Complex Permittivity Measurement of Dielectric Substrates at Millimeter-wave Frequencies

The understanding of the dielectric properties of materials used in the manufacturing of printed circuit boards (PCBs) is fundamental for reliable radio-frequency (RF) circuit designs, especially at millimeter-wave (mm-wave) frequencies. In this work, we present a transmission line method, aided with electromagnetic (EM) simulation, to measure the complex permittivity of dielectric substrates. Many methods for permittivity measurement already exist. However, most methods are not suitable for mm-wave frequencies. On the other hand, methods used at mm-wave frequencies are usually based on waveguide or resonator techniques, which can only operate for a limited frequency range or at discrete frequency points. The transmission line method we present in this work can measure dielectric substrates' complex permittivity over a continuous frequency range as low as hundreds of megahertz and up to mm-wave and beyond. The foundation of our method is to measure the propagation constant of a set of transmission lines via the multiline thru–reflect–line (mTRL) calibration. In addition, with the aid of EM simulations, we can estimate losses contributed by the conductor while accounting for surface roughness, which allows us to separate the dielectric loss from the overall losses in the measured propagation constant. Accordingly, we obtain an estimate of the effective complex permittivity of the transmission line. From the transmission line effective complex permittivity, we then derive the complex permittivity of the dielectric substrate. The mapping from the effective complex permittivity of the transmission line to the actual complex permittivity of the dielectric substrate is achieved through a proper polynomial function derived from the EM simulation. Equally important, the uncertainty in the measurement can be accounted for by the first-order error propagation method. We performed measurements on a low-temperature cofired ceramic (LTCC) substrate over a 0.2 – 85 GHz frequency range. We demonstrated that the obtained values for the complex permittivity of the LTCC substrate using our method agree with the measurements obtained via the split cavity resonator method within the defined uncertainty bound.