Presented By, Gaul Swapnil Narhari, M.Tech RF & Microwave, IIT Kharagpur.

1. Time Domain Modeling of Microwave Structures Presented By, Gaul SwapnilNarhari, [11EC63R05], RF & Microwave Engineering, Indian Institute of Technology , Kharagpur.

2. System Modeling Methodes: Time Domain Modeling Frequency Domain Modeling

3. Figure 1(a)Single Input Single Output (SISO) System (b)Transmission line as SISO System (ref.[4B])

4. Choice of Modeling Frequency Domain Modeling-computationally less efficient, provides higher stability and allows an analysis of more complex structures. Time-domain modeling is a more demanding task than the frequency-domain approach.

5. slide5 Analysis of electromagnetic field coupling to overhead wires of finite length based on the wire antenna theory. The TL model fails to predict resonances, to take into account properly the presence of a lossy ground and the effects at the line ends.

6. Integral Equations: To cast solution for the unknown current density, which is induced on the surface of the radiator/scatterer. Popular integral equations are, 1.Electric-field integral equation (EFIE) A.Hallenintegral equation B.Pocklingtonintegral equation 2.Magnetic field integral equation (MFIE)

7. Figure 2 Uniform plane wave obliquely incident on a conducting wire (ref.[1B])

8. Hallen’s Integral : From the Maxwell’s equations we can derive Electric field intensity,

9. Pocklington’s Integral:

10. The formulation based on the wire antenna theory in the frequency domain is based on the corresponding Pocklington equation, while the time domain formulation is based on the space-time Hallen integral equation.

11. slide6 The related integro-differential and integral relationships in the frequency and time domain, arising from the wire antenna theory are numerically handled via the frequency and time domain Galerkin-Bubnov scheme of the Indirect Boundary Element Method (GB-IBEM).

12. Fig. 3. Geometry of the straight wire ebedded in a dielectric half-space (ref.[2]) The spatial current is governed by the Pocklingtonintegro-differential equation(ref.[2] ),

13. Perform the straightforward convolution to the Pocklington integral equation to get the Hallen integral equation counterpart for a homogeneous lossless medium.

14. Transfer the Hallen integral equation for medium 1 into the laplace domain. After solving it, apply the inverse Laplace transform and the convolution theorem to get time domain Hallen equation.

15. Let us consider,the wire is illuminated by the transmitted part of the electro-magnetic pulse (EMP) incident waveform,

21. References: [1]. C. Y. Tham, A. McCowen, M. S. Towers, and D. Poljak, “Dynamic adaptive sampling technique in frequency-domain transient analyis,” IEEE Trans. Electromagn. Compat., vol. 44, no. 4, pp. 522–528, Nov. 2002. [2] DraganPoljakand Vicko Doric, “Time-Domain Modeling of Electromagnetic Field Coupling to Finite-Length Wires Embedded in a Dielectric Half-Space”, IEEE Trans. Electromagn. Compat., vol. 47, no. 2, 2 May 2005. [3]. Sadasiva M. Rao, Tapan K. Sarkar , , and SoheilA. Dianat, “ANovel Technique to the Solution of Transient Electromagnetic Scattering from Thin Wires”, IEEE Trans. On Antennas AndPropagation, Vol. Ap-34, No. 5, May 1986.

22. Referances: [1B] C. R. Paul Introduction to Electromagnetic Compatibility Second Edition,Wiley, New Jersey, 2006,Chapter 3,pg no.91. [2B] C.A.BalanisAntenna Theory,Analysis and Design Third Edition, Wiley,India, 2005, Chapter 8,pg no.433. [3B] Harrington R. F., Time-Harmonic Electromagnetic Fields, IEEE Press, 2001, Chapter 2,pg 37. [4B] C. R. Paul Multiwired Transmission Line,Chapter 8, pg.no. 342.

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