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Use of Transmission Line Methods for Antenna Analysis and Wave Propagation

The transmission line method (TLM) is almost ideally suited for computation of wave propagation in the presence of various media as well as to the representation of sources, including antennas. Being a time domain method, it requires few assumption on the shape or frequency of the source waveform. It can handle a variety of interface conditions as well as material properties including lossy media and perfect conductors. Following a brief introduction to the method and its formulation for perfect dielectrics and conductors we discuss the extension of the method for inclusion of lossy dielectrics, placing the method in perspective relative to other time-domain methods suitable for wave propagation and for modeling of antennas. In this paper we chose to emphasize the interaction of antenna fields and conducting grids with particular application to modeling of shielding effects in relatively widely spaced grids. This in turns has application to shielding of MRI signals. A second focus point of the paper is the use of the transmission line method for the design of antenna adaptive arrays including driving coefficients and beam shaping parameters. While we will constrain ourselves to simple linear arrays of dipoles, for which analytical solutions can be used for comparison, the method is fully expandable to any antenna element and array configuration. The TLM Method The transmission line matrix was proven to be a very powerful method in modeling complex geometries. This paper explores the capability of the method to deal with various types of input signals and in particular, signals related to antennas and wave propagation. The TLM method was introduced in 1971 [1]. The capabilities of the method in modeling of radar applications were demonstrated elsewhere [2]. The accuracy necessary for antenna applications required the development of a new type of node for an antenna with axial symmetry [3]. The TLM method is limited only by the amount of memory storage required, which depends on the complexity of the problem to be modeled. It was found that for the same problem a TLM model provides higher accuracy in solution compared with the Finite Difference Time Domain (FDTD) method [4]. The price for this is an increased number of computer operations as compared with FDTD. The TLM based model has other three major advantages compared to the FDTD model: the TLM method is an unconditionally stable numerical method; there are no restrictions on the geometries to be modeled and any type of field sources can be implemented in a TLM model. There is an equivalence between the field quantities (electric and magnetic field intensities) and the transmission line quantities (voltage and current) [5-7]. Based on these equivalencies the whole space can be treated as a network of lumped circuits. The smallest part of space that can be modeled is called node. For this node, the charge and flux conservation laws must be satisfied. The propagation properties of this node are described by the so called scattering matrix (Slm). The scattering matrix determines the output at all ports for a given input [6,7]. In a general form, this can be written as: