In this paper, a compact and single-mode X-band
dielectric-loaded matching section with constant tilt angle, blended
edges, and two discontinuities at both ends is analyzed by the
transmission line model. This matching section is designed as a
high-power injection coupler to a dielectric-loaded accelerating
structure (DLA). Although the transmission line model is a powerful
tool for single-mode structures, because of radial inhomogeneity and
lack of single value for characteristic impedance in
dielectric-loaded structures, this method is not applicable in
non-uniform dielectric-loaded structures. To solve this problem, it
is shown that a dielectric-loaded waveguide (DLW) can be modeled by
a dielectric-filled waveguide (DFW) with the same parameters of the
phase constant, power flow, and dielectric loss. The characteristic
impedance of a dielectric-filled waveguide can be determined by
three structural parameters of the real and imaginary parts of the
dielectric material and inner radius. These structural parameters
can be found by solving a non-linear equation system made by
equality of the parameters of the dielectric-loaded and
dielectric-filled waveguides. To analyze the matching section, it is
stratified to low thickness and uniform DLWs in the propagation
direction and every segment is substituted by its equal DFW
model. However, because of sharp variation in dielectric region at
two ends of the flared section, solving the non-linear equation
system is difficult at these points due to the lack of a proper
initial point for the answer. Therefore, two virtual sections are
added at the discontinuities to smoothen the variation of the
dielectric region. Then, the total transmission matrix and
scattering matrix parameters can be obtained without considering the
added virtual sections. Moreover, the matching section is simulated
by a full-wave electromagnetic software and the results of the
scattering matrix parameters are compared with the ones of the
proposed method. It is shown that there is a good agreement between
the total behavior of the simulation and analytical results and the
proposed method has acceptable accuracy.