Mode Theory Of Wavguides With Discontinuities

Waveguides with discontinuities have many applications in microwave, millimeter wave and optical circuits. The propagation characteristics of these waveguieds are important when analyzing them with numerical or analytical method. The geometry discontinuities cause field distortions, which are accounted for by higher order evanescent modes. So the electromagnetic filed components can be described by a linear combination of infinite terms of normal modes. The complexity of filed expression results in inconsistence on the mode type existing in the waveguide.Firstly, we define several types of mode with five field components, then investigate the relationships among boundary conditions of each individual mode, and obtain the conditions for each mode to propagate in the waveguide. The conditions are given in the forms of theorems. Therefore, a general theory of propagation modes in the waveguide with discontinuities is presented.Based on the theory, modes in ridged, step and dielectric waveguides are predicted. Comparison with opinions in previous literature is also presented. We develop the point of view that TE~X and TM~X modes may exist in ridged waveguide with inhomogeneous dielectric loading.The mode-matching technique (MMT) is direct and conforms closely to physical reality. But it is not usually recognized as a very flexible method because of the complex formulation. The general formulation we use let us analyze a class of waveguides with discontinuities in cascade, such as ridged and step waveguides.We divide the waveguide into I regions. The total fields in each region are expanded in terms of a complete set of normal modes whose amplitudes are adjusted so as to satisfy the boundary conditions.For ridged waveguide, the tangential fileds in each region are expressed in terms of the multiplication of several matrices, i. e., a functional matrix F(x) about x, a functional matrix G(y)about y and a column vector of amplitudes of the individual region. It is worth pointing out that several amplitudes in regions 1 and I (the regions attached to the waveguide narrow walls) are of zeros, which is differed from the expression customarily used. This is for the purpose of constructing the matrix form of field components in the above.To transform the boundary conditions into a set of linear equations, we take the inner products of G(y) with weight functions. While neither the eigenvalue nor theamplitudes can be solved directly form the equations. We make use of the waveguide boundary conditions of regions 1 and I to construct the eigen equation and solve the unknown amplitudes.The field expression and computational formulation given in the above have several advantages. First, it becomes much easier to get the linear equations from boundary conditions by simple matrix operation. Second, the formulation provides more flexibility in selecting different set of weight functions. Third, the relationship between the amplitudes in the adjacent regions represented by the transfer matrix can be easily obtained. By applying the cascading of transfer matrices, the amplitudes in arbitrary region can be expressed in terms of those in region 1. Only amplitudes in region 1 are needed solving when computing the fields.Two approaches to reduce the element value and condition number of matrix are proposed. One way is accomplished by normalizing the amplitudes, which entails subtle change in matrix F(x). Another way is diving each region into several subregions, this results in the reduction of waveguide width of individual region. Both can be easily programmed, and provide drastic performance.For step waveguide, we express the tangential fields in each region in terms of the product of a functional matrix F(x) about x, a functional matrix H(z) about z and a column vector of amplitudes of the individual region. To transform the boundary conditions into a set of linear equations, we take the inner products of F(x) with weight functions.Transmission matrix considering higher order evanescent modes are obtained. By applying the cascading of transm...