Envelope full-wave 3D finite element time domain method

9.

10.

11. 12.

13.

14. Figure 7 S-parameter modules of the FET obtained by CPGA. 兩S 11 兩 (-.-.-), 兩S 12 兩 (......), 兩S 21 兩 (----), 兩S 22 兩 (—)

15.

electromagnetics, IEEE Antennas Propagation Magazine 39 (1997), 7–25. S. Kent and T. Gu¨ nel, Dielectric permittivity estimation of cylindrical objects using genetic algorithms, J Microwave Power and Electromagn Energy 32 (1997), 109 –113. P.L. Werner, R. Mittra, and D.H. Werner, Extraction of equivalent circuits for microstrip components and discontinuities using the genetic algorithm, IEEE Microwave and Guided Wave Letters 8 (1998), 333–335. G.J. Klir and B. Yuan, Fuzzy sets and fuzzy logic: Theory and applications, Prentice Hall, 1995. T. Gu¨ nel, A new approach for the synthesis of nonreciprocal and nonsymmetric nonuniform transmission line impedance-matching sec¨ ) 52 (1998), 274 –276. tions, Int J Electron Commun (AEU T. Gu¨ nel, A hybrid approach to the synthesis of nonuniform lossy transmission-line impedance-matching sections, Microwave and Optical Technology Letters 24 (2000), 121–125. T. Gu¨ nel, A fuzzy hybrid approach for the synthesis of rectangular microstrip antenna elements with thick substrates, Microwave and Optical Technology Letters 26 (2000), 351–355. R.L. Haupt and S.E. Haupt, Practical genetic algorithms, New York, John Wiley & Sons, 1998.

© 2002 Wiley Periodicals, Inc.

ENVELOPE FULL-WAVE 3D FINITE ELEMENT TIME DOMAIN METHOD A. M. F. Frasson1 and H. E. Herna´ ndez-Figueroa2 1 Federal University of Espı´rito Santo (UFES) Electric Department (DEL) Av. Fernando Ferrari SN 29970-960, Vito´ ria-ES, Brazil 2 University of Campinas (UNICAMP) School of Electrical and Computer Engineering (FEEC) Department of Microwaves and Optics (DMO) Av. Albert Einstein 400 13083-970, Campinas-SP, Brazil Received 3 June 2002 Figure 8 S-parameter modules of the FET obtained by CHA. 兩S 11 兩 (-.-.-), 兩S 12 兩 (......), 兩S 21 兩 (----), 兩S 22 兩 (—)

fabricate the FET for a specified performance characteristic. This approach can also be used to determine the values of MESFET and HEMT model elements for the different power gain definitions. REFERENCES 1. G.D. Vendelin, Design of amplifiers and oscillators by the S-parameter method, Wiley, New York, 1982. 2. C. Paoloni, A simplified procedure to calculate the power gain definitions of FET’s, IEEE Trans Microwave Theory Tech MTT-48 (2000), 470 – 474. 3. C. Paoloni and S. D’Agostino, An approach to distributed amplifier based on a design-oriented FET model, IEEE Trans Microwave Theory Tech MTT-43 (1995), 272–277. 4. W.L. Price, Global optimization algorithms for a CAD workstation, J Optimization Theory Appl 55 (1987), 133–146. 5. J.H. Holland, Genetic algorithms, Scientific American, July (1992), 44 –50. 6. R.L. Haupt, An introduction to genetic algorithms for electromagnetics, IEEE Antennas and Propagation Magazine 37 (1995), 7–15. 7. D.S. Weile and E. Michielssen, Genetic algorithm optimization applied to electromagnetics: A review, IEEE Trans Antennas Propagat AP-45 (1997), 343–353. 8. J.M. Johnson and Y. Rahmat-Samii, Genetic algorithms in engineering

ABSTRACT: A three-dimensional finite-element time domain scheme based on the envelope approach is presented for the first time. In this approach the fast wave component or carrier is removed from the field and the envelope is solved instead. This strategy permits longer time steps than when the carrier is included, for the same spatial refinement. The unconditionally stable and second-order accurate Newmark scheme, in conjunction with tetrahedron edge elements and absorbing boundary condition (ABC) method was adopted. Key numerical results validate and show the efficiency and usefulness of the present algorithm. © 2002 Wiley Periodicals, Inc. Microwave Opt Technol Lett 35: 351–354, 2002; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.10604 Key words: finite element time domain method; full-wave analysis; 3D analysis 1. INTRODUCTION

