Nonuniform transmission-line synthesis using inverse eigenvalue analysis

Recent research on inverse eigenvalue problems for second-order differential equations on a finite interval has made it possible to reconstruct the coefficients in such an equation from spectral data. These data consist of the eigenvalues and the end values of the normalized eigenfunctions. This result is applied to reconstruct the axial profile of a finite transverse electromagnetic transmission line, and it is shown that the normalized scattering matrix of the line can also be expressed, in closed form, in terms of the spectral data. Asymptotic considerations indicate that for any continuous line the eigenvalues and end values will converge to those of a uniform line. This suggests that one should consider lines for which all the eigenvalues and all but the first n end values are equal to those of the uniform line. Numerical results show that this family of nonuniform lines contains members with useful and controllable transmission characteristics. Experimental results confirm the accuracy of the analysis