static nature of model is justified by the fact that coupling between contacts in close proximity (e.g., within the same functional block or between adjacent blocks) is what requires special attention, since guard rings are always introduced in the substrate to contain the extent of substrate-induced coupling. With regards to taking into account the impact of the finite conductivity of the substrate in the calculation of the electromagnetic response of the power grid, a frequency-dependent surface impedance is utilized at the Si/SiO2 interface. The development and implementation of the substrate surface impedance is discussed in [2].

26

2.3 Signal Interconnects Depicted in Fig. 2a is a signal wire sandwiched between a pair of power and ground wires. The signal wire together with its reference power and ground wires form a multi-conductor transmission line (MTL). The figure depicts the case where the driver is switching from high to low. The current flow in the signal and reference wires can be decomposed into its transmission-line (differential-mode) and common-mode currents as shown in Fig. 2b, where it is,

,d d d cP G S PI I I I I+ = = (2)

This decomposition suggests that the modeling of the switching currents in the interconnects can be effected through the combination of an MTL model for the differential-mode portion of the currents and the power grid model described in Section 2.1 for the common-mode portion of the current. It is well known that the MTL model is governed by the generalized telegrapher’s equations, the transmission properties of which are described in terms of the per-unit-length impedance and admittance matrices of the system of the signal wires and the associated return wires. These, in turn, are extracted using two-dimensional electrostatic and magneto-quasi-static fields solvers, taking into account frequency-dependent effects associated with skin effect ohmic loss in the metallization and semiconductor-induced ohmic loss for signal wires in the metallization layer closest to the Si substrate. The extraction of the frequency-dependent, per-unit-length MTL impedance and admittance matrices and the subsequent synthesis of circuit netlists for the development of SPICE-compatible models are well known and extensively documented in the literature.

Figure 2: A driven signal wire (S) sandwiched between a power (P) and a ground (G) wire. a) Depicted here is the situation when the driver is switching from high to low. b) Decomposition of the switching currents into transmission-line and common mode components.

dGI

IS IS

IG = IS

= +

cI cI

cI

cI dPI

dPI dGI

SI

(b)

P

IS

IG (a)

G

S

27

3. Case Study The case study presented next considers the transient response of a portion of the on-chip power grid during switching. The model includes the semiconductor substrate noise coupling model. The substrate consists of a 2-mm thick epi layer of conductivity 10 S/m backed by a 198-mm thick bulk layer of conductivity 10000 S/m, which is backed, in turn, by a PEC ground plate. In addition, a simplistic behavioral electrical model is provided for the connection of the power grid to the package as depicted in Fig. 3. The lumped circuit model includes pin parasitics and a lumped RLC model for the package power grid. The pins connect the package power grid to the top Vdd wires of the on-chip power grid depicted in Fig. 1. The lumped element values used for this specific model are Lpin = 0.1 nH, Cpin = 5.31 fF, Rpin = 20 mOhm, Lpkg = 2 nH, Cpkg = 0.5 pF , Rpkg = 100 mOhm .

Figure 3: Interconnection of lumped electrical models for pin parasitics (Rpin, Lpin, and Cpin) and package power grid (Rpkg, Lpkg, and Cpkg) to the top metallization layer of the on-chip power grid. The portion of the die considered included 264 drivers. Two thirds of these drivers were associated with a digital block and the remaining one third with an analog block. Each driver is connected to a 90-mm long interconnect terminated at a 0.1 pF capacitor. The cross-sectional dimensions of the interconnect are given in [3]. The on-chip portions of the power grids for the two blocks are kept separate. Thus, any interactions between them are solely due to the off-chip portion of the power distribution network and the semiconductor substrate. A total of 1050 substrate contacts are included in the model, 504 of which are power and 546 are ground. SPICE level 1 models were used for the drivers. The transconductance parameter is such that /k W L′ =150 mA/V2. This large value reflects the fact that each driver serves as a behavioral model for the switching of a large, functional sub-block. A threshold voltage of 0.3 V is assumed. Decoupling and bypass capacitance has been assigned throughout the die. A 25-pF capacitor is assigned between each pair of power and ground contacts, and a bypass capacitor of 1pF is assumed between each contact and global ground. The hybrid FDTD/SPICE transient simulator used is described in [3]. Figure 4 depicts power voltage fluctuation at a victim contact in the analog block due to a 5-GHz digital driver switching, with rise and fall times of 40 ps. The distance between the switching and the victim nodes is 120 mm. A peak-to-peak voltage fluctuation of 60 mV is detected in the victim contact. Three different coupling paths are responsible for the recorded noise. For example, during the fall time of the switching signal, the noise current injected in the ground contact finds its way to its accompanying power contact through the decoupling capacitor, and then on to the victim contact through the power-grid network. It also enters the neighboring ground-grid network, and arrives at the victim contact. The noise current may also reach the victim contact through the semiconductor substrate. Coupling during the rise time of the signal can be interpreted in a similar manner.

28

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35-0.02

-0.01

0

0.01

Time [ns]

Cur

rent

[V]

0 0.05 0.1 0.15 0.2 0.25 0.3 0.351.15

1.2

1.25

1.3

Time [ns]

Vol

tage

[V]

0 0.05 0.1 0.15 0.2 0.25 0.3 0.350

0.5

1

1.5

Time [ns]

Vol

tage

[V]

(a)

(b)

(c)

Figure 4: (a) Noise current in switching transistor, (b) Power voltage fluctuations; (c) Driver Input voltage. 4. Acknowledgments This work was supported in part by the Semiconductor Research Corporation and the Air Force Office for Scientific Research.