The precise design, analysis, and optimization of MonolithicMicrowave Circuits (MMIC), with high-speed motherboard, printed antennas, and passive microwave circuits, demand fullwave numerical techniques, which have to be highly accurate, efficient, and versatile. Although the most popular method for such kind of simulations, the finite-difference time domain suffers from the starcasing effect when analyzing arbitrary curved geometries [1]. Recent contributions on perfect matched layers (PML), absorbing boundary condition (ABC), and vectorial edge elements,

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have created conditions to the development of more competitive finite-element time domain (FETD) schemes. In order to improve the time stepping efficiency, the narrowband slow-wave approach was proposed in the integrated optics literature [2]. Recently, an improved technique, the full-band slow-wave or carrier-free (or, simply, envelope) approach, was proposed in [3]. However, this technique is restricted to the 2D scalar simulation of planar integrated optics structures and 2D microwave applications [4]. In this paper, the envelope approach is extended to the full-wave 3D situation and applied to practice microstrip circuits for the first time. First order ABCs were placed over the truncated surfaces far away from the discontinuities, in order to allow the corresponding mode to be well established. In addition, such a mode is assumed to be quasi-TEM. For the time marching process, the Newmark scheme [5] was adopted, due to its unconditional stability and second-order accuracy. 2. FORMULATION

The wave equation for the electric field, eជ , in a source-free region is given by ⵜ ⫻ 共关 ␯ r兴ⵜ ⫻ eជ 兲 ⫹

1 ⭸ eជ ⫽ 0, 2 关␧ r兴 c ⭸t 2

(1)

where A 1 is the surface (cross section) associated with the input port n ⫽ 2, . . . , N represents any other port’s cross sections and open surfaces, A n , and ␯ fn velocity of a plane wave on that location. Assuming a solution of the form eជ ⫽ Eជ e j␻0t,

where Eជ is the time dependent electric field envelope and ␻0 the carrier angular frequency. The incident field can be written in the form: eជ inc ⫽ e⫺ ␲ 共tB w/ 2兲 e j ␻ 0t Eជ inc,

冕冕冕

V

冖冖 冕冕冕

⫹

n⫽1

⫹

w ជ 䡠 nˆ ⫻ 共关 ␯ r兴ⵜ ⫻ eជ 兲dA

1 ⭸2 c 2 ⭸t 2

w ជ 䡠 关␧ r兴eជ dv ⫽ 0,

(2)

V

where w ជ is the test vector function and nˆ the unitary normal vector pointing outside the volume. Considering that input and output circuit ports are far enough from the discontinuities, only the dominant quasi-TEM modes are present over the ports and, consequently, first-order ABC can be adopted [6].

冉 冘 冉 冕冕

⫽

冊 冕冕冕

⭸ 1 ⭸2 ⫹ j2 ␻ ⫺ ␻ 2 c 2 ⭸t 2 ⭸t N

⫺

A

⫹

ⵜ⫻w ជ 䡠 共关 ␯ r兴ⵜ ⫻ Eជ 兲dv

V

where [ ␯ r ] ⫽ [ ␮ r ] is the inverse magnetic relative permeability tensor, [␧ r ] is the electric relative permittivity tensor, and c is the speed of light in free space. Applying the Galerkin technique, the weak equivalent integral form of Eq. (1) is obtained by

ⵜ⫻w ជ 䡠 共关 ␯ r兴ⵜ ⫻ eជ 兲dv ⫹

(6)

where Eជ inc is the incident field pattern on port 1, that may be calculated by a 2D eigenvalue code and B w is the bandwidth of the envelope. Plugging Eqs. (5) and (6) into (4), the following expression for the complex envelope Eជ is obtained:

⫺1

冕冕冕

(5)

j␻0 ␯ fn

冉

1 ␯ fn

冕冕

V

w ជ 䡠 nˆ ⫻ nˆ ⫻

An

w ជ 䡠 nˆ 䡠 nˆ ⫻ Eជ ndA

An

冊

␲ B w2 t ⫺␲共tBw/ 2兲2 2 j␻0 ⫺ e ␯f 1 2

关␧ r兴Eជ 䡠 w ជ dv

⭸Eជ n dA ⭸t

冊

冗

w ជ 䡠 A1

⭸Eជ 1inc dA. ⭸t

(7)

3. FINITE ELEMENT DISCRETIZATION

The domain is divided using tetrahedra and the electric field envelope is expanded in terms of the well known vector Whitney ជ j , [7], 1-form basis functions, N

