Determining the Stopband of a Periodic Bed of Nails From the Dispersion Relation Measurements Prediction

It is useful to determine the stopband of a bed of nails that can be used for packaging applications. The traditional methodology to identify the cell characteristics is to use the eigenmode solver, which is a numerical method that cannot be validated using a measurement setup. Here, we introduce a mathematical procedure to extract the dispersion relation out of the scattering parameters. The scattering parameters express the transmission and the reflection at the ports, which are functions of the phase constant of the propagating modes inside the device under test. A measurement setup is established by placing several successive cell rows inside a Ku -band rectangular waveguide. The proposed algorithm is validated through examples of well-known dispersion relations. The extracted dispersion relation with the introduced methodology is in good agreement with the one obtained from the eigenmode solver. The ride gap waveguide is used as an application example.