References [1] J.-Y. Ihm and A. C. Cangellaris, “Distributed on-chip power grid modeling; an electromagnetic

alternative to RLC extraction-based models,” Proc.2003 IEEE Topical Meeting on Electrical Performance of Electronic Packaging, Oct. 2003, pp. 37-40.

[2] J.-Y. Ihm and A. C. Cangellaris, “Modeling of semiconductor substrate on on-chip power grid switching,” 13th Topical Meeting on Electrical Performance of Electronic Packaging, Portland, OR, October 2004, pp. 265-268.

[3] J.-Y. Ihm, I. J. Chung, G. Manetas and A. C. Cangellaris, “Comprehensive Model for On-Chip Power Grid Transient Analysis and Power Grid-Induced Noise Prediction,” Proc. 55st Electronic Components and Technology Conference, May 31-June 3, 2005.

[4] G. Manetas and A. C. Cangellaris, “Methodology for Expedient Computation of Semiconductor Substrate Noise Coupling,” Proc. 13th Topical Meeting on Electrical Performance of Electronic Packaging, Portland, OR, Oct. 2004, pp.273-276.

29

Antenna and Systems Research in the Electromagnetics Laboratory: Enabling Multifunction Operation

in Portable Devices, Sensors, and High Performance Arrays

Prof. Jennifer T. Bernhard 1. Introduction The continued growth of wireless communication in both the commercial and defense sectors requires new kinds of enabling technology for antennas and RF circuitry to provide high speed, high reliability performance. The development of this technology requires contributions from industry, the military, and academia to meet the challenges presented by unpredictable and often hostile operating environments. Our research group addresses these fundamental, yet application-oriented problems by focusing on integrated and reconfigurable antennas with an emphasis on theoretical analysis and experimental investigation. 2. Multifunction Reconfigurable Antennas Our research implements reconfigurability in antenna structures to provide flexibility in operating frequency, bandwidth, and radiation pattern performance. Reconfigurability is accomplished using RF MEMS (microelectromechanical systems) [1-3], traditional microwave switches [4, 5], ferroelectric materials, or magnetic or mechanical actuation of antenna components [6, 7]. The new multi-function antennas developed in this research have the potential to reduce dramatically the number and size of large array-based antenna systems, improve system efficiency, and decrease system cost and weight. Intelligent Portable Antenna Systems High-speed (2-100 Mb/sec) wireless data communication - whether land- or satellite-based -- faces two challenges: (1) high error rates caused by interference and unpredictable environments, and (2) limited functionality and battery life at the portable unit. ‘Intelligent’ or ‘smart’ antenna systems that respond to changing operating conditions can help meet these challenges. Currently, smart antennas are implemented only on base stations. Portable units, however, remain the weakest components of the system. Indeed, the wireless research and industrial communities agree that the capabilities of portable units will constrain future high-speed wireless system performance. Therefore, portable units require new kinds of antenna capabilities that allow autonomous responses to local operating conditions while remaining practical and cost-effective. This research develops intelligent portable antenna systems to improve the reliability, throughput, and noise immunity of high-speed wireless communication networks. Specifically, this project implements new compact radiation-tunable antennas with a performance-driven fuzzy controller. This novel approach views portable antennas as dynamic components of the communication system, creating a new paradigm for antenna design and control.

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The new antennas for these systems are based on spiral microstrip antennas and thin microstrip radiators [1-5]. One design using thin microstrip radiators implemented with solid state switches is shown in Figure 1 [4]. In contrast to other designs, each individual antenna possesses reconfigurable radiation patterns. These patterns are achieved by using tuning elements that change the current distributions on the inner and outer portions of the spiral arm. In addition to the development of these novel antennas, this research also addresses the electromagnetic effects of antenna integration into a portable device or other packaging. Antenna diversity schemes using individual tunable antennas are being developed. Theoretical, experimental, and computational analyses of the integrated tunable antenna systems

provide the foundation for fuzzy control algorithms and also permit implementation of these antennas in reconfigurable arrays. Reconfigurable Antennas for High Data Rate Multibeam Communication Systems This project develops new individually-reconfigurable low-profile antenna array elements that can be adjusted to provide multiple beams while providing increased scan angles (even to endfire) and higher aperture efficiency than traditional diffraction-limited arrays. These antennas range from spiral microstrip elements developed for portable communication devices to cavity-backed slots and canted elements that change both resonant frequency and radiation properties with changes in length, coupling, and loading [8]. A photo of a 16-element reconfigurable phased array is shown in Figure 2. Recently, we have integrated commercial RF MEMS switches into some of our reconfigurable designs. With only minor changes to the switch packaging, the antennas operated in broadside and endfire modes over a common impedance bandwidth. Future work in this area includes the direct design and fabrication of specialized RF MEMS switches with the antennas in one fabrication process, eliminating the need to deal with package parasitics, bias line constraints, and impedance mismatches arising from switch design. Wideband Conformal Antennas and Arrays This project, sponsored by the U.S. Air Force Research Laboratory, investigates the fundamental characterization of suitable wideband conformal microstrip-based antennas as single elements and in arrays and explores possible approaches to expand the operating frequency bands and performance of planar and conformal arrays. These approaches encompass the use of novel substrates and antenna designs, array designs that allow wideband performance, such as random and connected array topologies, and implementation of antenna reconfiguration to enable wideband operation of planar and conformal arrays. 3. Aperiodic Arrays of Wideband and Narrowband Antennas Wideband Antennas in Aperiodic Arrays Planar microstrip antennas revolutionized phased array technology decades ago. To enable the next levels of array functionality, however, new array elements with expanded capabilities and

Figure 2: 16-element reconfigurable phased array

Figure 1: Reconfigurable microstrip parasitic array with solid state switches.

