S-parameters Based Transmission Line Modeling with Accurate Low-Frequency Response

Accurate transmission line modeling is required for multi-gigahertz designs. To capture high frequency effects such as frequency-dependent dielectric and conductor loss, S-parameters obtained from VNA measurement are commonly used to model transmission lines. Unfortunately, such method has not been very robust since the S-parameters from VNA measurement have a low frequency limit. In this paper, we present a method to obtain a broadband transmission line model with accurate low-frequency response. A conversion formale from the S-parameters to RLGC models is first derived for multi-conductor transmission lines. We then demonstrate the inaccuracy in transient waveforms of transmission line models due to inaccurate low frequency response. Finally we present a method to calculate the accurate low-frequency response using TDR time-domain measurements in addition to VNA frequency domain measurements