## 1. Introduction

[2] Coaxial waveguides are used very frequently for both ground and satellite microwave equipment. They have been studied in the past with a variety of approaches, including modern numerical techniques such as finite element and finite difference (FD). An important application of the coaxial technology is in the implementation of low-pass and bandpass filters. The correct design of this type of hardware requires the knowledge of the modal structure of the coaxial waveguide.

[3] The calculation of the modal fields of an uniform hollow conducting waveguide and the corresponding cutoff wave numbers is equivalent to the determination of the resonant modes and frequencies of a two-dimensional resonator [*Marcuvitz*, 1951]. Several numerical techniques have been developed for this purpose in the last decades. Most of these techniques may be grouped into two classes. The first consists of techniques based on the finite element method (or finite difference method) [*Itoh*, 1989], which leads to either large-size standard eigenvalue matrix problem or to multistep iterative schemes. The second class consists of techniques based upon the solution of integral equations by algorithms such as the method of moments [*Itoh*, 1989; *Conciauro et al.*, 1984], the null-field method, the point matching method, or the auxiliary source method. All these techniques lead to the solution of small-size nonalgebraic eigenvalue problems [*Spielman and Harrington*, 1972]. The techniques belonging to the former class require an “ad hoc” choice of the location, the shape, and the number of elements inside the cross section of the waveguide, particularly when irregular and pointed boundaries are to be dealt with. In addition, their application requires time consuming procedures and/or large computer memory availability.

[4] Storage requirements are strongly reduced for the techniques belonging to the latter class. Nevertheless, computational time is still fairly long (especially when many modes must be computed), due to the need of finding zeros of determinants of matrices whose elements are transcendental functions of the frequency (nonlinear eigenvalue problems).

[5] The modal analysis of a perfectly symmetrical coaxial cable can be found in literature [e.g., *Gimeno and Guglielmi*, 1997, but the modal analysis of an off-center coaxial cable has not yet been analyzed using techniques belonging to the latter class. By building junctions between two asymmetric coaxial cables it is possible to realize interesting devices such as filters whose behavior is different from the behavior of a filter realized with two perfectly symmetric coaxial cables. Moreover this work is interesting because using this theory it is possible to foresee the variations of the behavior of a symmetric coaxial cable when the offset of the inner conductor is due to manufacturing tolerance.