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appropriate array strategies are required to operate over wide frequency bands. While patch antennas have many desirable characteristics, their narrow impedance bandwidths make them unsuitable for wideband applications. Wideband antennas, on the other hand, promise increased bandwidth, but at the expense of greater physical size and/or reduced gain. This situation captures a fundamental physical limitation analogous to the gain-bandwidth tradeoff in electrical networks. In the case of antennas, this limitation is defined by gain-bandwidth and size. Therefore, in order to increase significantly the bandwidth of low-profile antennas, the effective volume occupied by the antenna structure must be increased. There are two alternatives: (a) increase the height, or (b) increase the lateral dimensions. These choices have implications not only for antenna design but also attainable array performance. In this project, sponsored by the U.S. Army Research Office, we are developing of a family of low-profile antennas and associated array methodologies for wideband applications where traditional periodic patch antenna arrays severely limit performance [9-11]. In particular, this work is exploring the possibilities as well as the limitations of these wide bandwidth elements in aperiodic arrays [12, 13]. Narrowband Antennas for Scatterable Sensor Systems Dependence on a small set of surface rovers for surface and atmospheric exploration exposes missions to higher than acceptable probabilities of failure. To mitigate this situation, we propose use of many small, highly specialized sensors that can be scattered from multiple orbiters or secondary craft and form networks. Information exchange within these networks requires antennas that fit into very small packages and radiate efficiently. Since antenna size is controlled mainly by the network’s operating frequency, however, the antenna will be the limiting factor in wireless sensor feasibility. Moreover, the power resident on any individual sensor will probably not to be enough to establish a link with distant receivers. In order to transfer data out of the local region, the sensors need to work together as a non-traditional communications array, combining their powers to achieve a detectable signal level at a remote receiver, which could be a satellite, orbiter, or surface-based relay station. In this project, sponsored by NASA Glenn Research Center through the Space Communications Project, we are developing size-appropriate, electrically small (miniaturized) antennas with moderate bandwidths for such sensors as well as processing algorithms for random arrays that enable the sensors to work together to communicate their data to remote collection sites regardless of their relative positions or orientations. One prototype antenna is shown in Figure 3. The array will configure itself to form a beam in a general direction that can be intercepted by a passing orbiter or directed to a particular satellite- or surface-based receiver. The project will culminate with a testbed demonstration using the developed antennas and processing algorithms. 4. Integrated Antennas for Portable Devices and Sensors This work centers on cutting-edge technology development and design techniques that will enable high data-rate wireless communication and wireless parallel computation. The research group investigates the effects of packaging on antenna performance and uses these results to develop design-oriented models for internal antennas, embedded antennas, and diversity schemes. The research also creates synthesis approaches for internal portable antenna systems that produce desired performance while reducing user exposure and battery usage.

Figure 3: Photograph of electrically small antenna for scatterable sensor systems.

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Antenna Solutions for Commercial Wireless Applications In response to consumer demand, manufacturers of next-generation wireless communication devices are moving toward internal antenna designs that reduce consumer exposure to radiated electromagnetic fields. These internal designs will be more rugged and aesthetically pleasing than existing external antennas while directing energy away from the user [14]. However, when an antenna is included in the chassis of a device, its operating characteristics can change substantially, resulting in a system with very poor performance. Therefore, the design of an internal antenna must incorporate fundamental operating characteristics as well as specific internal environments and potential operating scenarios unique to a particular device. Existing design rules and models for antennas are primarily limited to very basic antennas in ideal situations (free space) that do not include a chassis. While each individual internal antenna design is necessarily unique to its intended application, general rules and models for such designs would be extremely useful for extending the concept for an antenna design to another chassis or another application or predicting changes in operating characteristics caused by changes in materials or fabrication tolerances. Our research goal in this area is to develop general guidelines for internal antenna systems [14-19]. These advances will contribute to overall communication system improvements in reliability and battery life while reducing the consumer exposure to electromagnetic fields radiated from wireless devices. In particular, we are characterizing the electrical properties of pertinent chassis materials over appropriate frequency bands and evaluating a range of possible chassis integration positions in terms of available volume and dimensions for the antenna, material properties, and suitable electromagnetic visibility for connection quality and minimum user exposure. Our group uses a combination of simulations, measurements, and theoretical modeling to arrive at design rules that can be transferred to other frequency bands and chassis. Effects of internal shielding, chassis geometry and size, and probable position of the user are considered. Additionally, we evaluate prototype internal antennas in free space and in integrated positions to provide data for quality control procedure development. Design Theory and Procedure for Broadband Antennas In recent years the demand for broadband antennas has increased for use in high frequency and high-speed data communication. Printed antennas are economical and easily hidden inside packages, making them well suited for consumer applications. Unfortunately, a “classical” microstrip patch antenna has a very narrow frequency bandwidth that precludes its use in typical communication systems. However, if the frequency bandwidth could be widened, a broadband microstrip antenna would prove very useful in commercial applications such as the Universal Mobile Telecommunication System (UMTS), the General Packet Radio Service (GPRS) and Bluetooth personal networks. A wide operating bandwidth for a single-layer coaxially fed rectangular microstrip patch antenna can be obtained by cutting a U-shaped slot on the patch. This antenna structure has recently been found experimentally to provide impedance bandwidths of 10-40%, even with non-air substrates. In this project, we developed a set of simple design procedures for the rectangular U-slot microstrip patch antenna on microwave substrates through examination of the structure’s multiple resonant frequencies as well as the radiation and impedance properties of different antenna geometries [20]. These procedures provide antenna engineers with approximate rules that result in a good first-pass design with prescribed characteristics that requires only minimal tuning. Additionally, the accompanying parametric studies give direction for the selection and variation of the proper geometric and material parameters to achieve desired antenna behavior. This paper [20] has been awarded the 2004 H. A. Wheeler Prize Paper Award from the IEEE Antennas and Propagation Society. The H. A. Wheeler Award recognizes the paper

