An accurate calibration and calculation method of six-port circuit for microfluidic sensing application

In this paper, an accurate calibration and calculation method of six-port circuit is proposed and tested in a microfluidic sensing system. Based on the Levenberg-Marquardt algorithm, a nonlinear iteration calibration model with the removal of redundancy equations is employed to calculate the system parameters of the six-port circuit. The reflection coefficient of device under test is calculated by the same iteration algorithm. To confirm the general accuracy of the algorithm, a series of coaxial loads are measured by six-port reflectometer. The maximum error referring to a commercial VNA is 1.2 dB/7° at the lowest measured reflection coefficient magnitude of − 20 dB from 2.4 to 2.9 GHz. The mentioned calculation result of the reflection coefficient for the resonator is accurate enough to show little influence to the judgement of resonant frequency and quality factor. Utilizing the respective linear fitting curve, the real part and imaginary part of permittivity of an unknown microfluidic sample can be obtained by six-port reflectometer. The calculating range of permittivity and the average calculating error is (7.7,77.0) and 4.9 % in real part and (7.3,18.2) and 3.5 % in imaginary part. In general, this approach enhance the accuracy of reflection coefficient calculating by six-port and further improve the application value of six-port in low-cost microfluidic sensing systems.