冘 Ne

Eជ ⫽

1 ⭸eជi 2 ⭸eជinc i nˆ ⫻ ⵜ ⫻ eជ i ⫽ ⫺ nˆ ⫻ nˆ ⫻ ⫺ , ␯fi ⭸t ␯fi ⭸t

(3)

are the total field and the incident field, respecwhere eជ i and eជ inc i tively, on port i, and ␯ fi is the velocity of the dominant mode on the same port i. Assuming that the ports are defined over isotropic media, utilizing the condition of Eq. (3) in Eq. (2), the following expression is obtained:

ជ j, E jN

(8)

j⫽1

where, the coefficients E j are time depending and N e represents the total number of unknowns. For the test functions the set of basis functions are adopted. Defining

Q ij ⫽

冕冕冕

ជ i 䡠 共关 ␯ r兴ⵜ ⫻ N ជ j兲dv ⵜ⫻N

(9)

V

冕冕冕

ⵜ⫻w ជ 䡠 共关 ␯ r兴ⵜ ⫻ eជ 兲dv ⫹

V

冘 N

⫺

n⫽1

1 ␯ fn

冕冕

An

w ជ 䡠 nˆ ⫻ nˆ ⫻

1 ⭸2 c 2 ⭸t 2

冕冕冕

关␧ r兴eជ 䡠 w ជ dv

R ij ⫽

V

⭸eជ n 2 dA ⫽ ⫺ ⭸t ␯f 1

冕冕

A1

ជ i 䡠 关␧ r兴N ជ jdv N

(10)

ជ i 䡠 nˆ ⫻ nˆ ⫻ N ជ jdA N

(11)

V

w ជ䡠

⭸eជ1inc dA, ⭸t

⍀ nij ⫽

(4)

352

冕冕冕

MICROWAVE AND OPTICAL TECHNOLOGY LETTERS / Vol. 35, No. 5, December 5 2002

冕冕

An

⌫ fi ⫽

冕冕

ជ i 䡠 Eជ incdA, N

(12)

A1

Eq. (7) can be rewritten in the matrix form: 关M兴

⭸ 2兵E其 ⭸兵E其 ⫹ 关C兴 ⫹ 关K兴兵E其 ⫽ 兵b其, ⭸t 2 ⭸t

(13)

where 关M兴 ⫽

关C兴 ⫽

j2 ␻ 0 关R兴 ⫺ c2

关K兴 ⫽ 关Q兴 ⫺

兵b其 ⫽

1 关R兴 c2

冘 N

n⫽1

␻ 02 关R兴 ⫺ c2

冉

(14)

1 关⍀ 兴 ␯ fn N

冘 N

n⫽1

j␻0 关⍀ n兴 ␯ fn

冊

␲ B w2 t ⫺␲共tBw/ 2兲2 2 j␻0 ⫺ e 兵⌫ f其. ␯f 1 2

(15)

(16)

(17)

4. TIME MARCHING SCHEME

In order to solve Eq. (13), it is necessary to discretize the temporal derivatives. Applying the Newmark algorithm for the time dependence in (13) yields 兵关M兴 ⫹ ␥ ⌬t关C兴 ⫹ ␤ ⌬t 2关K兴其兵E其 m⫹1 ⫽ 兵2关M兴 ⫹ 共2 ␥ ⫺ 1兲⌬t关C兴 ⫹ 共0.5 ⫺ 2 ␤ ⫹ ␥ 兲⌬t 2关K兴其兵E其 m ⫹ 兵⫺关M兴 ⫹ 共1 ⫺ ␥兲⌬t关C兴 ⫹ 共0.5 ⫹ ␤ ⫺ ␥兲⌬t2 关K兴其兵E其m⫺1 ⫹ ␤⌬t2 兵b其m⫹1 ⫹ 共0.5 ⫺ 2␤ ⫹ ␥兲⌬t2 兵b其m ⫹ 共0.5 ⫹ ␤ ⫺ ␥兲⌬t2 兵b其m⫺1 , where m is the time index. The Newmark parameters ␤ and ␥ determine the stability and accuracy characteristics of the algorithm. For unconditional stability and second-order accuracy, 2␤ ⱖ ␥ ⱖ 0.5. Since the electric field distribution is known over the entire spatial domain for every time step, the voltages on input and output ports can readily be calculated. Then, the scattering parameters can be obtained over a frequency band, B w of Eq. (6), through the expressions: S 11 ⫽