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considered to be the best applications paper in the IEEE Transactions on Antennas and Propagation for the past year. Active Antennas for Reflectarrays and Repeaters The objective of this research is a new active antenna element for reflectarrays in military, space, and commercial applications. This new element incorporates signal reception, amplification, and transmission functions in a single fabrication layer by including a MMIC amplifier inside the footprint of a microstrip antenna [21]. Reflectarrays using these new antenna elements will improve spatial power combining by eliminating the need for complex feed networks and oscillator synchronization. With planar phase shifters, these new antenna elements will provide high power beam steering and scanning for satellite communication, radar, and smart antenna wireless applications. Additionally, compact, lightweight repeaters/transceivers using these elements will eliminate the need for line-of-sight paths between consumers and satellites and will reduce the need for large, high gain antennas on portable units. Use of MMIC amplifiers that have 50-ohm input/output impedances and simplified biasing techniques eliminates the need for complex matching networks, which would reduce bandwidth and possibly cause spurious radiation. By placing the amplifier inside the patch footprint between the two orthogonal feed locations, the element spacing is greatly reduced as well, since the amplifier does not need to be located between radiating elements. Compared to current designs, arrays composed of these elements will exhibit increased radiated power efficiency and higher polarization purity while possessing smaller size, weight, and fabrication complexity. Embedded Wireless Sensor Systems The nation’s civil transportation infrastructure of structural concrete bridges is aging and deteriorating -- principally as a result of the corrosion of the steel reinforcement tendons that give these structures their strength. Current estimates place the total cost of inspection, rehabilitation, and replacement of existing corroded structures in the US at $210 billion. Assessing the condition of the steel reinforcement is still based primarily on qualitative visual inspections and anticipated design lives, since the steel is typically buried beneath 1 to 2 inches or more of concrete. We are part of a multi-disciplinary team, with expertise in the areas of non-destructive evaluation (NDE), wireless communication, and structural modeling have joined with bridge designers and managers from the Illinois state department of transportation to develop a wireless embedded sensor system to examine corrosion of tendons in prestressed concrete girders. The results of this project have the potential to deliver advanced, accurate information about the internal condition of steel reinforcement as well as the efficacy of new materials and rehabilitation methods and could save the nation billions of dollars annually. The research plan consists of three thrust areas and a demonstration project. In Thrust 1, a corrosion detection and monitoring method is being developed that uses embedded sensors. Thrust 2 integrates the internal sensors with wireless systems for the harsh, embedded environment of a concrete girder. To date we have designed, fabricated, and embedded a broadband antenna into concrete blocks that possesses wide bandwidth capable of handling various properties of different concrete mixes [22]. One of these antennas is shown in Figure 4. Thrust 3 involves the development of a software program for relating embedded sensor data to changes in significant structural characteristics. Finally, in cooperation with the Illinois Department of Transportation, the embedded

Figure 4: Photograph of antenna for embedded wireless sensing in concrete.

