Lumped-Element Circuit Modelling of Microfluidic Channels in Microstrip Transmission Lines

A lumped-element equivalent circuit model (ECM) for a short length of microstrip transmission line incorporating a microfluidic channel filled with dielectric fluid is proposed. With this model, advanced microstrip circuits containing microfluidic channels can be designed in a fast and accurate manner. For verification, an ECM is extracted for a l-mm length of $50\,\Omega $ transmission line on a 1.5-mm thick substrate with $\epsilon _{r}=3.55$ that has a 0.5-mm long $\times\,0.5$-mm tall $\times\,6.9$-mm wide microfluidic channel underneath it filled with a dielectric fluid of $\epsilon _{r} = 81.$ The model parameter values are extracted using the structure’s two-port S-parameter response obtained through full-wave 3D electromagnetic simulation. The extracted ECM is then used to design a fluidic phase shifter.