ᑠ关共Vi ⫺ Vref兲ej ␻ 0t 兴 ᑠ共Vrefej ␻ 0t 兲

S 21 ⫽

ᑠ共Voutej ␻ 0t 兲 ᑠ共Vrefej ␻ 0t 兲

冑

Z0i , Z0o

(19)

(20)

where Z 0i and Z 0o are the characteristic impedance linked to the input and output ports, respectively, ᑠ is the Fourier transform, V i and V out are the voltages in time domain calculated on the input and output ports, respectively, and V ref is the references voltage in time domain, on the input port, computed considering the accessing input waveguide as being infinite.

Figure 1 S-parameters of a low-pass filter printed on an RT/Duroid substrate

5. RESULTS

For validation purposes, a low-pass filter printed on an RT/Duroid substrate with ␧ r ⫽ 2.2 (Fig. 1), was simulated using the present approach (called FETD for simplicity), and compared with the FDTD results in [8], for a frequency range of 20 GHz. This frequency range was divided into three bandwidths: f 0 ⫽ 2.0 GHz with B w ⫽ 2.0 GHz, f 0 ⫽ 7.5 GHz with B w ⫽ 7.5 GHz, and f 0 ⫽ 15.0 GHz with B w ⫽ 15.0 GHz. The mesh used consisted of 29,947 tetrahedra, producing a total of 38,195 unknowns. Each bandwidth simulation was carried out using 144 time steps, with a time step size of 0.15 the period of the central frequency. It is clear from Figure 1 that there is excellent agreement between the two methods over all frequency ranges, except the minimum value of S 11 , around 6 GHz. The total computational time required to obtain the entire curve was 1 h 13 min using a PENTIUM III, with 800-MHz, running GNU and LINUX operating systems. These computational resources were adopted in all simulations presented here. With the same mesh, the field (carrier and envelope) approach was also computed. To reach the same accuracy as the envelope approach, a time step size of 0.025 the period of central frequency was required. Each bandwidth simulation was carried out with 864 time steps. In spite of less computational effort at each time step, because the variables were all real, the total computation time to obtain the entire curve was 2 h 3 min. Another simulation for the field approach was performed using as input a 15-ps-wide Gaussian pulse. Due to the pulse’s wide band it was not necessary to divide the frequency range of 20 GHz. A time step of 0.66 ps was used to reach the same accuracy shown in Figure 1. The total time required to obtain the entire curve was 1 h 49 min. As a second example, a curved structure, extracted from [1], was chosen. This is a circular spiral inductor connected in shunt with a microstrip printed on alumina substrate, depicted in the inset of Figure 2. The alumina’s relative permittivity was, ␧ r ⫽ 9.8, and height of 0.635 mm. The other geometric parameters (see Fig. 2) are: w m ⫽ 0.635 mm, w d ⫽ 0.6 mm, w e ⫽ 0.2 mm, R 1 ⫽ 1.9 mm, R 2 ⫽ 1.3 mm, and R 3 ⫽ 0.7 mm. The center of the spiral is grounded using a planar conducting via. Our results (FETD), as seen in Figure 2, show a good agreement with those based on the frequency domain approach (FEFD), presented in [1]. There, a mesh with 43,588 tetrahedra and a total of 51,270 unknowns were used, while in the present scheme 21,749 tetrahedra and a total of 26,767 unknowns were used. Two bandwidths were used: f 0 ⫽

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AN OPTICAL RECEIVER CIRCUIT FOR ON-LINE FIBER-OPTIC CHARACTERISTICS MONITORING Wen-Ming Cheng and Shyh-Lin Tsao Institute of Electro-optical Science and Technology National Taiwan Normal University Taipei, 116, Taiwan, R.O.C. Received 4 June 2002

Figure 2 S-parameters of a spiral inductor connected by a shunt across a microstrip line printed on aluminum

1.0 GHz and B w ⫽ 2.0 GHz, and f 0 ⫽ 4.5 GHz with B w ⫽ 5.0 GHz, with a time step size of 0.1 the period of the central frequency. The total simulation time taken by the present scheme was 1 h 14 min, 57% of which was spent in the LU matrix decomposition.

