Equivalent waveguide of a SIW

As long as the radiation losses in the SIW structure are negligible (see next section), the two rows of via holes of the side walls of the SIW (separated a distance equal to w) can be substituted by authentic metallic walls separated a distance a_{eq}, where a_{eq} is the width of the equivalent rectangular waveguide, and the attenuation and dispersion characteristics in SIW are almost identical to the ones of its equivalent rectangular waveguide [YHWC05].

Electric fields

Electric field distribution of the fundamental mode in SIW (up) and in its equivalent waveguide (down).

These two parameters, a_{eq} and w, are related with the following closed form expression [HHC+05],
where s is the repetition period of the via holes (see previous section) and d is their diameter.