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sensor system will be installed in a prestressed girder during fabrication so that in-field measurements can be taken over an extended period of time to validate the effectiveness of this new embedded sensor system. Antennas for Wireless Sensors The emergence of wireless sensor systems promises to change the way we control our environments, make decisions, and promote health and safety. While numerous research projects on wireless sensors exist, very few address the critical technology of antennas that enable wireless communication. Several projects in this area propose to use standard off-the-shelf antennas, but this choice often limits the capabilities of the system by ignoring the unique requirements and environment of the application. In this project, sponsored by the U.S. Office of Naval Research through the NCASSR program with NCSA, we are developing both a general methodology for the development of antennas for wireless sensor systems as well as several designs for specific applications. 5. Systems-Related Antenna Research Wireless Wind Tunnel With a grant from the National Science Foundation and in collaboration with colleagues from UIUC’s Coordinated Science Lab, we are developing a facility for experimental evaluation of protocols for wireless networks. The facility’s design focuses on the creation of repeatable, controllable electromagnetic environments that mimic real-world conditions that can then be used to accurately and scientifically characterize the performance of wireless communication protocols [23]. A new anechoic chamber will be installed in the Electromagnetics Laboratory in 2006 as part of this project. Measuring BER Performance of Antennas Through the support of the DURIP program and the Army Research Office, Prof. Bernhard and her students have assembled a state-of-the-art phased array bit error rate (BER) testing system. The system can be configured for either traditional coherent continuous wave antenna testing or for bit error rate testing. The BER testing system can implement a variety of standard or user-defined modulations, noise impairments, and propagation models with the help of specialized software from Agilent. This unique facility will enable us to apply new findings to optimize system behavior and to create entirely new avenues of research into the relationships between antenna and array characteristics, signal processing, and achievable system performance [24]. The BER testing system includes a E4443A PSA Series Spectrum Analyzer, a E4438C ESG Vector Signal Generator, and a E8247C PSG CW Signal Generator, all from Agilent. 6. Conclusion Our goal to answer the fundamental questions presented by the wireless environment creates a rich research environment, where results from an industry-oriented design can be directly applicable to the design of wideband military arrays, and reconfigurable antennas designed for implementation in large arrays can also be used in commercial wireless communication systems. We are also expanding our research to encompass more than just the antenna, examining system and protocol behavior as a function of antenna characteristics. Through ongoing collaborations with other research groups in the UIUC Electromagnetics Laboratory, other academic institutions, industry, and defense agencies, we are looking forward to continued success and new breakthroughs.

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References [1] G. Huff, J. Feng, S. Zhang, and J. T. Bernhard, “A novel radiation pattern and frequency

reconfigurable single turn square microstrip spiral antenna,” IEEE Microwave and Wireless Components Letters, vol. 13, no. 2, pp. 57-59, February 2003.

[2] G. H. Huff, J. Feng, S. Zhang, and J. T. Bernhard, “Directional reconfigurable antennas on laptop

computers: simulation, measurement, and evaluation of candidate integration positions.” IEEE Transactions on Antennas and Propagation, vol. 52, pp. 3220-3227, December 2004.

[3] G. H. Huff and J. T. Bernhard, “Analysis of a radiation and frequency reconfigurable microstrip

antenna,” Finalist in student paper competition, Proc. 2004 Antenna Applications Symposium, Sept. 2004, pp. 175-191.

[4] S. Zhang, G. H. Huff, J. Feng and J. T. Bernhard, “A pattern reconfigurable microstrip parasitic

array,” IEEE Transactions on Antennas and Propagation, vol. 52, pp. 2773-2776, October 2004. [5] S. Zhang and J. T. Bernhard, “A pattern reconfigurable microstrip antenna using solid state

switches,” Proc. 2004 IEEE/URSI Int. Symp. on Antennas and Propagation, Monterey, CA, v. URSI, June 2004, p. 555-558

[6] J.-C. Langer, J. Zou, C. Liu, and J. T. Bernhard, “Reconfigurable out-of-plane microstrip patch

antenna using MEMS plastic deformation magnetic actuation.” IEEE Microwave and Wireless Components Letters, vol. 13, no. 3, pp. 120-122, March 2003.

[7] Keynote Address: J. T. Bernhard, “Reconfigurable Antennas and Apertures: State-of-the-Art and

Future Outlook,” Proc. SPIE Conf. on Smart Electronics, MEMS, BioMEMS, and Nanotechnology, vol. 5055, March 2003, pp. 1-9.

[8] G. H. Huff, J. Feng, S. Zhang, J. T. Bernhard, “Behavior of pattern and/or frequency

reconfigurable antennas in small arrays,” in Proc. 2003 IEEE/URSI Int. Symp. on Antennas and Propagation, URSI, June 2003, p. 151.

[9] G. Cung, J. Fladie, P. E. Mayes, and J. T. Bernhard, “Investigation of canted compound sector

antennas for wideband periodic arrays,” Proc. 2004 IEEE/URSI Int. Symp. on Antennas and Propagation, Monterey, CA, v. 2, June 2004, pp. 1887-1890.

[10] J. T. Bernhard, B. Herting, P. Mayes, N. Chen, and E. Michielssen, “Wideband low-profile

canted antennas for array applications,” in Proc. 2003 IEEE/URSI Int. Symp. on Antennas and Propagation, URSI, June 2003, p. 694.

[11] J. T. Bernhard, B. Herting, N.-W. Chen, P. Mayes, and E. Michielssen, “Low Profile Radiators

for Wideband Arrays,” Proc. GOMACTech-2003, Tampa, FL, April 2003. [12] K. C. Kerby and J. T. Bernhard, “Wideband periodic array of random subarrays,” Proc. 2004

IEEE/URSI Int. Symp. on Antennas and Propagation, Monterey, CA, v. 1, June 2004, pp. 555-558.

[13] K. C. Kerby and J. T. Bernhard, “Array of rotated random subarrays,” Proc. 2004 Antenna

Applications Symposium, Sept. 2004, pp. 293-307.

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[14] J. T. Bernhard and C. Tousignant, “Resonant frequencies of rectangular microstrip antennas with flush and spaced dielectric superstrates,” IEEE Transactions on Antennas and Propagation, vol. 47, no.2, Feb. 1999, pp. 302-308.

[15] K. H. Pan, J. T. Bernhard, and T. Moore, “Effects of lossy dielectric material on microstrip

antennas,” Proc. IEEE AP-S Conference on Antennas and Propagation for Wireless Communications, Nov. 2000, pp. 39-42.

