Determination of Characteristic Impedance of Planar Transmission Lines on Lossy/Dispersive Substrates by Using Series Resistor With Frequency-Dependent Inductance

This article presents a simple derivation and fast-solving scheme to extract the characteristic impedance of planar transmission lines (TLs) on lossy/dispersive substrates, by using a series resistor after one-tier multiline thru-reflect-line (TRL) calibration, for on-wafer calibration applications. The proposed method is based on the constant resistance condition of the series resistor and linear frequency response of the conductance of TL per unit length, where the parasitic inductance of the series resistor can be frequency-dependent; thus, the deviation caused by the constant inductance assumption can be observed in millimeter-wave frequencies. The proposed method is investigated using a coplanar waveguide (CPW) on a high-resistivity silicon substrate by using an integrated passive device (IPD) technology with verifications of the calibration comparison method in a frequency range of 2-110 GHz.