Broadband permittivity of liquids extracted from transmission line measurements of microfluidic channels

We present a semi-analytical procedure to extract the permittivity of fluids from measurements in our microfluidic-microelectronic platform. This platform consists of broadband coplanar waveguide transmission lines with integrated microfluidic channels for characterizing the dielectric properties of submicroliter fluid samples. On-wafer calibration techniques are used to obtain the S-parameters of the composite structure (transmission line and microfluid channel) up to 40 GHz. Using microwave network analysis theory, we isolated the response of the microfluidic channel. We modeled the microfluidic channel as a distributed transmission line segment and as a single RLCG elemental segment. Both approaches analytically yield the circuit capacitance C(F) and conductance G(F) per unit length of the segment incorporating the microfluidic channel. A finite element electromagnetic simulator is then used to obtain the permittivity of the fluid as a continuous function of frequency. We applied this technique to extract the permittivity of submicroliter liquid volumes. Here we present results on polystyrene latex beads suspended in an aqueous solution over the frequency range from 100 MHz to 40 GHz.