ABSTRACT: A low-cost optical receiver circuit, which includes a photodiode preamplifier, an active band-pass filter, and an instrumental amplifier is experimentally achieved. Using the proposed circuit for measurement and on-line automatic monitoring in this paper, the efficiency of fiber-optic characteristics monitoring can be enhanced and on-line noise interference can be suppressed. The transfer functions and frequency response of the optical receiver are derived. The signal-tonoise ratio of the on-line fiber-optic characteristics monitoring system can be improved using this low-cost optical receiver. © 2002 Wiley Periodicals, Inc. Microwave Opt Technol Lett 35: 354 –357, 2002; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.10605 Key words: optical receiver circuit; fiber optics; automatic measurement; on-line monitoring; monitoring efficiency 1. INTRODUCTION

6. CONCLUSION

In this paper, the envelope approach was applied to the solution of 3D electromagnetic time domain problems using the finite element method for the first time. Through the analysis of two key microstrip structures, it was clearly shown that the present scheme performs more efficiently than the conventional field (carrier and envelope) approach.

REFERENCES 1. A.C. Polycarpou, P.A. Tirkas, and C.A. Balanis, The finite-element method for modeling circuits and interconnects for electronic packaging, IEEE Trans Microwave Theory Tech 45 (1997), 1868 –1874. 2. R.Y. Chan and J.M. Liu, Time-domain wave propagation on optical structures, IEEE Photonics Technology Letters, 6 (1994), 1001–1003. 3. V.F. Rodrı´guez-Esquerre and H.E. Herna´ ndez-Figueroa, Novel wave propagation scheme for the time-domain simulation of photonic devices, IEEE Photonics Technol Lett 13 (2001), 311–313. 4. Y. Wang and T. Itoh, Envelope-finite-element (EVFE) technique: A more efficient time-domain scheme, IEEE Trans Microwave Theory Tech 49 (2001), 2241–2247. 5. T.J.R. Hughes, The FEM linear static and dynamic analysis, PrenticeHall, 1997. 6. J. Jin, The finite element method in electromagnetics, Wiley, New York, 1993. 7. A. Bossavit and I. Mayergoyz, Edge elements for scattering problems, IEEE Trans Magnetics 25 (1989), 2816 –2821. 8. D.M. Sheen, S.M. Ali, M.D. Abouzahra, and J. Kong, Application of the three-dimensional finite-difference time-domain method to the analysis of planar microstrip circuits, IEEE Trans Microwave Theory Tech 38 (1990), 849 – 857. 9. J.-F. Lee, R. Lee, and A. Cangellaris, Time-domain finite element methods, IEEE Trans Antenna Propagat 45 (1997), 430 – 441. © 2002 Wiley Periodicals, Inc.

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Many optical fiber sensors have been studied to measure variety of electrical, mechanical, and noise phenomena. It is an important issue to increase the linearity and sensitivity of optical sensors [1, 2]. However, little reports related fiber sensor has been disclosed for fiber coating automatic on-line monitoring, because fiber automatic on-line monitoring is very useful for mass production. We have reported a simplified formulation of bending loss for building up an on-line fiber-optic characteristics monitoring system, recently [3]. Such a system can coat the jacket with polymer along a 25 km fiber spool. The optical signal detection for such an automatic fabrication machine is very important. Some basic electrical circuits have been reported related the electrical amplifiers and electrical filters design [4], which may be used in optical receivers’ design. However, for a specific fiber coating machine with on-line fiber-optic characteristics monitoring, no commercial available optical receiver could be found. In this letter, we implement a specific optical receiver circuit with narrow band-pass active filter for on-line optical fiber characteristics monitoring of a fiber-coating machine. The system description of implementing such an on-line fiber-optic characteristics monitoring apparatus is described in the following section. 2. ON-LINE FIBER-OPTIC CHARACTERISTICS MONITORING SYSTEM DESCRIPTION

The block diagram and signal flow of our implemented fiber-optic bending loss measurement system is shown in Figure 1 [3]. The optical light carrier is sinusoidally modulated to 21.5 kHz at the pay-off terminal on the fiber coating machine. By using a freespace optical coupling device, the modulated signal carried on the 1.31 ␮m laser light can go through the moving fiber path on the fiber coating machine. At the other side, the take-up terminal receives the modulated signal carried by the 1.31 ␮m laser light through the free-space optical coupling device at the optical receiver circuit. The received 21.5-kHz signal in the optical receiver is filtered out by an active band-pass filter and amplified by an instrumental amplifier. The amplitude of the modulated light sig-

MICROWAVE AND OPTICAL TECHNOLOGY LETTERS / Vol. 35, No. 5, December 5 2002