Time Domain Modeling of Microwave Structures

Presented By,Gaul Swapnil Narhari,

[11EC63R05],RF & Microwave Engineering,

Indian Institute of Technology , Kharagpur.

System Modeling Methodes:

Time Domain Modeling

Frequency Domain Modeling

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

Choice of ModelingFrequency 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.

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.

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.Hallen integral equation B.Pocklington integral equation

2.Magnetic field integral equation (MFIE)

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

Hallen’s Integral :From the Maxwell’s equations we

can derive Electric field intensity,

Pocklington’s Integral:

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.

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).

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] ),

Perform the straightforward

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

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.

Let us consider,the wire is

illuminated by the transmitted part of the electro-magnetic pulse (EMP) incident waveform,

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] Dragan Poljak and 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 Soheil A. Dianat, “A Novel Technique to the Solution of Transient Electromagnetic Scattering from Thin Wires”, IEEE Trans. On Antennas And Propagation, Vol. Ap-34, No. 5, May 1986.

 

Referances:[1B] C. R. Paul Introduction to Electromagnetic

Compatibility Second Edition,Wiley, New Jersey, 2006,Chapter 3,pg no.91.

 [2B] C.A.Balanis Antenna 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.

THANK YOU..!