# 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 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.