Extracting Complex PCB Substrate Permittivity from a Transmission Line using the Finite Difference Integral Method from 10 GHz - 100 GHz

This paper presents a new numerical method to deduce the complex permittivity ${\underline\varepsilon}_{r}$ of PCB (printed circuit board) substrates. First, the attenuation and phase of an on board transmission line are measured with a vector network analyzer (VNA). The transmission line is then simulated with the finite difference integral method (FDI) with the substrate substituted by air. The measured and simulated phases are used, to calculate the effective permittivity and the real part of the complex permittivity ${\varepsilon}_{r}^{\prime}$. With known ${\varepsilon}_{r}^{\prime}$, the electromagnetic field distribution can be calculated, which is necessary to deduce the imaginary part of the permittivity. The shown algorithms can be used for frequencies up to 100 GHz and without any iterative processes.