[16] J. Haley, T. Moore, and J. T. Bernhard, “Experimental investigation of antenna-handset-feed

interaction during wireless product testing,” Microwave and Optical Technology Letters, vol. 34, no. 3, August 5, 2002, pp. 169-172.

[17] G. Huff and J. T. Bernhard, “Improvements in the performance of microstrip antennas on finite

ground planes through ground plane edge serrations,” IEEE Microwave and Wireless Components Letters, vol. 12, August 2002, pp. 308-310.

[18] B. Herting, A. Perrotta, and J. T. Bernhard, “Finite ground plane packaging effects on a dual-band

PIFA,” Proc. IEEE Topical Mtg. on Electrical Performance of Electronic Packaging, pp. 95-98. [19] G. Huff, S. Zhang, J. Feng, and J. T. Bernhard, “Performance and packaging issues of novel

reconfigurable antennas in laptop computers,” Proc. 2002 IEEE/URSI International Symposium on Antennas and Propagation, vol. URSI, p. 178.

[20] S. Weigand, G. H. Huff, K. Pan, and J. T. Bernhard, “Analysis and design of broadband single-

layer rectangular U-slot microstrip patch antennas,” IEEE Transactions on Antennas and Propagation, vol. 51, no. 3, pp. 457-468, February 2003.

[21] R. Clark, G. H. Huff, and J. T. Bernhard, “An integrated active microstrip reflectarray element

with an internal amplifier,” IEEE Transactions on Antennas and Propagation, vol. 51, no. 5, pp. 993-999, May 2003.

[22] J. T. Bernhard, E. C. George, K. Hietpas, P. Lee, A. Zoeteman, and J. Hill, “Embedding antennas

into concrete for sensing applications: a packaging adventure,” in Proc. 2003 IEEE/URSI Int. Symp. on Antennas and Propagation, URSI, June 2003, p. 299.

[23] N. H. Vaidya, J. Bernhard, V. Veeravalli, P. R. Kumar, R. Iyer, “Illinois Wireless Wind Tunnel:

A Testbed for Experimental Evaluation of Wireless Networks,” in Proc. SIGCOMM 2005, E-Wind Workshop, August 2005.

[24] G. H. Huff, N. Soldner, W. D. Palmer, and J. T. Bernhard, “Study of Error Vector Magnitude

Patterns (EVRP) for a Transmit/Receive Pair of Microstrip Patch Antennas,” Accepted for presentation at the 2006 IEEE/URSI International Symposium on Antennas and Propagation, July 2006.

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CHAPTER 3

PUBLICATIONS LIST AND SEMINAR SERIES Journal Publications List, 2005 1. X. Wang, M. M. Botha and J. M. Jin, “An error estimator for the moment method in electromagnetic

scattering,” Microwave Opt. Tech. Lett., vol. 44, no. 4, pp. 320-326, February 2005. 2. L. E. R. Petersson and J. M. Jin, “An efficient procedure for the projection of a given field onto

hierarachal vector basis functions of arbitrary order,” Electromagn., vol. 25, no. 2, pp. 81-91, February-March 2005.

3. C. S. Liang, D. A. Streater, J. M. Jin, E. Dunn and T. Rozendal, “A quantitative study of Luneberg

lens reflectors,” IEEE Antennas Propagat. Mag., vol. 47, no. 2, pp. 30-42, April 2005. 4. L. E. R. Petersson and J. M. Jin, “A two-dimensional time-domain finite element formulation for

periodic structures,” IEEE Trans. Antennas Propagat., vol. 53, no. 4, pp. 1480-1488, April 2005. 5. T. Ryland and J. M. Jin, “Perfectly matched layers in three dimensions for the time-domain finite

element method applied to radiation problems,” IEEE Trans. Antennas Propagat., vol. 53, no. 4, pp. 1489-1499, April 2005.

6. M. M. Botha and J. M. Jin, “Adaptive finite element-boundary integral analysis for electromagnetic

fields in 3D,” IEEE Trans. Antennas Propagat., vol. 53, no. 5, pp. 1710-1720, May 2005. 7. H. Grabinski and J. E. Schutt-Aine, “Foreword – contributions from the eighth workshop on signal

propagation on interconnects,” IEEE Trans. Adv. Packaging, vol. 28, pp. 150-151, May 2005. 8. R. Gao, Y. S. Mekonnen, W. Beyene and J. E. Schutt-Aine, “Black-box modeling of passive systems

by rational approximation,” IEEE Trans. Adv. Packaging, vol. 28, pp. 209-215, May 2005. 9. J. K. Byun and J. M. Jin, “Finite-element analysis of scattering from a complex BOR using spherical

infinite elements,” Electromagn., vol. 25, no. 4, pp. 267-304, May-June 2005. 10. S. Zhang, G. Huff, G. Cung and J. T. Bernhard, “Three variations of a pattern reconfigurable

microstrip parasitic array,” Microwave and Optical Technology Letters, vol. 45, pp. 369-372, June 2005.

11. Yun-Hui Chu and Weng Cho Chew, “A robust surface-integral-equation formulation for conductive

media,” Microwave and Optical Technology Letters,” vol. 46, no. 2, July 20, 2005. 12. I. T. Chiang and W. C. Chew, “Fast real-time convolution algorithm for microwave multiport

networks with nonlinear terminations,” IEEE Trans. Circuits Syst. II, vol. 52, no. 7, pp. 370-375, July 2005.

13. D. Correia and J. M. Jin, “A simple and efficient implementation of CFS-PML in the FDTD analysis

of periodic structures,” IEEE Microwave and Wireless Components Letters, vol. 15, no. 7, pp. 487-489, July 2005.

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14. J. M. Jin, “A highly robust and versatile finite element-boundary integral hybrid code for scattering by BOR objects,” IEEE Trans. Antennas Propagat., vol. 53, no. 7, pp. 2274-2281, July 2005.

15. D. Riley and J. M. Jin, “Modeling of magnetic loss in the finite-element time-domain method,”

Microwave Opt. Tech. Lett., vol. 46, no. 2, pp. 165-168, July 2005. 16. H. Reis, B. L. Ervin, D. A. Kuchma and J. T. Bernhard, “Estimation of corrosion damage in steel

reinforced mortar using waveguides,” ASME Journal of Pressure Vessel Technology, vol. 127, pp. 255-261, August 2005.

17. A. Rong, A. C. Cangellaris and L. Dong, “Comprehensive broad-band electromagnetic modeling of

on-chip interconnects with a surface discretization-based generalized PEEC model,” IEEE Trans. Advanced Packaging, vol. 28, no. 3, pp. 434-444, August 2005.

18. W. C. Chew, L. J. Jiang, Y. H. Chu, G. L. Wang, I. T. Chiang, Y. C. Pan and J. S. Zhao, “Toward a

more robust and accurate CEM fast intergral equation solver for IC applications,” IEEE Trans. Advanced Packaging, vol. 28, no. 3, pp. 449-464, August 2005.

19. K. Hietpas, B. Ervin, J. Banasiak, D. Pointer, D. Kuchma, H. Reis and J. T. Bernhard, “Ultrasonics

and electromagnetics for a wireless sensing system embedded in reinforced concrete girders,” Smart Structures and Systems, vol. 1, no. 3, pp. 267-282, September 2005.

20. A. E. Yilmaz, J. M. Jin and E. Michielssen, “A parallel FFT-accelerated transient field-circuit

simulator,” IEEE Trans. Microwave Theory Tech., vol. 53, no. 9, pp. 2851-2865, September 2005. 21. Z. Lou and J. M. Jin, “An accurate waveguide port boundary condition for the time-domain finite

element method,” IEEE Trans. Microwave Theory Tech., vol. 53, no. 9, pp. 3014-3023, September 2005.

22. L. J. Jiang and W. C. Chew, “A mixed-form fast multipole algorithm,” IEEE Trans. Antennas Propag.,

vol. AP-53, no. 12, pp. 4145-4156, December 2005. 23. Z. Lou and J. M. Jin, “Modeling and simulation of broadband antennas using the time-domain finite

element method,” IEEE Trans. Antennas Propagat., vol. 53, no. 12, pp. 4099-4110, December 2005. 24. D. Correia and J. M. Jin, “On the development of a higher-order PML,” IEEE Trans. Antennas

Propagat., vol. 53, no. 12, pp. 4157-4163, December 2005. 25. M. A. Kuroda, A. C. Cangellaris and J.-L. Leburton, “Nonlinear transport and heat dissipation in

metallic carbon nanotubes,” Phys. Rev. Lett., 95, 266803, 2005. 26. I. T. Chiang and W. C. Chew, “New formulation and iterative solution for low-frequency volume

integral equation,” J. Electromag. Wave Appl., vol. 19, no. 3, pp. 289-305, 2005. 27. Z. G. Qian, T. J. Cui, W. B. Lu, X. X. Yin, W. Hong and W. C. Chew, “An improved MOM model

for line-fed patch antennas and printed circuits,” IEEE Trans. on Antennas Propagation, vol. 53, no. 8, 2005.

28. S. Ohnuki, W. C. Chew and T. Hinata, “Monte Carlo simulation of 1-D rough surface scattering in 2-

D space,” JEMWA, vol. 19, no. 8, pp. 1085-1102, 2005.

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29. L. J. Jiang, W. C. Chew and Y. C. Pan, “Capacitance extraction in the multilayer medium using DCIM and SMFMA,” J. of Electromag. Waves and Appl., vol. 19, no. 14, pp. 1851-1864, 2005.

30. S. Ohnuki and W. C. Chew, “Error minimization for multipole expansion,” SIAM J. Scientific

Computing, vol. 26, no. 6, pp. 2047-2065, 2005. 31. W. C. Chew, Bin Hu, Y. C. Pan and L. J. Jiang, “Fast algorithm for layered medium,” Comptes

Rendus Physique, vol. 6, pp. 604-617, 2005. 32. Mei Song Tong and Weng Cho Chew, “A higher-order Nystrom scheme for electromagnetic

scattering by arbitrarily shaped surfaces,” IEEE Antennas and Wireless Propagation Letters, vol. 4, 2005.

33. J. V. Li, R. Q. Yang, C. J. Hill and S. L. Chuang, “Interband cascade detectors with room-temperature

photovoltaic operation,” Appl. Phys. Lett., vol. 86, pp. 101102-1 to 101102-3, 2005. 34. P. K. Kondratko, S. L. Chuang, J. Kim, G. Walter, N. Holonyak, Jr., R. D. Heller, X. B. Zhang and R.

D. Dupuis, “Gain narrowing and output behavior of InP/InGaA1P tunneling injection quantum-dot-well laser,” IEEE Photon. Technol. Lett., vol. 17, pp. 938-940, 2005.

35. J. V. Li, S. L. Chuang, O. V. Sulima and J. A. Cox, “Passivation of AlGaAsSb/InGaAsSb/GaSb

photodiodes using aqueous (NH4)2S solution and polyimide encapsulation,” J. Appl. Phys., vol. 97, pp. 104506-1 to 104506-5, 2005.

36. M. R. Fisher and S. L. Chuang, “Variable group delay and pulse shaping of high bandwidth optical

signals,” IEEE J. Quantum Electron, vol. 41, pp. 885-891, 2005. 37. J. Kim, P. K. Kondratko, S. L. Chuang, G. Walter, N. Holonyak, Jr., R. D. Heller, X. B. Zhang and R.

D. Dupuis, “Tunneling injection quantum-dot lasers with polarization-dependent photon-mediated carrier re-distribution and gain narrowing,” IEEE J. Quantum Electron, vol. 41, pp. 1369-1379, 2005.

38. S. W. Chang and S. L. Chuang, “Slow light based on population oscillation in quantum dots with

inhomogeneous broadening,” Phys. Rev. B., vol. 72, pp. 235330-1 to 235330-10, 2005. 39. S. W. Chang and S. L. Chuang, “Strain-induced enhancement of spin relaxation times in [110] and

[111] grown quantum wells,” Phys. Rev. B., vol. 72, pp. 115429-1 to 115429-9, 2005. 40. Z. Lou, L. E. R. Peterson, J. M. Jin and D. Riley, “Total-scattered-field decomposition technique for

the finite-element time-domain modeling of buried scatterers,” IEEE Antennas and Wireless Propagation Letters, vol. 4, pp. 133-137, 2005.

41. Z. Lou, L. E. R. Petersson, J. M. Jin and D. Riley, “Total- and scattered-field decomposition

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Electromagnetic Seminar Series, 2005 January 25, 2005, Prof. Jianming Jin, University of Illinois, A Quantitative Study of Luneberg Lens Reflectors. February 1, 2005, Prof. Levent Gurel, University of Illinois, Essays on the Iterative Solution of the combined-Field Integral Equation. February 8, 2005, Prof. Jose Schutt-Aine, University of Illinois, Perspectives and Challenges in the Future of Integration. February 15, 2005, Prof. Steven Boppart, University of Illinois, Molecular Imaging with Optical Coherence Tomography. March 1, 2005, Prof. Robert Adams, University of Kentucky, Well-conditioned Integral Equations for Electromagnetic Applications. March 8, 2005, Dr. John Huang, JPL, Recent Challenging Microstrip Array Work at JPL. March 15, 2005, Prof. Richard Blahut, University of Illinois, Maximum-Likelihood Photon-Differencing Methods of Imaging. March 29, 2005, Prof. Zhi-Pei Liang, University of Illinois, Magnetic Resonance Imaging: Challenges and Opportunities. April 5, 2005, Dr. Hans Steyskal, Hanscom AFRL, A Sampling of Antenna Research at AFRL. April 12, 2005, Prof. Glaucio Paulino, University of Illinois, 3D Boundary Element Modeling: Application To Nonhomogeneous Media. April 19, 2005, Dr. Jose Camberos, AFRL, Development and Progress of a Finite-Volume, Time-Domain Computational Electromagnetics Research Code for Multidisciplinary Applications. April 26, 2005, Prof. Erhan Kudeki, University of Illinois, Calibrating An MST Radar Using F-region ISR Returns and Magneto-ionic Propagation Effects. May 3, 2005, Prof. Kevin Webb, Purdue University, Imaging Potential of a Negative Refractive Index Lens. August 30, 2005, Prof. Amir Mortazawi, University of Michigan, Adaptive RF Circuits Based on Thin Film BST. September 6, 2005, Dr. Robert Burkholder, Ohio State University, Using Asymptotic Phasefront Extraction To Take Computational Electromagnetics To A New Level. September 13, 2005, Prof. Gary Eden, University of Illinois, Microcavity Plasma Devices and Arrays: A New Realm of Plasma Physics and Photonics Applications. September 20, 2005, Prof. Caicheng Lu, University of Kentucky, Simulation of Electromagnetic Heating of Cryopreserved Samples.

41

September 27, 2005, Prof. Leo Kempel, Michigan State University, Design, Measurement, and Applications of Magneto-Dielectric RF Polymers. October 4, 2005, Prof. Bobby Weikle, University of Virginia, Terahertz Integrated Circuits and Systems: Technologies for Exploring the SubmillimeterGap. October 11, 2005, Prof. Scott Carney, University of Illinois, Apertureless Near-Field Scanning Optical Microscopy and Tomography. November 1, 2005, Dr. Aop Sezginer, Invarium Inc., Introduction to Sub-Wavelength Optical Projection Lithography. November 8, 2005, Prof. Paul Coleman, University of Illinois, An Overview of the THz Spectral Range: The Last Spectral Fontier. November 15, 2005, Prof. George Eleftheriades, University of Toronto, Negative-Refraction Transmission-Line Metamaterials and Their Applications. November 29, 2005, Zhuohui Zhang, University of Illinois, An Extremely Broadband Antenna. November 29, 2005, Jacquelyn Martin, University of Illinois, Efficiency of Electrically Small Antennas Used In Animal Tracking.